TSTP Solution File: NUM437+5 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM437+5 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 11:47:45 EDT 2023

% Result   : Theorem 132.47s 18.33s
% Output   : Proof 132.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM437+5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n015.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.34  % CPULimit : 300
% 0.19/0.34  % WCLimit  : 300
% 0.19/0.34  % DateTime : Fri Aug 25 11:31:07 EDT 2023
% 0.19/0.34  % CPUTime  : 
% 0.19/0.60  ________       _____
% 0.19/0.60  ___  __ \_________(_)________________________________
% 0.19/0.60  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.60  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.60  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60  
% 0.19/0.60  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60  (2023-06-19)
% 0.19/0.60  
% 0.19/0.60  (c) Philipp Rümmer, 2009-2023
% 0.19/0.60  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60                Amanda Stjerna.
% 0.19/0.60  Free software under BSD-3-Clause.
% 0.19/0.60  
% 0.19/0.60  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60  
% 0.19/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.48/1.23  Prover 1: Preprocessing ...
% 3.48/1.23  Prover 4: Preprocessing ...
% 3.97/1.27  Prover 2: Preprocessing ...
% 3.97/1.27  Prover 0: Preprocessing ...
% 3.97/1.27  Prover 3: Preprocessing ...
% 3.97/1.27  Prover 6: Preprocessing ...
% 3.97/1.27  Prover 5: Preprocessing ...
% 10.46/2.20  Prover 5: Constructing countermodel ...
% 10.46/2.20  Prover 3: Constructing countermodel ...
% 10.46/2.21  Prover 1: Constructing countermodel ...
% 10.81/2.21  Prover 6: Proving ...
% 11.05/2.28  Prover 2: Proving ...
% 17.27/3.15  Prover 4: Constructing countermodel ...
% 18.18/3.26  Prover 0: Proving ...
% 72.05/10.34  Prover 2: stopped
% 72.05/10.35  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 72.79/10.44  Prover 7: Preprocessing ...
% 73.85/10.58  Prover 7: Constructing countermodel ...
% 99.08/13.96  Prover 5: stopped
% 99.08/13.96  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 99.68/14.04  Prover 8: Preprocessing ...
% 100.74/14.15  Prover 8: Warning: ignoring some quantifiers
% 100.74/14.15  Prover 8: Constructing countermodel ...
% 114.89/16.01  Prover 1: stopped
% 115.12/16.03  Prover 9: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 115.19/16.09  Prover 9: Preprocessing ...
% 119.93/16.70  Prover 9: Constructing countermodel ...
% 128.40/17.88  Prover 6: stopped
% 128.40/17.90  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.13/18.04  Prover 10: Preprocessing ...
% 130.27/18.10  Prover 10: Constructing countermodel ...
% 132.12/18.32  Prover 10: Found proof (size 35)
% 132.12/18.32  Prover 10: proved (423ms)
% 132.12/18.33  Prover 9: stopped
% 132.12/18.33  Prover 3: stopped
% 132.47/18.33  Prover 0: stopped
% 132.47/18.33  Prover 8: stopped
% 132.47/18.33  Prover 7: stopped
% 132.47/18.33  Prover 4: stopped
% 132.47/18.33  
% 132.47/18.33  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 132.47/18.33  
% 132.47/18.34  % SZS output start Proof for theBenchmark
% 132.47/18.34  Assumptions after simplification:
% 132.47/18.34  ---------------------------------
% 132.47/18.34  
% 132.47/18.34    (mArSeq)
% 132.55/18.37    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v2 |
% 132.55/18.37      v1 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1)
% 132.55/18.37      |  ~ $i(v0) |  ~ aSet0(v3) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |  ? [v4:
% 132.55/18.37        $i] : ($i(v4) & ( ~ aElementOf0(v4, v3) |  ~ sdteqdtlpzmzozddtrp0(v4, v0,
% 132.55/18.37            v1) |  ~ aInteger0(v4)) & (aElementOf0(v4, v3) |
% 132.55/18.37          (sdteqdtlpzmzozddtrp0(v4, v0, v1) & aInteger0(v4))))) &  ! [v0: $i] :  !
% 132.55/18.37    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = sz00 |  ~
% 132.55/18.37      (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 132.55/18.37      ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |
% 132.55/18.37      sdteqdtlpzmzozddtrp0(v3, v0, v1)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 132.55/18.37    :  ! [v3: $i] : (v1 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~
% 132.55/18.37      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~
% 132.55/18.37      aInteger0(v1) |  ~ aInteger0(v0) | aInteger0(v3)) &  ! [v0: $i] :  ! [v1:
% 132.55/18.37      $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = sz00 |  ~
% 132.55/18.37      (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 132.55/18.37      ~ $i(v0) |  ~ sdteqdtlpzmzozddtrp0(v3, v0, v1) |  ~ aInteger0(v3) |  ~
% 132.55/18.37      aInteger0(v1) |  ~ aInteger0(v0) | aElementOf0(v3, v2)) &  ! [v0: $i] :  !
