Princess---230619.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n032.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 11:47:51 EDT 2023

% Result   : Theorem 47.46s 7.03s
% Output   : Proof 154.41s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : NUM453+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.11  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Fri Aug 25 10:28:12 EDT 2023
% 0.10/0.31  % CPUTime  : 
% 0.16/0.52  ________       _____
% 0.16/0.52  ___  __ \_________(_)________________________________
% 0.16/0.52  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.16/0.52  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.16/0.52  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.16/0.52  
% 0.16/0.52  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.52  (2023-06-19)
% 0.16/0.52  
% 0.16/0.52  (c) Philipp Rümmer, 2009-2023
% 0.16/0.52  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.52                Amanda Stjerna.
% 0.16/0.52  Free software under BSD-3-Clause.
% 0.16/0.52  
% 0.16/0.52  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.52  
% 0.16/0.52  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.53  Running up to 7 provers in parallel.
% 0.16/0.54  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.54  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.54  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.54  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.54  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.54  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.54  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.41/1.26  Prover 1: Preprocessing ...
% 4.41/1.26  Prover 4: Preprocessing ...
% 4.65/1.29  Prover 5: Preprocessing ...
% 4.65/1.29  Prover 0: Preprocessing ...
% 4.65/1.29  Prover 6: Preprocessing ...
% 4.65/1.29  Prover 3: Preprocessing ...
% 4.65/1.29  Prover 2: Preprocessing ...
% 13.35/2.51  Prover 1: Constructing countermodel ...
% 13.35/2.53  Prover 3: Constructing countermodel ...
% 13.35/2.55  Prover 6: Proving ...
% 13.35/2.56  Prover 5: Proving ...
% 15.08/2.75  Prover 2: Proving ...
% 19.96/3.37  Prover 4: Constructing countermodel ...
% 20.82/3.47  Prover 0: Proving ...
% 47.46/7.01  Prover 6: proved (6465ms)
% 47.46/7.01  
% 47.46/7.03  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 47.46/7.03  
% 47.46/7.03  Prover 0: stopped
% 47.46/7.03  Prover 2: stopped
% 47.46/7.05  Prover 5: stopped
% 47.46/7.06  Prover 3: stopped
% 47.46/7.07  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 47.46/7.07  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 47.46/7.07  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 47.46/7.07  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 47.46/7.08  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 48.80/7.21  Prover 8: Preprocessing ...
% 48.80/7.23  Prover 7: Preprocessing ...
% 48.80/7.23  Prover 10: Preprocessing ...
% 49.38/7.30  Prover 11: Preprocessing ...
% 49.84/7.33  Prover 13: Preprocessing ...
% 50.83/7.45  Prover 8: Warning: ignoring some quantifiers
% 50.83/7.45  Prover 7: Warning: ignoring some quantifiers
% 50.83/7.47  Prover 8: Constructing countermodel ...
% 50.83/7.47  Prover 10: Warning: ignoring some quantifiers
% 50.83/7.47  Prover 7: Constructing countermodel ...
% 51.11/7.49  Prover 10: Constructing countermodel ...
% 52.16/7.71  Prover 13: Warning: ignoring some quantifiers
% 52.16/7.72  Prover 13: Constructing countermodel ...
% 55.88/8.14  Prover 11: Constructing countermodel ...
% 82.61/11.68  Prover 13: stopped
% 83.08/11.69  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 83.77/11.80  Prover 16: Preprocessing ...
% 84.25/12.03  Prover 16: Warning: ignoring some quantifiers
% 84.25/12.03  Prover 16: Constructing countermodel ...
% 114.94/15.88  Prover 1: stopped
% 114.94/15.89  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 115.60/15.97  Prover 19: Preprocessing ...
% 118.24/16.42  Prover 19: Warning: ignoring some quantifiers
% 118.24/16.44  Prover 19: Constructing countermodel ...
% 123.27/17.02  Prover 16: stopped
% 140.13/19.47  Prover 19: stopped
% 153.83/21.75  Prover 10: Found proof (size 323)
% 153.83/21.75  Prover 10: proved (14706ms)
% 153.92/21.76  Prover 4: stopped
% 153.92/21.76  Prover 7: stopped
% 153.92/21.76  Prover 8: stopped
% 153.92/21.76  Prover 11: stopped
% 153.92/21.76  
% 153.92/21.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 153.92/21.76  
% 153.92/21.78  % SZS output start Proof for theBenchmark
% 153.92/21.79  Assumptions after simplification:
% 153.92/21.79  ---------------------------------
% 153.92/21.79  
% 153.92/21.79    (mAddAsso)
% 154.17/21.82     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] :  ! [v4: $i] : ( ~
% 154.17/21.82      (sdtpldt0(v3, v2) = v4) |  ~ (sdtpldt0(v0, v1) = v3) |  ~ $i(v2) |  ~ $i(v1)
% 154.17/21.82      |  ~ $i(v0) |  ~ aInteger0(v2) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |  ?
% 154.17/21.82      [v5: $i] : (sdtpldt0(v1, v2) = v5 & sdtpldt0(v0, v5) = v4 & $i(v5) &
% 154.17/21.82        $i(v4)))
% 154.17/21.82  
% 154.17/21.82    (mAddComm)
% 154.17/21.82     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~
% 154.17/21.82      $i(v1) |  ~ $i(v0) |  ~ aInteger0(v1) |  ~ aInteger0(v0) | (sdtpldt0(v1, v0)
% 154.17/21.82        = v2 & $i(v2)))
% 154.17/21.82  
% 154.17/21.82    (mAddNeg)
% 154.17/21.82    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = sz00 |  ~
% 154.17/21.82      (sdtpldt0(v1, v0) = v2) |  ~ (smndt0(v0) = v1) |  ~ $i(v0) |  ~
% 154.17/21.82      aInteger0(v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtpldt0(v1,
% 154.17/21.82          v0) = v2) |  ~ (smndt0(v0) = v1) |  ~ $i(v0) |  ~ aInteger0(v0) |
% 154.17/21.82      sdtpldt0(v0, v1) = sz00)
% 154.17/21.82  
% 154.17/21.82    (mAddZero)
% 154.17/21.82    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1)
% 154.17/21.82      |  ~ $i(v0) |  ~ aInteger0(v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 154.17/21.82      (sdtpldt0(sz00, v0) = v1) |  ~ $i(v0) |  ~ aInteger0(v0) | sdtpldt0(v0,
% 154.17/21.82        sz00) = v0)
% 154.17/21.82  
% 154.17/21.82    (mArSeq)
% 154.17/21.83    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v3 = v2 |
% 154.17/21.83      v1 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v1)
% 154.17/21.83      |  ~ $i(v0) |  ~ aSet0(v3) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |  ? [v4:
% 154.17/21.83        $i] : ($i(v4) & ( ~ aElementOf0(v4, v3) |  ~ sdteqdtlpzmzozddtrp0(v4, v0,
% 154.17/21.83            v1) |  ~ aInteger0(v4)) & (aElementOf0(v4, v3) |
% 154.17/21.83          (sdteqdtlpzmzozddtrp0(v4, v0, v1) & aInteger0(v4))))) &  ! [v0: $i] :  !
% 154.17/21.83    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = sz00 |  ~
% 154.17/21.83      (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 154.17/21.83      ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |
% 154.17/21.83      sdteqdtlpzmzozddtrp0(v3, v0, v1)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i]
% 154.17/21.83    :  ! [v3: $i] : (v1 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~
% 154.17/21.83      $i(v3) |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~
% 154.17/21.83      aInteger0(v1) |  ~ aInteger0(v0) | aInteger0(v3)) &  ! [v0: $i] :  ! [v1:
% 154.17/21.83      $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = sz00 |  ~
% 154.17/21.83      (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~ $i(v1) | 
% 154.17/21.83      ~ $i(v0) |  ~ sdteqdtlpzmzozddtrp0(v3, v0, v1) |  ~ aInteger0(v3) |  ~
% 154.17/21.83      aInteger0(v1) |  ~ aInteger0(v0) | aElementOf0(v3, v2)) &  ! [v0: $i] :  !
% 154.17/21.83    [v1: $i] :  ! [v2: $i] : (v1 = sz00 |  ~ (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2)
% 154.17/21.83      |  ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |  ~ aInteger0(v1) |  ~ aInteger0(v0) |
% 154.17/21.83      aSet0(v2))
% 154.17/21.83  
% 154.17/21.83    (mEquModRef)
% 154.17/21.83    $i(sz00) &  ! [v0: $i] :  ! [v1: $i] : (v1 = sz00 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 154.17/21.83      aInteger0(v1) |  ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 154.17/21.83  
% 154.17/21.83    (mIntMult)
% 154.17/21.84     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~
% 154.17/21.84      $i(v1) |  ~ $i(v0) |  ~ aInteger0(v1) |  ~ aInteger0(v0) | aInteger0(v2))
% 154.17/21.84  
% 154.17/21.84    (mIntNeg)
% 154.17/21.84     ! [v0: $i] :  ! [v1: $i] : ( ~ (smndt0(v0) = v1) |  ~ $i(v0) |  ~
% 154.17/21.84      aInteger0(v0) | aInteger0(v1))
% 154.17/21.84  
% 154.17/21.84    (mIntOne)
% 154.17/21.84    $i(sz10) & aInteger0(sz10)
% 154.17/21.84  
% 154.17/21.84    (mIntPlus)
% 154.17/21.84     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |  ~
% 154.17/21.84      $i(v1) |  ~ $i(v0) |  ~ aInteger0(v1) |  ~ aInteger0(v0) | aInteger0(v2))
% 154.17/21.84  
% 154.17/21.84    (mIntZero)
% 154.17/21.84    $i(sz00) & aInteger0(sz00)
% 154.17/21.84  
% 154.17/21.84    (mMulMinOne)
% 154.17/21.84    $i(sz10) &  ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) &  ! [v1: $i] :  ! [v2:
% 154.17/21.84        $i] : ( ~ (sdtasdt0(v0, v1) = v2) |  ~ $i(v1) |  ~ aInteger0(v1) |
% 154.17/21.84        (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 154.17/21.84  
% 154.17/21.84    (mPrimeDivisor)
% 154.17/21.84    $i(sz10) &  ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) &  ! [v1: $i] : (v1 = v0
% 154.17/21.84        | v1 = sz10 |  ~ $i(v1) |  ~ aInteger0(v1) |  ? [v2: $i] : ($i(v2) &
% 154.17/21.84          isPrime0(v2) & aDivisorOf0(v2, v1))) &  ! [v1: $i] : ( ~ $i(v1) |  ~
% 154.17/21.84        isPrime0(v1) |  ~ aDivisorOf0(v1, v0) |  ~ aInteger0(v0)) &  ! [v1: $i] :
% 154.17/21.84      ( ~ $i(v1) |  ~ isPrime0(v1) |  ~ aDivisorOf0(v1, sz10) |  ~
% 154.17/21.84        aInteger0(sz10)))
% 154.17/21.84  
% 154.17/21.84    (mSubset)
% 154.17/21.85     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~ $i(v0) |
% 154.17/21.85       ~ aSubsetOf0(v1, v0) |  ~ aElementOf0(v2, v1) |  ~ aSet0(v0) |
% 154.17/21.85      aElementOf0(v2, v0)) &  ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) | 
% 154.17/21.85      ~ aSubsetOf0(v1, v0) |  ~ aSet0(v0) | aSet0(v1)) &  ! [v0: $i] :  ! [v1: $i]
% 154.17/21.85    : ( ~ $i(v1) |  ~ $i(v0) |  ~ aSet0(v1) |  ~ aSet0(v0) | aSubsetOf0(v1, v0) | 
% 154.17/21.85      ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) &  ~ aElementOf0(v2, v0)))
% 154.17/21.85  
% 154.17/21.85    (m__)
% 154.17/21.85    $i(xp) & $i(sz10) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ((v2 = sz10 &
% 154.17/21.85        sdtpldt0(sz10, v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 &
% 154.17/21.85        sdtpldt0(sz10, xp) = sz10))
% 154.17/21.85  
% 154.17/21.85    (m__2079)
% 154.17/21.85    $i(cS2076) & $i(xS) & $i(sz10) &  ? [v0: $i] :  ? [v1: $i] : (stldt0(v0) =
% 154.17/21.85      cS2076 & sbsmnsldt0(xS) = v0 & smndt0(sz10) = v1 & $i(v1) & $i(v0) &
% 154.17/21.85      aElementOf0(v1, cS2076) & aElementOf0(sz10, cS2076) & aSet0(v0) &
% 154.17/21.85      aSet0(cS2076) &  ! [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~
% 154.17/21.85        aElementOf0(v3, xS) |  ~ aElementOf0(v2, v3) |  ~ aInteger0(v2) |
% 154.17/21.85        aElementOf0(v2, v0)) &  ! [v2: $i] : (v2 = v1 | v2 = sz10 |  ~ $i(v2) |  ~
% 154.17/21.85        aElementOf0(v2, cS2076)) &  ! [v2: $i] : ( ~ $i(v2) |  ~ aElementOf0(v2,
% 154.17/21.85          v0) |  ~ aElementOf0(v2, cS2076)) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 154.17/21.85        aElementOf0(v2, v0) | aInteger0(v2)) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 154.17/21.85        aElementOf0(v2, v0) |  ? [v3: $i] : ($i(v3) & aElementOf0(v3, xS) &
% 154.17/21.85          aElementOf0(v2, v3))) &  ! [v2: $i] : ( ~ $i(v2) |  ~ aElementOf0(v2,
% 154.17/21.85          cS2076) | aInteger0(v2)) &  ! [v2: $i] : ( ~ $i(v2) |  ~ aInteger0(v2) |
% 154.17/21.85        aElementOf0(v2, v0) | aElementOf0(v2, cS2076)))
% 154.17/21.85  
% 154.17/21.85    (m__2144)
% 154.17/21.86    $i(xS) & $i(sz00) &  ? [v0: $i] :  ? [v1: $i] : (stldt0(v0) = v1 &
% 154.17/21.86      sbsmnsldt0(xS) = v0 & $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) &
% 154.17/21.86      aSet0(v0) &  ! [v2: $i] :  ! [v3: $i] : ( ~ (smndt0(v2) = v3) |  ~ $i(v2) | 
% 154.17/21.86        ~ aElementOf0(v2, v1) |  ? [v4: $i] :  ? [v5: $i] : ( ~ (v4 = sz00) &
% 154.17/21.86          szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) & aSubsetOf0(v5,
% 154.17/21.86            v1) & aSet0(v5) & aInteger0(v4) &  ! [v6: $i] :  ! [v7: $i] :  ! [v8:
% 154.17/21.86            $i] : ( ~ (sdtasdt0(v4, v8) = v7) |  ~ (sdtpldt0(v6, v3) = v7) |  ~
% 154.17/21.86            $i(v8) |  ~ $i(v6) |  ~ aInteger0(v8) |  ~ aInteger0(v6) |
% 154.17/21.86            aElementOf0(v6, v5)) &  ! [v6: $i] :  ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 154.17/21.86                v3) = v7) |  ~ $i(v6) |  ~ aElementOf0(v6, v5) |
% 154.17/21.86            sdteqdtlpzmzozddtrp0(v6, v2, v4)) &  ! [v6: $i] :  ! [v7: $i] : ( ~
% 154.17/21.86            (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~ aElementOf0(v6, v5) |
% 154.17/21.86            aDivisorOf0(v4, v7)) &  ! [v6: $i] :  ! [v7: $i] : ( ~ (sdtpldt0(v6,
% 154.17/21.86                v3) = v7) |  ~ $i(v6) |  ~ aElementOf0(v6, v5) | aInteger0(v6)) & 
% 154.17/21.86          ! [v6: $i] :  ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~
% 154.17/21.86            aElementOf0(v6, v5) |  ? [v8: $i] : (sdtasdt0(v4, v8) = v7 & $i(v8) &
% 154.17/21.86              $i(v7) & aInteger0(v8))) &  ! [v6: $i] :  ! [v7: $i] : ( ~
% 154.17/21.86            (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~ sdteqdtlpzmzozddtrp0(v6, v2,
% 154.17/21.86              v4) |  ~ aInteger0(v6) | aElementOf0(v6, v5)) &  ! [v6: $i] :  !
