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