% 132.55/18.37    [v1: $i] :  ! [v2: $i] : (v1 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2)
% 132.55/18.37      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |
% 132.55/18.37      aSet0(v2))
% 132.55/18.37  
% 132.55/18.37    (mEquModRef)
% 132.55/18.38    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] : (v1 = sz00 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 132.55/18.38      aInteger0(v1) |  ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 132.55/18.38  
% 132.55/18.38    (mIntZero)
% 132.55/18.38    $i(sz00) & aInteger0(sz00)
% 132.55/18.38  
% 132.55/18.38    (m__)
% 132.55/18.38    $i(xS) & $i(sz00) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (sbsmnsldt0(xS)
% 132.55/18.38      = v0 & smndt0(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) &
% 132.55/18.38      aSet0(v0) &  ~ isOpen0(v0) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  !
% 132.55/18.39      [v6: $i] :  ! [v7: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) =
% 132.55/18.39          v4) |  ~ (sdtasdt0(v3, v7) = v6) |  ~ (sdtpldt0(v5, v2) = v6) |  ~
% 132.55/18.39        $i(v7) |  ~ $i(v5) |  ~ $i(v3) |  ~ aInteger0(v7) |  ~ aInteger0(v5) |  ~
% 132.55/18.39        aInteger0(v3) | aElementOf0(v5, v4)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 132.55/18.39        $i] :  ! [v6: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4)
% 132.55/18.39        |  ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~ aElementOf0(v5,
% 132.55/18.39          v4) |  ~ aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5, v1, v3)) &  ! [v3: $i]
% 132.55/18.39      :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : (v3 = sz00 |  ~
% 132.55/18.39        (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ (sdtpldt0(v5, v2) = v6) |  ~
% 132.55/18.39        $i(v5) |  ~ $i(v3) |  ~ aElementOf0(v5, v4) |  ~ aInteger0(v3) |
% 132.55/18.39        aDivisorOf0(v3, v6)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6:
% 132.55/18.39        $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.39        (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~ aElementOf0(v5, v4) |
% 132.55/18.39         ~ aInteger0(v3) | aInteger0(v5)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5:
% 132.55/18.39        $i] :  ! [v6: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4)
% 132.55/18.39        |  ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~ aElementOf0(v5,
% 132.55/18.39          v4) |  ~ aInteger0(v3) |  ? [v7: $i] : (sdtasdt0(v3, v7) = v6 & $i(v7) &
% 132.55/18.39          $i(v6) & aInteger0(v7))) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  !
% 132.55/18.39      [v6: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.39        (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~
% 132.55/18.39        sdteqdtlpzmzozddtrp0(v5, v1, v3) |  ~ aInteger0(v5) |  ~ aInteger0(v3) |
% 132.55/18.39        aElementOf0(v5, v4)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6:
% 132.55/18.39        $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.39        (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~ aDivisorOf0(v3, v6) |
% 132.55/18.39         ~ aInteger0(v5) |  ~ aInteger0(v3) | aElementOf0(v5, v4)) &  ! [v3: $i] :
% 132.55/18.39       ! [v4: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.39        $i(v3) |  ~ aSubsetOf0(v4, v0) |  ~ aInteger0(v3)) &  ! [v3: $i] :  ! [v4:
% 132.55/18.39        $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ $i(v3) | 
% 132.55/18.39        ~ aInteger0(v3) | aSet0(v4)) &  ! [v3: $i] :  ! [v4: $i] : (v3 = sz00 |  ~
% 132.55/18.39        (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ $i(v3) |  ~ aInteger0(v3) |  ?
% 132.55/18.39        [v5: $i] : ($i(v5) & aElementOf0(v5, v4) &  ~ aElementOf0(v5, v0))) &  !
% 132.55/18.39      [v3: $i] :  ! [v4: $i] : ( ~ $i(v4) |  ~ $i(v3) |  ~ aElementOf0(v4, xS) | 
% 132.55/18.39        ~ aElementOf0(v3, v4) |  ~ aInteger0(v3) | aElementOf0(v3, v0)) &  ! [v3:
% 132.55/18.39        $i] : ( ~ $i(v3) |  ~ aElementOf0(v3, v0) | aInteger0(v3)) &  ! [v3: $i] :
% 132.55/18.39      ( ~ $i(v3) |  ~ aElementOf0(v3, v0) |  ? [v4: $i] : ($i(v4) &
% 132.55/18.39          aElementOf0(v4, xS) & aElementOf0(v3, v4))))
% 132.55/18.39  
% 132.55/18.39    (m__1750)
% 132.55/18.39    $i(xS) & $i(cS1395) & $i(sz00) & aSet0(xS) &  ! [v0: $i] :  ! [v1: $i] :  !
