TSTP Solution File: NUM489+3 by Princess---230619

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : NUM489+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n024.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 11:48:06 EDT 2023

% Result   : Theorem 9.19s 2.05s
% Output   : Proof 12.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM489+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34  % Computer : n024.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Fri Aug 25 16:05:24 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.61  ________       _____
% 0.19/0.61  ___  __ \_________(_)________________________________
% 0.19/0.61  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.19/0.61  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.19/0.61  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61  
% 0.19/0.61  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61  (2023-06-19)
% 0.19/0.61  
% 0.19/0.61  (c) Philipp Rümmer, 2009-2023
% 0.19/0.61  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61                Amanda Stjerna.
% 0.19/0.61  Free software under BSD-3-Clause.
% 0.19/0.61  
% 0.19/0.61  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61  
% 0.19/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.62  Running up to 7 provers in parallel.
% 0.19/0.64  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.72/1.21  Prover 4: Preprocessing ...
% 3.72/1.21  Prover 1: Preprocessing ...
% 3.89/1.24  Prover 2: Preprocessing ...
% 3.89/1.24  Prover 5: Preprocessing ...
% 3.89/1.24  Prover 6: Preprocessing ...
% 3.89/1.24  Prover 0: Preprocessing ...
% 3.89/1.24  Prover 3: Preprocessing ...
% 8.92/1.96  Prover 3: Constructing countermodel ...
% 8.92/1.97  Prover 1: Constructing countermodel ...
% 9.19/2.04  Prover 5: Constructing countermodel ...
% 9.19/2.04  Prover 5: proved (1401ms)
% 9.19/2.04  
% 9.19/2.05  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.19/2.05  
% 9.19/2.06  Prover 3: stopped
% 9.19/2.06  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.19/2.06  Prover 6: Proving ...
% 9.19/2.07  Prover 6: stopped
% 9.19/2.07  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.19/2.07  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.24/2.14  Prover 7: Preprocessing ...
% 10.24/2.15  Prover 8: Preprocessing ...
% 10.64/2.17  Prover 10: Preprocessing ...
% 10.64/2.20  Prover 1: Found proof (size 8)
% 10.64/2.20  Prover 1: proved (1571ms)
% 10.64/2.20  Prover 10: stopped
% 10.64/2.21  Prover 7: stopped
% 12.13/2.37  Prover 8: Warning: ignoring some quantifiers
% 12.13/2.38  Prover 8: Constructing countermodel ...
% 12.13/2.38  Prover 4: Constructing countermodel ...
% 12.13/2.40  Prover 8: stopped
% 12.58/2.42  Prover 4: stopped
% 12.58/2.42  Prover 2: Proving ...
% 12.58/2.43  Prover 2: stopped
% 12.87/2.49  Prover 0: Proving ...
% 12.87/2.49  Prover 0: stopped
% 12.87/2.49  
% 12.87/2.49  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.87/2.49  
% 12.87/2.49  % SZS output start Proof for theBenchmark
% 12.87/2.50  Assumptions after simplification:
% 12.87/2.50  ---------------------------------
% 12.87/2.50  
% 12.87/2.50    (m__)
% 12.87/2.52    $i(xr) & $i(xp) & $i(xn) &  ? [v0: $i] : ( ~ (v0 = xn) & sdtpldt0(xp, xr) = v0
% 12.87/2.52      & $i(v0))
% 12.87/2.52  
% 12.87/2.52    (m__1883)
% 12.87/2.52    sdtmndt0(xn, xp) = xr & sdtpldt0(xp, xr) = xn & aNaturalNumber0(xr) = 0 &
% 12.87/2.52    $i(xr) & $i(xp) & $i(xn)
% 12.87/2.52  
% 12.87/2.52    (function-axioms)
% 12.87/2.53     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.87/2.53      (sdtsldt0(v3, v2) = v1) |  ~ (sdtsldt0(v3, v2) = v0)) &  ! [v0:
% 12.87/2.53      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 12.87/2.53    : (v1 = v0 |  ~ (doDivides0(v3, v2) = v1) |  ~ (doDivides0(v3, v2) = v0)) &  !
