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PVS Bug 924


Synopsis:        20 <= 14? and 20 <= 17?
Severity:        serious
Priority:        medium
Responsible:     owre (Sam Owre)
State:           open
Class:           sw-bug
Arrival-Date:    Mon Nov 21 10:00:00 2005
Originator:      Hesselink
Organization:    rug.nl
Release:         PVS 3.2
Environment: 
 System:          
 Architecture: 

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  In the attached proof scripts, the lemmas lq7_rest and lq16_rest are 
  done with  (grind) but they remain unfinished with final sequents that 
  hold antecedents 20 <= 14 and 20 <= 17. Should not this be recognized as 
  false?
  
  Best regards,
  Wim
  
  -- 
  Wim H. Hesselink  
  
  Dept. of Computing Science | phone +31 50 3633933
  University of Groningen    |    or +31 50 3633939
  P.O.Box 800                | fax   +31 50 3633800
  9700 AV Groningen          | email: w.h.hesselink@rug.nl
  The Netherlands            | http://www.cs.rug.nl/~wim
  
  
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  %% PVS Version 3.2
  %% 6.2 [Linux (x86)] (Nov 3, 2004 23:30)
  $$$PVSHOME/.pvs.lisp
  
  $$$PVSHOME/.pvs.lisp
  
  $$$multiLLSC.pvs
  % Wim H. Hesselink, after Jayanti and Petrovic, Novemeber 2005
  
  multiLLSC: THEORY
  
  BEGIN
  
    Item: TYPE 
    N: posint
    Process: TYPE = below[N]
    Number: TYPE = below[2*N]
    Index: TYPE = below[3*N]
  
    state: TYPE = [#
      % shared variables
      absbuf: [nat -> Item] , % history var
      top: nat ,              % history var
      xind: Index ,
      xnr: Number ,
      xSet: pred[Process] ,
      buf: [Index -> Item] ,
      aux: pred[Process] ,
      hind, bb: [Process -> Index] ,
      bank: [Number -> Index] ,
      heSet: [Process -> pred[Process]] ,
      baSet: [Number -> pred[Process]] ,
      % history variables
      ptop, ltop, start, htop: [Process -> nat] ,
      % private variables
      ind: [Process -> Index] ,
      nr: [Process -> Number] ,
      loc: [Process -> Item] ,
      mybuf: [Process -> Index] ,
      result: [Process -> bool] ,
      pc: [Process -> nat]
    #]
  
    x, y: VAR state
    p, q, r: VAR Process
    i, j: VAR Number
  
    step11(p, x, y): bool =
      x`pc(p) = 11 AND 
      y = x WITH [
        `aux(p) := true ,
        `hind(p) := x`mybuf(p) ,
        `start(p) := x`top ,
        `pc(p) := 12
      ]
     
    step12(p, x, y): bool =
      (x`pc(p) = 12 OR x`pc(p) = 15) AND 
      y = x WITH [
        `ptop(p) := x`top ,
        `ltop(p) := x`top ,
        `ind(p) := x`xind ,
        `nr(p) := x`xnr ,
        `xSet := add(p, x`xSet) ,
        `pc(p) := x`pc(p) + 1
      ]
    
    step13(p, x, y): bool =
      (x`pc(p) = 13 OR x`pc(p) = 16) AND 
      y = x WITH [
        `loc(p) := x`buf(x`ind(p)) ,
        `pc(p) := x`pc(p) + 1
      ]
      
    step14(p, x, y): bool =
      x`pc(p) = 14 AND 
      y = x WITH [
        `bb(p) := x`hind(p) ,
        `heSet(p) := add(p, x`heSet(p)) ,
        `pc(p) := IF x`aux(p) THEN 18 ELSE 15 ENDIF 
      ]
     
    step17(p, x, y): bool =
      x`pc(p) = 17 AND 
      y = x WITH [
        `loc(p) := IF x`xSet(p) THEN x`loc(p) ELSE x`buf(x`bb(p)) ENDIF ,
        `ltop(p) := IF x`xSet(p) THEN x`ltop(p) ELSE x`htop(p) ENDIF ,
        `pc(p) := 18
      ]
     
    step18(p, x, y): bool =
      x`pc(p) = 18 AND 
      y = x WITH [
        `bb(p) := x`hind(p) ,
        `heSet(p) := add(p, x`heSet(p)) ,
        `pc(p) := IF x`aux(p) THEN 19 ELSE 20 ENDIF 
      ]
     
    step19(p, x, y): bool =
      x`pc(p) = 19 AND
      IF x`heSet(p)(p) THEN  
         y = x WITH [
          `aux(p) := false ,
          `hind(p) := x`bb(p) ,
          `heSet(p) := emptyset[Process] ,
          `pc(p) := 20
         ]
      ELSE y = x WITH [`pc(p) := 20] ENDIF
     
    step20(p, x, y): bool =
      x`pc(p) = 20 AND 
      y = x WITH [
        `mybuf(p) := x`hind(p) ,
        `pc(p) := 21
      ]
     
    step21(p, x, y): bool =
      x`pc(p) = 21 AND 
      y = x WITH [
        `buf(x`mybuf(p)) := x`loc(p) ,
        `pc(p) := 30
      ]
  
    step22(p, x, y): bool =
      x`pc(p) = 22 AND 
      y = x WITH [
        `baSet(x`nr(p)) := add(p, x`baSet(x`nr(p))) ,
        `pc(p) := IF x`bank(x`nr(p)) = x`ind(p) OR NOT x`xSet(p) THEN 24
                  ELSE 23 ENDIF 
      ]
  
    step23(p, x, y): bool =
      x`pc(p) = 23 AND
      IF x`baSet(x`nr(p))(p) THEN  
         y = x WITH [
          `bank(x`nr(p)) := x`ind(p) ,
          `baSet(x`nr(p)) := emptyset[Process] ,
          `pc(p) := 24
         ]
      ELSE y = x WITH [`pc(p) := 24] ENDIF
     
    step24(p, x, y): bool =
      x`pc(p) = 24 AND 
      y = x WITH [
        `ltop(p) := x`top ,
        `bb(p) := x`hind(rem(N)(x`nr(p))) ,
        `heSet(rem(N)(x`nr(p))) := add(p, x`heSet(rem(N)(x`nr(p)))) ,
        `pc(p) := IF x`aux(rem(N)(x`nr(p))) AND x`xSet(p) THEN 25 ELSE 27 ENDIF
  
      ]
     
    step25(p, x, y): bool =
      x`pc(p) = 25 AND 
      IF x`heSet(rem(N)(x`nr(p)))(p) THEN  
         y = x WITH [
          `aux(rem(N)(x`nr(p))) := false ,
          `hind(rem(N)(x`nr(p))) := x`mybuf(p) ,
          `htop(rem(N)(x`nr(p))) := x`ltop(p) ,
          `heSet(rem(N)(x`nr(p))) := emptyset[Process] ,
          `mybuf(p) := x`bb(p) ,
          `pc(p) := 27
         ]
      ELSE y = x WITH [`pc(p) := 27] ENDIF
  
    step27(p, x, y): bool =
      x`pc(p) = 27 AND 
      y = x WITH [
        `buf(x`mybuf(p)) := x`loc(p) ,
        `pc(p) := 28
      ]
  
    step28(p, x, y): bool =
      x`pc(p) = 28 AND 
      y = x WITH [
        `bb(p) := x`bank(rem(2*N)(x`nr(p)+1)) ,
        `pc(p) := 29
      ]
  
    step29(p, x, y): bool =
      x`pc(p) = 29 AND 
      IF x`xSet(p) THEN
         y = x WITH [
          `xind := x`mybuf(p) ,
          `xnr := rem(2*N)(x`nr(p)+1) ,
          `mybuf(p) := x`bb(p) ,
          `xSet := emptyset[Process] ,
          `absbuf(x`top + 1) := x`loc(p) ,
          `top := x`top + 1 ,
          `result(p) := true ,
          `pc(p) := 30
         ]
      ELSE y = x WITH [
          `pc(p) := 30 , `result(p) := false ]
      ENDIF
  
    step30(p, x, y): bool =
      x`pc(p) = 30 AND 
      EXISTS (newpc: nat, newloc: Item):
        (newpc = 11 OR newpc = 22) AND
        y = x WITH [
        `loc(p) := newloc ,
        `pc(p) := newpc
      ]
  
    step(p, x, y): bool =
        step11(p, x, y) OR step12(p, x, y) OR step13(p, x, y) 
        OR step14(p, x, y) OR step17(p, x, y) OR step18(p, x, y) 
        OR step19(p, x, y) OR step20(p, x, y) OR step21(p, x, y) 
        OR step22(p, x, y) OR step23(p, x, y) OR step24(p, x, y) 
        OR step25(p, x, y) OR step27(p, x, y) OR step28(p, x, y) 
        OR step29(p, x, y) OR step30(p, x, y) 
    
    step(x, y): bool = 
      EXISTS p: step(p, x, y)
  
    jq0(q, x): bool =
      x`aux(q) IMPLIES 12 <= x`pc(q) AND x`pc(q) < 20
  
    jq0_dif: LEMMA
      jq0(q, x) AND step(p, x, y) AND p /= q
      IMPLIES jq0(q, y)
  
    jq0_eq_rest: LEMMA
      jq0(p, x) AND step(p, x, y) AND x`pc(p) /= 19
      IMPLIES jq0(p, y)
  
    jq1(q, x): bool =
      x`pc(q) = 19 AND x`aux(q) IMPLIES x`heSet(q)(q)
  
    jq0_eq_19: LEMMA
      jq0(p, x) AND jq1(p, x) AND step(p, x, y) AND x`pc(p) = 19
      IMPLIES jq0(p, y)
  
    jq0_kept_valid: LEMMA
      jq0(q, x) AND jq1(q, x) AND step(p, x, y)
      IMPLIES jq0(q, y)
  
    jq1_kept_valid: LEMMA
      jq1(q, x) AND step(p, x, y)
      IMPLIES jq1(q, y)
  
    jq2(q, x): bool =
      x`aux(q) IMPLIES x`mybuf(q) = x`hind(q)
  
    jq2_dif: LEMMA
      jq2(q, x) AND step(p, x, y) AND p /= q
      IMPLIES jq2(q, y)
  
    jq2_eq_rest: LEMMA
      jq2(p, x) AND step(p, x, y) 
      IMPLIES jq2(p, y) OR x`pc(p) = 25 OR x`pc(p) = 29
  
    jq2_eq_25_29: LEMMA
      jq2(p, x) AND jq0(p, x) AND step(p, x, y) 
      AND (x`pc(p) = 25 OR x`pc(p) = 29)
      IMPLIES jq2(p, y)
  
    jq2_kept_valid: LEMMA
      jq2(q, x) AND jq0(q, x) AND step(p, x, y) 
      IMPLIES jq2(q, y)
  
    jq3(q, x): bool =
      x`pc(q) = 25 AND x`heSet(rem(N)(x`nr(q)))(q) IMPLIES 
      x`bb(q) = x`hind(rem(N)(x`nr(q))) AND x`aux(rem(N)(x`nr(q)))
  % by jq2 this implies x`bb(q) = x`mybuf(rem(N)(x`nr(q)))
  
    jq3_rest: LEMMA
      jq3(q, x) AND step(p, x, y) 
      IMPLIES jq3(q, y) OR rem(N)(x`nr(q)) = p
  
    jq3_adrem: LEMMA
      jq3(q, x) AND jq0(p, x) AND step(p, x, y) AND rem(N)(x`nr(q)) = p
      IMPLIES jq3(q, y)
  
    jq3_kept_valid: LEMMA
      jq3(q, x) AND jq0(p, x) AND step(p, x, y) 
      IMPLIES jq3(q, y)
  
    jq4(q, x): bool =
      x`xSet(q) IMPLIES x`ind(q) = x`xind AND x`nr(q) = x`xnr
  
    jq4_kept_valid: LEMMA
      jq4(q, x) AND step(p, x, y) 
      IMPLIES jq4(q, y)
  
    jq5(q, x): bool =
      x`pc(q) = 23 AND x`baSet(x`nr(q))(q) IMPLIES
      x`nr(q) = x`xnr AND x`ind(q) = x`xind AND x`bank(x`xnr) /= x`xind
  
    jq5_rest: LEMMA
      jq5(q, x) AND step(p, x, y) 
      IMPLIES jq5(q, y) OR x`pc(p) = 22 OR x`pc(p) = 29
  
    jq5_at22: LEMMA
      jq5(q, x) AND jq4(q, x) AND step(p, x, y) AND x`pc(p) = 22
      IMPLIES jq5(q, y)
  
    jq6(q, x): bool =
      x`xSet(q) AND 24 <= x`pc(q) AND x`pc(q) <= 29 IMPLIES 
      x`bank(x`xnr) = x`xind
  
    jq5_at29: LEMMA
      jq5(q, x) AND jq6(p, x) AND step(p, x, y) AND x`pc(p) = 29
      IMPLIES jq5(q, y)
  
    jq5_kept_valid: LEMMA
      jq5(q, x) AND jq4(q, x) AND jq6(p, x) AND step(p, x, y) 
      IMPLIES jq5(q, y) 
  
    jq6_rest: LEMMA
      jq6(q, x) AND step(p, x, y) 
      IMPLIES jq6(q, y) OR x`pc(p) = 22 OR x`pc(p) = 23
  
    jq6_at22: LEMMA
      jq6(q, x) AND jq4(q, x) AND step(p, x, y) AND x`pc(p) = 22 
      IMPLIES jq6(q, y)
  
    jq7(q, x): bool =
      x`pc(q) = 23 AND x`xSet(q) AND NOT x`baSet(x`xnr)(q) IMPLIES 
      x`bank(x`xnr) = x`xind
  
    jq6_at23: LEMMA
      jq6(q, x) AND jq4(q, x) AND jq5(p, x) AND jq7(p, x) 
      AND step(p, x, y) AND x`pc(p) = 23
      IMPLIES jq6(q, y)
  
    jq6_kept_valid: LEMMA
      jq6(q, x) AND jq4(q, x) AND jq5(p, x) AND jq7(p, x) 
      AND step(p, x, y)
      IMPLIES jq6(q, y)
  
    jq7_rest: LEMMA
      jq7(q, x) AND step(p, x, y) 
      IMPLIES jq7(q, y) OR x`pc(p) = 22 OR x`pc(p) = 23
  
    jq7_at22: LEMMA
      jq7(q, x) AND jq4(q, x) AND step(p, x, y) AND x`pc(p) = 22 
      IMPLIES jq7(q, y)
  
    jq7_at23: LEMMA
      jq7(q, x) AND jq5(p, x) AND step(p, x, y) AND x`pc(p) = 23
      IMPLIES jq7(q, y)
  
    jq7_kept_valid: LEMMA
      jq7(q, x) AND jq4(q, x) AND jq5(p, x)
      AND step(p, x, y)
      IMPLIES jq7(q, y)
  
    m: VAR posnat
    k: VAR int
  
    add1mod: LEMMA
      m >= 2 IMPLIES rem(m)(k+1) /= k
  
    jq8(q, x): bool =
      x`pc(q) = 29 AND x`xSet(q) IMPLIES 
      x`bb(q) = x`bank(rem(2*N)(x`xnr +1))
  
    jq8_rest: LEMMA
      jq8(q, x) AND step(p, x, y) 
      IMPLIES jq8(q, y) OR x`pc(p) = 23 OR x`pc(p) = 28
  
    jq8_at23: LEMMA     
      jq8(q, x) AND jq5(p, x) AND step23(p, x, y)
      IMPLIES jq8(q, y)
  
    reduce12: LEMMA
      step(p, x, y) AND (x`pc(p) = 12 OR x`pc(p) = 15) IMPLIES step12(p, x, y)
  
    reduce13: LEMMA
      step(p, x, y) AND (x`pc(p) = 13 OR x`pc(p) = 16) IMPLIES step13(p, x, y)
  
    reduce19: LEMMA
      step(p, x, y) AND x`pc(p) = 19 IMPLIES step19(p, x, y)
  