% 132.55/18.39    [v2: $i] : ( ~ (smndt0(v1) = v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1,
% 132.55/18.39        v0) |  ~ aElementOf0(v0, xS) |  ? [v3: $i] :  ? [v4: $i] : ( ~ (v3 = sz00)
% 132.55/18.39        & szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4 & $i(v4) & $i(v3) & aSubsetOf0(v4,
% 132.55/18.39          v0) & aSet0(v4) & aInteger0(v3) &  ! [v5: $i] :  ! [v6: $i] :  ! [v7:
% 132.55/18.39          $i] : ( ~ (sdtasdt0(v3, v7) = v6) |  ~ (sdtpldt0(v5, v2) = v6) |  ~
% 132.55/18.39          $i(v7) |  ~ $i(v5) |  ~ aInteger0(v7) |  ~ aInteger0(v5) |
% 132.55/18.39          aElementOf0(v5, v4)) &  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5, v2)
% 132.55/18.39            = v6) |  ~ $i(v5) |  ~ aElementOf0(v5, v4) | sdteqdtlpzmzozddtrp0(v5,
% 132.55/18.39            v1, v3)) &  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) | 
% 132.55/18.39          ~ $i(v5) |  ~ aElementOf0(v5, v4) | aDivisorOf0(v3, v6)) &  ! [v5: $i] :
% 132.55/18.39         ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ aElementOf0(v5,
% 132.55/18.39            v4) | aInteger0(v5)) &  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5,
% 132.55/18.39              v2) = v6) |  ~ $i(v5) |  ~ aElementOf0(v5, v4) |  ? [v7: $i] :
% 132.55/18.39          (sdtasdt0(v3, v7) = v6 & $i(v7) & $i(v6) & aInteger0(v7))) &  ! [v5: $i]
% 132.55/18.39        :  ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~
% 132.55/18.39          sdteqdtlpzmzozddtrp0(v5, v1, v3) |  ~ aInteger0(v5) | aElementOf0(v5,
% 132.55/18.39            v4)) &  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~
% 132.55/18.39          $i(v5) |  ~ aDivisorOf0(v3, v6) |  ~ aInteger0(v5) | aElementOf0(v5,
% 132.55/18.39            v4)) &  ! [v5: $i] : ( ~ $i(v5) |  ~ aElementOf0(v5, v4) |
% 132.55/18.39          aElementOf0(v5, v0)))) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~
% 132.55/18.39      $i(v0) |  ~ aElementOf0(v1, v0) |  ~ aElementOf0(v0, xS) | aElementOf0(v1,
% 132.55/18.39        cS1395)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 132.55/18.39      aElementOf0(v1, cS1395) |  ~ aElementOf0(v0, xS) | aInteger0(v1)) &  ! [v0:
% 132.55/18.39      $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v0, xS) |  ~
% 132.55/18.39      aInteger0(v1) | aElementOf0(v1, cS1395)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 132.55/18.39      aElementOf0(v0, xS) | isOpen0(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 132.55/18.39      aElementOf0(v0, xS) | aSubsetOf0(v0, cS1395)) &  ! [v0: $i] : ( ~ $i(v0) | 
% 132.55/18.39      ~ aElementOf0(v0, xS) | aSet0(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 132.55/18.39      aElementOf0(v0, xS) | aSet0(cS1395))
% 132.55/18.39  
% 132.55/18.39  Further assumptions not needed in the proof:
% 132.55/18.39  --------------------------------------------
% 132.55/18.39  mAddAsso, mAddComm, mAddNeg, mAddZero, mClosed, mComplement, mDistrib, mDivisor,
% 132.55/18.39  mElements, mEquMod, mEquModMul, mEquModSym, mEquModTrn, mFinSet, mIntMult,
% 132.55/18.39  mIntNeg, mIntOne, mIntPlus, mIntegers, mIntersection, mMulAsso, mMulComm,
% 132.55/18.39  mMulMinOne, mMulOne, mMulZero, mOpen, mPrime, mPrimeDivisor, mSets, mSubset,
% 132.55/18.39  mUnion, mUnionSet, mZeroDiv
% 132.55/18.39  
% 132.55/18.39  Those formulas are unsatisfiable:
% 132.55/18.39  ---------------------------------
% 132.55/18.39  
% 132.55/18.39  Begin of proof
% 132.55/18.39  | 
% 132.55/18.39  | ALPHA: (mIntZero) implies:
% 132.55/18.39  |   (1)  aInteger0(sz00)
% 132.55/18.39  | 
% 132.55/18.39  | ALPHA: (mEquModRef) implies:
% 132.55/18.40  |   (2)   ! [v0: $i] :  ! [v1: $i] : (v1 = sz00 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 132.55/18.40  |          aInteger0(v1) |  ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 132.55/18.40  | 
% 132.55/18.40  | ALPHA: (mArSeq) implies:
% 132.55/18.40  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = sz00 |  ~
% 132.55/18.40  |          (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 132.55/18.40  |          $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~ aInteger0(v1) |  ~
% 132.55/18.40  |          aInteger0(v0) | aInteger0(v3))
% 132.55/18.40  | 
% 132.55/18.40  | ALPHA: (m__1750) implies:
% 132.55/18.40  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (smndt0(v1) = v2) |  ~
% 132.55/18.40  |          $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1, v0) |  ~ aElementOf0(v0, xS)
% 132.55/18.40  |          |  ? [v3: $i] :  ? [v4: $i] : ( ~ (v3 = sz00) &
% 132.55/18.40  |            szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4 & $i(v4) & $i(v3) &
% 132.55/18.40  |            aSubsetOf0(v4, v0) & aSet0(v4) & aInteger0(v3) &  ! [v5: $i] :  !