% 154.17/21.86          [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~ aDivisorOf0(v4,
% 154.17/21.86              v7) |  ~ aInteger0(v6) | aElementOf0(v6, v5)) &  ! [v6: $i] : ( ~
% 154.17/21.86            $i(v6) |  ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) &  ! [v2: $i]
% 154.17/21.86      :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ aElementOf0(v3, xS) |  ~
% 154.17/21.86        aElementOf0(v2, v3) |  ~ aInteger0(v2) | aElementOf0(v2, v0)) &  ! [v2:
% 154.17/21.86        $i] : ( ~ $i(v2) |  ~ aElementOf0(v2, v1) |  ~ aElementOf0(v2, v0)) &  !
% 154.17/21.86      [v2: $i] : ( ~ $i(v2) |  ~ aElementOf0(v2, v1) | aInteger0(v2)) &  ! [v2:
% 154.17/21.86        $i] : ( ~ $i(v2) |  ~ aElementOf0(v2, v0) | aInteger0(v2)) &  ! [v2: $i] :
% 154.17/21.86      ( ~ $i(v2) |  ~ aElementOf0(v2, v0) |  ? [v3: $i] : ($i(v3) &
% 154.17/21.86          aElementOf0(v3, xS) & aElementOf0(v2, v3))) &  ! [v2: $i] : ( ~ $i(v2) |
% 154.17/21.86         ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2, v0)))
% 154.17/21.86  
% 154.17/21.86    (m__2171)
% 154.17/21.87    $i(xp) & $i(xS) & $i(sz10) & $i(sz00) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2:
% 154.17/21.87      $i] :  ? [v3: $i] : ( ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0
% 154.17/21.87      & stldt0(v2) = v3 & sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) &
% 154.17/21.87      $i(v2) & $i(v1) & $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) &
% 154.17/21.87      aInteger0(xp) &  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtasdt0(xp,
% 154.17/21.87            v6) = v5) |  ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v6) |  ~ $i(v4) |  ~
% 154.17/21.87        aInteger0(v6) |  ~ aInteger0(v4) | aElementOf0(v4, v0)) &  ! [v4: $i] :  !
% 154.17/21.87      [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aElementOf0(v4, v0)
% 154.17/21.87        | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) &  ! [v4: $i] :  ! [v5: $i] : ( ~
% 154.17/21.87        (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aElementOf0(v4, v0) |
% 154.17/21.87        aDivisorOf0(xp, v5)) &  ! [v4: $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) =
% 154.17/21.87          v5) |  ~ $i(v4) |  ~ aElementOf0(v4, v0) | aInteger0(v4)) &  ! [v4: $i]
% 154.17/21.87      :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aElementOf0(v4,
% 154.17/21.87          v0) |  ? [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) &
% 154.17/21.87          aInteger0(v6))) &  ! [v4: $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) =
% 154.17/21.87          v5) |  ~ $i(v4) |  ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp) |  ~
% 154.17/21.87        aInteger0(v4) | aElementOf0(v4, v0)) &  ! [v4: $i] :  ! [v5: $i] : ( ~
% 154.17/21.87        (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aDivisorOf0(xp, v5) |  ~
% 154.17/21.87        aInteger0(v4) | aElementOf0(v4, v0)) &  ! [v4: $i] :  ! [v5: $i] : ( ~
% 154.17/21.87        $i(v5) |  ~ $i(v4) |  ~ aElementOf0(v5, xS) |  ~ aElementOf0(v4, v5) |  ~
% 154.17/21.87        aInteger0(v4) | aElementOf0(v4, v2)) &  ! [v4: $i] : ( ~ $i(v4) |  ~
% 154.17/21.87        aElementOf0(v4, v3) |  ~ aElementOf0(v4, v2)) &  ! [v4: $i] : ( ~ $i(v4) |
% 154.17/21.87         ~ aElementOf0(v4, v3) | aInteger0(v4)) &  ! [v4: $i] : ( ~ $i(v4) |  ~
% 154.17/21.87        aElementOf0(v4, v2) | aInteger0(v4)) &  ! [v4: $i] : ( ~ $i(v4) |  ~
% 154.17/21.87        aElementOf0(v4, v2) |  ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) &
% 154.17/21.87          aElementOf0(v4, v5))) &  ! [v4: $i] : ( ~ $i(v4) |  ~ aElementOf0(v4,
% 154.17/21.87          v0) | aElementOf0(v4, v3)) &  ! [v4: $i] : ( ~ $i(v4) |  ~ aInteger0(v4)
% 154.17/21.87        | aElementOf0(v4, v3) | aElementOf0(v4, v2)))
% 154.17/21.87  
% 154.17/21.87    (m__2232)
% 154.17/21.87    $i(xp) & $i(sz10) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ?
% 154.17/21.87    [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :
% 154.17/21.87    (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v3 & sdtasdt0(xp, v8) = v2 & sdtasdt0(xp,
% 154.17/21.87        v7) = v6 & sdtpldt0(v5, v1) = v6 & sdtpldt0(v0, v1) = v2 & sdtpldt0(sz10,
% 154.17/21.87        v4) = v5 & sdtpldt0(sz10, xp) = v0 & smndt0(xp) = v4 & smndt0(sz10) = v1 &
% 154.17/21.87      $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 154.17/21.87      $i(v0) & aElementOf0(v5, v3) & aElementOf0(v0, v3) &
% 154.17/21.87      sdteqdtlpzmzozddtrp0(v5, sz10, xp) & sdteqdtlpzmzozddtrp0(v0, sz10, xp) &
% 154.17/21.87      aDivisorOf0(xp, v6) & aDivisorOf0(xp, v2) & aInteger0(v8) & aInteger0(v7))
% 154.17/21.87  
% 154.17/21.87    (function-axioms)
% 154.17/21.88     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.17/21.88      (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) |  ~ (szAzrzSzezqlpdtcmdtrp0(v3, v2) =
% 154.17/21.88        v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 | 
% 154.17/21.88      ~ (sdtslmnbsdt0(v3, v2) = v1) |  ~ (sdtslmnbsdt0(v3, v2) = v0)) &  ! [v0:
% 154.17/21.88      $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.17/21.88      (sdtbsmnsldt0(v3, v2) = v1) |  ~ (sdtbsmnsldt0(v3, v2) = v0)) &  ! [v0: $i]
% 154.17/21.88    :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtasdt0(v3, v2) =
% 154.17/21.88        v1) |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2:
% 154.17/21.88      $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3,
% 154.17/21.88          v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 154.17/21.88      (stldt0(v2) = v1) |  ~ (stldt0(v2) = v0)) &  ! [v0: $i] :  ! [v1: $i] :  !
% 154.17/21.88    [v2: $i] : (v1 = v0 |  ~ (sbsmnsldt0(v2) = v1) |  ~ (sbsmnsldt0(v2) = v0)) & 
% 154.17/21.88    ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (smndt0(v2) = v1) |  ~
% 154.17/21.88      (smndt0(v2) = v0))
% 154.17/21.88  
% 154.17/21.88  Further assumptions not needed in the proof:
% 154.17/21.88  --------------------------------------------
% 154.17/21.88  mArSeqClosed, mClosed, mComplement, mDistrib, mDivisor, mElements, mEquMod,
% 154.17/21.88  mEquModMul, mEquModSym, mEquModTrn, mFinSet, mIntegers, mInterOpen,
% 154.17/21.88  mIntersection, mMulAsso, mMulComm, mMulOne, mMulZero, mOpen, mPrime, mSets,
% 154.17/21.88  mUnion, mUnionClosed, mUnionOpen, mUnionSClosed, mUnionSet, mZeroDiv, m__2046,
% 154.17/21.88  m__2117
% 154.17/21.88  
% 154.17/21.88  Those formulas are unsatisfiable:
% 154.17/21.88  ---------------------------------
% 154.17/21.88  
% 154.17/21.88  Begin of proof
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mIntZero) implies:
% 154.17/21.88  |   (1)  aInteger0(sz00)
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mIntOne) implies:
% 154.17/21.88  |   (2)  aInteger0(sz10)
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mAddZero) implies:
% 154.17/21.88  |   (3)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) | 
% 154.17/21.88  |          ~ $i(v0) |  ~ aInteger0(v0))
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mAddNeg) implies:
% 154.17/21.88  |   (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v2 = sz00 |  ~ (sdtpldt0(v1,
% 154.17/21.88  |              v0) = v2) |  ~ (smndt0(v0) = v1) |  ~ $i(v0) |  ~ aInteger0(v0))
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mMulMinOne) implies:
% 154.17/21.88  |   (5)   ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) &  ! [v1: $i] :  ! [v2: $i] :
% 154.17/21.88  |          ( ~ (sdtasdt0(v0, v1) = v2) |  ~ $i(v1) |  ~ aInteger0(v1) |
% 154.17/21.88  |            (sdtasdt0(v1, v0) = v2 & smndt0(v1) = v2 & $i(v2))))
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mEquModRef) implies:
% 154.17/21.88  |   (6)   ! [v0: $i] :  ! [v1: $i] : (v1 = sz00 |  ~ $i(v1) |  ~ $i(v0) |  ~
% 154.17/21.88  |          aInteger0(v1) |  ~ aInteger0(v0) | sdteqdtlpzmzozddtrp0(v0, v0, v1))
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mPrimeDivisor) implies:
% 154.17/21.88  |   (7)   ? [v0: $i] : (smndt0(sz10) = v0 & $i(v0) &  ! [v1: $i] : (v1 = v0 | v1
% 154.17/21.88  |            = sz10 |  ~ $i(v1) |  ~ aInteger0(v1) |  ? [v2: $i] : ($i(v2) &
% 154.17/21.88  |              isPrime0(v2) & aDivisorOf0(v2, v1))) &  ! [v1: $i] : ( ~ $i(v1) |
% 154.17/21.88  |             ~ isPrime0(v1) |  ~ aDivisorOf0(v1, v0) |  ~ aInteger0(v0)) &  !
% 154.17/21.88  |          [v1: $i] : ( ~ $i(v1) |  ~ isPrime0(v1) |  ~ aDivisorOf0(v1, sz10) | 
% 154.17/21.88  |            ~ aInteger0(sz10)))
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mSubset) implies:
% 154.17/21.88  |   (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~ $i(v2) |  ~ $i(v1) |  ~
% 154.17/21.88  |          $i(v0) |  ~ aSubsetOf0(v1, v0) |  ~ aElementOf0(v2, v1) |  ~
% 154.17/21.88  |          aSet0(v0) | aElementOf0(v2, v0))
% 154.17/21.88  | 
% 154.17/21.88  | ALPHA: (mArSeq) implies:
% 154.17/21.89  |   (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = sz00 |  ~
% 154.17/21.89  |          (szAzrzSzezqlpdtcmdtrp0(v0, v1) = v2) |  ~ $i(v3) |  ~ $i(v2) |  ~
% 154.17/21.89  |          $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v3, v2) |  ~ aInteger0(v1) |  ~
% 154.17/21.89  |          aInteger0(v0) | aInteger0(v3))
% 154.17/21.89  | 
% 154.17/21.89  | ALPHA: (m__2079) implies:
% 154.17/21.89  |   (10)   ? [v0: $i] :  ? [v1: $i] : (stldt0(v0) = cS2076 & sbsmnsldt0(xS) = v0
% 154.17/21.89  |           & smndt0(sz10) = v1 & $i(v1) & $i(v0) & aElementOf0(v1, cS2076) &
% 154.17/21.89  |           aElementOf0(sz10, cS2076) & aSet0(v0) & aSet0(cS2076) &  ! [v2: $i]
% 154.17/21.89  |           :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ aElementOf0(v3, xS) |  ~
% 154.17/21.89  |             aElementOf0(v2, v3) |  ~ aInteger0(v2) | aElementOf0(v2, v0)) &  !