    reduce21: LEMMA
      step(p, x, y) AND x`pc(p) = 21 IMPLIES step21(p, x, y)
  
    reduce23: LEMMA
      step(p, x, y) AND x`pc(p) = 23 IMPLIES step23(p, x, y)
  
    reduce25: LEMMA
      step(p, x, y) AND x`pc(p) = 25 IMPLIES step25(p, x, y)
  
    reduce27: LEMMA
      step(p, x, y) AND x`pc(p) = 27 IMPLIES step27(p, x, y)
  
    reduce29: LEMMA
      step(p, x, y) AND x`pc(p) = 29 IMPLIES step29(p, x, y)
  
    jq8_at28: LEMMA
      jq8(q, x) AND jq4(q, x) AND step(p, x, y) AND x`pc(p) = 28
      IMPLIES jq8(q, y)
  
    jq8_kept_valid: LEMMA
      jq8(q, x) AND jq4(q, x) AND jq5(p, x) AND step(p, x, y)
      IMPLIES jq8(q, y)
  
    jq9(q, x): bool =
      x`pc(q) = 19 AND x`heSet(q)(q) IMPLIES 
      x`bb(q) = x`hind(q)
  
    jq9_kept_valid: LEMMA
      jq9(q, x) AND step(p, x, y) 
      IMPLIES jq9(q, y) 
  
    mb(q, x): Index =
      IF 12 <= x`pc(q) AND x`pc(q) <= 20 THEN x`hind(q) ELSE x`mybuf(q) ENDIF
  
    iq0(q, r, x): bool =
      mb(q, x) = mb(r, x) IMPLIES q = r 
  
    iq0_dif_rest: LEMMA
      iq0(q, r, x) AND step(p, x, y) AND p /= q AND p /= r
      IMPLIES iq0(q, r, y) OR x`pc(p) = 25
  
    iq0_dif_25d: LEMMA
      iq0(q, r, x) AND rem(N)(x`nr(p)) /= q AND rem(N)(x`nr(p)) /= r
      AND step25(p, x, y) AND p /= q AND p /= r
      IMPLIES iq0(q, r, y)
  
    iq0_dif_25de: LEMMA
      iq0(q, r, x) AND iq0(p, r, x) AND rem(N)(x`nr(p)) = q AND jq3(p, x) 
      AND jq0(q, x) AND step25(p, x, y) AND p /= r
      IMPLIES iq0(q, r, y)
  
    iq0_dif: LEMMA 
      iq0(q, r, x) AND iq0(p, q, x) AND iq0(p, r, x) AND jq3(p, x) 
      AND jq0(rem(N)(x`nr(p)), x) AND step(p, x, y) AND p /= q AND p /= r
      IMPLIES iq0(q, r, y)
  
    iq0_eq_rest: LEMMA 
      iq0(p, r, x) AND step(p, x, y)
      IMPLIES iq0(p, r, y) OR x`pc(p) = 19 OR x`pc(p) = 25 OR x`pc(p) = 29
  
    iq0_eq_19: LEMMA
      iq0(p, r, x) AND jq9(p, x) AND step19(p, x, y)
      IMPLIES iq0(p, r, y)
  
    iq0_eq_25: LEMMA
      iq0(p, r, x) AND iq0(rem(N)(x`nr(p)), r, x) AND jq0(rem(N)(x`nr(p)), x) 
      AND jq3(p, x) AND step25(p, x, y)
      IMPLIES iq0(p, r, y)
  
    iq1(q, x): bool =
      FORALL (k: Number): mb(q, x) = x`bank(k) IMPLIES k = x`xnr
  
    iq0_eq_29: LEMMA     
      iq0(p, r, x) AND iq1(r, x) AND jq8(p, x) AND step29(p, x, y)
      IMPLIES iq0(p, r, y)
  
    iq0_eq: LEMMA
      iq0(p, r, x) AND jq8(p, x) AND jq3(p, x) AND jq9(p, x) 
      AND iq0(rem(N)(x`nr(p)), r, x) AND jq0(rem(N)(x`nr(p)), x) AND iq1(r, x)
      AND step(p, x, y)
      IMPLIES iq0(p, r, y)
  
    iq0_kept_valid: LEMMA 
      iq0(q, r, x) AND iq0(p, q, x) AND iq0(p, r, x) AND jq3(p, x) 
      AND jq8(p, x) AND jq9(p, x) AND jq0(rem(N)(x`nr(p)), x) 
      AND iq0(rem(N)(x`nr(p)), q, x) AND iq0(rem(N)(x`nr(p)), r, x)
      AND iq1(q, x) AND iq1(r, x) AND step(p, x, y) 
      IMPLIES iq0(q, r, y)
  
    n: VAR Number
  
    iq1(q, n, x): bool =
      mb(q, x) = x`bank(n) IMPLIES n = x`xnr
  
    iq1_dif_rest: LEMMA
      iq1(q, n, x) AND step(p, x, y) IMPLIES 
      iq1(q, n, y) OR p = q OR x`pc(p) = 23 OR x`pc(p) = 25 OR x`pc(p) = 29
  
    iq1_at_23: LEMMA
      iq1(q, n, x) AND jq5(p, x) AND step23(p, x, y) IMPLIES 
      iq1(q, n, y)
  
    iq1_dif_25: LEMMA
      iq1(q, n, x) AND iq1(p, n, x) AND step25(p, x, y) IMPLIES 
      iq1(q, n, y) OR p = q 
  
    iq2(q, x): bool =
      mb(q, x) /= x`xind
  
    iq3(x): bool =
      FORALL (i, j): x`bank(i) = x`bank(j) IMPLIES i = j
  
    iq1_dif_29: LEMMA
      iq1(q, n, x) AND jq6(p, x) AND iq2(q, x) AND step29(p, x, y) IMPLIES 
      iq1(q, n, y) OR p = q 
  
    iq1_dif: LEMMA
      iq1(q, n, x) AND jq5(p, x) AND iq1(p, n, x) AND jq6(p, x) AND iq2(q, x) 
      AND step(p, x, y) IMPLIES 
      iq1(q, n, y) OR p = q
  
    iq1_eq_rest: LEMMA
      iq1(p, n, x) AND step(p, x, y) IMPLIES 
      iq1(p, n, y) OR x`pc(p) = 19 OR x`pc(p) = 23 OR x`pc(p) = 25 
      OR x`pc(p) = 29
  
    iq1_eq_19: LEMMA
      iq1(p, n, x) AND jq9(p, x) AND step19(p, x, y) IMPLIES 
      iq1(p, n, y)
  
    iq1_eq_25: LEMMA
      iq1(p, n, x) AND iq1(rem(N)(x`nr(p)), n, x) AND jq0(rem(N)(x`nr(p)), x) 
      AND jq3(p, x) AND step25(p, x, y) IMPLIES 
      iq1(p, n, y)
  
    iq1_eq_29: LEMMA
      iq1(p, n, x) AND iq3(x) AND jq4(p, x) AND jq8(p, x) 
      AND step29(p, x, y) IMPLIES 
      iq1(p, n, y)
  
    iq1_eq: LEMMA
      iq1(p, n, x) AND iq3(x) AND jq4(p, x) AND jq5(p, x) AND jq8(p, x) 
      AND jq9(p, x) AND iq1(rem(N)(x`nr(p)), n, x) AND jq0(rem(N)(x`nr(p)), x) 
      AND jq3(p, x) AND step(p, x, y) IMPLIES 
      iq1(p, n, y)
  
    iq1_kept_valid: LEMMA
      iq1(q, n, x) AND iq3(x) AND jq4(p, x) AND jq5(p, x) AND jq8(p, x) 
      AND jq9(p, x) AND iq1(rem(N)(x`nr(p)), n, x) AND jq0(rem(N)(x`nr(p)), x) 
      AND jq3(p, x) AND iq1(p, n, x) AND jq6(p, x) AND iq2(q, x) 
      AND step(p, x, y) IMPLIES 
      iq1(q, n, y)
  
    iq2_dif_rest: LEMMA
      iq2(q, x) AND step(p, x, y) IMPLIES 
      iq2(q, y) OR p = q OR x`pc(p) = 25 OR x`pc(p) = 29
  
    iq2_dif_25: LEMMA
      iq2(q, x) AND iq2(p, x) AND step25(p, x, y) IMPLIES 
      iq2(q, y) OR p = q
  
    iq2_dif_29: LEMMA
      iq2(q, x) AND iq0(p, q, x) AND step29(p, x, y) IMPLIES 
      iq2(q, y) OR p = q
  
    iq2_dif: LEMMA
      iq2(q, x) AND iq0(p, q, x) AND iq2(p, x) AND step(p, x, y) IMPLIES 
      iq2(q, y) OR p = q
  
    iq2_eq_rest: LEMMA
      iq2(p, x) AND step(p, x, y) IMPLIES 
      iq2(p, y) OR x`pc(p) = 19 OR x`pc(p) = 25 OR x`pc(p) = 29
  
    iq2_eq_19: LEMMA
      iq2(p, x) AND jq9(p, x) AND step19(p, x, y) IMPLIES 
      iq2(p, y)
  
    iq2_eq_25: LEMMA
      iq2(p, x) AND iq2(rem(N)(x`nr(p)), x) AND jq0(rem(N)(x`nr(p)), x) 
      AND jq3(p, x) AND step25(p, x, y) IMPLIES 
      iq2(p, y)
  
    iq2_eq_29: LEMMA
      iq2(p, x) AND jq8(p, x) AND iq1(p, x) AND step29(p, x, y) IMPLIES 
      iq2(p, y)
  
    iq2_eq: LEMMA
      iq2(p, x) AND iq2(rem(N)(x`nr(p)), x) AND jq0(rem(N)(x`nr(p)), x) 
      AND jq3(p, x) AND jq8(p, x) AND jq9(p, x) AND iq1(p, x) 
      AND step(p, x, y) IMPLIES 
      iq2(p, y)
  
    iq2_kept_valid: LEMMA
      iq2(q, x) AND iq0(p, q, x) AND iq2(p, x) AND iq2(rem(N)(x`nr(p)), x) 
      AND jq0(rem(N)(x`nr(p)), x) AND jq3(p, x) AND jq8(p, x) AND jq9(p, x) 
      AND iq1(p, x)  AND step(p, x, y) IMPLIES 
      iq2(q, y)
  
    iq3(i, j, x): bool =
      x`bank(i) = x`bank(j) IMPLIES i = j 
  
    iq3_rest: LEMMA
      iq3(i, j, x) AND step(p, x, y) IMPLIES 
      iq3(i, j, y) OR x`pc(p) = 23
  
    iq4(i, x): bool =
      x`bank(i) = x`xind IMPLIES i = x`xnr
    
    iq3_at23: LEMMA
      iq3(i, j, x) AND jq5(p, x) AND iq4(i, x) AND iq4(j, x) 
      AND step23(p, x, y) IMPLIES 
      iq3(i, j, y)
  
    iq3_kept_valid: LEMMA
      iq3(i, j, x) AND jq5(p, x) AND iq4(i, x) AND iq4(j, x) 
      AND step(p, x, y) IMPLIES 
      iq3(i, j, y)
  
    iq4_rest: LEMMA
      iq4(i, x) AND step(p, x, y) IMPLIES 
      iq4(i, y) OR x`pc(p) = 23 OR x`pc(p) = 29
  
    iq4_at_23: LEMMA
      iq4(i, x) AND jq5(p, x) AND step23(p, x, y) IMPLIES 
      iq4(i, y) 
  
    iq4_at_29: LEMMA
      iq4(i, x) AND iq1(p, i, x) AND iq2(p, x) AND jq6(p, x) AND jq8(p, x) 
      AND step29(p, x, y) IMPLIES 
      iq4(i, y) 
  
    iq4_kept_valid: LEMMA
      iq4(i, x) AND iq1(p, i, x) AND iq2(p, x) AND jq5(p, x) 
      AND jq6(p, x) AND jq8(p, x) AND step(p, x, y) IMPLIES 
      iq4(i, y) 
  
    kq0(x): bool = 
      x`xnr = rem(2 * N)(x`top) AND x`buf(x`xind) = x`absbuf(x`top)
  
    kq0_rest: LEMMA
      kq0(x) AND step(p, x, y) IMPLIES 
      kq0(y) OR x`pc(p) = 21 OR x`pc(p) = 27 OR x`pc(p) = 29
  
    kq0_at_21: LEMMA
      kq0(x) AND iq2(p, x) AND step21(p, x, y) IMPLIES 
      kq0(y)
  
    kq0_at_27: LEMMA
      kq0(x) AND iq2(p, x) AND step27(p, x, y) IMPLIES 
      kq0(y)
  
    kq1(q, x): bool =
      x`pc(q) = 28 OR x`pc(q) = 29 IMPLIES x`buf(x`mybuf(q)) = x`loc(q)
  
    kq0_at_29: LEMMA
      kq0(x) AND kq1(p, x) AND jq4(p, x) AND step29(p, x, y) IMPLIES 
      kq0(y)
  
    kq0_kept_valid: LEMMA
      kq0(x) AND kq1(p, x) AND iq2(p, x) AND jq4(p, x) 
      AND step(p, x, y) IMPLIES 
      kq0(y)
  
    kq1_dif_rest: LEMMA
      kq1(q, x) AND step(p, x, y) IMPLIES 
      kq1(q, y) OR p = q OR x`pc(p) = 21 OR x`pc(p) = 27
  
    kq1_dif_21: LEMMA
      kq1(q, x) AND iq0(p, q, x) AND step21(p, x, y) IMPLIES 
      kq1(q, y) OR p = q
  
    kq1_dif_27: LEMMA
      kq1(q, x) AND iq0(p, q, x) AND step27(p, x, y) IMPLIES 
      kq1(q, y) OR p = q
  
    kq1_dif: LEMMA
      kq1(q, x) AND iq0(p, q, x) AND step(p, x, y) IMPLIES 
      kq1(q, y) OR p = q
  
    kq1_eq: LEMMA
      kq1(p, x) AND step(p, x, y) IMPLIES 
      kq1(p, y)
  
    kq1_kept_valid: LEMMA
      kq1(q, x) AND iq0(p, q, x) AND step(p, x, y) IMPLIES 
      kq1(q, y)
  
    kq2(q, x): bool =
      x`nr(q) = rem(2*N)(x`ptop(q))
  
    kq2_rest: LEMMA
      kq2(q, x) AND step(p, x, y) IMPLIES 
      kq2(q, y) OR x`pc(p) = 12 OR x`pc(p) = 15
  
    kq2_at_12_15: LEMMA
      kq2(q, x) AND kq0(x) AND step12(p, x, y) IMPLIES 
      kq2(q, y)
  
    kq2_kept_valid: LEMMA
      kq2(q, x) AND kq0(x) AND step(p, x, y) IMPLIES 
      kq2(q, y)
  
    kq3(q, x): bool =
      x`xSet(q) AND (14 = x`pc(q) OR (17 <= x`pc(q)AND x`pc(q) <= 21)) IMPLIES
      x`loc(q) = x`absbuf(x`top)
  
    kq3_rest: LEMMA
      kq3(q, x) AND step(p, x, y) IMPLIES 
      kq3(q, y) OR x`pc(p) = 13 OR x`pc(p) = 16
  
    kq3_at_13_16: LEMMA
      kq3(q, x) AND jq4(q, x) AND kq0(x) AND step13(p, x, y) IMPLIES 
      kq3(q, y)
  
    kq3_kept_valid: LEMMA
      kq3(q, x) AND jq4(q, x) AND kq0(x) AND step(p, x, y) IMPLIES 
      kq3(q, y)
  
    kq4(q, x): bool =
      x`xSet(q) AND (30 = x`pc(q) OR (22 <= x`pc(q)AND x`pc(q) <= 25)) IMPLIES
      x`buf(x`mybuf(q)) = x`absbuf(x`top)
  
    kq4_rest: LEMMA
      kq4(q, x) AND step(p, x, y) IMPLIES 
      kq4(q, y) OR x`pc(p) = 21 OR x`pc(p) = 27
  
    kq4_at_21: LEMMA
      kq4(q, x) AND kq3(q, x) AND iq0(p, q, x) AND step21(p, x, y) IMPLIES 
      kq4(q, y)
  
    kq4_at_27: LEMMA
      kq4(q, x) AND iq0(p, q, x) AND step27(p, x, y) IMPLIES 
      kq4(q, y)
  
    kq4_kept_valid: LEMMA
      kq4(q, x) AND kq3(q, x) AND iq0(p, q, x) AND step(p, x, y) IMPLIES 
      kq4(q, y)
  
  
  END multiLLSC
  
  $$$multiLLSC.prf
  (multiLLSC
   (jq0_dif 0
    (jq0_dif-1 nil 3340950086 3341130885 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil))
     7037 6420 nil nil))
   (jq0_eq_rest 0
    (jq0_eq_rest-1 nil 3340950086 3341130888 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil))
     3495 3230 nil nil))
   (jq0_eq_19 0
    (jq0_eq_19-1 nil 3340950086 3341130889
     ("" (skosimp)
      (("" (expand "jq0")
        (("" (expand "step")
          (("" (expand "step11")
            (("" (expand "step12")
              (("" (expand "step13")
                (("" (expand "step14")
                  (("" (expand "step17")
                    (("" (expand "step18")
                      (("" (expand "step19")
                        (("" (expand "step20")
                          (("" (expand "step21")
                            (("" (expand "step22")
                              (("" (expand "step23")
                                ((""
                                  (expand "step24")
                                  ((""
                                    (expand "step25")
                                    ((""
                                      (expand "step27")
                                      ((""
                                        (expand "step28")
                                        ((""
                                          (expand "step29")
                                          ((""
                                            (expand "step30")
                                            ((""
                                              (assert)
                                              ((""
                                                (expand "jq1")
                                                ((""
                                                  (split -3)
                                                  (("1"
                                                    (flatten)
                                                    (("1"
                                                      (replace
  
                                                       -2
                                                       :hide?
  