% 132.55/18.40  |            [v6: $i] :  ! [v7: $i] : ( ~ (sdtasdt0(v3, v7) = v6) |  ~
% 132.55/18.40  |              (sdtpldt0(v5, v2) = v6) |  ~ $i(v7) |  ~ $i(v5) |  ~
% 132.55/18.40  |              aInteger0(v7) |  ~ aInteger0(v5) | aElementOf0(v5, v4)) &  ! [v5:
% 132.55/18.40  |              $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~
% 132.55/18.40  |              aElementOf0(v5, v4) | sdteqdtlpzmzozddtrp0(v5, v1, v3)) &  ! [v5:
% 132.55/18.40  |              $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~
% 132.55/18.40  |              aElementOf0(v5, v4) | aDivisorOf0(v3, v6)) &  ! [v5: $i] :  !
% 132.55/18.40  |            [v6: $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~
% 132.55/18.40  |              aElementOf0(v5, v4) | aInteger0(v5)) &  ! [v5: $i] :  ! [v6: $i]
% 132.55/18.40  |            : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ aElementOf0(v5, v4)
% 132.55/18.40  |              |  ? [v7: $i] : (sdtasdt0(v3, v7) = v6 & $i(v7) & $i(v6) &
% 132.55/18.40  |                aInteger0(v7))) &  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtpldt0(v5,
% 132.55/18.40  |                  v2) = v6) |  ~ $i(v5) |  ~ sdteqdtlpzmzozddtrp0(v5, v1, v3) |
% 132.55/18.40  |               ~ aInteger0(v5) | aElementOf0(v5, v4)) &  ! [v5: $i] :  ! [v6:
% 132.55/18.40  |              $i] : ( ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~
% 132.55/18.40  |              aDivisorOf0(v3, v6) |  ~ aInteger0(v5) | aElementOf0(v5, v4)) & 
% 132.55/18.40  |            ! [v5: $i] : ( ~ $i(v5) |  ~ aElementOf0(v5, v4) | aElementOf0(v5,
% 132.55/18.40  |                v0))))
% 132.55/18.40  | 
% 132.55/18.40  | ALPHA: (m__) implies:
% 132.55/18.40  |   (5)  $i(sz00)
% 132.55/18.41  |   (6)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (sbsmnsldt0(xS) = v0 &
% 132.55/18.41  |          smndt0(v1) = v2 & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v1, v0) &
% 132.55/18.41  |          aSet0(v0) &  ~ isOpen0(v0) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i]
% 132.55/18.41  |          :  ! [v6: $i] :  ! [v7: $i] : (v3 = sz00 |  ~
% 132.55/18.41  |            (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ (sdtasdt0(v3, v7) = v6)
% 132.55/18.41  |            |  ~ (sdtpldt0(v5, v2) = v6) |  ~ $i(v7) |  ~ $i(v5) |  ~ $i(v3) | 
% 132.55/18.41  |            ~ aInteger0(v7) |  ~ aInteger0(v5) |  ~ aInteger0(v3) |
% 132.55/18.41  |            aElementOf0(v5, v4)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  !
% 132.55/18.41  |          [v6: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.41  |            (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~
% 132.55/18.41  |            aElementOf0(v5, v4) |  ~ aInteger0(v3) | sdteqdtlpzmzozddtrp0(v5,
% 132.55/18.41  |              v1, v3)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i]
% 132.55/18.41  |          : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.41  |            (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~
% 132.55/18.41  |            aElementOf0(v5, v4) |  ~ aInteger0(v3) | aDivisorOf0(v3, v6)) &  !
% 132.55/18.41  |          [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : (v3 = sz00 |  ~
% 132.55/18.41  |            (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ (sdtpldt0(v5, v2) = v6)
% 132.55/18.41  |            |  ~ $i(v5) |  ~ $i(v3) |  ~ aElementOf0(v5, v4) |  ~ aInteger0(v3)
% 132.55/18.41  |            | aInteger0(v5)) &  ! [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  !
% 132.55/18.41  |          [v6: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.41  |            (sdtpldt0(v5, v2) = v6) |  ~ $i(v5) |  ~ $i(v3) |  ~
% 132.55/18.41  |            aElementOf0(v5, v4) |  ~ aInteger0(v3) |  ? [v7: $i] :
% 132.55/18.41  |            (sdtasdt0(v3, v7) = v6 & $i(v7) & $i(v6) & aInteger0(v7))) &  !