% 154.17/21.89  |           [v2: $i] : (v2 = v1 | v2 = sz10 |  ~ $i(v2) |  ~ aElementOf0(v2,
% 154.17/21.89  |               cS2076)) &  ! [v2: $i] : ( ~ $i(v2) |  ~ aElementOf0(v2, v0) | 
% 154.17/21.89  |             ~ aElementOf0(v2, cS2076)) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 154.17/21.89  |             aElementOf0(v2, v0) | aInteger0(v2)) &  ! [v2: $i] : ( ~ $i(v2) | 
% 154.17/21.89  |             ~ aElementOf0(v2, v0) |  ? [v3: $i] : ($i(v3) & aElementOf0(v3,
% 154.17/21.89  |                 xS) & aElementOf0(v2, v3))) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 154.17/21.89  |             aElementOf0(v2, cS2076) | aInteger0(v2)) &  ! [v2: $i] : ( ~
% 154.17/21.89  |             $i(v2) |  ~ aInteger0(v2) | aElementOf0(v2, v0) | aElementOf0(v2,
% 154.17/21.89  |               cS2076)))
% 154.17/21.89  | 
% 154.17/21.89  | ALPHA: (m__2144) implies:
% 154.17/21.90  |   (11)   ? [v0: $i] :  ? [v1: $i] : (stldt0(v0) = v1 & sbsmnsldt0(xS) = v0 &
% 154.17/21.90  |           $i(v1) & $i(v0) & isClosed0(v0) & isOpen0(v1) & aSet0(v0) &  ! [v2:
% 154.17/21.90  |             $i] :  ! [v3: $i] : ( ~ (smndt0(v2) = v3) |  ~ $i(v2) |  ~
% 154.17/21.90  |             aElementOf0(v2, v1) |  ? [v4: $i] :  ? [v5: $i] : ( ~ (v4 = sz00)
% 154.17/21.90  |               & szAzrzSzezqlpdtcmdtrp0(v2, v4) = v5 & $i(v5) & $i(v4) &
% 154.17/21.90  |               aSubsetOf0(v5, v1) & aSet0(v5) & aInteger0(v4) &  ! [v6: $i] : 
% 154.17/21.90  |               ! [v7: $i] :  ! [v8: $i] : ( ~ (sdtasdt0(v4, v8) = v7) |  ~
% 154.17/21.90  |                 (sdtpldt0(v6, v3) = v7) |  ~ $i(v8) |  ~ $i(v6) |  ~
% 154.17/21.90  |                 aInteger0(v8) |  ~ aInteger0(v6) | aElementOf0(v6, v5)) &  !
% 154.17/21.90  |               [v6: $i] :  ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~ $i(v6)
% 154.17/21.90  |                 |  ~ aElementOf0(v6, v5) | sdteqdtlpzmzozddtrp0(v6, v2, v4)) &
% 154.17/21.90  |                ! [v6: $i] :  ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~
% 154.17/21.90  |                 $i(v6) |  ~ aElementOf0(v6, v5) | aDivisorOf0(v4, v7)) &  !
% 154.17/21.90  |               [v6: $i] :  ! [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~ $i(v6)
% 154.17/21.90  |                 |  ~ aElementOf0(v6, v5) | aInteger0(v6)) &  ! [v6: $i] :  !
% 154.17/21.90  |               [v7: $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~
% 154.17/21.90  |                 aElementOf0(v6, v5) |  ? [v8: $i] : (sdtasdt0(v4, v8) = v7 &
% 154.17/21.90  |                   $i(v8) & $i(v7) & aInteger0(v8))) &  ! [v6: $i] :  ! [v7:
% 154.17/21.90  |                 $i] : ( ~ (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~
% 154.17/21.90  |                 sdteqdtlpzmzozddtrp0(v6, v2, v4) |  ~ aInteger0(v6) |
% 154.17/21.90  |                 aElementOf0(v6, v5)) &  ! [v6: $i] :  ! [v7: $i] : ( ~
% 154.17/21.90  |                 (sdtpldt0(v6, v3) = v7) |  ~ $i(v6) |  ~ aDivisorOf0(v4, v7) |
% 154.17/21.90  |                  ~ aInteger0(v6) | aElementOf0(v6, v5)) &  ! [v6: $i] : ( ~
% 154.17/21.90  |                 $i(v6) |  ~ aElementOf0(v6, v5) | aElementOf0(v6, v1)))) &  !
% 154.17/21.90  |           [v2: $i] :  ! [v3: $i] : ( ~ $i(v3) |  ~ $i(v2) |  ~ aElementOf0(v3,
% 154.17/21.90  |               xS) |  ~ aElementOf0(v2, v3) |  ~ aInteger0(v2) |
% 154.17/21.90  |             aElementOf0(v2, v0)) &  ! [v2: $i] : ( ~ $i(v2) |  ~
% 154.17/21.90  |             aElementOf0(v2, v1) |  ~ aElementOf0(v2, v0)) &  ! [v2: $i] : ( ~
% 154.17/21.90  |             $i(v2) |  ~ aElementOf0(v2, v1) | aInteger0(v2)) &  ! [v2: $i] : (
% 154.17/21.90  |             ~ $i(v2) |  ~ aElementOf0(v2, v0) | aInteger0(v2)) &  ! [v2: $i] :
% 154.17/21.90  |           ( ~ $i(v2) |  ~ aElementOf0(v2, v0) |  ? [v3: $i] : ($i(v3) &
% 154.17/21.90  |               aElementOf0(v3, xS) & aElementOf0(v2, v3))) &  ! [v2: $i] : ( ~
% 154.17/21.90  |             $i(v2) |  ~ aInteger0(v2) | aElementOf0(v2, v1) | aElementOf0(v2,
% 154.17/21.90  |               v0)))
% 154.17/21.90  | 
% 154.17/21.90  | ALPHA: (m__2171) implies:
% 154.17/21.90  |   (12)  $i(sz00)
% 154.17/21.90  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] : ( ~ (xp =
% 154.17/21.90  |             sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v0 & stldt0(v2) = v3 &
% 154.17/21.90  |           sbsmnsldt0(xS) = v2 & smndt0(sz10) = v1 & $i(v3) & $i(v2) & $i(v1) &
% 154.17/21.90  |           $i(v0) & aSubsetOf0(v0, v3) & aSet0(v2) & aSet0(v0) & aInteger0(xp)
% 154.17/21.90  |           &  ! [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtasdt0(xp, v6) =
% 154.17/21.90  |               v5) |  ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v6) |  ~ $i(v4) |  ~
% 154.17/21.90  |             aInteger0(v6) |  ~ aInteger0(v4) | aElementOf0(v4, v0)) &  ! [v4:
% 154.17/21.90  |             $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~
% 154.17/21.90  |             aElementOf0(v4, v0) | sdteqdtlpzmzozddtrp0(v4, sz10, xp)) &  !
% 154.17/21.90  |           [v4: $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) | 
% 154.17/21.90  |             ~ aElementOf0(v4, v0) | aDivisorOf0(xp, v5)) &  ! [v4: $i] :  !
% 154.17/21.90  |           [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~
% 154.17/21.90  |             aElementOf0(v4, v0) | aInteger0(v4)) &  ! [v4: $i] :  ! [v5: $i] :
% 154.17/21.90  |           ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aElementOf0(v4, v0) | 
% 154.17/21.90  |             ? [v6: $i] : (sdtasdt0(xp, v6) = v5 & $i(v6) & $i(v5) &
% 154.17/21.90  |               aInteger0(v6))) &  ! [v4: $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4,
% 154.17/21.90  |                 v1) = v5) |  ~ $i(v4) |  ~ sdteqdtlpzmzozddtrp0(v4, sz10, xp)
% 154.17/21.90  |             |  ~ aInteger0(v4) | aElementOf0(v4, v0)) &  ! [v4: $i] :  ! [v5:
% 154.17/21.90  |             $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aDivisorOf0(xp,
% 154.17/21.90  |               v5) |  ~ aInteger0(v4) | aElementOf0(v4, v0)) &  ! [v4: $i] :  !
% 154.17/21.90  |           [v5: $i] : ( ~ $i(v5) |  ~ $i(v4) |  ~ aElementOf0(v5, xS) |  ~
% 154.17/21.90  |             aElementOf0(v4, v5) |  ~ aInteger0(v4) | aElementOf0(v4, v2)) &  !
% 154.17/21.90  |           [v4: $i] : ( ~ $i(v4) |  ~ aElementOf0(v4, v3) |  ~ aElementOf0(v4,
% 154.17/21.90  |               v2)) &  ! [v4: $i] : ( ~ $i(v4) |  ~ aElementOf0(v4, v3) |
% 154.17/21.90  |             aInteger0(v4)) &  ! [v4: $i] : ( ~ $i(v4) |  ~ aElementOf0(v4, v2)
% 154.17/21.90  |             | aInteger0(v4)) &  ! [v4: $i] : ( ~ $i(v4) |  ~ aElementOf0(v4,
% 154.17/21.90  |               v2) |  ? [v5: $i] : ($i(v5) & aElementOf0(v5, xS) &
% 154.17/21.90  |               aElementOf0(v4, v5))) &  ! [v4: $i] : ( ~ $i(v4) |  ~
% 154.17/21.90  |             aElementOf0(v4, v0) | aElementOf0(v4, v3)) &  ! [v4: $i] : ( ~
% 154.17/21.91  |             $i(v4) |  ~ aInteger0(v4) | aElementOf0(v4, v3) | aElementOf0(v4,
% 154.17/21.91  |               v2)))
% 154.17/21.91  | 
% 154.17/21.91  | ALPHA: (m__2232) implies:
% 154.17/21.91  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 154.17/21.91  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :
% 154.17/21.91  |         (szAzrzSzezqlpdtcmdtrp0(sz10, xp) = v3 & sdtasdt0(xp, v8) = v2 &
% 154.17/21.91  |           sdtasdt0(xp, v7) = v6 & sdtpldt0(v5, v1) = v6 & sdtpldt0(v0, v1) =
% 154.17/21.91  |           v2 & sdtpldt0(sz10, v4) = v5 & sdtpldt0(sz10, xp) = v0 & smndt0(xp)
% 154.17/21.91  |           = v4 & smndt0(sz10) = v1 & $i(v8) & $i(v7) & $i(v6) & $i(v5) &
% 154.17/21.91  |           $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aElementOf0(v5, v3) &
% 154.17/21.91  |           aElementOf0(v0, v3) & sdteqdtlpzmzozddtrp0(v5, sz10, xp) &
% 154.17/21.91  |           sdteqdtlpzmzozddtrp0(v0, sz10, xp) & aDivisorOf0(xp, v6) &
% 154.17/21.91  |           aDivisorOf0(xp, v2) & aInteger0(v8) & aInteger0(v7))
% 154.17/21.91  | 
% 154.17/21.91  | ALPHA: (m__) implies:
% 154.17/21.91  |   (15)  $i(sz10)
% 154.17/21.91  |   (16)  $i(xp)
% 154.17/21.91  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : ((v2 = sz10 & sdtpldt0(sz10,
% 154.17/21.91  |               v1) = sz10 & smndt0(xp) = v1 & $i(v1)) | (v0 = sz10 &
% 154.17/21.91  |             sdtpldt0(sz10, xp) = sz10))
% 154.17/21.91  | 
% 154.17/21.91  | ALPHA: (function-axioms) implies:
% 154.17/21.91  |   (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (smndt0(v2) =
% 154.17/21.91  |             v1) |  ~ (smndt0(v2) = v0))
% 154.17/21.91  |   (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~
% 154.17/21.91  |           (sbsmnsldt0(v2) = v1) |  ~ (sbsmnsldt0(v2) = v0))
% 154.17/21.91  |   (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : (v1 = v0 |  ~ (stldt0(v2) =
% 154.17/21.91  |             v1) |  ~ (stldt0(v2) = v0))
% 154.17/21.91  |   (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.17/21.91  |           (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 154.17/21.91  |   (22)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.17/21.91  |           (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v1) |  ~
% 154.17/21.91  |           (szAzrzSzezqlpdtcmdtrp0(v3, v2) = v0))
% 154.17/21.91  | 
% 154.17/21.91  | DELTA: instantiating (17) with fresh symbols all_36_0, all_36_1, all_36_2
% 154.17/21.91  |        gives:
% 154.17/21.91  |   (23)  (all_36_0 = sz10 & sdtpldt0(sz10, all_36_1) = sz10 & smndt0(xp) =
% 154.17/21.91  |           all_36_1 & $i(all_36_1)) | (all_36_2 = sz10 & sdtpldt0(sz10, xp) =
% 154.17/21.91  |           sz10)
% 154.17/21.91  | 
% 154.17/21.91  | DELTA: instantiating (5) with fresh symbol all_37_0 gives:
% 154.17/21.91  |   (24)  smndt0(sz10) = all_37_0 & $i(all_37_0) &  ! [v0: $i] :  ! [v1: $i] : (
% 154.17/21.91  |           ~ (sdtasdt0(all_37_0, v0) = v1) |  ~ $i(v0) |  ~ aInteger0(v0) |
% 154.17/21.91  |           (sdtasdt0(v0, all_37_0) = v1 & smndt0(v0) = v1 & $i(v1)))
% 154.17/21.91  | 
% 154.17/21.91  | ALPHA: (24) implies:
% 154.17/21.91  |   (25)  smndt0(sz10) = all_37_0