                                                       t)
                                                      (("1"
                                                        (assert)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (flatten)
                                                    (("2"
                                                      (replace
  
                                                       -1
                                                       :hide?
  
                                                       t)
                                                      (("2"
                                                        (grind)
                                                        nil
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((jq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (jq1 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil))
     1303 1210 nil nil))
   (jq0_kept_valid 0
    (jq0_kept_valid-1 nil 3340950086 3341130890
     ("" (skosimp)
      (("" (use "jq0_dif")
        (("" (assert)
          (("" (use "jq0_eq_rest")
            (("" (assert)
              (("" (use "jq0_eq_19") (("" (assert) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((jq0_dif formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq0_eq_rest formula-decl nil multiLLSC nil)
      (jq0_eq_19 formula-decl nil multiLLSC nil))
     131 100 nil nil))
   (jq1_kept_valid 0
    (jq1_kept_valid-1 nil 3340950086 3341130902 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq1 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     12007 10310 nil nil))
   (jq2_dif 0
    (jq2_dif-1 nil 3340950086 3341130906 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq2 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil))
     4425 4170 nil nil))
   (jq2_eq_rest 0
    (jq2_eq_rest-1 nil 3340950086 3341130908 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq2 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     2134 2010 nil nil))
   (jq2_eq_25_29 0
    (jq2_eq_25_29-1 nil 3340950086 3341130912 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq2 const-decl "bool" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     3443 3270 nil nil))
   (jq2_kept_valid 0
    (jq2_kept_valid-1 nil 3340950086 3341130912
     ("" (skosimp)
      (("" (use "jq2_dif")
        (("" (use "jq2_eq_rest")
          (("" (use "jq2_eq_25_29") (("" (ground) nil nil)) nil)) nil))
        nil))
      nil)
     unchecked
     ((jq2_dif formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq2_eq_25_29 formula-decl nil multiLLSC nil)
      (jq2_eq_rest formula-decl nil multiLLSC nil))
     208 180 nil nil))
   (jq3_rest 0
    (jq3_rest-1 nil 3340950086 3341130973 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     61292 58670 nil nil))
   (jq3_adrem 0
    (jq3_adrem-1 nil 3340950086 3341131032 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (emptyset const-decl "set" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     59138 55580 nil nil))
   (jq3_kept_valid 0
    (jq3_kept_valid-1 nil 3340950086 3341131033
     ("" (skosimp)
      (("" (use "jq3_rest")
        (("" (use "jq3_adrem") (("" (prop) nil nil)) nil)) nil))
      nil)
     unchecked
     ((jq3_rest formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq3_adrem formula-decl nil multiLLSC nil))
     610 580 nil nil))
   (jq4_kept_valid 0
    (jq4_kept_valid-1 nil 3340950086 3341131041 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     7955 6680 nil nil))
   (jq5_rest 0
    (jq5_rest-1 nil 3340950086 3341131086 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (emptyset const-decl "set" sets nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     45298 43140 nil nil))
   (jq5_at22 0
    (jq5_at22-1 nil 3340950086 3341131100 ("" (grind) nil nil) unchecked
     ((Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     13408 11900 nil nil))
   (jq5_at29 0
    (jq5_at29-1 nil 3340950086 3341131106 ("" (grind) nil nil) unchecked
     ((Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     6216 5950 nil nil))
   (jq5_kept_valid 0
    (jq5_kept_valid-1 nil 3340950086 3341131106
     ("" (skosimp)
      (("" (use "jq5_rest")
        (("" (use "jq5_at22")
          (("" (use "jq5_at29") (("" (prop) nil nil)) nil)) nil))
        nil))
      nil)
     unchecked
     ((jq5_rest formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq5_at29 formula-decl nil multiLLSC nil)
      (jq5_at22 formula-decl nil multiLLSC nil))
     186 150 nil nil))
   (jq6_rest 0
    (jq6_rest-1 nil 3340950086 3341131118 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     11800 11150 nil nil))
   (jq6_at22 0
    (jq6_at22-1 nil 3340950086 3341131121 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     3060 2900 nil nil))
   (jq6_at23 0
    (jq6_at23-1 nil 3340950086 3341131125 ("" (grind) nil nil) unchecked
     ((Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (jq7 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     3689 3510 nil nil))
   (jq6_kept_valid 0
    (jq6_kept_valid-1 nil 3340950086 3341131125
     ("" (skosimp)
      (("" (use "jq6_rest")
        (("" (use "jq6_at22")
          (("" (use "jq6_at23") (("" (prop) nil nil)) nil)) nil))
        nil))
      nil)
     unchecked
     ((jq6_rest formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq6_at23 formula-decl nil multiLLSC nil)
      (jq6_at22 formula-decl nil multiLLSC nil))
     194 160 nil nil))
   (jq7_rest 0
    (jq7_rest-1 nil 3340950086 3341131142 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq7 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     17116 16300 nil nil))
   (jq7_at22 0
    (jq7_at22-1 nil 3340950086 3341131147 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (jq7 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     4639 4370 nil nil))
   (jq7_at23 0
    (jq7_at23-1 nil 3340950086 3341131149 ("" (grind) nil nil) unchecked
     ((Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil)
      (jq7 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     2861 2730 nil nil))
   (jq7_kept_valid 0
    (jq7_kept_valid-1 nil 3340950086 3341131150
     ("" (skosimp)
      (("" (use "jq7_rest")
        (("" (use "jq7_at22")
          (("" (use "jq7_at23") (("" (prop) nil nil)) nil)) nil))
        nil))
      nil)
     unchecked
     ((jq7_rest formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq7_at23 formula-decl nil multiLLSC nil)
      (jq7_at22 formula-decl nil multiLLSC nil))
     188 150 nil nil))
   (add1mod 0
    (add1mod-1 nil 3341029782 3341131150
     ("" (skosimp)
      (("" (typepred "rem(m!1)(k!1 + 1)")
        (("" (skolem!)
          (("" (replace -4 :hide? t)
            (("" (assert)
              (("" (use "product_1")
                (("" (assert)
                  (("" (use "neg_times_le") (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil)
      (product_1 formula-decl nil real_props nil)
      (neg_times_le formula-decl nil real_props nil))
     607 560 t shostak))
   (jq8_rest 0
    (jq8_rest-1 nil 3340950086 3341131172 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq8 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     21814 20050 nil nil))
   (jq8_at23 0
    (jq8_at23-1 nil 3340950086 3341131174
     ("" (skosimp)
      (("" (expand "step23")
        (("" (ground)
          (("1" (replace -2 :hide? t)
            (("1" (expand "jq8")
              (("1" (expand "jq5")
                (("1" (flatten)
                  (("1" (assert)
                    (("1" (case "p!1=q!1")
                      (("1" (assert) nil nil)
                       ("2" (assert)
                        (("2"
                          (case "x!1`nr(p!1) = rem(2 * N)(1 + x!1`xnr)")
                          (("1" (assert)
                            (("1" (hide-all-but -1)
                              (("1" (use "add1mod")
                                (("1" (assert) nil nil)) nil))
                              nil))
                            nil)
                           ("2" (assert) nil nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (grind) nil nil))
          nil))
        nil))
      nil)
     unchecked
     ((step23 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (add1mod formula-decl nil multiLLSC nil)
      (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (Item type-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq8 const-decl "bool" multiLLSC nil))
     1486 1390 t nil))
   (reduce12 0
    (reduce12-1 nil 3341131682 3341131722
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     39989 3720 t shostak))
   (reduce13 0
    (reduce13-1 nil 3341139112 3341139126
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     14102 2980 t shostak))
   (reduce19 0
    (reduce19-1 nil 3340970943 3341131175
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     933 910 t shostak))
   (reduce21 0
    (reduce21-1 nil 3341131768 3341131783
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     15104 1260 t shostak))
   (reduce23 0
    (reduce23-1 nil 3340950086 3341131175
     ("" (skosimp)
      (("" (expand "step")
        (("" (assert) (("" (hide +) (("" (grind) nil nil)) nil)) nil))
        nil))
      nil)
     unchecked
     ((step30 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil))
     926 890 t nil))
   (reduce25 0
    (reduce25-1 nil 3340967827 3341131176
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     931 880 t shostak))
   (reduce27 0
    (reduce27-1 nil 3341131789 3341131803
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     14249 1270 t shostak))
   (reduce29 0
    (reduce29-1 nil 3340970969 3341131177
     ("" (skosimp)
      (("" (expand "step") (("" (assert) (("" (grind) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     915 890 t shostak))
   (jq8_at28 0
    (jq8_at28-1 nil 3340950086 3341131181 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (jq8 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     3655 3520 nil nil))
   (jq8_kept_valid 0
    (jq8_kept_valid-1 nil 3340950086 3341131181
     ("" (skosimp)
      (("" (use "jq8_rest")
        (("" (assert)
          (("" (use "jq8_at28")
            (("" (prop)
              (("" (use "reduce23")
                (("" (assert)
                  (("" (use "jq8_at23") (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((jq8_rest formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq8_at28 formula-decl nil multiLLSC nil)
      (reduce23 formula-decl nil multiLLSC nil)
      (jq8_at23 formula-decl nil multiLLSC nil))
     201 170 nil nil))
   (jq9_kept_valid 0
    (jq9_kept_valid-1 nil 3340950096 3341131202 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (emptyset const-decl "set" sets nil)
      (jq9 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     21225 20180 t shostak))
   (iq0_dif_rest 0
    (iq0_dif_rest-1 nil 3340965641 3341131272 ("" (grind) nil nil)
     unchecked
     ((Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil))
     69707 64030 t shostak))
   (iq0_dif_25d 0
    (iq0_dif_25d-1 nil 3340966269 3341131276 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (step25 const-decl "bool" multiLLSC nil))
     3777 3580 t shostak))
   (iq0_dif_25de 0
    (iq0_dif_25de-1 nil 3340966633 3341131280
     ("" (grind)
      (("1" (postpone) nil nil) ("2" (postpone) nil nil)
       ("3" (postpone) nil nil))
      nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil))
     4095 3850 t shostak))
   (iq0_dif 0
    (iq0_dif-1 nil 3340968054 3341131281
     ("" (skosimp)
      (("" (use "iq0_dif_rest" ("p" "p!1" "y" "y!1"))
        (("" (assert)
          (("" (use "reduce25")
            (("" (assert)
              (("" (use "iq0_dif_25d" ("y" "y!1"))
                (("" (assert)
                  ((""
                    (use "iq0_dif_25de"
                         ("p" "p!1" "q" "q!1" "r" "r!1" "x" "x!1" "y"
                          "y!1"))
                    ((""
                      (use "iq0_dif_25de"
                           ("p" "p!1" "q" "r!1" "r" "q!1" "x" "x!1" "y"
                            "y!1"))
                      (("" (assert)
                        (("" (case "rem(N)(x!1`nr(p!1)) = q!1")
                          (("1" (assert) nil nil)
                           ("2" (assert)
                            (("2" (replace 3)
                              (("2" (assert)
                                (("2"
                                  (hide-all-but (-1 -4 5))
                                  (("2"
                                    (expand "iq0")
                                    (("2" (assert) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq0_dif_rest formula-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (Item type-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (iq0_dif_25d formula-decl nil multiLLSC nil)
      (iq0_dif_25de formula-decl nil multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil))
     895 780 t shostak))
   (iq0_eq_rest 0
    (iq0_eq_rest-1 nil 3340969628 3341131310 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     29202 27630 t shostak))
   (iq0_eq_19 0
    (iq0_eq_19-1 nil 3340969860 3341131311 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (jq9 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil))
     658 600 t shostak))
   (iq0_eq_25 0
    (iq0_eq_25-1 nil 3340970137 3341131317 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil))
     5967 4830 t shostak))
   (iq0_eq_29 0
    (iq0_eq_29-1 nil 3340970512 3341131319
     ("" (skosimp)
      (("" (expand "step29")
        (("" (flatten)
          (("" (split)
            (("1" (flatten)
              (("1" (replace -2 :hide? t)
                (("1" (expand "iq0")
                  (("1" (expand "jq8")
                    (("1" (assert)
                      (("1" (expand "mb")
                        (("1" (flatten)
                          (("1" (assert)
                            (("1" (expand "iq1")
                              (("1" (inst?)
                                (("1"
                                  (expand "mb")
                                  (("1"
                                    (use "add1mod")
                                    (("1"
                                      (assert)
                                      (("1" (grind) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (grind) nil nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((step29 const-decl "bool" multiLLSC nil)
      (jq8 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (< const-decl "bool" reals nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (add1mod formula-decl nil multiLLSC nil)
      (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (iq0 const-decl "bool" multiLLSC nil))
     2219 2110 t shostak))
   (iq0_eq 0
    (iq0_eq-1 nil 3340970993 3341131320
     ("" (skosimp)
      (("" (use "iq0_eq_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "iq0_eq_19" ("y" "y!1"))
            (("" (assert)
              (("" (use "iq0_eq_25" ("y" "y!1"))
                (("" (assert)
                  (("" (use "iq0_eq_29" ("y" "y!1"))
                    (("" (assert)
                      (("" (use "reduce19")
                        (("" (use "reduce25")
                          (("" (use "reduce29") (("" (prop) nil nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq0_eq_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (iq0_eq_19 formula-decl nil multiLLSC nil)
      (iq0_eq_25 formula-decl nil multiLLSC nil)
      (iq0_eq_29 formula-decl nil multiLLSC nil)
      (reduce19 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil))
     593 530 t shostak))
   (iq0_kept_valid 0
    (iq0_kept_valid-1 nil 3340971412 3341131320
     ("" (skosimp)
      (("" (use "iq0_dif" ("y" "y!1"))
        (("" (assert)
          (("" (case "p!1=q!1")
            (("1" (assert)
              (("1" (use "iq0_eq" ("y" "y!1")) (("1" (assert) nil nil))
                nil))
              nil)
             ("2" (assert)
              (("2"
                (use "iq0_eq" ("p" "p!1" "r" "q!1" "x" "x!1" "y" "y!1"))
                (("2" (assert)
                  (("2" (hide-all-but (-1 2 3))
                    (("2" (expand "iq0") (("2" (ground) nil nil)) nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq0_dif formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (iq0_eq formula-decl nil multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil))
     777 710 t shostak))
   (iq1_dif_rest 0
    (iq1_dif_rest-1 nil 3341030688 3341131350 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     29357 27850 t shostak))
   (iq1_at_23 0
    (iq1_at_23-1 nil 3341030777 3341131354 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil))
     4623 4350 t shostak))
   (iq1_dif_25 0
    (iq1_dif_25-1 nil 3341030790 3341131360 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil))
     5516 5260 t shostak))
   (iq1_dif_29 0
    (iq1_dif_29-1 nil 3341030813 3341131370 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil))
     10030 8780 t shostak))
   (iq1_dif 0
    (iq1_dif-1 nil 3341030903 3341131370
     ("" (skosimp)
      (("" (use "iq1_dif_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce23")
            (("" (use "reduce25")
              (("" (use "reduce29")
                (("" (assert)
                  (("" (use "iq1_at_23" ("y" "y!1"))
                    (("" (use "iq1_dif_25" ("y" "y!1"))
                      (("" (use "iq1_dif_29" ("y" "y!1"))
                        (("" (prop) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq1_dif_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (reduce23 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (iq1_at_23 formula-decl nil multiLLSC nil)
      (iq1_dif_29 formula-decl nil multiLLSC nil)
      (iq1_dif_25 formula-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil))
     458 420 t shostak))
   (iq1_eq_rest 0
    (iq1_eq_rest-1 nil 3341031002 3341131392 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     21094 19940 t shostak))
   (iq1_eq_19 0