% 132.55/18.41  |          [v3: $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : (v3 = sz00 |  ~
% 132.55/18.41  |            (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ (sdtpldt0(v5, v2) = v6)
% 132.55/18.41  |            |  ~ $i(v5) |  ~ $i(v3) |  ~ sdteqdtlpzmzozddtrp0(v5, v1, v3) |  ~
% 132.55/18.41  |            aInteger0(v5) |  ~ aInteger0(v3) | aElementOf0(v5, v4)) &  ! [v3:
% 132.55/18.41  |            $i] :  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : (v3 = sz00 |  ~
% 132.55/18.41  |            (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~ (sdtpldt0(v5, v2) = v6)
% 132.55/18.41  |            |  ~ $i(v5) |  ~ $i(v3) |  ~ aDivisorOf0(v3, v6) |  ~ aInteger0(v5)
% 132.55/18.41  |            |  ~ aInteger0(v3) | aElementOf0(v5, v4)) &  ! [v3: $i] :  ! [v4:
% 132.55/18.41  |            $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.41  |            $i(v3) |  ~ aSubsetOf0(v4, v0) |  ~ aInteger0(v3)) &  ! [v3: $i] : 
% 132.55/18.41  |          ! [v4: $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) | 
% 132.55/18.41  |            ~ $i(v3) |  ~ aInteger0(v3) | aSet0(v4)) &  ! [v3: $i] :  ! [v4:
% 132.55/18.41  |            $i] : (v3 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v1, v3) = v4) |  ~
% 132.55/18.41  |            $i(v3) |  ~ aInteger0(v3) |  ? [v5: $i] : ($i(v5) & aElementOf0(v5,
% 132.55/18.41  |                v4) &  ~ aElementOf0(v5, v0))) &  ! [v3: $i] :  ! [v4: $i] : (
% 132.55/18.41  |            ~ $i(v4) |  ~ $i(v3) |  ~ aElementOf0(v4, xS) |  ~ aElementOf0(v3,
% 132.55/18.41  |              v4) |  ~ aInteger0(v3) | aElementOf0(v3, v0)) &  ! [v3: $i] : ( ~
% 132.55/18.41  |            $i(v3) |  ~ aElementOf0(v3, v0) | aInteger0(v3)) &  ! [v3: $i] : (
% 132.55/18.41  |            ~ $i(v3) |  ~ aElementOf0(v3, v0) |  ? [v4: $i] : ($i(v4) &
% 132.55/18.41  |              aElementOf0(v4, xS) & aElementOf0(v3, v4))))
% 132.55/18.41  | 
% 132.55/18.41  | DELTA: instantiating (6) with fresh symbols all_38_0, all_38_1, all_38_2
% 132.55/18.41  |        gives:
% 132.55/18.42  |   (7)  sbsmnsldt0(xS) = all_38_2 & smndt0(all_38_1) = all_38_0 & $i(all_38_0)
% 132.55/18.42  |        & $i(all_38_1) & $i(all_38_2) & aElementOf0(all_38_1, all_38_2) &
% 132.55/18.42  |        aSet0(all_38_2) &  ~ isOpen0(all_38_2) &  ! [v0: $i] :  ! [v1: $i] :  !
% 132.55/18.42  |        [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : (v0 = sz00 |  ~
% 132.55/18.42  |          (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~ (sdtasdt0(v0, v4) =
% 132.55/18.42  |            v3) |  ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 132.55/18.42  |          $i(v0) |  ~ aInteger0(v4) |  ~ aInteger0(v2) |  ~ aInteger0(v0) |
% 132.55/18.42  |          aElementOf0(v2, v1)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  !
% 132.55/18.42  |        [v3: $i] : (v0 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1)
% 132.55/18.42  |          |  ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2) |  ~ $i(v0) |  ~
% 132.55/18.42  |          aElementOf0(v2, v1) |  ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v2,
% 132.55/18.42  |            all_38_1, v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3:
% 132.55/18.42  |          $i] : (v0 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | 
% 132.55/18.42  |          ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2) |  ~ $i(v0) |  ~
% 132.55/18.42  |          aElementOf0(v2, v1) |  ~ aInteger0(v0) | aDivisorOf0(v0, v3)) &  !
% 132.55/18.42  |        [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v0 = sz00 |  ~
% 132.55/18.42  |          (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~ (sdtpldt0(v2,
% 132.55/18.42  |              all_38_0) = v3) |  ~ $i(v2) |  ~ $i(v0) |  ~ aElementOf0(v2, v1)
% 132.55/18.42  |          |  ~ aInteger0(v0) | aInteger0(v2)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 132.55/18.42  |        [v2: $i] :  ! [v3: $i] : (v0 = sz00 |  ~
% 132.55/18.42  |          (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~ (sdtpldt0(v2,
% 132.55/18.42  |              all_38_0) = v3) |  ~ $i(v2) |  ~ $i(v0) |  ~ aElementOf0(v2, v1)
% 132.55/18.42  |          |  ~ aInteger0(v0) |  ? [v4: $i] : (sdtasdt0(v0, v4) = v3 & $i(v4) &
% 132.55/18.42  |            $i(v3) & aInteger0(v4))) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 132.55/18.42  |        :  ! [v3: $i] : (v0 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) =
% 132.55/18.42  |            v1) |  ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2) |  ~ $i(v0) |  ~
% 132.55/18.42  |          sdteqdtlpzmzozddtrp0(v2, all_38_1, v0) |  ~ aInteger0(v2) |  ~
% 132.55/18.42  |          aInteger0(v0) | aElementOf0(v2, v1)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 132.55/18.42  |        [v2: $i] :  ! [v3: $i] : (v0 = sz00 |  ~
% 132.55/18.42  |          (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~ (sdtpldt0(v2,
% 132.55/18.42  |              all_38_0) = v3) |  ~ $i(v2) |  ~ $i(v0) |  ~ aDivisorOf0(v0, v3)
% 132.55/18.42  |          |  ~ aInteger0(v2) |  ~ aInteger0(v0) | aElementOf0(v2, v1)) &  !