% 154.17/21.91  | 
% 154.17/21.91  | DELTA: instantiating (7) with fresh symbol all_40_0 gives:
% 154.17/21.92  |   (26)  smndt0(sz10) = all_40_0 & $i(all_40_0) &  ! [v0: any] : (v0 = all_40_0
% 154.17/21.92  |           | v0 = sz10 |  ~ $i(v0) |  ~ aInteger0(v0) |  ? [v1: $i] : ($i(v1) &
% 154.17/21.92  |             isPrime0(v1) & aDivisorOf0(v1, v0))) &  ! [v0: $i] : ( ~ $i(v0) | 
% 154.17/21.92  |           ~ isPrime0(v0) |  ~ aDivisorOf0(v0, all_40_0) |  ~
% 154.17/21.92  |           aInteger0(all_40_0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ isPrime0(v0) | 
% 154.17/21.92  |           ~ aDivisorOf0(v0, sz10) |  ~ aInteger0(sz10))
% 154.17/21.92  | 
% 154.17/21.92  | ALPHA: (26) implies:
% 154.17/21.92  |   (27)  $i(all_40_0)
% 154.17/21.92  |   (28)  smndt0(sz10) = all_40_0
% 154.17/21.92  |   (29)   ! [v0: any] : (v0 = all_40_0 | v0 = sz10 |  ~ $i(v0) |  ~
% 154.17/21.92  |           aInteger0(v0) |  ? [v1: $i] : ($i(v1) & isPrime0(v1) &
% 154.17/21.92  |             aDivisorOf0(v1, v0)))
% 154.17/21.92  | 
% 154.17/21.92  | DELTA: instantiating (14) with fresh symbols all_43_0, all_43_1, all_43_2,
% 154.17/21.92  |        all_43_3, all_43_4, all_43_5, all_43_6, all_43_7, all_43_8 gives:
% 154.17/21.92  |   (30)  szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_5 & sdtasdt0(xp, all_43_0) =
% 154.17/21.92  |         all_43_6 & sdtasdt0(xp, all_43_1) = all_43_2 & sdtpldt0(all_43_3,
% 154.17/21.92  |           all_43_7) = all_43_2 & sdtpldt0(all_43_8, all_43_7) = all_43_6 &
% 154.17/21.92  |         sdtpldt0(sz10, all_43_4) = all_43_3 & sdtpldt0(sz10, xp) = all_43_8 &
% 154.17/21.92  |         smndt0(xp) = all_43_4 & smndt0(sz10) = all_43_7 & $i(all_43_0) &
% 154.17/21.92  |         $i(all_43_1) & $i(all_43_2) & $i(all_43_3) & $i(all_43_4) &
% 154.17/21.92  |         $i(all_43_5) & $i(all_43_6) & $i(all_43_7) & $i(all_43_8) &
% 154.17/21.92  |         aElementOf0(all_43_3, all_43_5) & aElementOf0(all_43_8, all_43_5) &
% 154.17/21.92  |         sdteqdtlpzmzozddtrp0(all_43_3, sz10, xp) &
% 154.17/21.92  |         sdteqdtlpzmzozddtrp0(all_43_8, sz10, xp) & aDivisorOf0(xp, all_43_2) &
% 154.17/21.92  |         aDivisorOf0(xp, all_43_6) & aInteger0(all_43_0) & aInteger0(all_43_1)
% 154.17/21.92  | 
% 154.17/21.92  | ALPHA: (30) implies:
% 154.17/21.92  |   (31)  aInteger0(all_43_1)
% 154.17/21.92  |   (32)  aInteger0(all_43_0)
% 154.17/21.92  |   (33)  aElementOf0(all_43_8, all_43_5)
% 154.17/21.92  |   (34)  aElementOf0(all_43_3, all_43_5)
% 154.17/21.92  |   (35)  $i(all_43_8)
% 154.17/21.92  |   (36)  $i(all_43_4)
% 154.17/21.92  |   (37)  $i(all_43_3)
% 154.17/21.92  |   (38)  $i(all_43_1)
% 154.17/21.92  |   (39)  $i(all_43_0)
% 154.17/21.92  |   (40)  smndt0(sz10) = all_43_7
% 154.17/21.92  |   (41)  smndt0(xp) = all_43_4
% 154.17/21.92  |   (42)  sdtpldt0(sz10, xp) = all_43_8
% 154.17/21.92  |   (43)  sdtpldt0(sz10, all_43_4) = all_43_3
% 154.17/21.92  |   (44)  sdtpldt0(all_43_8, all_43_7) = all_43_6
% 154.17/21.92  |   (45)  sdtpldt0(all_43_3, all_43_7) = all_43_2
% 154.17/21.92  |   (46)  sdtasdt0(xp, all_43_1) = all_43_2
% 154.17/21.92  |   (47)  sdtasdt0(xp, all_43_0) = all_43_6
% 154.17/21.92  |   (48)  szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_43_5
% 154.17/21.92  | 
% 154.17/21.92  | DELTA: instantiating (10) with fresh symbols all_45_0, all_45_1 gives:
% 154.17/21.93  |   (49)  stldt0(all_45_1) = cS2076 & sbsmnsldt0(xS) = all_45_1 & smndt0(sz10) =
% 154.17/21.93  |         all_45_0 & $i(all_45_0) & $i(all_45_1) & aElementOf0(all_45_0, cS2076)
% 154.17/21.93  |         & aElementOf0(sz10, cS2076) & aSet0(all_45_1) & aSet0(cS2076) &  !
% 154.17/21.93  |         [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1,
% 154.17/21.93  |             xS) |  ~ aElementOf0(v0, v1) |  ~ aInteger0(v0) | aElementOf0(v0,
% 154.17/21.93  |             all_45_1)) &  ! [v0: any] : (v0 = all_45_0 | v0 = sz10 |  ~ $i(v0)
% 154.17/21.93  |           |  ~ aElementOf0(v0, cS2076)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 154.17/21.93  |           aElementOf0(v0, all_45_1) |  ~ aElementOf0(v0, cS2076)) &  ! [v0:
% 154.17/21.93  |           $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_45_1) | aInteger0(v0)) & 
% 154.17/21.93  |         ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_45_1) |  ? [v1: $i] :
% 154.17/21.93  |           ($i(v1) & aElementOf0(v1, xS) & aElementOf0(v0, v1))) &  ! [v0: $i]
% 154.17/21.93  |         : ( ~ $i(v0) |  ~ aElementOf0(v0, cS2076) | aInteger0(v0)) &  ! [v0:
% 154.17/21.93  |           $i] : ( ~ $i(v0) |  ~ aInteger0(v0) | aElementOf0(v0, all_45_1) |
% 154.17/21.93  |           aElementOf0(v0, cS2076))
% 154.17/21.93  | 
% 154.17/21.93  | ALPHA: (49) implies:
% 154.17/21.93  |   (50)  aSet0(cS2076)
% 154.17/21.93  |   (51)  smndt0(sz10) = all_45_0
% 154.17/21.93  |   (52)  sbsmnsldt0(xS) = all_45_1
% 154.17/21.93  |   (53)  stldt0(all_45_1) = cS2076
% 154.17/21.93  |   (54)   ! [v0: any] : (v0 = all_45_0 | v0 = sz10 |  ~ $i(v0) |  ~
% 154.17/21.93  |           aElementOf0(v0, cS2076))
% 154.17/21.93  | 
% 154.17/21.93  | DELTA: instantiating (13) with fresh symbols all_48_0, all_48_1, all_48_2,
% 154.17/21.93  |        all_48_3 gives:
% 154.17/21.93  |   (55)   ~ (xp = sz00) & szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_48_3 &
% 154.17/21.93  |         stldt0(all_48_1) = all_48_0 & sbsmnsldt0(xS) = all_48_1 & smndt0(sz10)
% 154.17/21.93  |         = all_48_2 & $i(all_48_0) & $i(all_48_1) & $i(all_48_2) & $i(all_48_3)
% 154.17/21.93  |         & aSubsetOf0(all_48_3, all_48_0) & aSet0(all_48_1) & aSet0(all_48_3) &
% 154.17/21.93  |         aInteger0(xp) &  ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] : ( ~
% 154.17/21.93  |           (sdtasdt0(xp, v2) = v1) |  ~ (sdtpldt0(v0, all_48_2) = v1) |  ~
% 154.17/21.93  |           $i(v2) |  ~ $i(v0) |  ~ aInteger0(v2) |  ~ aInteger0(v0) |
% 154.17/21.93  |           aElementOf0(v0, all_48_3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 154.17/21.93  |           (sdtpldt0(v0, all_48_2) = v1) |  ~ $i(v0) |  ~ aElementOf0(v0,
% 154.17/21.93  |             all_48_3) | sdteqdtlpzmzozddtrp0(v0, sz10, xp)) &  ! [v0: $i] :  !
% 154.17/21.93  |         [v1: $i] : ( ~ (sdtpldt0(v0, all_48_2) = v1) |  ~ $i(v0) |  ~
% 154.17/21.93  |           aElementOf0(v0, all_48_3) | aDivisorOf0(xp, v1)) &  ! [v0: $i] :  !
% 154.17/21.93  |         [v1: $i] : ( ~ (sdtpldt0(v0, all_48_2) = v1) |  ~ $i(v0) |  ~
% 154.17/21.93  |           aElementOf0(v0, all_48_3) | aInteger0(v0)) &  ! [v0: $i] :  ! [v1:
% 154.17/21.93  |           $i] : ( ~ (sdtpldt0(v0, all_48_2) = v1) |  ~ $i(v0) |  ~
% 154.17/21.93  |           aElementOf0(v0, all_48_3) |  ? [v2: $i] : (sdtasdt0(xp, v2) = v1 &
% 154.17/21.93  |             $i(v2) & $i(v1) & aInteger0(v2))) &  ! [v0: $i] :  ! [v1: $i] : (
% 154.17/21.93  |           ~ (sdtpldt0(v0, all_48_2) = v1) |  ~ $i(v0) |  ~
% 154.17/21.93  |           sdteqdtlpzmzozddtrp0(v0, sz10, xp) |  ~ aInteger0(v0) |
% 154.17/21.93  |           aElementOf0(v0, all_48_3)) &  ! [v0: $i] :  ! [v1: $i] : ( ~
% 154.17/21.93  |           (sdtpldt0(v0, all_48_2) = v1) |  ~ $i(v0) |  ~ aDivisorOf0(xp, v1) |
% 154.17/21.93  |            ~ aInteger0(v0) | aElementOf0(v0, all_48_3)) &  ! [v0: $i] :  !
% 154.17/21.93  |         [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~ aElementOf0(v1, xS) |  ~
% 154.17/21.93  |           aElementOf0(v0, v1) |  ~ aInteger0(v0) | aElementOf0(v0, all_48_1))
% 154.17/21.93  |         &  ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_48_0) |  ~
% 154.17/21.93  |           aElementOf0(v0, all_48_1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 154.17/21.93  |           aElementOf0(v0, all_48_0) | aInteger0(v0)) &  ! [v0: $i] : ( ~
% 154.17/21.93  |           $i(v0) |  ~ aElementOf0(v0, all_48_1) | aInteger0(v0)) &  ! [v0: $i]
% 154.17/21.93  |         : ( ~ $i(v0) |  ~ aElementOf0(v0, all_48_1) |  ? [v1: $i] : ($i(v1) &
% 154.17/21.93  |             aElementOf0(v1, xS) & aElementOf0(v0, v1))) &  ! [v0: $i] : ( ~
% 154.17/21.93  |           $i(v0) |  ~ aElementOf0(v0, all_48_3) | aElementOf0(v0, all_48_0)) &
% 154.17/21.93  |          ! [v0: $i] : ( ~ $i(v0) |  ~ aInteger0(v0) | aElementOf0(v0,
% 154.17/21.94  |             all_48_0) | aElementOf0(v0, all_48_1))
% 154.17/21.94  | 
% 154.17/21.94  | ALPHA: (55) implies:
% 154.17/21.94  |   (56)   ~ (xp = sz00)
% 154.17/21.94  |   (57)  aInteger0(xp)
% 154.17/21.94  |   (58)  aSubsetOf0(all_48_3, all_48_0)
% 154.17/21.94  |   (59)  $i(all_48_3)
% 154.17/21.94  |   (60)  $i(all_48_0)
% 154.17/21.94  |   (61)  smndt0(sz10) = all_48_2
% 154.17/21.94  |   (62)  sbsmnsldt0(xS) = all_48_1
% 154.17/21.94  |   (63)  stldt0(all_48_1) = all_48_0
% 154.17/21.94  |   (64)  szAzrzSzezqlpdtcmdtrp0(sz10, xp) = all_48_3
% 154.17/21.94  |   (65)   ! [v0: $i] : ( ~ $i(v0) |  ~ aInteger0(v0) | aElementOf0(v0,
% 154.17/21.94  |             all_48_0) | aElementOf0(v0, all_48_1))
% 154.17/21.94  | 
% 154.17/21.94  | DELTA: instantiating (11) with fresh symbols all_51_0, all_51_1 gives:
% 154.17/21.94  |   (66)  stldt0(all_51_1) = all_51_0 & sbsmnsldt0(xS) = all_51_1 & $i(all_51_0)
% 154.17/21.94  |         & $i(all_51_1) & isClosed0(all_51_1) & isOpen0(all_51_0) &
% 154.17/21.94  |         aSet0(all_51_1) &  ! [v0: $i] :  ! [v1: $i] : ( ~ (smndt0(v0) = v1) | 
% 154.17/21.94  |           ~ $i(v0) |  ~ aElementOf0(v0, all_51_0) |  ? [v2: $i] :  ? [v3: $i]
% 154.17/21.94  |           : ( ~ (v2 = sz00) & szAzrzSzezqlpdtcmdtrp0(v0, v2) = v3 & $i(v3) &
% 154.17/21.94  |             $i(v2) & aSubsetOf0(v3, all_51_0) & aSet0(v3) & aInteger0(v2) &  !
% 154.17/21.94  |             [v4: $i] :  ! [v5: $i] :  ! [v6: $i] : ( ~ (sdtasdt0(v2, v6) = v5)
% 154.17/21.94  |               |  ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v6) |  ~ $i(v4) |  ~
% 154.17/21.94  |               aInteger0(v6) |  ~ aInteger0(v4) | aElementOf0(v4, v3)) &  !
% 154.17/21.94  |             [v4: $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |
% 154.17/21.94  |                ~ aElementOf0(v4, v3) | sdteqdtlpzmzozddtrp0(v4, v0, v2)) &  !