    (iq1_eq_19-1 nil 3341031034 3341131393 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (jq9 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil))
     1262 1150 t shostak))
   (iq1_eq_25 0
    (iq1_eq_25-1 nil 3341031043 3341131399 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil))
     5954 5730 t shostak))
   (iq1_eq_29 0
    (iq1_eq_29-1 nil 3341031058 3341131400
     ("" (skosimp)
      (("" (expand "step29")
        (("" (flatten)
          (("" (split)
            (("1" (flatten)
              (("1" (replace -2 :hide? t)
                (("1" (expand "iq1")
                  (("1" (expand "mb")
                    (("1" (flatten)
                      (("1" (assert)
                        (("1" (expand "jq8")
                          (("1" (replace -5 :hide? t)
                            (("1" (expand "iq3")
                              (("1"
                                (inst - "rem(2 * N)(1 + x!1`xnr)" "n!1")
                                (("1"
                                  (assert)
                                  (("1"
                                    (expand "jq4")
                                    (("1" (propax) nil nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (grind) nil nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((step29 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (< const-decl "bool" reals nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (jq8 const-decl "bool" multiLLSC nil))
     1266 1190 t shostak))
   (iq1_eq 0
    (iq1_eq-1 nil 3341031209 3341131401
     ("" (skosimp)
      (("" (use "iq1_eq_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce19")
            (("" (use "reduce23")
              (("" (use "reduce25")
                (("" (use "reduce29")
                  (("" (assert)
                    (("" (use "iq1_eq_19" ("y" "y!1"))
                      (("" (use "iq1_eq_25" ("y" "y!1"))
                        (("" (use "iq1_eq_29" ("y" "y!1"))
                          (("" (use "iq1_at_23" ("y" "y!1"))
                            (("" (prop) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq1_eq_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (reduce19 formula-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (iq1_eq_25 formula-decl nil multiLLSC nil)
      (iq1_at_23 formula-decl nil multiLLSC nil)
      (iq1_eq_29 formula-decl nil multiLLSC nil)
      (iq1_eq_19 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (reduce23 formula-decl nil multiLLSC nil))
     736 680 t shostak))
   (iq1_kept_valid 0
    (iq1_kept_valid-1 nil 3341031305 3341131401
     ("" (skosimp)
      (("" (use "iq1_dif" ("y" "y!1"))
        (("" (assert)
          (("" (replace -1 :hide? t)
            (("" (use "iq1_eq" ("y" "y!1")) (("" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq1_dif formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (iq1_eq formula-decl nil multiLLSC nil))
     586 540 t shostak))
   (iq2_dif_rest 0
    (iq2_dif_rest-1 nil 3341052917 3341131424 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     22417 20290 t shostak))
   (iq2_dif_25 0
    (iq2_dif_25-1 nil 3341053050 3341131427 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil))
     3564 3400 t shostak))
   (iq2_dif_29 0
    (iq2_dif_29-1 nil 3341053173 3341131431 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil))
     3933 3780 t shostak))
   (iq2_dif 0
    (iq2_dif-1 nil 3341053230 3341131432
     ("" (skosimp)
      (("" (use "iq2_dif_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce25")
            (("" (use "reduce29")
              (("" (assert)
                (("" (use "iq2_dif_25" ("y" "y!1"))
                  (("" (use "iq2_dif_29" ("y" "y!1"))
                    (("" (prop) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq2_dif_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (iq2_dif_29 formula-decl nil multiLLSC nil)
      (iq2_dif_25 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil))
     290 240 t shostak))
   (iq2_eq_rest 0
    (iq2_eq_rest-1 nil 3341053461 3341131445 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     13005 12240 t shostak))
   (iq2_eq_19 0
    (iq2_eq_19-1 nil 3341053578 3341131445 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (jq9 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil))
     379 340 t shostak))
   (iq2_eq_25 0
    (iq2_eq_25-1 nil 3341053767 3341131449 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil))
     3635 3460 t shostak))
   (iq2_eq_29 0
    (iq2_eq_29-1 nil 3341053966 3341131451
     ("" (grind) (("" (use "add1mod") (("" (assert) nil nil)) nil)) nil)
     unchecked
     ((add1mod formula-decl nil multiLLSC nil)
      (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (Item type-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (jq8 const-decl "bool" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil))
     2541 2450 t shostak))
   (iq2_eq 0
    (iq2_eq-1 nil 3341054103 3341131452
     ("" (skosimp)
      (("" (use "iq2_eq_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce19")
            (("" (use "reduce25")
              (("" (use "reduce29")
                (("" (assert)
                  (("" (use "iq2_eq_19" ("y" "y!1"))
                    (("" (use "iq2_eq_29" ("y" "y!1"))
                      (("" (use "iq2_eq_25" ("y" "y!1"))
                        (("" (prop) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq2_eq_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce19 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (iq2_eq_19 formula-decl nil multiLLSC nil)
      (iq2_eq_25 formula-decl nil multiLLSC nil)
      (iq2_eq_29 formula-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil))
     669 630 t shostak))
   (iq2_kept_valid 0
    (iq2_kept_valid-1 nil 3341054292 3341131453
     ("" (skosimp)
      (("" (use "iq2_dif" ("y" "y!1"))
        (("" (assert)
          (("" (replace -1 :hide? t)
            (("" (use "iq2_eq" ("y" "y!1")) (("" (assert) nil nil)) nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq2_dif formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (iq2_eq formula-decl nil multiLLSC nil))
     516 500 t shostak))
   (iq3_rest 0
    (iq3_rest-1 nil 3341054536 3341131455
     ("" (grind)
      (("1" (postpone) nil nil) ("2" (postpone) nil nil)
       ("3" (postpone) nil nil) ("4" (postpone) nil nil)
       ("5" (postpone) nil nil) ("6" (postpone) nil nil)
       ("7" (postpone) nil nil) ("8" (postpone) nil nil)
       ("9" (postpone) nil nil) ("10" (postpone) nil nil)
       ("11" (postpone) nil nil) ("12" (postpone) nil nil)
       ("13" (postpone) nil nil) ("14" (postpone) nil nil)
       ("15" (postpone) nil nil) ("16" (postpone) nil nil)
       ("17" (postpone) nil nil) ("18" (postpone) nil nil)
       ("19" (postpone) nil nil) ("20" (postpone) nil nil)
       ("21" (postpone) nil nil) ("22" (postpone) nil nil)
       ("23" (postpone) nil nil) ("24" (postpone) nil nil)
       ("25" (postpone) nil nil) ("26" (postpone) nil nil)
       ("27" (postpone) nil nil) ("28" (postpone) nil nil)
       ("29" (postpone) nil nil) ("30" (postpone) nil nil)
       ("31" (postpone) nil nil) ("32" (postpone) nil nil)
       ("33" (postpone) nil nil) ("34" (postpone) nil nil)
       ("35" (postpone) nil nil) ("36" (postpone) nil nil)
       ("37" (postpone) nil nil) ("38" (postpone) nil nil)
       ("39" (postpone) nil nil) ("40" (postpone) nil nil)
       ("41" (postpone) nil nil) ("42" (postpone) nil nil)
       ("43" (postpone) nil nil) ("44" (postpone) nil nil)
       ("45" (postpone) nil nil) ("46" (postpone) nil nil)
       ("47" (postpone) nil nil) ("48" (postpone) nil nil)
       ("49" (postpone) nil nil) ("50" (postpone) nil nil)
       ("51" (postpone) nil nil) ("52" (postpone) nil nil)
       ("53" (postpone) nil nil) ("54" (postpone) nil nil)
       ("55" (postpone) nil nil) ("56" (postpone) nil nil)
       ("57" (postpone) nil nil) ("58" (postpone) nil nil)
       ("59" (postpone) nil nil) ("60" (postpone) nil nil)
       ("61" (postpone) nil nil) ("62" (postpone) nil nil)
       ("63" (postpone) nil nil) ("64" (postpone) nil nil)
       ("65" (postpone) nil nil) ("66" (postpone) nil nil)
       ("67" (postpone) nil nil) ("68" (postpone) nil nil)
       ("69" (postpone) nil nil) ("70" (postpone) nil nil)
       ("71" (postpone) nil nil) ("72" (postpone) nil nil)
       ("73" (postpone) nil nil) ("74" (postpone) nil nil)
       ("75" (postpone) nil nil) ("76" (postpone) nil nil)
       ("77" (postpone) nil nil) ("78" (postpone) nil nil)
       ("79" (postpone) nil nil) ("80" (postpone) nil nil)
       ("81" (postpone) nil nil) ("82" (postpone) nil nil)
       ("83" (postpone) nil nil) ("84" (postpone) nil nil)
       ("85" (postpone) nil nil) ("86" (postpone) nil nil)
       ("87" (postpone) nil nil))
      nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     2288 2190 t shostak))
   (iq3_at23 0
    (iq3_at23-1 nil 3341055641 3341131896 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (iq4 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil))
     47612 2930 t shostak))
   (iq3_kept_valid 0
    (iq3_kept_valid-1 nil 3341131909 3341131949
     ("" (skosimp)
      (("" (use "iq3_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce23")
            (("" (assert)
              (("" (use "iq3_at23" ("y" "y!1")) (("" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq3_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (reduce23 formula-decl nil multiLLSC nil)
      (iq3_at23 formula-decl nil multiLLSC nil))
     39404 810 t shostak))
   (iq4_rest 0
    (iq4_rest-1 nil 3341131958 3341131968 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (iq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     10551 6360 t shostak))
   (iq4_at_23 0
    (iq4_at_23-1 nil 3341131974 3341131985 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (iq4 const-decl "bool" multiLLSC nil)
      (/= const-decl "boolean" notequal nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil))
     10845 1110 t shostak))
   (iq4_at_29 0
    (iq4_at_29-1 nil 3341131992 3341131998 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (iq4 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (jq8 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil))
     5606 1890 t shostak))
   (iq4_kept_valid 0
    (iq4_kept_valid-1 nil 3341132007 3341132051
     ("" (skosimp)
      (("" (use "iq4_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce23")
            (("" (use "reduce29")
              (("" (assert)
                (("" (use "iq4_at_23" ("y" "y!1"))
                  (("" (use "iq4_at_29" ("y" "y!1"))
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((iq4_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (reduce23 formula-decl nil multiLLSC nil)
      (iq4_at_29 formula-decl nil multiLLSC nil)
      (iq4_at_23 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil))
     43846 1070 t shostak))
   (kq0_rest 0
    (kq0_rest-1 nil 3341132061 3341132071 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     9655 4610 t shostak))
   (kq0_at_21 0
    (kq0_at_21-1 nil 3341132079 3341132082 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil))
     3734 770 t shostak))
   (kq0_at_27 0
    (kq0_at_27-1 nil 3341132088 3341132092 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil))
     4499 770 t shostak))
   (kq0_at_29 0
    (kq0_at_29-1 nil 3341132100 3341132144
     ("" (grind) (("" (use "rem_sum2") nil nil)) nil) unchecked
     ((posnat nonempty-type-eq-decl nil integers nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (Item type-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (rem_sum2 formula-decl nil modulo_arithmetic nil)
      (boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (kq1 const-decl "bool" multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil))
     43546 2010 t shostak))
   (kq0_kept_valid 0
    (kq0_kept_valid-1 nil 3341132151 3341132205
     ("" (skosimp)
      (("" (use "kq0_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce21")
            (("" (use "reduce27")
              (("" (use "reduce29")
                (("" (assert)
                  (("" (use "kq0_at_29" ("y" "y!1"))
                    (("" (use "kq0_at_27" ("y" "y!1"))
                      (("" (use "kq0_at_21" ("y" "y!1"))
                        (("" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((kq0_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce21 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (kq0_at_29 formula-decl nil multiLLSC nil)
      (kq0_at_21 formula-decl nil multiLLSC nil)
      (kq0_at_27 formula-decl nil multiLLSC nil)
      (reduce27 formula-decl nil multiLLSC nil))
     54065 1100 t shostak))
   (kq1_dif_rest 0
    (kq1_dif_rest-1 nil 3341132214 3341132230 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq1 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     16224 11390 t shostak))
   (kq1_dif_21 0
    (kq1_dif_21-1 nil 3341132241 3341132245 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq1 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil))
     3717 430 t shostak))
   (kq1_dif_27 0
    (kq1_dif_27-1 nil 3341132253 3341132256 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq1 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil))
     3187 410 t shostak))
   (kq1_dif 0
    (kq1_dif-1 nil 3341132262 3341132317
     ("" (skosimp)
      (("" (use "kq1_dif_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce21")
            (("" (use "reduce27")
              (("" (assert)
                (("" (use "kq1_dif_21" ("y" "y!1"))
                  (("" (use "kq1_dif_27" ("y" "y!1"))
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((kq1_dif_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce21 formula-decl nil multiLLSC nil)
      (kq1_dif_27 formula-decl nil multiLLSC nil)
      (kq1_dif_21 formula-decl nil multiLLSC nil)
      (reduce27 formula-decl nil multiLLSC nil))
     54481 920 t shostak))
   (kq1_eq 0
    (kq1_eq-1 nil 3341132348 3341132359 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq1 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     10916 7280 t shostak))
   (kq1_kept_valid 0
    (kq1_kept_valid-1 nil 3341132364 3341132399
     ("" (skosimp)
      (("" (use "kq1_dif" ("y" "y!1"))
        (("" (use "kq1_eq" ("y" "y!1")) (("" (assert) nil nil)) nil))
        nil))
      nil)
     unchecked
     ((kq1_dif formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (kq1_eq formula-decl nil multiLLSC nil))
     35043 380 t shostak))
   (kq2_rest 0
    (kq2_rest-1 nil 3341132408 3341132414 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq2 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     6089 2570 t shostak))
   (kq2_at_12_15 0
    (kq2_at_12_15-1 nil 3341132425 3341132429 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq2 const-decl "bool" multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil))
     4563 1590 t shostak))
   (kq2_kept_valid 0
    (kq2_kept_valid-1 nil 3341132444 3341132613
     ("" (skosimp)
      (("" (use " kq2_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce12")
            (("" (assert)
              (("" (use "kq2_at_12_15" ("y" "y!1")) (("" (prop) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((kq2_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce12 formula-decl nil multiLLSC nil)
      (kq2_at_12_15 formula-decl nil multiLLSC nil))
     168471 1740 t shostak))
   (kq3_rest 0
    (kq3_rest-1 nil 3341138418 3341138982 ("" (grind) nil nil) unchecked
     ((step30 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (kq3 const-decl "bool" multiLLSC nil)
      (emptyset const-decl "set" sets nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (< const-decl "bool" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number nonempty-type-decl nil numbers nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (boolean nonempty-type-decl nil booleans nil))
     35708 23340 t shostak))
   (kq3_at_13_16 0
    (kq3_at_13_16-1 nil 3341138819 3341138827 ("" (grind) nil nil)
     unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq3 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil))
     7869 2530 t shostak))
   (kq3_kept_valid 0
    (kq3_kept_valid-1 nil 3341139015 3341139176
     ("" (skosimp)
      (("" (use "kq3_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce13")
            (("" (assert)
              (("" (use "kq3_at_13_16" ("y" "y!1")) (("" (prop) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     unchecked
     ((kq3_at_13_16 formula-decl nil multiLLSC nil)
      (reduce13 formula-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (Item type-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (kq3_rest formula-decl nil multiLLSC nil))
     39219 560 t shostak))
   (kq4_rest 0
    (kq4_rest-1 nil 3341139459 3341139492 ("" (grind) nil nil) unchecked
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (emptyset const-decl "set" sets nil)
      (kq4 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil))
     32837 26110 t shostak))
   (kq4_at_21 0
    (kq4_at_21-1 nil 3341139547 3341139608
     ("" (grind)
      (("1" (postpone) nil nil) ("2" (postpone) nil nil)
       ("3" (postpone) nil nil) ("4" (postpone) nil nil))
      nil)
     unchecked nil 60633 2090 t shostak))
   (kq4_at_27 0
    (kq4_at_27-1 nil 3341139769 3341139812
     ("" (grind) (("1" (postpone) nil nil) ("2" (postpone) nil nil)) nil)
     unfinished nil 43234 1880 t shostak))
   (kq4_kept_valid 0
    (kq4_kept_valid-1 nil 3341139902 3341139996
     ("" (skosimp)
      (("" (use "kq4_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce21")
            (("" (use "reduce27")
              (("" (assert)
                (("" (use "kq4_at_21" ("y" "y!1"))
                  (("" (use "kq4_at_27" ("y" "y!1"))
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((kq4_rest formula-decl nil multiLLSC nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce21 formula-decl nil multiLLSC nil)
      (kq4_at_27 formula-decl nil multiLLSC nil)
      (kq4_at_21 formula-decl nil multiLLSC nil)
      (reduce27 formula-decl nil multiLLSC nil))
     94277 920 t shostak)))
  