% 132.55/18.42  |        [v0: $i] :  ! [v1: $i] : (v0 = sz00 |  ~
% 132.55/18.42  |          (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~ $i(v0) |  ~
% 132.55/18.42  |          aSubsetOf0(v1, all_38_2) |  ~ aInteger0(v0)) &  ! [v0: $i] :  ! [v1:
% 132.55/18.42  |          $i] : (v0 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) | 
% 132.55/18.42  |          ~ $i(v0) |  ~ aInteger0(v0) | aSet0(v1)) &  ! [v0: $i] :  ! [v1: $i]
% 132.55/18.42  |        : (v0 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~
% 132.55/18.42  |          $i(v0) |  ~ aInteger0(v0) |  ? [v2: $i] : ($i(v2) & aElementOf0(v2,
% 132.55/18.42  |              v1) &  ~ aElementOf0(v2, all_38_2))) &  ! [v0: $i] :  ! [v1: $i]
% 132.55/18.42  |        : ( ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1, xS) |  ~ aElementOf0(v0,
% 132.55/18.42  |            v1) |  ~ aInteger0(v0) | aElementOf0(v0, all_38_2)) &  ! [v0: $i] :
% 132.55/18.42  |        ( ~ $i(v0) |  ~ aElementOf0(v0, all_38_2) | aInteger0(v0)) &  ! [v0:
% 132.55/18.42  |          $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_38_2) |  ? [v1: $i] :
% 132.55/18.42  |          ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1)))
% 132.55/18.42  | 
% 132.55/18.42  | ALPHA: (7) implies:
% 132.55/18.42  |   (8)  aElementOf0(all_38_1, all_38_2)
% 132.55/18.42  |   (9)  $i(all_38_1)
% 132.55/18.42  |   (10)  smndt0(all_38_1) = all_38_0
% 132.55/18.42  |   (11)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_38_2) |  ? [v1: $i]
% 132.55/18.42  |           : ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1)))
% 132.55/18.42  |   (12)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_38_2) |
% 132.55/18.42  |           aInteger0(v0))
% 132.55/18.42  |   (13)   ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 132.55/18.42  |           aElementOf0(v1, xS) |  ~ aElementOf0(v0, v1) |  ~ aInteger0(v0) |
% 132.55/18.42  |           aElementOf0(v0, all_38_2))
% 132.55/18.42  |   (14)   ! [v0: $i] :  ! [v1: $i] : (v0 = sz00 |  ~
% 132.55/18.42  |           (szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1) |  ~ $i(v0) |  ~
% 132.55/18.42  |           aInteger0(v0) |  ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) &  ~
% 132.55/18.42  |             aElementOf0(v2, all_38_2)))
% 132.55/18.42  | 
% 132.55/18.42  | GROUND_INST: instantiating (12) with all_38_1, simplifying with (8), (9)
% 132.55/18.42  |              gives:
% 132.55/18.42  |   (15)  aInteger0(all_38_1)
% 132.55/18.42  | 
% 132.55/18.42  | GROUND_INST: instantiating (11) with all_38_1, simplifying with (8), (9)
% 132.55/18.42  |              gives:
% 132.55/18.42  |   (16)   ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & aElementOf0(all_38_1,
% 132.55/18.42  |             v0))
% 132.55/18.42  | 
% 132.55/18.42  | DELTA: instantiating (16) with fresh symbol all_51_0 gives:
% 132.55/18.42  |   (17)  $i(all_51_0) & aElementOf0(all_51_0, xS) & aElementOf0(all_38_1,
% 132.55/18.42  |           all_51_0)
% 132.55/18.42  | 
% 132.55/18.42  | ALPHA: (17) implies:
% 132.55/18.42  |   (18)  aElementOf0(all_38_1, all_51_0)
% 132.55/18.42  |   (19)  aElementOf0(all_51_0, xS)
% 132.55/18.42  |   (20)  $i(all_51_0)
% 132.55/18.42  | 
% 132.55/18.43  | GROUND_INST: instantiating (4) with all_51_0, all_38_1, all_38_0, simplifying
% 132.55/18.43  |              with (9), (10), (18), (19), (20) gives:
% 132.55/18.43  |   (21)   ? [v0: $i] :  ? [v1: $i] : ( ~ (v0 = sz00) &
% 132.55/18.43  |           szAzrzSzezqlpdtcmdtrp0(all_38_1, v0) = v1 & $i(v1) & $i(v0) &
% 132.55/18.43  |           aSubsetOf0(v1, all_51_0) & aSet0(v1) & aInteger0(v0) &  ! [v2: $i] :
% 132.55/18.43  |            ! [v3: $i] :  ! [v4: $i] : ( ~ (sdtasdt0(v0, v4) = v3) |  ~
% 132.55/18.43  |             (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v4) |  ~ $i(v2) |  ~
% 132.55/18.43  |             aInteger0(v4) |  ~ aInteger0(v2) | aElementOf0(v2, v1)) &  ! [v2:
% 132.55/18.43  |             $i] :  ! [v3: $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2)
% 132.55/18.43  |             |  ~ aElementOf0(v2, v1) | sdteqdtlpzmzozddtrp0(v2, all_38_1, v0))
% 132.55/18.43  |           &  ! [v2: $i] :  ! [v3: $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) |  ~
% 132.55/18.43  |             $i(v2) |  ~ aElementOf0(v2, v1) | aDivisorOf0(v0, v3)) &  ! [v2:
% 132.55/18.43  |             $i] :  ! [v3: $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2)
% 132.55/18.43  |             |  ~ aElementOf0(v2, v1) | aInteger0(v2)) &  ! [v2: $i] :  ! [v3:
% 132.55/18.43  |             $i] : ( ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2) |  ~
% 132.55/18.43  |             aElementOf0(v2, v1) |  ? [v4: $i] : (sdtasdt0(v0, v4) = v3 &
% 132.55/18.43  |               $i(v4) & $i(v3) & aInteger0(v4))) &  ! [v2: $i] :  ! [v3: $i] :
% 132.55/18.43  |           ( ~ (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2) |  ~
% 132.55/18.43  |             sdteqdtlpzmzozddtrp0(v2, all_38_1, v0) |  ~ aInteger0(v2) |
% 132.55/18.43  |             aElementOf0(v2, v1)) &  ! [v2: $i] :  ! [v3: $i] : ( ~
% 132.55/18.43  |             (sdtpldt0(v2, all_38_0) = v3) |  ~ $i(v2) |  ~ aDivisorOf0(v0, v3)
% 132.55/18.43  |             |  ~ aInteger0(v2) | aElementOf0(v2, v1)) &  ! [v2: $i] : ( ~
% 132.55/18.43  |             $i(v2) |  ~ aElementOf0(v2, v1) | aElementOf0(v2, all_51_0)))
% 132.55/18.43  | 
% 132.55/18.43  | DELTA: instantiating (21) with fresh symbols all_61_0, all_61_1 gives:
% 132.55/18.43  |   (22)   ~ (all_61_1 = sz00) & szAzrzSzezqlpdtcmdtrp0(all_38_1, all_61_1) =
% 132.55/18.43  |         all_61_0 & $i(all_61_0) & $i(all_61_1) & aSubsetOf0(all_61_0,
% 132.55/18.43  |           all_51_0) & aSet0(all_61_0) & aInteger0(all_61_1) &  ! [v0: $i] :  !
% 132.55/18.43  |         [v1: $i] :  ! [v2: $i] : ( ~ (sdtasdt0(all_61_1, v2) = v1) |  ~
% 132.55/18.43  |           (sdtpldt0(v0, all_38_0) = v1) |  ~ $i(v2) |  ~ $i(v0) |  ~
% 132.55/18.43  |           aInteger0(v2) |  ~ aInteger0(v0) | aElementOf0(v0, all_61_0)) &  !
% 132.55/18.43  |         [v0: $i] :  ! [v1: $i] : ( ~ (sdtpldt0(v0, all_38_0) = v1) |  ~ $i(v0)
% 132.55/18.43  |           |  ~ aElementOf0(v0, all_61_0) | sdteqdtlpzmzozddtrp0(v0, all_38_1,
% 132.55/18.43  |             all_61_1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (sdtpldt0(v0,
% 132.55/18.43  |               all_38_0) = v1) |  ~ $i(v0) |  ~ aElementOf0(v0, all_61_0) |
% 132.55/18.43  |           aDivisorOf0(all_61_1, v1)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 132.55/18.43  |           (sdtpldt0(v0, all_38_0) = v1) |  ~ $i(v0) |  ~ aElementOf0(v0,
% 132.55/18.43  |             all_61_0) | aInteger0(v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 132.55/18.43  |           (sdtpldt0(v0, all_38_0) = v1) |  ~ $i(v0) |  ~ aElementOf0(v0,
% 132.55/18.43  |             all_61_0) |  ? [v2: $i] : (sdtasdt0(all_61_1, v2) = v1 & $i(v2) &
% 132.55/18.43  |             $i(v1) & aInteger0(v2))) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 132.55/18.43  |           (sdtpldt0(v0, all_38_0) = v1) |  ~ $i(v0) |  ~
% 132.55/18.43  |           sdteqdtlpzmzozddtrp0(v0, all_38_1, all_61_1) |  ~ aInteger0(v0) |
% 132.55/18.43  |           aElementOf0(v0, all_61_0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 132.55/18.43  |           (sdtpldt0(v0, all_38_0) = v1) |  ~ $i(v0) |  ~ aDivisorOf0(all_61_1,
% 132.55/18.43  |             v1) |  ~ aInteger0(v0) | aElementOf0(v0, all_61_0)) &  ! [v0: $i]
% 132.55/18.43  |         : ( ~ $i(v0) |  ~ aElementOf0(v0, all_61_0) | aElementOf0(v0,
% 132.55/18.43  |             all_51_0))
% 132.55/18.43  | 
% 132.55/18.43  | ALPHA: (22) implies:
% 132.55/18.43  |   (23)   ~ (all_61_1 = sz00)
% 132.55/18.43  |   (24)  aInteger0(all_61_1)
% 132.55/18.43  |   (25)  $i(all_61_1)
% 132.55/18.43  |   (26)  $i(all_61_0)
% 132.55/18.43  |   (27)  szAzrzSzezqlpdtcmdtrp0(all_38_1, all_61_1) = all_61_0
% 132.55/18.43  |   (28)   ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_61_0) |