% 154.17/21.94  |             [v4: $i] :  ! [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |
% 154.17/21.94  |                ~ aElementOf0(v4, v3) | aDivisorOf0(v2, v5)) &  ! [v4: $i] :  !
% 154.17/21.94  |             [v5: $i] : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~
% 154.17/21.94  |               aElementOf0(v4, v3) | aInteger0(v4)) &  ! [v4: $i] :  ! [v5: $i]
% 154.17/21.94  |             : ( ~ (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aElementOf0(v4, v3)
% 154.17/21.94  |               |  ? [v6: $i] : (sdtasdt0(v2, v6) = v5 & $i(v6) & $i(v5) &
% 154.17/21.94  |                 aInteger0(v6))) &  ! [v4: $i] :  ! [v5: $i] : ( ~
% 154.17/21.94  |               (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~
% 154.17/21.94  |               sdteqdtlpzmzozddtrp0(v4, v0, v2) |  ~ aInteger0(v4) |
% 154.17/21.94  |               aElementOf0(v4, v3)) &  ! [v4: $i] :  ! [v5: $i] : ( ~
% 154.17/21.94  |               (sdtpldt0(v4, v1) = v5) |  ~ $i(v4) |  ~ aDivisorOf0(v2, v5) | 
% 154.17/21.94  |               ~ aInteger0(v4) | aElementOf0(v4, v3)) &  ! [v4: $i] : ( ~
% 154.17/21.94  |               $i(v4) |  ~ aElementOf0(v4, v3) | aElementOf0(v4, all_51_0)))) &
% 154.17/21.94  |          ! [v0: $i] :  ! [v1: $i] : ( ~ $i(v1) |  ~ $i(v0) |  ~
% 154.17/21.94  |           aElementOf0(v1, xS) |  ~ aElementOf0(v0, v1) |  ~ aInteger0(v0) |
% 154.17/21.94  |           aElementOf0(v0, all_51_1)) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 154.17/21.94  |           aElementOf0(v0, all_51_0) |  ~ aElementOf0(v0, all_51_1)) &  ! [v0:
% 154.17/21.94  |           $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_51_0) | aInteger0(v0)) & 
% 154.17/21.94  |         ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0, all_51_1) |
% 154.17/21.94  |           aInteger0(v0)) &  ! [v0: $i] : ( ~ $i(v0) |  ~ aElementOf0(v0,
% 154.17/21.94  |             all_51_1) |  ? [v1: $i] : ($i(v1) & aElementOf0(v1, xS) &
% 154.17/21.94  |             aElementOf0(v0, v1))) &  ! [v0: $i] : ( ~ $i(v0) |  ~
% 154.17/21.94  |           aInteger0(v0) | aElementOf0(v0, all_51_0) | aElementOf0(v0,
% 154.17/21.94  |             all_51_1))
% 154.17/21.94  | 
% 154.17/21.94  | ALPHA: (66) implies:
% 154.17/21.94  |   (67)  sbsmnsldt0(xS) = all_51_1
% 154.17/21.94  |   (68)  stldt0(all_51_1) = all_51_0
% 154.17/21.94  | 
% 154.17/21.94  | GROUND_INST: instantiating (18) with all_40_0, all_43_7, sz10, simplifying
% 154.17/21.94  |              with (28), (40) gives:
% 154.17/21.94  |   (69)  all_43_7 = all_40_0
% 154.17/21.94  | 
% 154.17/21.94  | GROUND_INST: instantiating (18) with all_45_0, all_48_2, sz10, simplifying
% 154.17/21.94  |              with (51), (61) gives:
% 154.17/21.94  |   (70)  all_48_2 = all_45_0
% 154.17/21.94  | 
% 154.17/21.94  | GROUND_INST: instantiating (18) with all_43_7, all_48_2, sz10, simplifying
% 154.17/21.94  |              with (40), (61) gives:
% 154.17/21.94  |   (71)  all_48_2 = all_43_7
% 154.17/21.94  | 
% 154.17/21.94  | GROUND_INST: instantiating (18) with all_37_0, all_48_2, sz10, simplifying
% 154.17/21.94  |              with (25), (61) gives:
% 154.17/21.94  |   (72)  all_48_2 = all_37_0
% 154.17/21.94  | 
% 154.17/21.94  | GROUND_INST: instantiating (19) with all_48_1, all_51_1, xS, simplifying with
% 154.17/21.94  |              (62), (67) gives:
% 154.17/21.94  |   (73)  all_51_1 = all_48_1
% 154.17/21.94  | 
% 154.17/21.94  | GROUND_INST: instantiating (19) with all_45_1, all_51_1, xS, simplifying with
% 154.17/21.94  |              (52), (67) gives:
% 154.17/21.94  |   (74)  all_51_1 = all_45_1
% 154.17/21.94  | 
% 154.17/21.95  | GROUND_INST: instantiating (22) with all_43_5, all_48_3, xp, sz10, simplifying
% 154.17/21.95  |              with (48), (64) gives:
% 154.17/21.95  |   (75)  all_48_3 = all_43_5
% 154.17/21.95  | 
% 154.17/21.95  | COMBINE_EQS: (73), (74) imply:
% 154.17/21.95  |   (76)  all_48_1 = all_45_1
% 154.17/21.95  | 
% 154.17/21.95  | COMBINE_EQS: (70), (71) imply:
% 154.17/21.95  |   (77)  all_45_0 = all_43_7
% 154.17/21.95  | 
% 154.17/21.95  | COMBINE_EQS: (70), (72) imply:
% 154.17/21.95  |   (78)  all_45_0 = all_37_0
% 154.17/21.95  | 
% 154.17/21.95  | COMBINE_EQS: (77), (78) imply:
% 154.17/21.95  |   (79)  all_43_7 = all_37_0
% 154.17/21.95  | 
% 154.17/21.95  | SIMP: (79) implies:
% 154.17/21.95  |   (80)  all_43_7 = all_37_0
% 154.17/21.95  | 
% 154.17/21.95  | COMBINE_EQS: (69), (80) imply:
% 154.17/21.95  |   (81)  all_40_0 = all_37_0
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (68), (74) imply:
% 154.17/21.95  |   (82)  stldt0(all_45_1) = all_51_0
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (63), (76) imply:
% 154.17/21.95  |   (83)  stldt0(all_45_1) = all_48_0
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (45), (80) imply:
% 154.17/21.95  |   (84)  sdtpldt0(all_43_3, all_37_0) = all_43_2
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (44), (80) imply:
% 154.17/21.95  |   (85)  sdtpldt0(all_43_8, all_37_0) = all_43_6
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (59), (75) imply:
% 154.17/21.95  |   (86)  $i(all_43_5)
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (27), (81) imply:
% 154.17/21.95  |   (87)  $i(all_37_0)
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (58), (75) imply:
% 154.17/21.95  |   (88)  aSubsetOf0(all_43_5, all_48_0)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (20) with cS2076, all_51_0, all_45_1, simplifying
% 154.17/21.95  |              with (53), (82) gives:
% 154.17/21.95  |   (89)  all_51_0 = cS2076
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (20) with all_48_0, all_51_0, all_45_1, simplifying
% 154.17/21.95  |              with (82), (83) gives:
% 154.17/21.95  |   (90)  all_51_0 = all_48_0
% 154.17/21.95  | 
% 154.17/21.95  | COMBINE_EQS: (89), (90) imply:
% 154.17/21.95  |   (91)  all_48_0 = cS2076
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (60), (91) imply:
% 154.17/21.95  |   (92)  $i(cS2076)
% 154.17/21.95  | 
% 154.17/21.95  | REDUCE: (88), (91) imply:
% 154.17/21.95  |   (93)  aSubsetOf0(all_43_5, cS2076)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (29) with sz00, simplifying with (1), (12) gives:
% 154.17/21.95  |   (94)  all_40_0 = sz00 | sz10 = sz00 |  ? [v0: $i] : ($i(v0) & isPrime0(v0) &
% 154.17/21.95  |           aDivisorOf0(v0, sz00))
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (65) with sz00, simplifying with (1), (12) gives:
% 154.17/21.95  |   (95)  aElementOf0(sz00, all_48_0) | aElementOf0(sz00, all_48_1)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (8) with cS2076, all_43_5, all_43_8, simplifying
% 154.17/21.95  |              with (33), (35), (50), (86), (92), (93) gives:
% 154.17/21.95  |   (96)  aElementOf0(all_43_8, cS2076)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (mIntNeg) with sz10, all_37_0, simplifying with
% 154.17/21.95  |              (2), (15), (25) gives:
% 154.17/21.95  |   (97)  aInteger0(all_37_0)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (mIntNeg) with xp, all_43_4, simplifying with (16),
% 154.17/21.95  |              (41), (57) gives:
% 154.17/21.95  |   (98)  aInteger0(all_43_4)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (mIntPlus) with sz10, xp, all_43_8, simplifying
% 154.17/21.95  |              with (2), (15), (16), (42), (57) gives:
% 154.17/21.95  |   (99)  aInteger0(all_43_8)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (mAddComm) with sz10, xp, all_43_8, simplifying
% 154.17/21.95  |              with (2), (15), (16), (42), (57) gives:
% 154.17/21.95  |   (100)  sdtpldt0(xp, sz10) = all_43_8 & $i(all_43_8)
% 154.17/21.95  | 
% 154.17/21.95  | ALPHA: (100) implies:
% 154.17/21.95  |   (101)  sdtpldt0(xp, sz10) = all_43_8
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (mIntMult) with xp, all_43_1, all_43_2, simplifying
% 154.17/21.95  |              with (16), (31), (38), (46), (57) gives:
% 154.17/21.95  |   (102)  aInteger0(all_43_2)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (mIntMult) with xp, all_43_0, all_43_6, simplifying
% 154.17/21.95  |              with (16), (32), (39), (47), (57) gives:
% 154.17/21.95  |   (103)  aInteger0(all_43_6)
% 154.17/21.95  | 
% 154.17/21.95  | GROUND_INST: instantiating (9) with sz10, xp, all_43_5, all_43_3, simplifying
% 154.17/21.95  |              with (2), (15), (16), (34), (37), (48), (57), (86) gives:
% 154.17/21.95  |   (104)  xp = sz00 | aInteger0(all_43_3)
% 154.17/21.95  | 
% 154.17/21.95  | BETA: splitting (104) gives:
% 154.17/21.95  | 
% 154.17/21.95  | Case 1:
% 154.17/21.95  | | 
% 154.17/21.95  | |   (105)  aInteger0(all_43_3)
% 154.17/21.95  | | 
% 154.17/21.95  | | GROUND_INST: instantiating (mAddAsso) with sz10, xp, all_37_0, all_43_8,
% 154.17/21.95  | |              all_43_6, simplifying with (2), (15), (16), (42), (57), (85),
% 154.17/21.95  | |              (87), (97) gives:
% 154.17/21.95  | |   (106)   ? [v0: $i] : (sdtpldt0(xp, all_37_0) = v0 & sdtpldt0(sz10, v0) =
% 154.17/21.95  | |            all_43_6 & $i(v0) & $i(all_43_6))
% 154.17/21.95  | | 
% 154.17/21.95  | | GROUND_INST: instantiating (mAddComm) with all_43_8, all_37_0, all_43_6,
% 154.17/21.95  | |              simplifying with (35), (85), (87), (97), (99) gives:
% 154.17/21.95  | |   (107)  sdtpldt0(all_37_0, all_43_8) = all_43_6 & $i(all_43_6)
% 154.17/21.95  | | 
% 154.17/21.95  | | ALPHA: (107) implies:
% 154.17/21.95  | |   (108)  sdtpldt0(all_37_0, all_43_8) = all_43_6
% 154.17/21.95  | | 
% 154.17/21.95  | | GROUND_INST: instantiating (29) with all_43_8, simplifying with (35), (99)
% 154.17/21.95  | |              gives:
% 154.17/21.96  | |   (109)  all_43_8 = all_40_0 | all_43_8 = sz10 |  ? [v0: $i] : ($i(v0) &
% 154.17/21.96  | |            isPrime0(v0) & aDivisorOf0(v0, all_43_8))
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (mAddAsso) with sz10, all_43_4, all_37_0,
% 154.17/21.96  | |              all_43_3, all_43_2, simplifying with (2), (15), (36), (43),
% 154.17/21.96  | |              (84), (87), (97), (98) gives:
% 154.17/21.96  | |   (110)   ? [v0: $i] : (sdtpldt0(all_43_4, all_37_0) = v0 & sdtpldt0(sz10,
% 154.17/21.96  | |              v0) = all_43_2 & $i(v0) & $i(all_43_2))
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (mAddComm) with sz10, all_43_4, all_43_3,
% 154.17/21.96  | |              simplifying with (2), (15), (36), (43), (98) gives:
% 154.17/21.96  | |   (111)  sdtpldt0(all_43_4, sz10) = all_43_3 & $i(all_43_3)
% 154.17/21.96  | | 
% 154.17/21.96  | | ALPHA: (111) implies:
% 154.17/21.96  | |   (112)  sdtpldt0(all_43_4, sz10) = all_43_3
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (29) with all_43_4, simplifying with (36), (98)
% 154.17/21.96  | |              gives:
% 154.17/21.96  | |   (113)  all_43_4 = all_40_0 | all_43_4 = sz10 |  ? [v0: $i] : ($i(v0) &
% 154.17/21.96  | |            isPrime0(v0) & aDivisorOf0(v0, all_43_4))
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (mAddComm) with all_43_3, all_37_0, all_43_2,
% 154.17/21.96  | |              simplifying with (37), (84), (87), (97), (105) gives:
% 154.17/21.96  | |   (114)  sdtpldt0(all_37_0, all_43_3) = all_43_2 & $i(all_43_2)
% 154.17/21.96  | | 
% 154.17/21.96  | | ALPHA: (114) implies:
% 154.17/21.96  | |   (115)  $i(all_43_2)
% 154.17/21.96  | |   (116)  sdtpldt0(all_37_0, all_43_3) = all_43_2
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (6) with all_43_2, xp, simplifying with (16),
% 154.17/21.96  | |              (57), (102), (115) gives:
% 154.17/21.96  | |   (117)  xp = sz00 | sdteqdtlpzmzozddtrp0(all_43_2, all_43_2, xp)
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (54) with all_43_8, simplifying with (35), (96)
% 154.17/21.96  | |              gives:
% 154.17/21.96  | |   (118)  all_45_0 = all_43_8 | all_43_8 = sz10
% 154.17/21.96  | | 
% 154.17/21.96  | | GROUND_INST: instantiating (mAddAsso) with xp, sz10, all_37_0, all_43_8,
% 154.17/21.96  | |              all_43_6, simplifying with (2), (15), (16), (57), (85), (87),
% 154.17/21.96  | |              (97), (101) gives:
% 154.17/21.96  | |   (119)   ? [v0: $i] : (sdtpldt0(xp, v0) = all_43_6 & sdtpldt0(sz10,
% 154.17/21.96  | |              all_37_0) = v0 & $i(v0) & $i(all_43_6))
% 154.17/21.96  | | 
% 154.17/21.96  | | DELTA: instantiating (110) with fresh symbol all_129_0 gives:
% 154.17/21.96  | |   (120)  sdtpldt0(all_43_4, all_37_0) = all_129_0 & sdtpldt0(sz10,
% 154.17/21.96  | |            all_129_0) = all_43_2 & $i(all_129_0) & $i(all_43_2)
% 154.17/21.96  | | 
% 154.17/21.96  | | ALPHA: (120) implies:
% 154.17/21.96  | |   (121)  sdtpldt0(sz10, all_129_0) = all_43_2
% 154.17/21.96  | |   (122)  sdtpldt0(all_43_4, all_37_0) = all_129_0
% 154.17/21.96  | | 
% 154.17/21.96  | | DELTA: instantiating (106) with fresh symbol all_131_0 gives:
% 154.17/21.96  | |   (123)  sdtpldt0(xp, all_37_0) = all_131_0 & sdtpldt0(sz10, all_131_0) =
% 154.17/21.96  | |          all_43_6 & $i(all_131_0) & $i(all_43_6)
% 154.17/21.96  | | 
% 154.17/21.96  | | ALPHA: (123) implies:
% 154.17/21.96  | |   (124)  sdtpldt0(sz10, all_131_0) = all_43_6
% 154.17/21.96  | |   (125)  sdtpldt0(xp, all_37_0) = all_131_0
% 154.17/21.96  | | 
% 154.17/21.96  | | DELTA: instantiating (119) with fresh symbol all_133_0 gives:
% 154.17/21.96  | |   (126)  sdtpldt0(xp, all_133_0) = all_43_6 & sdtpldt0(sz10, all_37_0) =
% 154.17/21.96  | |          all_133_0 & $i(all_133_0) & $i(all_43_6)
% 154.17/21.96  | | 
% 154.17/21.96  | | ALPHA: (126) implies:
% 154.17/21.96  | |   (127)  sdtpldt0(sz10, all_37_0) = all_133_0
% 154.17/21.96  | |   (128)  sdtpldt0(xp, all_133_0) = all_43_6
% 154.17/21.96  | | 
% 154.17/21.96  | | BETA: splitting (117) gives:
% 154.17/21.96  | | 
% 154.17/21.96  | | Case 1:
% 154.17/21.96  | | | 
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mIntPlus) with sz10, all_37_0, all_133_0,
% 154.17/21.96  | | |              simplifying with (2), (15), (87), (97), (127) gives:
% 154.17/21.96  | | |   (129)  aInteger0(all_133_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mAddComm) with sz10, all_37_0, all_133_0,
% 154.17/21.96  | | |              simplifying with (2), (15), (87), (97), (127) gives:
% 154.17/21.96  | | |   (130)  sdtpldt0(all_37_0, sz10) = all_133_0 & $i(all_133_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | ALPHA: (130) implies:
% 154.17/21.96  | | |   (131)  sdtpldt0(all_37_0, sz10) = all_133_0
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mIntPlus) with xp, all_37_0, all_131_0,
% 154.17/21.96  | | |              simplifying with (16), (57), (87), (97), (125) gives:
% 154.17/21.96  | | |   (132)  aInteger0(all_131_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mAddComm) with xp, all_37_0, all_131_0,
% 154.17/21.96  | | |              simplifying with (16), (57), (87), (97), (125) gives:
% 154.17/21.96  | | |   (133)  sdtpldt0(all_37_0, xp) = all_131_0 & $i(all_131_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | ALPHA: (133) implies:
% 154.17/21.96  | | |   (134)  $i(all_131_0)
% 154.17/21.96  | | |   (135)  sdtpldt0(all_37_0, xp) = all_131_0
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mAddAsso) with all_43_4, sz10, all_37_0,
% 154.17/21.96  | | |              all_43_3, all_43_2, simplifying with (2), (15), (36), (84),
% 154.17/21.96  | | |              (87), (97), (98), (112) gives:
% 154.17/21.96  | | |   (136)   ? [v0: $i] : (sdtpldt0(all_43_4, v0) = all_43_2 & sdtpldt0(sz10,
% 154.17/21.96  | | |              all_37_0) = v0 & $i(v0) & $i(all_43_2))
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mIntPlus) with all_43_4, all_37_0, all_129_0,
% 154.17/21.96  | | |              simplifying with (36), (87), (97), (98), (122) gives:
% 154.17/21.96  | | |   (137)  aInteger0(all_129_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | GROUND_INST: instantiating (mAddComm) with all_43_4, all_37_0, all_129_0,
% 154.17/21.96  | | |              simplifying with (36), (87), (97), (98), (122) gives:
% 154.17/21.96  | | |   (138)  sdtpldt0(all_37_0, all_43_4) = all_129_0 & $i(all_129_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | ALPHA: (138) implies:
% 154.17/21.96  | | |   (139)  $i(all_129_0)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | DELTA: instantiating (136) with fresh symbol all_181_0 gives:
% 154.17/21.96  | | |   (140)  sdtpldt0(all_43_4, all_181_0) = all_43_2 & sdtpldt0(sz10,
% 154.17/21.96  | | |            all_37_0) = all_181_0 & $i(all_181_0) & $i(all_43_2)
% 154.17/21.96  | | | 
% 154.17/21.96  | | | ALPHA: (140) implies:
% 154.17/21.97  | | |   (141)  sdtpldt0(sz10, all_37_0) = all_181_0
% 154.17/21.97  | | |   (142)  sdtpldt0(all_43_4, all_181_0) = all_43_2
% 154.17/21.97  | | | 
% 154.17/21.97  | | | GROUND_INST: instantiating (21) with all_133_0, all_181_0, all_37_0, sz10,
% 154.17/21.97  | | |              simplifying with (127), (141) gives:
% 154.17/21.97  | | |   (143)  all_181_0 = all_133_0
% 154.17/21.97  | | | 
% 154.17/21.97  | | | REDUCE: (142), (143) imply:
% 154.17/21.97  | | |   (144)  sdtpldt0(all_43_4, all_133_0) = all_43_2
% 154.17/21.97  | | | 
% 154.17/21.97  | | | BETA: splitting (23) gives:
% 154.17/21.97  | | | 
% 154.17/21.97  | | | Case 1:
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | |   (145)  all_36_0 = sz10 & sdtpldt0(sz10, all_36_1) = sz10 & smndt0(xp)
% 154.17/21.97  | | | |          = all_36_1 & $i(all_36_1)
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | ALPHA: (145) implies:
% 154.17/21.97  | | | |   (146)  smndt0(xp) = all_36_1
% 154.17/21.97  | | | |   (147)  sdtpldt0(sz10, all_36_1) = sz10
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | GROUND_INST: instantiating (18) with all_43_4, all_36_1, xp, simplifying
% 154.17/21.97  | | | |              with (41), (146) gives:
% 154.17/21.97  | | | |   (148)  all_43_4 = all_36_1
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (144), (148) imply:
% 154.17/21.97  | | | |   (149)  sdtpldt0(all_36_1, all_133_0) = all_43_2
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (122), (148) imply:
% 154.17/21.97  | | | |   (150)  sdtpldt0(all_36_1, all_37_0) = all_129_0
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (112), (148) imply:
% 154.17/21.97  | | | |   (151)  sdtpldt0(all_36_1, sz10) = all_43_3
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (43), (148) imply:
% 154.17/21.97  | | | |   (152)  sdtpldt0(sz10, all_36_1) = all_43_3
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (36), (148) imply:
% 154.17/21.97  | | | |   (153)  $i(all_36_1)
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (98), (148) imply:
% 154.17/21.97  | | | |   (154)  aInteger0(all_36_1)
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | GROUND_INST: instantiating (21) with sz10, all_43_3, all_36_1, sz10,
% 154.17/21.97  | | | |              simplifying with (147), (152) gives:
% 154.17/21.97  | | | |   (155)  all_43_3 = sz10
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (116), (155) imply:
% 154.17/21.97  | | | |   (156)  sdtpldt0(all_37_0, sz10) = all_43_2
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (151), (155) imply:
% 154.17/21.97  | | | |   (157)  sdtpldt0(all_36_1, sz10) = sz10
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | GROUND_INST: instantiating (21) with all_133_0, all_43_2, sz10,
% 154.17/21.97  | | | |              all_37_0, simplifying with (131), (156) gives:
% 154.17/21.97  | | | |   (158)  all_133_0 = all_43_2
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (149), (158) imply:
% 154.17/21.97  | | | |   (159)  sdtpldt0(all_36_1, all_43_2) = all_43_2
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | REDUCE: (128), (158) imply:
% 154.17/21.97  | | | |   (160)  sdtpldt0(xp, all_43_2) = all_43_6
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | BETA: splitting (95) gives:
% 154.17/21.97  | | | | 
% 154.17/21.97  | | | | Case 1:
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | |   (161)  aElementOf0(sz00, all_48_0)
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | REDUCE: (91), (161) imply:
% 154.17/21.97  | | | | |   (162)  aElementOf0(sz00, cS2076)
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | GROUND_INST: instantiating (6) with all_131_0, xp, simplifying with
% 154.17/21.97  | | | | |              (16), (57), (132), (134) gives:
% 154.17/21.97  | | | | |   (163)  xp = sz00 | sdteqdtlpzmzozddtrp0(all_131_0, all_131_0, xp)
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | GROUND_INST: instantiating (54) with sz00, simplifying with (12),
% 154.17/21.97  | | | | |              (162) gives:
% 154.17/21.97  | | | | |   (164)  all_45_0 = sz00 | sz10 = sz00
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | GROUND_INST: instantiating (mAddAsso) with sz10, all_36_1, all_129_0,
% 154.17/21.97  | | | | |              sz10, all_43_2, simplifying with (2), (15), (121), (137),
% 154.17/21.97  | | | | |              (139), (147), (153), (154) gives:
% 154.17/21.97  | | | | |   (165)   ? [v0: $i] : (sdtpldt0(all_36_1, all_129_0) = v0 &
% 154.17/21.97  | | | | |            sdtpldt0(sz10, v0) = all_43_2 & $i(v0) & $i(all_43_2))
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | GROUND_INST: instantiating (mAddAsso) with all_36_1, sz10, xp, sz10,
% 154.17/21.97  | | | | |              all_43_8, simplifying with (2), (15), (16), (42), (57),
% 154.17/21.97  | | | | |              (153), (154), (157) gives:
% 154.17/21.97  | | | | |   (166)   ? [v0: $i] : (sdtpldt0(all_36_1, v0) = all_43_8 &
% 154.17/21.97  | | | | |            sdtpldt0(sz10, xp) = v0 & $i(v0) & $i(all_43_8))
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | GROUND_INST: instantiating (4) with sz10, all_37_0, all_43_2,
% 154.17/21.97  | | | | |              simplifying with (2), (15), (25), (156) gives:
% 154.17/21.97  | | | | |   (167)  all_43_2 = sz00
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | DELTA: instantiating (165) with fresh symbol all_243_0 gives:
% 154.17/21.97  | | | | |   (168)  sdtpldt0(all_36_1, all_129_0) = all_243_0 & sdtpldt0(sz10,
% 154.17/21.97  | | | | |            all_243_0) = all_43_2 & $i(all_243_0) & $i(all_43_2)
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | ALPHA: (168) implies:
% 154.17/21.97  | | | | |   (169)  $i(all_243_0)
% 154.17/21.97  | | | | |   (170)  sdtpldt0(sz10, all_243_0) = all_43_2
% 154.17/21.97  | | | | |   (171)  sdtpldt0(all_36_1, all_129_0) = all_243_0
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | DELTA: instantiating (166) with fresh symbol all_247_0 gives:
% 154.17/21.97  | | | | |   (172)  sdtpldt0(all_36_1, all_247_0) = all_43_8 & sdtpldt0(sz10, xp)
% 154.17/21.97  | | | | |          = all_247_0 & $i(all_247_0) & $i(all_43_8)
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | ALPHA: (172) implies:
% 154.17/21.97  | | | | |   (173)  $i(all_247_0)
% 154.17/21.97  | | | | |   (174)  sdtpldt0(sz10, xp) = all_247_0
% 154.17/21.97  | | | | |   (175)  sdtpldt0(all_36_1, all_247_0) = all_43_8
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | REDUCE: (159), (167) imply:
% 154.17/21.97  | | | | |   (176)  sdtpldt0(all_36_1, sz00) = sz00
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | REDUCE: (160), (167) imply:
% 154.17/21.97  | | | | |   (177)  sdtpldt0(xp, sz00) = all_43_6
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | REDUCE: (167), (170) imply:
% 154.17/21.97  | | | | |   (178)  sdtpldt0(sz10, all_243_0) = sz00
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | BETA: splitting (163) gives:
% 154.17/21.97  | | | | | 
% 154.17/21.97  | | | | | Case 1:
% 154.17/21.97  | | | | | | 
% 154.17/21.97  | | | | | | 
% 154.17/21.97  | | | | | | GROUND_INST: instantiating (21) with all_43_8, all_247_0, xp, sz10,
% 154.17/21.97  | | | | | |              simplifying with (42), (174) gives:
% 154.17/21.97  | | | | | |   (179)  all_247_0 = all_43_8
% 154.17/21.97  | | | | | | 
% 154.17/21.97  | | | | | | REDUCE: (175), (179) imply:
% 154.17/21.97  | | | | | |   (180)  sdtpldt0(all_36_1, all_43_8) = all_43_8
% 154.17/21.97  | | | | | | 
% 154.17/21.97  | | | | | | BETA: splitting (94) gives:
% 154.17/21.97  | | | | | | 
% 154.17/21.97  | | | | | | Case 1:
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | |   (181)  all_40_0 = sz00
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | COMBINE_EQS: (81), (181) imply:
% 154.17/21.97  | | | | | | |   (182)  all_37_0 = sz00
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | SIMP: (182) implies:
% 154.17/21.97  | | | | | | |   (183)  all_37_0 = sz00
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | COMBINE_EQS: (78), (183) imply:
% 154.17/21.97  | | | | | | |   (184)  all_45_0 = sz00
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | REDUCE: (85), (183) imply:
% 154.17/21.97  | | | | | | |   (185)  sdtpldt0(all_43_8, sz00) = all_43_6
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | REDUCE: (108), (183) imply:
% 154.17/21.97  | | | | | | |   (186)  sdtpldt0(sz00, all_43_8) = all_43_6
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | REDUCE: (135), (183) imply:
% 154.17/21.97  | | | | | | |   (187)  sdtpldt0(sz00, xp) = all_131_0
% 154.17/21.97  | | | | | | | 
% 154.17/21.97  | | | | | | | REDUCE: (150), (183) imply:
% 154.17/21.97  | | | | | | |   (188)  sdtpldt0(all_36_1, sz00) = all_129_0
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | REDUCE: (125), (183) imply:
% 154.17/21.98  | | | | | | |   (189)  sdtpldt0(xp, sz00) = all_131_0
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | GROUND_INST: instantiating (21) with all_43_6, all_131_0, sz00,
% 154.17/21.98  | | | | | | |              xp, simplifying with (177), (189) gives:
% 154.17/21.98  | | | | | | |   (190)  all_131_0 = all_43_6
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | GROUND_INST: instantiating (21) with sz00, all_129_0, sz00,
% 154.17/21.98  | | | | | | |              all_36_1, simplifying with (176), (188) gives:
% 154.17/21.98  | | | | | | |   (191)  all_129_0 = sz00
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | REDUCE: (171), (191) imply:
% 154.17/21.98  | | | | | | |   (192)  sdtpldt0(all_36_1, sz00) = all_243_0
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | REDUCE: (187), (190) imply:
% 154.17/21.98  | | | | | | |   (193)  sdtpldt0(sz00, xp) = all_43_6
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | GROUND_INST: instantiating (21) with sz00, all_243_0, sz00,
% 154.17/21.98  | | | | | | |              all_36_1, simplifying with (176), (192) gives:
% 154.17/21.98  | | | | | | |   (194)  all_243_0 = sz00
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | REDUCE: (178), (194) imply:
% 154.17/21.98  | | | | | | |   (195)  sdtpldt0(sz10, sz00) = sz00
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | BETA: splitting (118) gives:
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | Case 1:
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | |   (196)  all_45_0 = all_43_8
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | COMBINE_EQS: (184), (196) imply:
% 154.17/21.98  | | | | | | | |   (197)  all_43_8 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | SIMP: (197) implies:
% 154.17/21.98  | | | | | | | |   (198)  all_43_8 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (186), (198) imply:
% 154.17/21.98  | | | | | | | |   (199)  sdtpldt0(sz00, sz00) = all_43_6
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | GROUND_INST: instantiating (3) with sz00, all_43_6, simplifying
% 154.17/21.98  | | | | | | | |              with (1), (12), (199) gives:
% 154.17/21.98  | | | | | | | |   (200)  all_43_6 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | GROUND_INST: instantiating (3) with xp, all_43_6, simplifying
% 154.17/21.98  | | | | | | | |              with (16), (57), (193) gives:
% 154.17/21.98  | | | | | | | |   (201)  all_43_6 = xp
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | COMBINE_EQS: (200), (201) imply:
% 154.17/21.98  | | | | | | | |   (202)  xp = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | SIMP: (202) implies:
% 154.17/21.98  | | | | | | | |   (203)  xp = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (56), (203) imply:
% 154.17/21.98  | | | | | | | |   (204)  $false
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | CLOSE: (204) is inconsistent.
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | Case 2:
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | |   (205)  all_43_8 = sz10