  
  $$$multiLLSC1.pvs
  % Wim H. Hesselink, after Jayanti and Petrovic, November 2005
  
  multiLLSC1: THEORY
  
  BEGIN
    IMPORTING multiLLSC
  
    x, y: VAR state
    p, q, r: VAR Process
    i, j: VAR Number
    n: VAR int
  
    kq5(q, x): bool =
      x`ptop(q) <= x`top 
  
    kq5_kept_valid: LEMMA
      kq5(q, x) AND step(p, x, y) IMPLIES 
      kq5(q, y)
  
    kq6(q, x): bool =
      x`ptop(q) = x`top IFF x`xSet(q)
  
    kq6_kept_valid: LEMMA % kq5 is needed at 29
      kq6(q, x) AND kq5(q, x) AND step(p, x, y) IMPLIES 
      kq6(q, y)
  
    same_rem_bounded: LEMMA
      FORALL (x, y, z: nat): 
        x <= y AND y < x+z AND rem(z)(x) = rem(z)(y) IMPLIES x = y
  
    kq7(q, x): bool =
      x`ptop(q) < x`top AND x`top < x`ptop(q) + 2*N IMPLIES
      x`bank(x`nr(q)) = x`ind(q)
  
    kq7_rest: LEMMA 
      kq7(q, x) AND step(p, x, y) IMPLIES 
      kq7(q, y) OR x`pc(p) = 23  OR x`pc(p) = 29
  
    kq7_at_23: LEMMA 
      kq7(q, x) AND kq0(x) AND kq2(q, x) AND jq5(p, x) 
      AND step23(p, x, y) IMPLIES 
      kq7(q, y)
  
    kq7_at_29: LEMMA 
      kq7(q, x) AND kq6(q, x) AND jq4(q, x) AND jq6(p, x)
      AND step29(p, x, y) IMPLIES 
      kq7(q, y)
  
    kq7_kept_valid: LEMMA 
      kq7(q, x) AND kq0(x) AND kq2(q, x) AND kq6(q, x) AND jq4(q, x) 
      AND jq5(p, x)  AND jq6(p, x) AND step(p, x, y) IMPLIES 
      kq7(q, y)
    
    kq8(q, x): bool =
      (x`pc(q) = 13 OR x`pc(q) = 16) AND x`top < x`ptop(q) + 2*N IMPLIES
      x`buf(x`ind(q)) = x`absbuf(x`ptop(q))
  
    kq8_rest: LEMMA 
      kq8(q, x) AND step(p, x, y) IMPLIES 
      kq8(q, y) OR x`pc(p) = 12 OR x`pc(p) = 15 OR x`pc(p) = 21 
      OR x`pc(p) = 27 OR x`pc(p) = 29
  
    kq8_at_12_15: LEMMA 
      kq8(q, x) AND kq0(x) AND step12(p, x, y) IMPLIES 
      kq8(q, y)
  
    kq8_at_21: LEMMA 
      kq8(q, x) AND kq0(x) AND kq2(q, x) AND kq5(q, x) AND kq6(q, x) 
      AND kq7(q, x) AND iq1(p, x) AND iq2(p, x) AND jq4(q, x) 
      AND step21(p, x, y) IMPLIES 
      kq8(q, y)
  
    kq8_at_27: LEMMA 
      kq8(q, x) AND iq1(p, x) AND iq2(p, x) AND kq0(x) AND kq2(q, x) 
      AND kq5(q, x) AND kq6(q, x) AND kq7(q, x) AND jq4(q, x) 
      AND step27(p, x, y) IMPLIES 
      kq8(q, y)
  
    kq8_at_29: LEMMA 
      kq8(q, x) AND kq5(q, x) 
      AND step29(p, x, y) IMPLIES 
      kq8(q, y)
  
    kq8_kept_valid: LEMMA 
      kq8(q, x) AND iq1(p, x) AND iq2(p, x) AND kq0(x) AND kq2(q, x) 
      AND kq5(q, x) AND kq6(q, x) AND kq7(q, x) AND jq4(q, x) 
      AND step(p, x, y) IMPLIES 
      kq8(q, y)
  
    lq0(q, n, x): bool =
      x`aux(q) AND (x`pc(q) = 13 OR x`pc(q) = 14) AND x`ptop(q) < n
      AND rem(N)(n) = q IMPLIES x`top <= n
  
    lq1(q, r, n, x): bool =
      x`aux(q) AND (x`pc(q) = 13 OR x`pc(q) = 14) AND x`ptop(q) < n
      AND rem(N)(n) = q AND x`top = n AND 27 <= x`pc(r) AND x`pc(r) <= 29
      IMPLIES NOT x`xSet(r)
  
    lq0_rest: LEMMA 
      lq0(q, n, x) AND step(p, x, y) IMPLIES 
      lq0(q, n, y) OR x`pc(p) = 29
  
    lq0_at_29: LEMMA 
      lq0(q, n, x) AND lq1(q, p, n, x) AND step29(p, x, y) IMPLIES 
      lq0(q, n, y)
  
    lq0_kept_valid: LEMMA 
      lq0(q, n, x) AND lq1(q, p, n, x) AND step(p, x, y) IMPLIES 
      lq0(q, n, y)
  
    rem_of_bigger_rem: LEMMA
      FORALL (p, q: posnat), (x: int): rem(p)(rem(q*p)(x)) = rem(p)(x)
  
    lq1_rest: LEMMA 
      lq1(q, r, n, x) AND step(p, x, y) IMPLIES 
      lq1(q, r, n, y) OR x`pc(p) = 24 OR x`pc(p) = 25
  
    lq1_at_24: LEMMA 
      lq1(q, r, n, x) AND jq4(p, x) AND kq0(x) AND step24(p, x, y) 
      IMPLIES lq1(q, r, n, y)
  
    reduce11: LEMMA
      step(p, x, y) AND x`pc(p) = 11 IMPLIES step11(p, x, y)
  
    reduce14: LEMMA
      step(p, x, y) AND x`pc(p) = 14 IMPLIES step14(p, x, y)
  
    reduce17: LEMMA
      step(p, x, y) AND x`pc(p) = 17 IMPLIES step17(p, x, y)
  
    reduce24: LEMMA
      step(p, x, y) AND x`pc(p) = 24 IMPLIES step24(p, x, y)
  
    lq2(q, x): bool =
      x`xSet(q) AND x`pc(q) = 25 AND x`aux(rem(N)(x`xnr)) 
      AND (x`pc(rem(N)(x`xnr)) = 13 OR x`pc(rem(N)(x`xnr)) = 14) 
      IMPLIES x`heSet(rem(N)(x`xnr))(q) OR x`xSet(rem(N)(x`xnr))
  
    lq1_at_25: LEMMA 
      lq1(q, r, n, x) AND jq4(p, x) AND lq2(p, x) AND kq0(x) 
      AND kq6(q, x) AND step25(p, x, y) IMPLIES 
      lq1(q, r, n, y)
  
    lq1_kept_valid: LEMMA 
      lq1(q, r, n, x) AND jq4(p, x) AND lq2(p, x) AND kq0(x) 
      AND kq6(q, x) AND step(p, x, y) IMPLIES 
      lq1(q, r, n, y)
  
    lq2_rest: LEMMA   %   TAKES TIME
      lq2(q, x) AND step(p, x, y) IMPLIES 
      lq2(q, y) OR x`pc(p) = 24
  
    lq2_at_24: LEMMA 
      lq2(q, x) AND jq4(q, x) AND step24(p, x, y) IMPLIES 
      lq2(q, y)
  
    lq2_kept_valid: LEMMA 
      lq2(q, x) AND jq4(q, x) AND step(p, x, y) IMPLIES 
      lq2(q, y)
  
    lq3(q, x): bool =
      x`pc(q) = 25 AND x`heSet(rem(N)(x`nr(q)))(q) IMPLIES 
      x`start(rem(N)(x`nr(q))) <= x`ltop(q)
  
    lq3_rest: LEMMA 
      lq3(q, x) AND step(p, x, y) IMPLIES 
      lq3(q, y) OR x`pc(p) = 11 OR x`pc(p) = 24
  
    lq3_at_11: LEMMA 
      lq3(q, x) AND jq3(q, x) AND jq0(p, x) AND step11(p, x, y) IMPLIES 
      lq3(q, y)
  
    lq4(q, x): bool =
      x`start(q) <= x`top
  
    lq6(q, x): bool =
      x`ltop(q) <= x`top
  
    lq8(q, x): bool =
      x`htop(q) <= x`top
  
    lq3_at_24: LEMMA 
      lq3(q, x) AND lq4(rem(N)(x`nr(q)), x) AND step24(p, x, y) IMPLIES 
      lq3(q, y)
  
    lq3_kept_valid: LEMMA 
      lq3(q, x) AND jq3(q, x) AND jq0(p, x) AND lq4(rem(N)(x`nr(q)), x) 
      AND step(p, x, y) IMPLIES 
      lq3(q, y)
  
    lq4_kept_valid: LEMMA 
      lq4(q, x) AND step(p, x, y) IMPLIES 
      lq4(q, y)
  
    lq5(q, x): bool =
      x`pc(q) = 25 IMPLIES x`buf(x`mybuf(q)) = x`absbuf(x`ltop(q))
  
    lq5_rest: LEMMA 
      lq5(q, x) AND step(p, x, y) IMPLIES 
      lq5(q, y) OR x`pc(p) = 21 OR x`pc(p) = 24 OR x`pc(p) = 27 OR x`pc(p) = 29
  
    lq5_at_21: LEMMA 
      lq5(q, x) AND iq0(p, q, x) AND step21(p, x, y) IMPLIES 
      lq5(q, y)
  
    lq5_at_24: LEMMA 
      lq5(q, x) AND kq4(p, x) AND step24(p, x, y) IMPLIES 
      lq5(q, y)
  
    lq5_at_27: LEMMA 
      lq5(q, x) AND iq0(p, q, x) AND step27(p, x, y) IMPLIES 
      lq5(q, y)
  
    lq5_at_29: LEMMA 
      lq5(q, x) AND lq6(q, x) 
      AND iq0(p, q, x) AND step29(p, x, y) IMPLIES 
      lq5(q, y)
  
    lq5_kept_valid: LEMMA 
      lq5(q, x) AND iq0(p, q, x) AND kq4(p, x) AND lq6(q, x) 
      AND step(p, x, y) IMPLIES 
      lq5(q, y)
   
    lq6_kept_valid: LEMMA 
      lq6(q, x) AND lq8(p, x) AND step(p, x, y) IMPLIES 
      lq6(q, y)
  
    lq7(q, x): bool = 
      12 <= x`pc(q) AND x`pc(q) <= 14 IMPLIES 
      x`buf(x`hind(q)) = x`absbuf(x`htop(q)) OR x`aux(q)
  
    lq7_rest: LEMMA 
      lq7(q, x) AND step(p, x, y) IMPLIES 
      lq7(q, y) OR x`pc(p) = 21 OR x`pc(p) = 25 
      OR x`pc(p) = 27 OR x`pc(p) = 29
  
    lq7_at_21: LEMMA 
      lq7(q, x) AND iq0(p, q, x) AND step21(p, x, y) IMPLIES 
      lq7(q, y)
  
    lq7_at_25: LEMMA 
      lq7(q, x) AND lq5(p, x) AND step25(p, x, y) IMPLIES 
      lq7(q, y)
  
    lq7_at_27: LEMMA 
      lq7(q, x) AND iq0(p, q, x) AND step27(p, x, y) IMPLIES 
      lq7(q, y)
  
    lq7_at_29: LEMMA 
      lq7(q, x) AND lq8(q, x) AND iq0(p, q, x) AND step29(p, x, y) IMPLIES 
      lq7(q, y)
  
    lq7_kept_valid: LEMMA
      lq7(q, x) AND lq5(p, x) AND lq8(q, x) AND iq0(p, q, x) 
      AND step(p, x, y) IMPLIES 
      lq7(q, y)
  
    lq8_rest: LEMMA 
      lq8(q, x) AND step(p, x, y) IMPLIES 
      lq8(q, y) OR x`pc(p) = 25
  
    lq8_at_25: LEMMA 
      lq8(q, x) AND lq6(p, x) AND step25(p, x, y) IMPLIES 
      lq8(q, y)
  
    lq8_kept_valid: LEMMA 
      lq8(q, x) AND lq6(p, x) AND step(p, x, y) IMPLIES 
      lq8(q, y)
  
    lq9(q, x): bool =
      15 <= x`pc(q) AND x`pc(q) <= 17 IMPLIES 
      x`buf(x`bb(q)) = x`absbuf(x`htop(q))
  
    lq10(q, x): bool =
      15 <= x`pc(q) AND x`pc(q) <= 17 IMPLIES 
      x`bb(q) = x`hind(q)
  
    lq11(q, x): bool =
      15 <= x`pc(q) AND x`pc(q) <= 17 IMPLIES 
      NOT x`aux(q) 
  
    lq9_rest: LEMMA 
      lq9(q, x) AND step(p, x, y) IMPLIES 
      lq9(q, y) OR x`pc(p) = 14 OR x`pc(p) = 21 OR x`pc(p) = 25 
      OR x`pc(p) = 27 OR x`pc(p) = 29
  
    lq9_at_14: LEMMA 
      lq9(q, x) AND lq7(q, x) AND step14(p, x, y) IMPLIES 
      lq9(q, y)
  
    lq9_at_21: LEMMA 
      lq9(q, x) AND iq0(p, q, x) AND lq10(q, x) AND step21(p, x, y) IMPLIES 
      lq9(q, y)
  
