TSTP Solution File: NUM530+1 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM530+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n019.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 11:48:24 EDT 2023

% Result   : Theorem 6.84s 1.69s
% Output   : Proof 11.04s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM530+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.32  % Computer : n019.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Aug 25 10:05:13 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.17/0.59  ________       _____
% 0.17/0.59  ___  __ \_________(_)________________________________
% 0.17/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.17/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.17/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.17/0.59  
% 0.17/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.59  (2023-06-19)
% 0.17/0.59  
% 0.17/0.59  (c) Philipp Rümmer, 2009-2023
% 0.17/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.59                Amanda Stjerna.
% 0.17/0.59  Free software under BSD-3-Clause.
% 0.17/0.59  
% 0.17/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.59  
% 0.17/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.17/0.60  Running up to 7 provers in parallel.
% 0.17/0.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.61  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.61  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.61  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.61  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.61  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.17/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.65/1.20  Prover 1: Preprocessing ...
% 3.65/1.20  Prover 4: Preprocessing ...
% 3.65/1.24  Prover 5: Preprocessing ...
% 3.65/1.24  Prover 0: Preprocessing ...
% 3.65/1.24  Prover 3: Preprocessing ...
% 3.65/1.24  Prover 2: Preprocessing ...
% 3.65/1.24  Prover 6: Preprocessing ...
% 6.84/1.64  Prover 3: Constructing countermodel ...
% 6.84/1.64  Prover 6: Constructing countermodel ...
% 6.84/1.69  Prover 6: proved (1070ms)
% 6.84/1.69  
% 6.84/1.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.84/1.69  
% 7.28/1.70  Prover 3: stopped
% 7.28/1.70  Prover 0: stopped
% 7.28/1.71  Prover 5: Constructing countermodel ...
% 7.28/1.71  Prover 5: stopped
% 7.28/1.72  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.28/1.72  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.28/1.72  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.28/1.72  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.78/1.76  Prover 2: Constructing countermodel ...
% 7.78/1.76  Prover 2: stopped
% 7.78/1.78  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.33/1.85  Prover 1: Constructing countermodel ...
% 8.33/1.88  Prover 7: Preprocessing ...
% 8.33/1.89  Prover 8: Preprocessing ...
% 8.33/1.89  Prover 10: Preprocessing ...
% 8.33/1.91  Prover 13: Preprocessing ...
% 8.33/1.93  Prover 11: Preprocessing ...
% 9.06/2.05  Prover 1: Found proof (size 8)
% 9.06/2.05  Prover 1: proved (1443ms)
% 9.06/2.06  Prover 11: stopped
% 9.06/2.07  Prover 8: Warning: ignoring some quantifiers
% 9.06/2.10  Prover 8: Constructing countermodel ...
% 9.06/2.12  Prover 10: Constructing countermodel ...
% 9.06/2.13  Prover 8: stopped
% 9.06/2.14  Prover 10: stopped
% 9.99/2.16  Prover 7: Constructing countermodel ...
% 9.99/2.17  Prover 13: Constructing countermodel ...
% 9.99/2.18  Prover 7: stopped
% 9.99/2.19  Prover 13: stopped
% 11.04/2.22  Prover 4: Constructing countermodel ...
% 11.04/2.24  Prover 4: stopped
% 11.04/2.25  
% 11.04/2.25  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.04/2.25  
% 11.04/2.25  % SZS output start Proof for theBenchmark
% 11.04/2.25  Assumptions after simplification:
% 11.04/2.25  ---------------------------------
% 11.04/2.25  
% 11.04/2.25    (m__3025)
% 11.04/2.27    isPrime0(xp) = 0 & $i(xp)
% 11.04/2.27  
% 11.04/2.27    (m__3161)
% 11.04/2.27    $i(xp) &  ? [v0: int] : ( ~ (v0 = 0) & isPrime0(xp) = v0)
% 11.04/2.27  
% 11.04/2.27    (function-axioms)
% 11.04/2.28     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 11.04/2.28      (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0)) &  ! [v0:
% 11.04/2.28      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 11.04/2.28    : (v1 = v0 |  ~ (doDivides0(v3, v2) = v1) |  ~ (doDivides0(v3, v2) = v0)) &  !
% 11.04/2.28    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 11.04/2.28      $i] : (v1 = v0 |  ~ (iLess0(v3, v2) = v1) |  ~ (iLess0(v3, v2) = v0)) &  !
% 11.04/2.28    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 11.04/2.28      (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0)) &  ! [v0:
% 11.04/2.28      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 11.04/2.28    : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~ (sdtlseqdt0(v3, v2) = v0)) &  !
% 11.04/2.28    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 11.04/2.28      (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 11.04/2.28    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |
% 11.04/2.28       ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 11.04/2.28      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (isPrime0(v2) = v1) |  ~
% 11.04/2.28      (isPrime0(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 11.04/2.28      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1)
% 11.04/2.28      |  ~ (aNaturalNumber0(v2) = v0))
% 11.04/2.28  
% 11.04/2.28  Further assumptions not needed in the proof:
% 11.04/2.28  --------------------------------------------
% 11.04/2.28  mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime,
% 11.04/2.28  mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym,
% 11.04/2.28  mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso,
% 11.04/2.28  mMulCanc, mMulComm, mNatSort, mPDP, mPrimDiv, mSortsB, mSortsB_02, mSortsC,
% 11.04/2.28  mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__2963,
% 11.04/2.28  m__2987, m__3014, m__3046, m__3059, m__3082, m__3124
% 11.04/2.28  
% 11.04/2.28  Those formulas are unsatisfiable:
% 11.04/2.28  ---------------------------------
% 11.04/2.28  
% 11.04/2.28  Begin of proof
% 11.04/2.28  | 
% 11.04/2.28  | ALPHA: (m__3025) implies:
% 11.04/2.29  |   (1)  isPrime0(xp) = 0
% 11.04/2.29  | 
% 11.04/2.29  | ALPHA: (m__3161) implies:
% 11.04/2.29  |   (2)   ? [v0: int] : ( ~ (v0 = 0) & isPrime0(xp) = v0)
% 11.04/2.29  | 
% 11.04/2.29  | ALPHA: (function-axioms) implies:
% 11.04/2.29  |   (3)   ! [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :
% 11.04/2.29  |        (v1 = v0 |  ~ (isPrime0(v2) = v1) |  ~ (isPrime0(v2) = v0))
% 11.04/2.29  | 
% 11.04/2.29  | DELTA: instantiating (2) with fresh symbol all_40_0 gives:
% 11.04/2.29  |   (4)   ~ (all_40_0 = 0) & isPrime0(xp) = all_40_0
% 11.04/2.29  | 
% 11.04/2.29  | ALPHA: (4) implies:
% 11.04/2.29  |   (5)   ~ (all_40_0 = 0)
% 11.04/2.29  |   (6)  isPrime0(xp) = all_40_0
% 11.04/2.29  | 
% 11.04/2.29  | GROUND_INST: instantiating (3) with 0, all_40_0, xp, simplifying with (1), (6)
% 11.04/2.29  |              gives:
% 11.04/2.29  |   (7)  all_40_0 = 0
% 11.04/2.29  | 
% 11.04/2.29  | REDUCE: (5), (7) imply:
% 11.04/2.29  |   (8)  $false
% 11.04/2.29  | 
% 11.04/2.29  | CLOSE: (8) is inconsistent.
% 11.04/2.29  | 
% 11.04/2.29  End of proof
% 11.04/2.29  % SZS output end Proof for theBenchmark
% 11.04/2.29  
% 11.04/2.29  1707ms
%------------------------------------------------------------------------------