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (185), (205) imply:
% 154.17/21.98  | | | | | | | |   (206)  sdtpldt0(sz10, sz00) = all_43_6
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | GROUND_INST: instantiating (21) with sz00, all_43_6, sz00, sz10,
% 154.17/21.98  | | | | | | | |              simplifying with (195), (206) gives:
% 154.17/21.98  | | | | | | | |   (207)  all_43_6 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (193), (207) imply:
% 154.17/21.98  | | | | | | | |   (208)  sdtpldt0(sz00, xp) = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (208) are inconsistent by
% 154.17/21.98  | | | | | | | |            sub-proof #1.
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | End of split
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | Case 2:
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | |   (209)   ~ (all_40_0 = sz00)
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | REDUCE: (81), (209) imply:
% 154.17/21.98  | | | | | | |   (210)   ~ (all_37_0 = sz00)
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | BETA: splitting (164) gives:
% 154.17/21.98  | | | | | | | 
% 154.17/21.98  | | | | | | | Case 1:
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | |   (211)  all_45_0 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | COMBINE_EQS: (78), (211) imply:
% 154.17/21.98  | | | | | | | |   (212)  all_37_0 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | SIMP: (212) implies:
% 154.17/21.98  | | | | | | | |   (213)  all_37_0 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (210), (213) imply:
% 154.17/21.98  | | | | | | | |   (214)  $false
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | CLOSE: (214) is inconsistent.
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | Case 2:
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | |   (215)  sz10 = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (178), (215) imply:
% 154.17/21.98  | | | | | | | |   (216)  sdtpldt0(sz00, all_243_0) = sz00
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | REDUCE: (42), (215) imply:
% 154.17/21.98  | | | | | | | |   (217)  sdtpldt0(sz00, xp) = all_43_8
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | BETA: splitting (118) gives:
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | | Case 1:
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | |   (218)  all_45_0 = all_43_8
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | COMBINE_EQS: (78), (218) imply:
% 154.17/21.98  | | | | | | | | |   (219)  all_43_8 = all_37_0
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | REDUCE: (180), (219) imply:
% 154.17/21.98  | | | | | | | | |   (220)  sdtpldt0(all_36_1, all_37_0) = all_37_0
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | GROUND_INST: instantiating (21) with all_129_0, all_37_0,
% 154.17/21.98  | | | | | | | | |              all_37_0, all_36_1, simplifying with (150), (220)
% 154.17/21.98  | | | | | | | | |              gives:
% 154.17/21.98  | | | | | | | | |   (221)  all_129_0 = all_37_0
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | REDUCE: (171), (221) imply:
% 154.17/21.98  | | | | | | | | |   (222)  sdtpldt0(all_36_1, all_37_0) = all_243_0
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | GROUND_INST: instantiating (21) with all_37_0, all_243_0,
% 154.17/21.98  | | | | | | | | |              all_37_0, all_36_1, simplifying with (220), (222)
% 154.17/21.98  | | | | | | | | |              gives:
% 154.17/21.98  | | | | | | | | |   (223)  all_243_0 = all_37_0
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | REDUCE: (216), (223) imply:
% 154.17/21.98  | | | | | | | | |   (224)  sdtpldt0(sz00, all_37_0) = sz00
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | GROUND_INST: instantiating (3) with all_37_0, sz00, simplifying
% 154.17/21.98  | | | | | | | | |              with (87), (97), (224) gives:
% 154.17/21.98  | | | | | | | | |   (225)  all_37_0 = sz00
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | COMBINE_EQS: (78), (225) imply:
% 154.17/21.98  | | | | | | | | |   (226)  all_45_0 = sz00
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | BETA: splitting (118) gives:
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | Case 1:
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | COMBINE_EQS: (218), (226) imply:
% 154.17/21.98  | | | | | | | | | |   (227)  all_43_8 = sz00
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | REDUCE: (217), (227) imply:
% 154.17/21.98  | | | | | | | | | |   (228)  sdtpldt0(sz00, xp) = sz00
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (228) are inconsistent by
% 154.17/21.98  | | | | | | | | | |            sub-proof #1.
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | Case 2:
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | |   (229)  all_43_8 = sz10
% 154.17/21.98  | | | | | | | | | |   (230)   ~ (all_45_0 = all_43_8)
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | COMBINE_EQS: (215), (229) imply:
% 154.17/21.98  | | | | | | | | | |   (231)  all_43_8 = sz00
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | REDUCE: (226), (230), (231) imply:
% 154.17/21.98  | | | | | | | | | |   (232)  $false
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | | CLOSE: (232) is inconsistent.
% 154.17/21.98  | | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | End of split
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | Case 2:
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | |   (233)  all_43_8 = sz10
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | COMBINE_EQS: (215), (233) imply:
% 154.17/21.98  | | | | | | | | |   (234)  all_43_8 = sz00
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | REDUCE: (217), (234) imply:
% 154.17/21.98  | | | | | | | | |   (235)  sdtpldt0(sz00, xp) = sz00
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (235) are inconsistent by
% 154.17/21.98  | | | | | | | | |            sub-proof #1.
% 154.17/21.98  | | | | | | | | | 
% 154.17/21.98  | | | | | | | | End of split
% 154.17/21.98  | | | | | | | | 
% 154.17/21.98  | | | | | | | End of split
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | End of split
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | Case 2:
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | |   (236)  xp = sz00
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | REDUCE: (56), (236) imply:
% 154.17/21.99  | | | | | |   (237)  $false
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | CLOSE: (237) is inconsistent.
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | End of split
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | Case 2:
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | |   (238)   ~ aElementOf0(sz00, all_48_0)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | REDUCE: (91), (238) imply:
% 154.17/21.99  | | | | |   (239)   ~ aElementOf0(sz00, cS2076)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_129_0, all_43_2,
% 154.17/21.99  | | | | |              simplifying with (2), (15), (121), (137), (139) gives:
% 154.17/21.99  | | | | |   (240)  sdtpldt0(all_129_0, sz10) = all_43_2 & $i(all_43_2)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (6) with all_131_0, xp, simplifying with
% 154.17/21.99  | | | | |              (16), (57), (132), (134) gives:
% 154.17/21.99  | | | | |   (241)  xp = sz00 | sdteqdtlpzmzozddtrp0(all_131_0, all_131_0, xp)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (mAddAsso) with sz10, all_36_1, all_129_0,
% 154.17/21.99  | | | | |              sz10, all_43_2, simplifying with (2), (15), (121), (137),
% 154.17/21.99  | | | | |              (139), (147), (153), (154) gives:
% 154.17/21.99  | | | | |   (242)   ? [v0: $i] : (sdtpldt0(all_36_1, all_129_0) = v0 &
% 154.17/21.99  | | | | |            sdtpldt0(sz10, v0) = all_43_2 & $i(v0) & $i(all_43_2))
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (mAddComm) with xp, all_43_2, all_43_6,
% 154.17/21.99  | | | | |              simplifying with (16), (57), (102), (115), (160) gives:
% 154.17/21.99  | | | | |   (243)  sdtpldt0(all_43_2, xp) = all_43_6 & $i(all_43_6)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | ALPHA: (243) implies:
% 154.17/21.99  | | | | |   (244)  sdtpldt0(all_43_2, xp) = all_43_6
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (mAddAsso) with all_36_1, sz10, xp, sz10,
% 154.17/21.99  | | | | |              all_43_8, simplifying with (2), (15), (16), (42), (57),
% 154.17/21.99  | | | | |              (153), (154), (157) gives:
% 154.17/21.99  | | | | |   (245)   ? [v0: $i] : (sdtpldt0(all_36_1, v0) = all_43_8 &
% 154.17/21.99  | | | | |            sdtpldt0(sz10, xp) = v0 & $i(v0) & $i(all_43_8))
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (mAddComm) with all_36_1, all_43_2,
% 154.17/21.99  | | | | |              all_43_2, simplifying with (102), (115), (153), (154),
% 154.17/21.99  | | | | |              (159) gives:
% 154.17/21.99  | | | | |   (246)  sdtpldt0(all_43_2, all_36_1) = all_43_2
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | GROUND_INST: instantiating (4) with sz10, all_37_0, all_43_2,
% 154.17/21.99  | | | | |              simplifying with (2), (15), (25), (156) gives:
% 154.17/21.99  | | | | |   (247)  all_43_2 = sz00
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | DELTA: instantiating (245) with fresh symbol all_241_0 gives:
% 154.17/21.99  | | | | |   (248)  sdtpldt0(all_36_1, all_241_0) = all_43_8 & sdtpldt0(sz10, xp)
% 154.17/21.99  | | | | |          = all_241_0 & $i(all_241_0) & $i(all_43_8)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | ALPHA: (248) implies:
% 154.17/21.99  | | | | |   (249)  sdtpldt0(sz10, xp) = all_241_0
% 154.17/21.99  | | | | |   (250)  sdtpldt0(all_36_1, all_241_0) = all_43_8
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | DELTA: instantiating (242) with fresh symbol all_249_0 gives:
% 154.17/21.99  | | | | |   (251)  sdtpldt0(all_36_1, all_129_0) = all_249_0 & sdtpldt0(sz10,
% 154.17/21.99  | | | | |            all_249_0) = all_43_2 & $i(all_249_0) & $i(all_43_2)
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | ALPHA: (251) implies:
% 154.17/21.99  | | | | |   (252)  $i(all_249_0)
% 154.17/21.99  | | | | |   (253)  sdtpldt0(all_36_1, all_129_0) = all_249_0
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | REDUCE: (246), (247) imply:
% 154.17/21.99  | | | | |   (254)  sdtpldt0(sz00, all_36_1) = sz00
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | REDUCE: (244), (247) imply:
% 154.17/21.99  | | | | |   (255)  sdtpldt0(sz00, xp) = all_43_6
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | REDUCE: (156), (247) imply:
% 154.17/21.99  | | | | |   (256)  sdtpldt0(all_37_0, sz10) = sz00
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | BETA: splitting (241) gives:
% 154.17/21.99  | | | | | 
% 154.17/21.99  | | | | | Case 1:
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | GROUND_INST: instantiating (21) with all_43_8, all_241_0, xp, sz10,
% 154.17/21.99  | | | | | |              simplifying with (42), (249) gives:
% 154.17/21.99  | | | | | |   (257)  all_241_0 = all_43_8
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | REDUCE: (250), (257) imply:
% 154.17/21.99  | | | | | |   (258)  sdtpldt0(all_36_1, all_43_8) = all_43_8
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | BETA: splitting (109) gives:
% 154.17/21.99  | | | | | | 
% 154.17/21.99  | | | | | | Case 1:
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | |   (259)  all_43_8 = all_40_0
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | COMBINE_EQS: (81), (259) imply:
% 154.17/21.99  | | | | | | |   (260)  all_43_8 = all_37_0
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | REDUCE: (258), (260) imply:
% 154.17/21.99  | | | | | | |   (261)  sdtpldt0(all_36_1, all_37_0) = all_37_0
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | REDUCE: (96), (260) imply:
% 154.17/21.99  | | | | | | |   (262)  aElementOf0(all_37_0, cS2076)
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | GROUND_INST: instantiating (21) with all_129_0, all_37_0,
% 154.17/21.99  | | | | | | |              all_37_0, all_36_1, simplifying with (150), (261)
% 154.17/21.99  | | | | | | |              gives:
% 154.17/21.99  | | | | | | |   (263)  all_129_0 = all_37_0
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | REDUCE: (253), (263) imply:
% 154.17/21.99  | | | | | | |   (264)  sdtpldt0(all_36_1, all_37_0) = all_249_0
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | GROUND_INST: instantiating (21) with all_37_0, all_249_0,
% 154.17/21.99  | | | | | | |              all_37_0, all_36_1, simplifying with (261), (264)
% 154.17/21.99  | | | | | | |              gives:
% 154.17/21.99  | | | | | | |   (265)  all_249_0 = all_37_0
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | BETA: splitting (113) gives:
% 154.17/21.99  | | | | | | | 
% 154.17/21.99  | | | | | | | Case 1:
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | |   (266)  all_43_4 = all_40_0
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | COMBINE_EQS: (148), (266) imply:
% 154.17/21.99  | | | | | | | |   (267)  all_40_0 = all_36_1
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | COMBINE_EQS: (81), (267) imply:
% 154.17/21.99  | | | | | | | |   (268)  all_37_0 = all_36_1
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | SIMP: (268) implies:
% 154.17/21.99  | | | | | | | |   (269)  all_37_0 = all_36_1
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | REDUCE: (262), (269) imply:
% 154.17/21.99  | | | | | | | |   (270)  aElementOf0(all_36_1, cS2076)
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | GROUND_INST: instantiating (3) with all_36_1, sz00, simplifying
% 154.17/21.99  | | | | | | | |              with (153), (154), (254) gives:
% 154.17/21.99  | | | | | | | |   (271)  all_36_1 = sz00
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | REDUCE: (270), (271) imply:
% 154.17/21.99  | | | | | | | |   (272)  aElementOf0(sz00, cS2076)
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | PRED_UNIFY: (239), (272) imply:
% 154.17/21.99  | | | | | | | |   (273)  $false
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | CLOSE: (273) is inconsistent.