    lq9_at_25: LEMMA 
      lq9(q, x) AND jq3(p, x) AND lq11(q, x) AND step25(p, x, y) IMPLIES 
      lq9(q, y)
  
    lq9_at_27: LEMMA 
      lq9(q, x) AND iq0(p, q, x) AND lq10(q, x) AND step27(p, x, y) IMPLIES 
      lq9(q, y)
  
    lq9_at_29: LEMMA 
      lq9(q, x) AND iq0(p, q, x) AND lq8(q, x) AND lq10(q, x) 
      AND step29(p, x, y) IMPLIES 
      lq9(q, y)
  
    lq9_kept_valid: LEMMA 
      lq9(q, x) AND iq0(p, q, x) AND jq3(p, x) AND lq7(q, x) AND lq8(q, x) 
      AND lq10(q, x) AND lq11(q, x) AND step(p, x, y) IMPLIES 
      lq9(q, y)
  
    lq10_rest: LEMMA 
      lq10(q, x) AND step(p, x, y) IMPLIES 
      lq10(q, y) OR x`pc(p) = 25 
  
    lq10_at_25: LEMMA 
      lq10(q, x) AND jq3(p, x)  AND lq11(q, x) AND step25(p, x, y) IMPLIES 
      lq10(q, y)
  
    lq10_kept_valid: LEMMA 
      lq10(q, x) AND jq3(p, x)  AND lq11(q, x) AND step(p, x, y) IMPLIES 
      lq10(q, y)
  
    lq11_kept_valid: LEMMA 
      lq11(q, x) AND step(p, x, y) IMPLIES 
      lq11(q, y)
  
    lq12(q, x): bool =
      18 <= x`pc(q) AND x`pc(q) <= 21 IMPLIES 
      x`loc(q) = x`absbuf(x`ltop(q))
  
    lq12_rest: LEMMA 
      lq12(q, x) AND step(p, x, y) IMPLIES 
      lq12(q, y) OR x`pc(p) = 14 OR x`pc(p) = 17 OR x`pc(p) = 29
  
    lq13(q, x): bool =
      13 <= x`pc(q) AND x`pc(q) <= 17 IMPLIES x`ltop(q) = x`ptop(q)
  
    lq14(q, x): bool =
      x`pc(q) = 14 AND x`aux(q) IMPLIES x`loc(q) = x`absbuf(x`ptop(q))
  
    lq12_at_14: LEMMA 
      lq12(q, x) AND lq13(q, x) AND lq14(q, x)
      AND step14(p, x, y) IMPLIES 
      lq12(q, y)
  
    lq12_at_17: LEMMA 
      lq12(q, x) AND kq3(q, x) AND kq6(q, x) AND lq9(q, x) AND lq13(q, x) 
      AND step17(p, x, y) IMPLIES 
      lq12(q, y)
  
    lq12_at_29: LEMMA 
      lq12(q, x) AND lq6(q, x)
      AND step29(p, x, y) IMPLIES 
      lq12(q, y)
  
    lq12_kept_valid: LEMMA 
      lq12(q, x) AND kq3(q, x) AND kq6(q, x) AND lq6(q, x) AND lq9(q, x) 
      AND lq13(q, x) AND lq14(q, x) AND step(p, x, y) IMPLIES 
      lq12(q, y)
  
    lq13_kept_valid: LEMMA 
      lq13(q, x) AND step(p, x, y) IMPLIES 
      lq13(q, y)
  
    lq14_rest: LEMMA 
      lq14(q, x) AND step(p, x, y) IMPLIES 
      lq14(q, y) OR x`pc(p) = 13 OR x`pc(p) = 29
  
    lq14_at_29: LEMMA 
      lq14(q, x) AND kq5(q, x) AND step29(p, x, y) IMPLIES 
      lq14(q, y)
  
    lq0_plus(q, x): bool =
      x`pc(q) = 13 AND x`aux(q) IMPLIES x`top < x`ptop(q) + 2*N
  
    lq14_at_13: LEMMA 
      lq14(q, x) AND kq8(q, x) AND lq0_plus(q, x) AND step13(p, x, y) IMPLIES 
      lq14(q, y)
  
    lq14_kept_valid: LEMMA 
      lq14(q, x) AND kq5(q, x) AND kq8(q, x) AND lq0_plus(q, x) 
      AND step(p, x, y) IMPLIES 
      lq14(q, y)
  
    lq15(q, x): bool =
      13 <= x`pc(q) AND x`pc(q) <= 21 IMPLIES x`start(q) <= x`ltop(q)
  
    lq15_rest: LEMMA 
      lq15(q, x) AND step(p, x, y) IMPLIES 
      lq15(q, y) OR x`pc(p) = 12 OR x`pc(p) = 15 OR x`pc(p) = 17
  
    lq15_at_12: LEMMA     %    also at 15!
      lq15(q, x) AND kq5(q, x) AND lq4(q, x) AND step12(p, x, y) IMPLIES 
      lq15(q, y)
  
    lq16(q, x): bool =
      12 <= x`pc(q) AND x`pc(q) <= 17 IMPLIES 
      x`start(q) <= x`htop(q) OR x`aux(q)
  
    lq15_at_17: LEMMA 
      lq15(q, x) AND lq11(q, x) AND lq16(q, x) AND step17(p, x, y) IMPLIES 
      lq15(q, y)
  
    lq15_kept_valid: LEMMA 
      lq15(q, x) AND kq5(q, x) AND lq4(q, x) AND lq11(q, x) AND lq16(q, x) 
      AND step(p, x, y) IMPLIES 
      lq15(q, y)
  
    lq16_rest: LEMMA 
      lq16(q, x) AND step(p, x, y) IMPLIES 
      lq16(q, y) OR x`pc(p) = 25
  
    lq16_at_25: LEMMA 
      lq16(q, x) AND lq3(p, x) AND step25(p, x, y) IMPLIES 
      lq16(q, y)
  
    lq16_kept_valid: LEMMA 
      lq16(q, x) AND lq3(p, x) AND step(p, x, y) IMPLIES 
      lq16(q, y)
  
  
  END multiLLSC1
  
  $$$multiLLSC1.prf
  (multiLLSC1
   (kq5_kept_valid 0
    (kq5_kept_valid-1 nil 3341552674 3341558612 ("" (grind) nil nil)
     proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     2947 2700 nil nil))
   (kq6_kept_valid 0
    (kq6_kept_valid-1 nil 3341552674 3341558624 ("" (grind) nil nil)
     proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (emptyset const-decl "set" sets nil)
      (kq6 const-decl "bool" multiLLSC1 nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     11118 10590 nil nil))
   (same_rem_bounded_TCC1 0
    (same_rem_bounded_TCC1-1 nil 3341552674 3341558624
     ("" (subtype-tcc) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (>= const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil))
     256 240 nil nil))
   (same_rem_bounded 0
    (same_rem_bounded-1 nil 3341554295 3341558625
     ("" (skosimp)
      (("" (name "d" "y!1-x!1")
        (("" (case "y!1 = x!1+d")
          (("1" (replace -1 :hide? t)
            (("1" (assert)
              (("1" (use "same_remainder" ("x" "d+x!1"))
                (("1" (assert)
                  (("1" (expand "divides")
                    (("1" (skolem!)
                      (("1" (case "d>= 0")
                        (("1" (hide -3 -4)
                          (("1" (case "d < z!1")
                            (("1" (hide -4 -5)
                              (("1" (case "z!1 > 0")
                                (("1"
                                  (case "x!2>= 1")
                                  (("1"
                                    (use
                                     "both_sides_times_pos_ge2"
                                     ("pz" "z!1"))
                                    (("1" (assert) nil nil))
                                    nil)
                                   ("2"
                                    (case "x!2 = 0")
                                    (("1" (assert) nil nil)
                                     ("2"
                                      (use "neg_times_lt")
                                      (("2" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil)
                                 ("2" (assert) nil nil))
                                nil))
                              nil)
                             ("2" (assert) nil nil))
                            nil))
                          nil)
                         ("2" (assert) nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil)
           ("2" (assert) nil nil))
          nil))
        nil))
      nil)
     proved
     ((nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (- const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (same_remainder formula-decl nil modulo_arithmetic nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (divides const-decl "bool" divides nil)
      (< const-decl "bool" reals nil)
      (neg_times_lt formula-decl nil real_props nil)
      (posreal nonempty-type-eq-decl nil real_types nil)
      (nonneg_real nonempty-type-eq-decl nil real_types nil)
      (both_sides_times_pos_ge2 formula-decl nil real_props nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields
         nil))
     909 840 t shostak))
   (kq7_rest 0
    (kq7_rest-1 nil 3341552674 3341558639 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq7 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     14581 12990 nil nil))
   (kq7_at_23 0
    (kq7_at_23-1 nil 3341552674 3341558641
     ("" (skosimp)
      (("" (expand "step23")
        (("" (flatten)
          (("" (split)
            (("1" (flatten)
              (("1" (replace -2 :hide? t)
                (("1" (expand "kq7")
                  (("1" (flatten)
                    (("1" (expand "jq5")
                      (("1" (assert)
                        (("1" (flatten)
                          (("1" (assert)
                            (("1" (expand "kq0")
                              (("1" (expand "kq2")
                                (("1"
                                  (flatten)
                                  (("1"
                                    (hide -4)
                                    (("1"
                                      (case "x!1`nr(q!1) = x!1`xnr")
                                      (("1"
                                        (replace* -1 -5)
                                        (("1"
                                          (assert)
                                          (("1"
                                            (hide-all-but (-4 -9 -10))
                                            (("1"
                                              (name-replace
                                               "aa"
                                               "x!1`ptop(q!1)")
                                              (("1"
                                                (use "same_rem_bounded")
                                                (("1" (assert) nil nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil)
                                       ("2" (assert) nil nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (grind) nil nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((step23 const-decl "bool" multiLLSC nil)
      (kq2 const-decl "bool" multiLLSC nil)
      (same_rem_bounded formula-decl nil multiLLSC1 nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (jq5 const-decl "bool" multiLLSC nil)
      (kq7 const-decl "bool" multiLLSC1 nil)
      (/= const-decl "boolean" notequal nil))
     1565 1500 t nil))
   (kq7_at_29 0
    (kq7_at_29-1 nil 3341552674 3341558642
     ("" (skosimp)
      (("" (expand "step29")
        (("" (flatten)
          (("" (split)
            (("1" (flatten)
              (("1" (replace -2 :hide? t)
                (("1" (expand "kq7")
                  (("1" (assert)
                    (("1" (flatten)
                      (("1" (expand "kq6")
                        (("1" (expand "jq4")
                          (("1" (expand "jq6")
                            (("1" (assert)
                              (("1" (flatten) (("1" (assert) nil nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (grind) nil nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((step29 const-decl "bool" multiLLSC nil)
      (kq6 const-decl "bool" multiLLSC1 nil)
      (jq6 const-decl "bool" multiLLSC nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (kq7 const-decl "bool" multiLLSC1 nil))
     1055 1030 t nil))
   (kq7_kept_valid 0
    (kq7_kept_valid-1 nil 3341552674 3341558642
     ("" (skosimp)
      (("" (use "kq7_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce23")
            (("" (use "reduce29")
              (("" (assert)
                (("" (use "kq7_at_29" ("y" "y!1"))
                  (("" (use "kq7_at_23" ("y" "y!1"))
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((kq7_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce23 formula-decl nil multiLLSC nil)
      (kq7_at_23 formula-decl nil multiLLSC1 nil)
      (kq7_at_29 formula-decl nil multiLLSC1 nil)
      (reduce29 formula-decl nil multiLLSC nil))
     375 320 t nil))
   (kq8_rest 0
    (kq8_rest-1 nil 3341552674 3341558671 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq8 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     28107 27060 t nil))
   (kq8_at_12_15 0
    (kq8_at_12_15-1 nil 3341552674 3341558674 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq8 const-decl "bool" multiLLSC1 nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil))
     3594 3410 t nil))
   (kq8_at_21 0
    (kq8_at_21-1 nil 3341552674 3341558677
     ("" (skosimp)
      (("" (expand "step21")
        (("" (flatten)
          (("" (replace -11 :hide? t)
            (("" (expand "kq8")
              (("" (flatten)
                (("" (case "p!1=q!1")
                  (("1" (grind) nil nil)
                   ("2" (assert)
                    (("2" (split -1)
                      (("1" (case "x!1`mybuf(p!1)= x!1`ind(q!1)")
                        (("1" (assert)
                          (("1" (expand "kq7")
                            (("1" (split)
                              (("1" (expand "iq2")
                                (("1"
                                  (expand "iq1")
                                  (("1"
                                    (inst?)
                                    (("1"
                                      (expand "mb")
                                      (("1"
                                        (assert)
                                        (("1"
                                          (expand "kq0")
                                          (("1"
                                            (expand "kq2")
                                            (("1"
                                              (expand "kq6")
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (expand "jq4")
                                                    (("1"
                                                      (assert)
                                                      (("1"
                                                        (replace* -4 -6)
                                                        (("1"
                                                          (expand "kq5")
                                                          (("1"
                                                            (hide-all-but
                                                             (-7
                                                              -8
                                                              -11
                                                              2))
                                                            (("1"
                                                              (use
                                                               "same_rem_bounde
 d")
                                                              (("1"
                                                                (assert)
                                                                nil
                                                                nil))
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2" (grind) nil nil))
                              nil))
                            nil))
                          nil)
                         ("2" (grind) nil nil))
                        nil)
                       ("2" (propax) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((step21 const-decl "bool" multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (same_rem_bounded formula-decl nil multiLLSC1 nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (iq1 const-decl "bool" multiLLSC nil)
      (mb const-decl "Index" multiLLSC nil)
      (kq7 const-decl "bool" multiLLSC1 nil)
      (kq6 const-decl "bool" multiLLSC1 nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (kq2 const-decl "bool" multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq8 const-decl "bool" multiLLSC1 nil))
     2628 2510 t nil))
   (kq8_at_27 0
    (kq8_at_27-1 nil 3341555094 3341558679
     ("" (skosimp)
      (("" (expand "step27")
        (("" (flatten)
          (("" (replace -11 :hide? t)
            (("" (expand "kq8")
              (("" (case "q!1 = p!1")
                (("1" (grind) nil nil)
                 ("2" (flatten)
                  (("2" (assert)
                    (("2" (split -1)
                      (("1" (case "x!1`mybuf(p!1)=x!1`ind(q!1)")
                        (("1" (assert)
                          (("1" (expand "jq4")
                            (("1" (expand "kq7")
                              (("1" (expand "kq6")
                                (("1"
                                  (expand "kq5")
                                  (("1"
                                    (expand "iq2")
                                    (("1"
                                      (expand "iq1")
                                      (("1"
                                        (expand "mb")
                                        (("1"
                                          (assert)
                                          (("1"
                                            (assert)
                                            (("1"
                                              (expand "kq0")
                                              (("1"
                                                (expand "kq2")
                                                (("1"
                                                  (flatten)
                                                  (("1"
                                                    (inst?)
                                                    (("1"
                                                      (replace* -1 -4 -6)
                                                      (("1"
                                                        (assert)
                                                        (("1"
                                                          (hide-all-but
                                                           (-3 -7 -11 3))
                                                          (("1"
                                                            (use
                                                             "same_rem_bounded"
 )
                                                            (("1"
                                                              (assert)
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil)
                         ("2" (grind) nil nil))
                        nil)
                       ("2" (propax) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((step27 const-decl "bool" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq1 const-decl "bool" multiLLSC nil)
      (iq2 const-decl "bool" multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (kq2 const-decl "bool" multiLLSC nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (kq6 const-decl "bool" multiLLSC1 nil)
      (kq7 const-decl "bool" multiLLSC1 nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (same_rem_bounded formula-decl nil multiLLSC1 nil)
      (kq8 const-decl "bool" multiLLSC1 nil))
     2419 2340 t shostak))
   (kq8_at_29 0
    (kq8_at_29-1 nil 3341555641 3341558684 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (kq8 const-decl "bool" multiLLSC1 nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (step29 const-decl "bool" multiLLSC nil))
     4947 4810 t shostak))
   (kq8_kept_valid 0
    (kq8_kept_valid-1 nil 3341555664 3341558685
     ("" (skosimp)
      (("" (use "kq8_rest")
        (("" (assert)
          (("" (use "reduce12")
            (("" (use "reduce21")
              (("" (use "reduce27")
                (("" (use "reduce29")
                  (("" (assert)
                    (("" (use "kq8_at_12_15" ("y" "y!1"))
                      (("" (use "kq8_at_21" ("y" "y!1"))
                        (("" (use "kq8_at_27" ("y" "y!1"))
                          (("" (use "kq8_at_29" ("y" "y!1"))
                            (("" (assert) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((kq8_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce12 formula-decl nil multiLLSC nil)
      (reduce27 formula-decl nil multiLLSC nil)
      (kq8_at_21 formula-decl nil multiLLSC1 nil)
      (kq8_at_29 formula-decl nil multiLLSC1 nil)
      (kq8_at_27 formula-decl nil multiLLSC1 nil)
      (kq8_at_12_15 formula-decl nil multiLLSC1 nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (reduce21 formula-decl nil multiLLSC nil))
     716 650 t shostak))
   (lq0_rest 0
    (lq0_rest-1 nil 3341555796 3341558716 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq0 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     31269 29060 t shostak))
   (lq0_at_29 0
    (lq0_at_29-1 nil 3341555884 3341558720 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq0 const-decl "bool" multiLLSC1 nil)
      (lq1 const-decl "bool" multiLLSC1 nil)
      (step29 const-decl "bool" multiLLSC nil))
     4035 3850 t shostak))
   (lq0_kept_valid 0
    (lq0_kept_valid-1 nil 3341555902 3341558720
     ("" (skosimp)
      (("" (use "lq0_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce29")
            (("" (assert)
              (("" (use "lq0_at_29" ("y" "y!1")) (("" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq0_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (lq0_at_29 formula-decl nil multiLLSC1 nil))
     146 120 t shostak))
   (rem_of_bigger_rem 0
    (rem_of_bigger_rem-1 nil 3341552674 3341558722
     ("" (skosimp)
      (("" (name "z" "rem(q!1 * p!1)(x!1)")
        (("" (replace -1)
          (("" (use "same_remainder")
            (("" (assert)
              (("" (hide 2)
                (("" (expand "divides")
                  (("" (typepred "rem(q!1 * p!1)(x!1)")
                    (("" (skolem!)
                      (("" (replace -3)
                        (("" (replace -2)
                          (("" (assert)
                            (("" (inst + "-1*q!1*q!2")
                              (("" (assert) nil nil)) nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (same_remainder formula-decl nil modulo_arithmetic nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (- const-decl "[numfield -> numfield]" number_fields nil)
      (divides const-decl "bool" divides nil))
     1993 1940 t nil))
   (lq1_rest 0
    (lq1_rest-1 nil 3341556098 3341558812 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil) (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (emptyset const-decl "set" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (lq1 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     89683 83380 t shostak))
   (lq1_at_24 0
    (lq1_at_24-1 nil 3341552674 3341558817
     ("" (skosimp)
      (("" (expand "step24")
        (("" (flatten)
          (("" (replace -5 :hide? t)
            (("" (expand "lq1")
              (("" (case "p!1 = q!1")
                (("1" (grind) nil nil)
                 ("2" (assert)
                  (("2" (flatten)
                    (("2" (case "p!1=r!1")
                      (("1" (assert)
                        (("1" (expand "jq4")
                          (("1" (expand "kq0")
                            (("1" (flatten)
                              (("1" (assert)
                                (("1"
                                  (lift-if)
                                  (("1"
                                    (split -13)
                                    (("1" (assert) nil nil)
                                     ("2"
                                      (flatten)
                                      (("2"
                                        (assert)
                                        (("2"
                                          (replace -5 :hide? t)
                                          (("2"
                                            (replace -11 :hide? t)
                                            (("2"
                                              (replace -4 :hide? t)
                                              (("2"
                                                (hide-all-but (-9 -6 1))
                                                (("2"
                                                  (use
                                                   "rem_of_bigger_rem")
                                                  (("2"
                                                    (assert)
                                                    nil
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil))
                              nil))
                            nil))
                          nil))
                        nil)
                       ("2" (grind) nil nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((step24 const-decl "bool" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (rem_of_bigger_rem formula-decl nil multiLLSC1 nil)
      (lq1 const-decl "bool" multiLLSC1 nil))
     5036 4760 nil nil))
   (reduce11 0
    (reduce11-1 nil 3341552674 3341558818
     ("" (skosimp)
      (("" (expand "step")
        (("" (assert) (("" (hide +) (("" (grind) nil nil)) nil)) nil))
        nil))
      nil)
     proved
     ((step const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil))
     1021 990 nil nil))
   (reduce14 0
    (reduce14-1 nil 3341552674 3341558819
     ("" (skosimp)
      (("" (expand "step")
        (("" (assert) (("" (hide +) (("" (grind) nil nil)) nil)) nil))
        nil))
      nil)
     proved
     ((step const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil))
     1014 980 nil nil))
   (reduce17 0
    (reduce17-1 nil 3341552674 3341558820
     ("" (skosimp)
      (("" (expand "step")
        (("" (assert) (("" (hide +) (("" (grind) nil nil)) nil)) nil))
        nil))
      nil)
     proved
     ((step const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil))
     1017 990 nil nil))
   (reduce24 0
    (reduce24-1 nil 3341552674 3341558821
     ("" (skosimp)
      (("" (expand "step")
        (("" (assert) (("" (hide +) (("" (grind) nil nil)) nil)) nil))
        nil))
      nil)
     proved
     ((step const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil))
     1002 970 nil nil))
   (lq1_at_25 0
    (lq1_at_25-1 nil 3341552674 3341558837
     ("" (skosimp)
      (("" (expand "step25")
        (("" (flatten)
          (("" (case "p!1=r!1")
            (("1" (replace -1 :hide? t)
              (("1" (expand "lq1")
                (("1" (flatten)
                  (("1" (expand "jq4")
                    (("1" (assert)
                      (("1" (split -2)
                        (("1" (expand "kq0")
                          (("1" (flatten)
                            (("1" (case "y!1`top = x!1`top")
                              (("1" (replace -1 :hide? t)
                                (("1"
                                  (replace* -11 -2)
                                  (("1"
                                    (expand "lq2")
                                    (("1"
                                      (assert)
                                      (("1"
                                        (expand "kq6")
                                        (("1"
                                          (split -8)
                                          (("1"
                                            (flatten)
                                            (("1"
                                              (replace -2 :hide? t)
                                              (("1"
                                                (assert)
                                                (("1"
                                                  (case
                                                   "rem(N)(x!1`xnr) = q!1")
                                                  (("1" (assert) nil nil)
                                                   ("2"
                                                    (replace -5)
                                                    (("2"
                                                      (replace -11)
                                                      (("2"
                                                        (replace
  