% 12.87/2.53    [v0: MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3:
% 12.87/2.53      $i] : (v1 = v0 |  ~ (iLess0(v3, v2) = v1) |  ~ (iLess0(v3, v2) = v0)) &  !
% 12.87/2.53    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.87/2.53      (sdtmndt0(v3, v2) = v1) |  ~ (sdtmndt0(v3, v2) = v0)) &  ! [v0:
% 12.87/2.53      MultipleValueBool] :  ! [v1: MultipleValueBool] :  ! [v2: $i] :  ! [v3: $i]
% 12.87/2.53    : (v1 = v0 |  ~ (sdtlseqdt0(v3, v2) = v1) |  ~ (sdtlseqdt0(v3, v2) = v0)) &  !
% 12.87/2.53    [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.87/2.53      (sdtasdt0(v3, v2) = v1) |  ~ (sdtasdt0(v3, v2) = v0)) &  ! [v0: $i] :  !
% 12.87/2.53    [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (sdtpldt0(v3, v2) = v1) |
% 12.87/2.53       ~ (sdtpldt0(v3, v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 12.87/2.53      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (isPrime0(v2) = v1) |  ~
% 12.87/2.53      (isPrime0(v2) = v0)) &  ! [v0: MultipleValueBool] :  ! [v1:
% 12.87/2.53      MultipleValueBool] :  ! [v2: $i] : (v1 = v0 |  ~ (aNaturalNumber0(v2) = v1)
% 12.87/2.53      |  ~ (aNaturalNumber0(v2) = v0))
% 12.87/2.53  
% 12.87/2.53  Further assumptions not needed in the proof:
% 12.87/2.53  --------------------------------------------
% 12.87/2.53  mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime,
% 12.87/2.53  mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym,
% 12.87/2.53  mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso,
% 12.87/2.53  mMulCanc, mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC,
% 12.87/2.53  mSortsC_01, mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799,
% 12.87/2.53  m__1837, m__1860, m__1870, m__1894
% 12.87/2.53  
% 12.87/2.53  Those formulas are unsatisfiable:
% 12.87/2.53  ---------------------------------
% 12.87/2.53  
% 12.87/2.53  Begin of proof
% 12.87/2.53  | 
% 12.87/2.53  | ALPHA: (m__1883) implies:
% 12.87/2.54  |   (1)  sdtpldt0(xp, xr) = xn
% 12.87/2.54  | 
% 12.87/2.54  | ALPHA: (m__) implies:
% 12.87/2.54  |   (2)   ? [v0: $i] : ( ~ (v0 = xn) & sdtpldt0(xp, xr) = v0 & $i(v0))
% 12.87/2.54  | 
% 12.87/2.54  | ALPHA: (function-axioms) implies:
% 12.87/2.54  |   (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 12.87/2.54  |          (sdtpldt0(v3, v2) = v1) |  ~ (sdtpldt0(v3, v2) = v0))
% 12.87/2.54  | 
% 12.87/2.54  | DELTA: instantiating (2) with fresh symbol all_40_0 gives:
% 12.87/2.54  |   (4)   ~ (all_40_0 = xn) & sdtpldt0(xp, xr) = all_40_0 & $i(all_40_0)
% 12.87/2.54  | 
% 12.87/2.54  | ALPHA: (4) implies:
% 12.87/2.54  |   (5)   ~ (all_40_0 = xn)
% 12.87/2.54  |   (6)  sdtpldt0(xp, xr) = all_40_0
% 12.87/2.54  | 
% 12.87/2.54  | GROUND_INST: instantiating (3) with xn, all_40_0, xr, xp, simplifying with
% 12.87/2.54  |              (1), (6) gives:
% 12.87/2.54  |   (7)  all_40_0 = xn
% 12.87/2.54  | 
% 12.87/2.54  | REDUCE: (5), (7) imply:
% 12.87/2.54  |   (8)  $false
% 12.87/2.54  | 
% 12.87/2.54  | CLOSE: (8) is inconsistent.
% 12.87/2.54  | 
% 12.87/2.54  End of proof
% 12.87/2.54  % SZS output end Proof for theBenchmark
% 12.87/2.54  
% 12.87/2.54  1938ms
%------------------------------------------------------------------------------