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | Case 2:
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | GROUND_INST: instantiating (3) with xp, all_43_6, simplifying
% 154.17/21.99  | | | | | | | |              with (16), (57), (255) gives:
% 154.17/21.99  | | | | | | | |   (274)  all_43_6 = xp
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | GROUND_INST: instantiating (mAddAsso) with sz00, all_36_1, xp,
% 154.17/21.99  | | | | | | | |              sz00, all_43_6, simplifying with (1), (12), (16),
% 154.17/21.99  | | | | | | | |              (57), (153), (154), (254), (255) gives:
% 154.17/21.99  | | | | | | | |   (275)   ? [v0: $i] : (sdtpldt0(all_36_1, xp) = v0 &
% 154.17/21.99  | | | | | | | |            sdtpldt0(sz00, v0) = all_43_6 & $i(v0) &
% 154.17/21.99  | | | | | | | |            $i(all_43_6))
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | GROUND_INST: instantiating (3) with all_36_1, sz00, simplifying
% 154.17/21.99  | | | | | | | |              with (153), (154), (254) gives:
% 154.17/21.99  | | | | | | | |   (276)  all_36_1 = sz00
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | DELTA: instantiating (275) with fresh symbol all_1020_0 gives:
% 154.17/21.99  | | | | | | | |   (277)  sdtpldt0(all_36_1, xp) = all_1020_0 & sdtpldt0(sz00,
% 154.17/21.99  | | | | | | | |            all_1020_0) = all_43_6 & $i(all_1020_0) &
% 154.17/21.99  | | | | | | | |          $i(all_43_6)
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | ALPHA: (277) implies:
% 154.17/21.99  | | | | | | | |   (278)  $i(all_43_6)
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | REDUCE: (146), (276) imply:
% 154.17/21.99  | | | | | | | |   (279)  smndt0(xp) = sz00
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | GROUND_INST: instantiating (4) with xp, sz00, all_43_6,
% 154.17/21.99  | | | | | | | |              simplifying with (16), (57), (255), (279) gives:
% 154.17/21.99  | | | | | | | |   (280)  all_43_6 = sz00
% 154.17/21.99  | | | | | | | | 
% 154.17/21.99  | | | | | | | | COMBINE_EQS: (274), (280) imply:
% 154.17/22.00  | | | | | | | |   (281)  xp = sz00
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | REDUCE: (56), (281) imply:
% 154.17/22.00  | | | | | | | |   (282)  $false
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | CLOSE: (282) is inconsistent.
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | End of split
% 154.17/22.00  | | | | | | | 
% 154.17/22.00  | | | | | | Case 2:
% 154.17/22.00  | | | | | | | 
% 154.17/22.00  | | | | | | |   (283)   ~ (all_43_8 = all_40_0)
% 154.17/22.00  | | | | | | | 
% 154.17/22.00  | | | | | | | REDUCE: (81), (283) imply:
% 154.17/22.00  | | | | | | |   (284)   ~ (all_43_8 = all_37_0)
% 154.17/22.00  | | | | | | | 
% 154.17/22.00  | | | | | | | BETA: splitting (118) gives:
% 154.17/22.00  | | | | | | | 
% 154.17/22.00  | | | | | | | Case 1:
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | |   (285)  all_45_0 = all_43_8
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | COMBINE_EQS: (78), (285) imply:
% 154.17/22.00  | | | | | | | |   (286)  all_43_8 = all_37_0
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | REDUCE: (284), (286) imply:
% 154.17/22.00  | | | | | | | |   (287)  $false
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | CLOSE: (287) is inconsistent.
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | Case 2:
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | |   (288)  all_43_8 = sz10
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | REDUCE: (108), (288) imply:
% 154.17/22.00  | | | | | | | |   (289)  sdtpldt0(all_37_0, sz10) = all_43_6
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | GROUND_INST: instantiating (21) with sz00, all_43_6, sz10,
% 154.17/22.00  | | | | | | | |              all_37_0, simplifying with (256), (289) gives:
% 154.17/22.00  | | | | | | | |   (290)  all_43_6 = sz00
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | REDUCE: (255), (290) imply:
% 154.17/22.00  | | | | | | | |   (291)  sdtpldt0(sz00, xp) = sz00
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | | REF_CLOSE: (3), (16), (56), (57), (291) are inconsistent by
% 154.17/22.00  | | | | | | | |            sub-proof #1.
% 154.17/22.00  | | | | | | | | 
% 154.17/22.00  | | | | | | | End of split
% 154.17/22.00  | | | | | | | 
% 154.17/22.00  | | | | | | End of split
% 154.17/22.00  | | | | | | 
% 154.17/22.00  | | | | | Case 2:
% 154.17/22.00  | | | | | | 
% 154.17/22.00  | | | | | |   (292)  xp = sz00
% 154.17/22.00  | | | | | | 
% 154.17/22.00  | | | | | | REDUCE: (56), (292) imply:
% 154.17/22.00  | | | | | |   (293)  $false
% 154.17/22.00  | | | | | | 
% 154.17/22.00  | | | | | | CLOSE: (293) is inconsistent.
% 154.17/22.00  | | | | | | 
% 154.17/22.00  | | | | | End of split
% 154.17/22.00  | | | | | 
% 154.17/22.00  | | | | End of split
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | Case 2:
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | |   (294)  all_36_2 = sz10 & sdtpldt0(sz10, xp) = sz10
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | ALPHA: (294) implies:
% 154.17/22.00  | | | |   (295)  sdtpldt0(sz10, xp) = sz10
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | GROUND_INST: instantiating (21) with all_43_8, sz10, xp, sz10,
% 154.17/22.00  | | | |              simplifying with (42), (295) gives:
% 154.17/22.00  | | | |   (296)  all_43_8 = sz10
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | REDUCE: (108), (296) imply:
% 154.17/22.00  | | | |   (297)  sdtpldt0(all_37_0, sz10) = all_43_6
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | GROUND_INST: instantiating (21) with all_133_0, all_43_6, sz10,
% 154.17/22.00  | | | |              all_37_0, simplifying with (131), (297) gives:
% 154.17/22.00  | | | |   (298)  all_133_0 = all_43_6
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | REDUCE: (128), (298) imply:
% 154.17/22.00  | | | |   (299)  sdtpldt0(xp, all_43_6) = all_43_6
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | GROUND_INST: instantiating (mAddComm) with sz10, all_131_0, all_43_6,
% 154.17/22.00  | | | |              simplifying with (2), (15), (124), (132), (134) gives:
% 154.17/22.00  | | | |   (300)  sdtpldt0(all_131_0, sz10) = all_43_6 & $i(all_43_6)
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | ALPHA: (300) implies:
% 154.17/22.00  | | | |   (301)  $i(all_43_6)
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | GROUND_INST: instantiating (mAddComm) with xp, all_43_6, all_43_6,
% 154.17/22.00  | | | |              simplifying with (16), (57), (103), (299), (301) gives:
% 154.17/22.00  | | | |   (302)  sdtpldt0(all_43_6, xp) = all_43_6
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | GROUND_INST: instantiating (4) with sz10, all_37_0, all_43_6,
% 154.17/22.00  | | | |              simplifying with (2), (15), (25), (297) gives:
% 154.17/22.00  | | | |   (303)  all_43_6 = sz00
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | REDUCE: (302), (303) imply:
% 154.17/22.00  | | | |   (304)  sdtpldt0(sz00, xp) = sz00
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | | REF_CLOSE: (3), (16), (56), (57), (304) are inconsistent by sub-proof
% 154.17/22.00  | | | |            #1.
% 154.17/22.00  | | | | 
% 154.17/22.00  | | | End of split
% 154.17/22.00  | | | 
% 154.17/22.00  | | Case 2:
% 154.17/22.00  | | | 
% 154.17/22.00  | | |   (305)  xp = sz00
% 154.17/22.00  | | | 
% 154.17/22.00  | | | REDUCE: (56), (305) imply:
% 154.17/22.00  | | |   (306)  $false
% 154.17/22.00  | | | 
% 154.17/22.00  | | | CLOSE: (306) is inconsistent.
% 154.17/22.00  | | | 
% 154.17/22.00  | | End of split
% 154.17/22.00  | | 
% 154.17/22.00  | Case 2:
% 154.17/22.00  | | 
% 154.17/22.00  | |   (307)  xp = sz00
% 154.17/22.00  | | 
% 154.17/22.00  | | REDUCE: (56), (307) imply:
% 154.17/22.00  | |   (308)  $false
% 154.17/22.00  | | 
% 154.17/22.00  | | CLOSE: (308) is inconsistent.
% 154.17/22.00  | | 
% 154.17/22.00  | End of split
% 154.17/22.00  | 
% 154.17/22.00  End of proof
% 154.17/22.00  
% 154.17/22.00  Sub-proof #1 shows that the following formulas are inconsistent:
% 154.17/22.00  ----------------------------------------------------------------
% 154.41/22.00    (1)   ! [v0: $i] :  ! [v1: $i] : (v1 = v0 |  ~ (sdtpldt0(sz00, v0) = v1) |  ~
% 154.41/22.00           $i(v0) |  ~ aInteger0(v0))
% 154.41/22.00    (2)  aInteger0(xp)
% 154.41/22.00    (3)  sdtpldt0(sz00, xp) = sz00
% 154.41/22.00    (4)  $i(xp)
% 154.41/22.00    (5)   ~ (xp = sz00)
% 154.41/22.00  
% 154.41/22.00  Begin of proof
% 154.41/22.00  | 
% 154.41/22.00  | GROUND_INST: instantiating (1) with xp, sz00, simplifying with (2), (3), (4)
% 154.41/22.00  |              gives:
% 154.41/22.00  |   (6)  xp = sz00
% 154.41/22.00  | 
% 154.41/22.00  | REDUCE: (5), (6) imply:
% 154.41/22.00  |   (7)  $false
% 154.41/22.00  | 
% 154.41/22.00  | CLOSE: (7) is inconsistent.
% 154.41/22.00  | 
% 154.41/22.00  End of proof
% 154.41/22.00  % SZS output end Proof for theBenchmark
% 154.41/22.00  
% 154.41/22.00  21481ms
%------------------------------------------------------------------------------