                                                         -10
                                                         *
  
                                                         rl)
                                                        (("2"
                                                          (hide -)
                                                          (("2"
                                                            (hide 2)
                                                            (("2"
                                                              (use
                                                               "rem_of_bigger_r
 em")
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil)
                                           ("2"
                                            (flatten)
                                            (("2"
                                              (replace -1 :hide? t)
                                              (("2"
                                                (assert)
                                                (("2"
                                                  (case
                                                   "rem(N)(x!1`xnr) = q!1")
                                                  (("1"
                                                    (replace -1)
                                                    (("1"
                                                      (assert)
                                                      nil
                                                      nil))
                                                    nil)
                                                   ("2"
                                                    (assert)
                                                    (("2"
                                                      (replace -4)
                                                      (("2"
                                                        (replace -11)
                                                        (("2"
                                                          (replace
  
                                                           -10
                                                           *
  
                                                           rl)
                                                          (("2"
                                                            (hide-all-but
                                                             1)
                                                            (("2"
                                                              (use
                                                               "rem_of_bigger_r
 em")
                                                              nil
                                                              nil))
                                                            nil))
                                                          nil))
                                                        nil))
                                                      nil))
                                                    nil))
                                                  nil))
                                                nil))
                                              nil))
                                            nil))
                                          nil))
                                        nil))
                                      nil))
                                    nil))
                                  nil))
                                nil)
                               ("2" (grind) nil nil))
                              nil))
                            nil))
                          nil)
                         ("2" (grind) nil nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil)
             ("2" (grind) nil nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((step25 const-decl "bool" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (= const-decl "[T, T -> boolean]" equalities nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (lq1 const-decl "bool" multiLLSC1 nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (lq2 const-decl "bool" multiLLSC1 nil)
      (kq6 const-decl "bool" multiLLSC1 nil)
      (rem_of_bigger_rem formula-decl nil multiLLSC1 nil)
      (posnat nonempty-type-eq-decl nil integers nil)
      (mod nonempty-type-eq-decl nil euclidean_division nil)
      (numfield nonempty-type-eq-decl nil number_fields nil)
      (+ const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (* const-decl "[numfield, numfield -> numfield]" number_fields nil)
      (rem const-decl "{r: mod(b) | EXISTS q: x = b * q + r}"
           modulo_arithmetic nil)
      (Item type-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (kq0 const-decl "bool" multiLLSC nil))
     15590 14930 nil nil))
   (lq1_kept_valid 0
    (lq1_kept_valid-1 nil 3341552674 3341558837
     ("" (skosimp)
      (("" (use "lq1_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce24")
            (("" (use "reduce25")
              (("" (assert)
                (("" (use "lq1_at_24" ("y" "y!1"))
                  (("" (use "lq1_at_25" ("y" "y!1"))
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq1_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce24 formula-decl nil multiLLSC1 nil)
      (lq1_at_25 formula-decl nil multiLLSC1 nil)
      (lq1_at_24 formula-decl nil multiLLSC1 nil)
      (reduce25 formula-decl nil multiLLSC nil))
     331 310 nil nil))
   (lq2_rest 0
    (lq2_rest-1 nil 3341552674 3341558955 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (emptyset const-decl "set" sets nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (lq2 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     117947 111680 nil nil))
   (lq2_at_24 0
    (lq2_at_24-1 nil 3341552674 3341558983 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (lq2 const-decl "bool" multiLLSC1 nil)
      (jq4 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil))
     27998 27120 nil nil))
   (lq2_kept_valid 0
    (lq2_kept_valid-1 nil 3341552674 3341558983
     ("" (skosimp)
      (("" (use "lq2_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce24")
            (("" (assert)
              (("" (use "lq2_at_24" ("y" "y!1")) (("" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq2_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce24 formula-decl nil multiLLSC1 nil)
      (lq2_at_24 formula-decl nil multiLLSC1 nil))
     166 150 nil nil))
   (lq3_rest 0
    (lq3_rest-1 nil 3341552674 3341559007 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (emptyset const-decl "set" sets nil)
      (member const-decl "bool" sets nil)
      (add const-decl "(nonempty?)" sets nil)
      (lq3 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     23290 22420 nil nil))
   (lq3_at_11 0
    (lq3_at_11-1 nil 3341552674 3341559008 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq3 const-decl "bool" multiLLSC1 nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (jq0 const-decl "bool" multiLLSC nil)
      (step11 const-decl "bool" multiLLSC nil))
     1294 1220 nil nil))
   (lq3_at_24 0
    (lq3_at_24-1 nil 3341552674 3341559018 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (add const-decl "(nonempty?)" sets nil)
      (member const-decl "bool" sets nil)
      (lq3 const-decl "bool" multiLLSC1 nil)
      (lq4 const-decl "bool" multiLLSC1 nil)
      (step24 const-decl "bool" multiLLSC nil))
     10270 9000 nil nil))
   (lq3_kept_valid 0
    (lq3_kept_valid-1 nil 3341552674 3341559019
     ("" (skosimp)
      (("" (use "lq3_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce11")
            (("" (use "reduce24")
              (("" (assert)
                (("" (use "lq3_at_11" ("y" "y!1"))
                  (("" (use "lq3_at_24" ("y" "y!1"))
                    (("" (assert) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq3_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce11 formula-decl nil multiLLSC1 nil)
      (lq3_at_24 formula-decl nil multiLLSC1 nil)
      (lq3_at_11 formula-decl nil multiLLSC1 nil)
      (reduce24 formula-decl nil multiLLSC1 nil))
     678 640 nil nil))
   (lq4_kept_valid 0
    (lq4_kept_valid-1 nil 3341552674 3341559021 ("" (grind) nil nil)
     proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq4 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     2298 2220 nil nil))
   (lq5_rest 0
    (lq5_rest-1 nil 3341552674 3341559032 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq5 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     10893 10440 nil nil))
   (lq5_at_21 0
    (lq5_at_21-1 nil 3341552674 3341559033 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq5 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil))
     626 570 nil nil))
   (lq5_at_24 0
    (lq5_at_24-1 nil 3341552674 3341559036 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq5 const-decl "bool" multiLLSC1 nil)
      (kq4 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil))
     3370 3190 nil nil))
   (lq5_at_27 0
    (lq5_at_27-1 nil 3341552674 3341559037 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq5 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil))
     623 580 nil nil))
   (lq5_at_29 0
    (lq5_at_29-1 nil 3341552674 3341559040 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq5 const-decl "bool" multiLLSC1 nil)
      (lq6 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil))
     3780 3620 nil nil))
   (lq5_kept_valid 0
    (lq5_kept_valid-1 nil 3341552674 3341559041
     ("" (skosimp)
      (("" (use "lq5_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce21")
            (("" (use "reduce24")
              (("" (use "reduce27")
                (("" (use "reduce29")
                  (("" (assert)
                    (("" (use "lq5_at_21" ("y" "y!1"))
                      (("" (use "lq5_at_24" ("y" "y!1"))
                        (("" (use "lq5_at_27" ("y" "y!1"))
                          (("" (use "lq5_at_29" ("y" "y!1"))
                            (("" (assert) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq5_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce21 formula-decl nil multiLLSC nil)
      (reduce27 formula-decl nil multiLLSC nil)
      (lq5_at_24 formula-decl nil multiLLSC1 nil)
      (lq5_at_29 formula-decl nil multiLLSC1 nil)
      (lq5_at_27 formula-decl nil multiLLSC1 nil)
      (lq5_at_21 formula-decl nil multiLLSC1 nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (reduce24 formula-decl nil multiLLSC1 nil))
     443 370 nil nil))
   (lq6_kept_valid 0
    (lq6_kept_valid-1 nil 3341552674 3341559045 ("" (grind) nil nil)
     proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq6 const-decl "bool" multiLLSC1 nil)
      (lq8 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     4487 4320 nil nil))
   (lq7_rest 0
    (lq7_rest-1 nil 3341552674 3341559365
     ("" (grind)
      (("1" (postpone) nil nil) ("2" (postpone) nil nil)
       ("3" (postpone) nil nil))
      nil)
     unfinished nil 62912 13510 t nil))
   (lq7_at_21 0
    (lq7_at_21-1 nil 3341552674 3341559060 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq7 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil))
     888 820 nil nil))
   (lq7_at_25 0
    (lq7_at_25-1 nil 3341552674 3341559063 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq7 const-decl "bool" multiLLSC1 nil)
      (lq5 const-decl "bool" multiLLSC1 nil)
      (step25 const-decl "bool" multiLLSC nil))
     3007 2880 nil nil))
   (lq7_at_27 0
    (lq7_at_27-1 nil 3341552674 3341559064 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq7 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil))
     860 800 nil nil))
   (lq7_at_29 0
    (lq7_at_29-1 nil 3341552674 3341559068 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq7 const-decl "bool" multiLLSC1 nil)
      (lq8 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil))
     3560 3400 nil nil))
   (lq7_kept_valid 0
    (lq7_kept_valid-1 nil 3341552674 3341559068
     ("" (skosimp)
      (("" (use "lq7_rest")
        (("" (assert)
          (("" (use "reduce21")
            (("" (use "reduce25")
              (("" (use "reduce27")
                (("" (use "reduce29")
                  (("" (assert)
                    (("" (use "lq7_at_21" ("y" "y!1"))
                      (("" (use "lq7_at_25" ("y" "y!1"))
                        (("" (use "lq7_at_27" ("y" "y!1"))
                          (("" (use "lq7_at_29" ("y" "y!1"))
                            (("" (assert) nil nil)) nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq7_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce21 formula-decl nil multiLLSC nil)
      (reduce27 formula-decl nil multiLLSC nil)
      (lq7_at_25 formula-decl nil multiLLSC1 nil)
      (lq7_at_29 formula-decl nil multiLLSC1 nil)
      (lq7_at_27 formula-decl nil multiLLSC1 nil)
      (lq7_at_21 formula-decl nil multiLLSC1 nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (reduce25 formula-decl nil multiLLSC nil))
     333 310 nil nil))
   (lq8_rest 0
    (lq8_rest-1 nil 3341552674 3341559070 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq8 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     2129 2030 nil nil))
   (lq8_at_25 0
    (lq8_at_25-1 nil 3341552674 3341559071 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq8 const-decl "bool" multiLLSC1 nil)
      (lq6 const-decl "bool" multiLLSC1 nil)
      (step25 const-decl "bool" multiLLSC nil))
     1010 950 nil nil))
   (lq8_kept_valid 0
    (lq8_kept_valid-1 nil 3341552674 3341559071
     ("" (skosimp)
      (("" (use "lq8_rest")
        (("" (assert)
          (("" (use "reduce25")
            (("" (assert)
              (("" (use "lq8_at_25" ("y" "y!1")) (("" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq8_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (lq8_at_25 formula-decl nil multiLLSC1 nil))
     132 130 nil nil))
   (lq9_rest 0