% 132.55/18.43  |           aElementOf0(v0, all_51_0))
% 132.55/18.43  | 
% 132.55/18.43  | GROUND_INST: instantiating (2) with sz00, all_61_1, simplifying with (1), (5),
% 132.55/18.43  |              (24), (25) gives:
% 132.55/18.43  |   (29)  all_61_1 = sz00 | sdteqdtlpzmzozddtrp0(sz00, sz00, all_61_1)
% 132.55/18.43  | 
% 132.55/18.43  | GROUND_INST: instantiating (14) with all_61_1, all_61_0, simplifying with
% 132.55/18.43  |              (24), (25), (27) gives:
% 132.55/18.44  |   (30)  all_61_1 = sz00 |  ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_61_0) & 
% 132.55/18.44  |           ~ aElementOf0(v0, all_38_2))
% 132.55/18.44  | 
% 132.55/18.44  | BETA: splitting (30) gives:
% 132.55/18.44  | 
% 132.55/18.44  | Case 1:
% 132.55/18.44  | | 
% 132.55/18.44  | |   (31)  all_61_1 = sz00
% 132.55/18.44  | | 
% 132.55/18.44  | | REDUCE: (23), (31) imply:
% 132.55/18.44  | |   (32)  $false
% 132.55/18.44  | | 
% 132.55/18.44  | | CLOSE: (32) is inconsistent.
% 132.55/18.44  | | 
% 132.55/18.44  | Case 2:
% 132.55/18.44  | | 
% 132.55/18.44  | |   (33)   ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_61_0) &  ~
% 132.55/18.44  | |           aElementOf0(v0, all_38_2))
% 132.55/18.44  | | 
% 132.55/18.44  | | DELTA: instantiating (33) with fresh symbol all_91_0 gives:
% 132.55/18.44  | |   (34)  $i(all_91_0) & aElementOf0(all_91_0, all_61_0) &  ~
% 132.55/18.44  | |         aElementOf0(all_91_0, all_38_2)
% 132.55/18.44  | | 
% 132.55/18.44  | | ALPHA: (34) implies:
% 132.55/18.44  | |   (35)   ~ aElementOf0(all_91_0, all_38_2)
% 132.55/18.44  | |   (36)  aElementOf0(all_91_0, all_61_0)
% 132.55/18.44  | |   (37)  $i(all_91_0)
% 132.55/18.44  | | 
% 132.55/18.44  | | BETA: splitting (29) gives:
% 132.55/18.44  | | 
% 132.55/18.44  | | Case 1:
% 132.55/18.44  | | | 
% 132.55/18.44  | | | 
% 132.55/18.44  | | | GROUND_INST: instantiating (3) with all_38_1, all_61_1, all_61_0,
% 132.55/18.44  | | |              all_91_0, simplifying with (9), (15), (24), (25), (26), (27),
% 132.55/18.44  | | |              (36), (37) gives:
% 132.55/18.44  | | |   (38)  all_61_1 = sz00 | aInteger0(all_91_0)
% 132.55/18.44  | | | 
% 132.55/18.44  | | | GROUND_INST: instantiating (28) with all_91_0, simplifying with (36), (37)
% 132.55/18.44  | | |              gives:
% 132.55/18.44  | | |   (39)  aElementOf0(all_91_0, all_51_0)
% 132.55/18.44  | | | 
% 132.55/18.44  | | | BETA: splitting (38) gives:
% 132.55/18.44  | | | 
% 132.55/18.44  | | | Case 1:
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | |   (40)  aInteger0(all_91_0)
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | | GROUND_INST: instantiating (13) with all_91_0, all_51_0, simplifying
% 132.55/18.44  | | | |              with (19), (20), (35), (37), (39), (40) gives:
% 132.55/18.44  | | | |   (41)  $false
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | | CLOSE: (41) is inconsistent.
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | Case 2:
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | |   (42)  all_61_1 = sz00
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | | REDUCE: (23), (42) imply:
% 132.55/18.44  | | | |   (43)  $false
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | | CLOSE: (43) is inconsistent.
% 132.55/18.44  | | | | 
% 132.55/18.44  | | | End of split
% 132.55/18.44  | | | 
% 132.55/18.44  | | Case 2:
% 132.55/18.44  | | | 
% 132.55/18.44  | | |   (44)  all_61_1 = sz00
% 132.55/18.44  | | | 
% 132.55/18.44  | | | REDUCE: (23), (44) imply:
% 132.55/18.44  | | |   (45)  $false
% 132.55/18.44  | | | 
% 132.55/18.44  | | | CLOSE: (45) is inconsistent.
% 132.55/18.44  | | | 
% 132.55/18.44  | | End of split
% 132.55/18.44  | | 
% 132.55/18.44  | End of split
% 132.55/18.44  | 
% 132.55/18.44  End of proof
% 132.55/18.44  % SZS output end Proof for theBenchmark
% 132.55/18.44  
% 132.55/18.44  17836ms
%------------------------------------------------------------------------------