    (lq9_rest-1 nil 3341552674 3341559085 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     13679 12070 nil nil))
   (lq9_at_14 0
    (lq9_at_14-1 nil 3341552674 3341559088 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (lq7 const-decl "bool" multiLLSC1 nil)
      (step14 const-decl "bool" multiLLSC nil))
     3175 3000 nil nil))
   (lq9_at_21 0
    (lq9_at_21-1 nil 3341552674 3341559089 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (lq10 const-decl "bool" multiLLSC1 nil)
      (step21 const-decl "bool" multiLLSC nil))
     970 910 nil nil))
   (lq9_at_25 0
    (lq9_at_25-1 nil 3341552674 3341559091 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (lq11 const-decl "bool" multiLLSC1 nil)
      (step25 const-decl "bool" multiLLSC nil))
     1868 1770 nil nil))
   (lq9_at_27 0
    (lq9_at_27-1 nil 3341552674 3341559092 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (lq10 const-decl "bool" multiLLSC1 nil)
      (step27 const-decl "bool" multiLLSC nil))
     995 880 nil nil))
   (lq9_at_29 0
    (lq9_at_29-1 nil 3341552674 3341559095 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (mb const-decl "Index" multiLLSC nil)
      (iq0 const-decl "bool" multiLLSC nil)
      (lq8 const-decl "bool" multiLLSC1 nil)
      (lq10 const-decl "bool" multiLLSC1 nil)
      (step29 const-decl "bool" multiLLSC nil))
     3267 3110 nil nil))
   (lq9_kept_valid 0
    (lq9_kept_valid-1 nil 3341552674 3341559096
     ("" (skosimp)
      (("" (use "lq9_rest" ("y" "y!1"))
        (("" (assert)
          (("" (use "reduce14")
            (("" (use "reduce21")
              (("" (use "reduce25")
                (("" (use "reduce27")
                  (("" (use "reduce29")
                    (("" (assert)
                      (("" (use "lq9_at_14" ("y" "y!1"))
                        (("" (use "lq9_at_21" ("y" "y!1"))
                          (("" (use "lq9_at_25" ("y" "y!1"))
                            (("" (use "lq9_at_27" ("y" "y!1"))
                              (("" (use "lq9_at_29" ("y" "y!1"))
                                (("" (assert) nil nil)) nil))
                              nil))
                            nil))
                          nil))
                        nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq9_rest formula-decl nil multiLLSC1 nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (Item type-decl nil multiLLSC nil)
      (number nonempty-type-decl nil numbers nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (>= const-decl "bool" reals nil) (< const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Number type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (state type-eq-decl nil multiLLSC nil)
      (reduce14 formula-decl nil multiLLSC1 nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (reduce29 formula-decl nil multiLLSC nil)
      (lq9_at_14 formula-decl nil multiLLSC1 nil)
      (lq9_at_25 formula-decl nil multiLLSC1 nil)
      (lq9_at_29 formula-decl nil multiLLSC1 nil)
      (lq9_at_27 formula-decl nil multiLLSC1 nil)
      (lq9_at_21 formula-decl nil multiLLSC1 nil)
      (reduce27 formula-decl nil multiLLSC nil)
      (reduce21 formula-decl nil multiLLSC nil))
     603 550 nil nil))
   (lq10_rest 0
    (lq10_rest-1 nil 3341552674 3341559112 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq10 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     15807 15020 nil nil))
   (lq10_at_25 0
    (lq10_at_25-1 nil 3341552674 3341559114 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq10 const-decl "bool" multiLLSC1 nil)
      (jq3 const-decl "bool" multiLLSC nil)
      (lq11 const-decl "bool" multiLLSC1 nil)
      (step25 const-decl "bool" multiLLSC nil))
     1962 1860 nil nil))
   (lq10_kept_valid 0
    (lq10_kept_valid-1 nil 3341552674 3341559114
     ("" (skosimp)
      (("" (use "lq10_rest")
        (("" (assert)
          (("" (use "reduce25")
            (("" (assert)
              (("" (use "lq10_at_25" ("y" "y!1")) (("" (assert) nil nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq10_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (lq10_at_25 formula-decl nil multiLLSC1 nil))
     140 140 nil nil))
   (lq11_kept_valid 0
    (lq11_kept_valid-1 nil 3341552674 3341559124 ("" (grind) nil nil)
     proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq11 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     9911 9370 nil nil))
   (lq12_rest 0
    (lq12_rest-1 nil 3341552674 3341559137 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq12 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     13051 11360 nil nil))
   (lq12_at_14 0
    (lq12_at_14-1 nil 3341552674 3341559140 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq12 const-decl "bool" multiLLSC1 nil)
      (lq13 const-decl "bool" multiLLSC1 nil)
      (lq14 const-decl "bool" multiLLSC1 nil)
      (step14 const-decl "bool" multiLLSC nil))
     2742 2570 nil nil))
   (lq12_at_17 0
    (lq12_at_17-1 nil 3341552674 3341559146 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq12 const-decl "bool" multiLLSC1 nil)
      (kq3 const-decl "bool" multiLLSC nil)
      (kq6 const-decl "bool" multiLLSC1 nil)
      (lq9 const-decl "bool" multiLLSC1 nil)
      (lq13 const-decl "bool" multiLLSC1 nil)
      (step17 const-decl "bool" multiLLSC nil))
     6710 6350 nil nil))
   (lq12_at_29 0
    (lq12_at_29-1 nil 3341552674 3341559148 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq12 const-decl "bool" multiLLSC1 nil)
      (lq6 const-decl "bool" multiLLSC1 nil)
      (step29 const-decl "bool" multiLLSC nil))
     2111 2020 nil nil))
   (lq12_kept_valid 0
    (lq12_kept_valid-1 nil 3341552674 3341559149
     ("" (skosimp)
      (("" (use "lq12_rest")
        (("" (assert)
          (("" (use "reduce14")
            (("" (use "reduce29")
              (("" (use "reduce17")
                (("" (assert)
                  (("" (use "lq12_at_14" ("y" "y!1"))
                    (("" (use "lq12_at_17" ("y" "y!1"))
                      (("" (use "lq12_at_29" ("y" "y!1"))
                        (("" (assert) nil nil)) nil))
                      nil))
                    nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq12_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce14 formula-decl nil multiLLSC1 nil)
      (reduce17 formula-decl nil multiLLSC1 nil)
      (lq12_at_14 formula-decl nil multiLLSC1 nil)
      (lq12_at_29 formula-decl nil multiLLSC1 nil)
      (lq12_at_17 formula-decl nil multiLLSC1 nil)
      (reduce29 formula-decl nil multiLLSC nil))
     405 340 nil nil))
   (lq13_kept_valid 0
    (lq13_kept_valid-1 nil 3341552674 3341559161 ("" (grind) nil nil)
     proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq13 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     12278 11660 nil nil))
   (lq14_rest 0
    (lq14_rest-1 nil 3341552674 3341559173 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq14 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     12166 11550 nil nil))
   (lq14_at_29 0
    (lq14_at_29-1 nil 3341552674 3341559175 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq14 const-decl "bool" multiLLSC1 nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (step29 const-decl "bool" multiLLSC nil))
     2079 1990 nil nil))
   (lq14_at_13 0
    (lq14_at_13-1 nil 3341552674 3341559177 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq14 const-decl "bool" multiLLSC1 nil)
      (kq8 const-decl "bool" multiLLSC1 nil)
      (lq0_plus const-decl "bool" multiLLSC1 nil)
      (step13 const-decl "bool" multiLLSC nil))
     1764 1650 nil nil))
   (lq14_kept_valid 0
    (lq14_kept_valid-1 nil 3341552674 3341559177
     ("" (skosimp)
      (("" (use "lq14_rest")
        (("" (assert)
          (("" (use "reduce13")
            (("" (use "reduce29")
              (("" (assert)
                (("" (use "lq14_at_29" ("y" "y!1"))
                  (("" (use "lq14_at_13" ("y" "y!1"))
                    (("" (ground) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq14_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce13 formula-decl nil multiLLSC nil)
      (lq14_at_13 formula-decl nil multiLLSC1 nil)
      (lq14_at_29 formula-decl nil multiLLSC1 nil)
      (reduce29 formula-decl nil multiLLSC nil))
     300 250 nil nil))
   (lq15_rest 0
    (lq15_rest-1 nil 3341552674 3341559190 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq15 const-decl "bool" multiLLSC1 nil)
      (step11 const-decl "bool" multiLLSC nil)
      (step12 const-decl "bool" multiLLSC nil)
      (step13 const-decl "bool" multiLLSC nil)
      (step14 const-decl "bool" multiLLSC nil)
      (step17 const-decl "bool" multiLLSC nil)
      (step18 const-decl "bool" multiLLSC nil)
      (step19 const-decl "bool" multiLLSC nil)
      (step20 const-decl "bool" multiLLSC nil)
      (step21 const-decl "bool" multiLLSC nil)
      (step22 const-decl "bool" multiLLSC nil)
      (step23 const-decl "bool" multiLLSC nil)
      (step24 const-decl "bool" multiLLSC nil)
      (step25 const-decl "bool" multiLLSC nil)
      (step27 const-decl "bool" multiLLSC nil)
      (step28 const-decl "bool" multiLLSC nil)
      (step29 const-decl "bool" multiLLSC nil)
      (step30 const-decl "bool" multiLLSC nil)
      (step const-decl "bool" multiLLSC nil))
     12846 11180 nil nil))
   (lq15_at_12 0
    (lq15_at_12-1 nil 3341552674 3341559192 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq15 const-decl "bool" multiLLSC1 nil)
      (kq5 const-decl "bool" multiLLSC1 nil)
      (lq4 const-decl "bool" multiLLSC1 nil)
      (step12 const-decl "bool" multiLLSC nil))
     1390 1330 nil nil))
   (lq15_at_17 0
    (lq15_at_17-1 nil 3341552674 3341559194 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq15 const-decl "bool" multiLLSC1 nil)
      (lq11 const-decl "bool" multiLLSC1 nil)
      (lq16 const-decl "bool" multiLLSC1 nil)
      (step17 const-decl "bool" multiLLSC nil))
     2282 2170 nil nil))
   (lq15_kept_valid 0
    (lq15_kept_valid-1 nil 3341552674 3341559194
     ("" (skosimp)
      (("" (use "lq15_rest")
        (("" (assert)
          (("" (use "reduce12")
            (("" (use "reduce17")
              (("" (assert)
                (("" (use "lq15_at_12" ("y" "y!1"))
                  (("" (use "lq15_at_17" ("y" "y!1"))
                    (("" (ground) nil nil)) nil))
                  nil))
                nil))
              nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq15_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce12 formula-decl nil multiLLSC nil)
      (lq15_at_17 formula-decl nil multiLLSC1 nil)
      (lq15_at_12 formula-decl nil multiLLSC1 nil)
      (reduce17 formula-decl nil multiLLSC1 nil))
     262 240 nil nil))
   (lq16_rest 0
    (lq16_rest-1 nil 3341552674 3341559455
     ("" (grind) (("1" (postpone) nil nil) ("2" (postpone) nil nil)) nil)
     unfinished nil 49855 12120 t nil))
   (lq16_at_25 0
    (lq16_at_25-1 nil 3341552674 3341559210 ("" (grind) nil nil) proved
     ((boolean nonempty-type-decl nil booleans nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (NOT const-decl "[bool -> bool]" booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (real nonempty-type-from-decl nil reals nil)
      (< const-decl "bool" reals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (int nonempty-type-eq-decl nil integers nil)
      (>= const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (N const-decl "posint" multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (lq16 const-decl "bool" multiLLSC1 nil)
      (lq3 const-decl "bool" multiLLSC1 nil)
      (step25 const-decl "bool" multiLLSC nil))
     3176 3050 nil nil))
   (lq16_kept_valid 0
    (lq16_kept_valid-1 nil 3341552674 3341559210
     ("" (skosimp)
      (("" (use "lq16_rest")
        (("" (assert)
          (("" (use "reduce25")
            (("" (assert)
              (("" (use "lq16_at_25") (("" (assert) nil nil)) nil)) nil))
            nil))
          nil))
        nil))
      nil)
     proved
     ((lq16_rest formula-decl nil multiLLSC1 nil)
      (state type-eq-decl nil multiLLSC nil)
      (Index type-eq-decl nil multiLLSC nil)
      (Number type-eq-decl nil multiLLSC nil)
      (pred type-eq-decl nil defined_types nil)
      (Item type-decl nil multiLLSC nil)
      (Process type-eq-decl nil multiLLSC nil)
      (N const-decl "posint" multiLLSC nil)
      (posint nonempty-type-eq-decl nil integers nil)
      (> const-decl "bool" reals nil)
      (nonneg_int nonempty-type-eq-decl nil integers nil)
      (< const-decl "bool" reals nil)
      (nat nonempty-type-eq-decl nil naturalnumbers nil)
      (>= const-decl "bool" reals nil)
      (bool nonempty-type-eq-decl nil booleans nil)
      (int nonempty-type-eq-decl nil integers nil)
      (integer_pred const-decl "[rational -> boolean]" integers nil)
      (rational nonempty-type-from-decl nil rationals nil)
      (rational_pred const-decl "[real -> boolean]" rationals nil)
      (real nonempty-type-from-decl nil reals nil)
      (real_pred const-decl "[number_field -> boolean]" reals nil)
      (number_field nonempty-type-from-decl nil number_fields nil)
      (number_field_pred const-decl "[number -> boolean]" number_fields
       nil)
      (boolean nonempty-type-decl nil booleans nil)
      (number nonempty-type-decl nil numbers nil)
      (reduce25 formula-decl nil multiLLSC nil)
      (lq16_at_25 formula-decl nil multiLLSC1 nil))
     151 130 nil nil)))
  
  
  --------------070603020302040201040400--

How-To-Repeat: 

Fix: 

This is a known problem with the current decision procedures, which are
heavily modified versions of Shostak's original code.  Shankar will look
into it, but I expect that this problem will not be solved until we
integrate a new decision procedure.  The basic problem is that the
decision procedures are sensitive to the order assertions are made, and
occasionally miss false assertions such as these.  The workaround is to
use the :flush?  argument to assert, which clears the decision procedure
database (for this sequent) before asserting everything again.

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