TSTP Solution File: NUM484+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM484+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 : n011.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 11:48:05 EDT 2023
% Result : Theorem 6.49s 1.65s
% Output : Proof 10.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM484+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 16:12:38 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 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
% 3.25/1.16 Prover 1: Preprocessing ...
% 3.25/1.17 Prover 4: Preprocessing ...
% 3.71/1.20 Prover 6: Preprocessing ...
% 3.71/1.20 Prover 3: Preprocessing ...
% 3.71/1.20 Prover 5: Preprocessing ...
% 3.71/1.20 Prover 0: Preprocessing ...
% 3.71/1.20 Prover 2: Preprocessing ...
% 6.49/1.61 Prover 3: Constructing countermodel ...
% 6.49/1.61 Prover 6: Constructing countermodel ...
% 6.49/1.64 Prover 3: proved (1016ms)
% 6.49/1.64
% 6.49/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.49/1.65
% 7.09/1.65 Prover 6: proved (1009ms)
% 7.09/1.65
% 7.09/1.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.09/1.65
% 7.09/1.65 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.09/1.65 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.09/1.67 Prover 5: Constructing countermodel ...
% 7.09/1.67 Prover 5: stopped
% 7.28/1.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.62/1.72 Prover 7: Preprocessing ...
% 7.62/1.76 Prover 10: Preprocessing ...
% 7.62/1.78 Prover 2: Constructing countermodel ...
% 7.62/1.78 Prover 2: stopped
% 7.62/1.78 Prover 0: Constructing countermodel ...
% 7.62/1.78 Prover 0: stopped
% 7.62/1.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 7.62/1.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 7.62/1.80 Prover 1: Constructing countermodel ...
% 7.62/1.80 Prover 8: Preprocessing ...
% 8.29/1.85 Prover 13: Preprocessing ...
% 8.29/1.86 Prover 11: Preprocessing ...
% 8.89/1.91 Prover 1: Found proof (size 8)
% 8.89/1.91 Prover 1: proved (1283ms)
% 8.89/1.93 Prover 13: stopped
% 8.89/1.94 Prover 11: stopped
% 9.32/1.98 Prover 10: Constructing countermodel ...
% 9.32/2.00 Prover 10: stopped
% 9.69/2.02 Prover 8: Warning: ignoring some quantifiers
% 9.69/2.02 Prover 7: Constructing countermodel ...
% 9.69/2.03 Prover 8: Constructing countermodel ...
% 10.00/2.05 Prover 7: stopped
% 10.00/2.05 Prover 8: stopped
% 10.48/2.16 Prover 4: Constructing countermodel ...
% 10.48/2.18 Prover 4: stopped
% 10.48/2.18
% 10.48/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.48/2.18
% 10.48/2.19 % SZS output start Proof for theBenchmark
% 10.73/2.20 Assumptions after simplification:
% 10.73/2.20 ---------------------------------
% 10.73/2.20
% 10.73/2.20 (m__1725)
% 10.73/2.23 $i(xk) & ? [v0: int] : ( ~ (v0 = 0) & isPrime0(xk) = v0)
% 10.73/2.23
% 10.73/2.23 (m__1737)
% 10.73/2.24 isPrime0(xk) = 0 & $i(xk)
% 10.73/2.24
% 10.73/2.24 (function-axioms)
% 10.73/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.73/2.24 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0:
% 10.73/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.73/2.24 : (v1 = v0 | ~ (doDivides0(v3, v2) = v1) | ~ (doDivides0(v3, v2) = v0)) & !
% 10.73/2.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.73/2.24 $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & !
% 10.73/2.24 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.73/2.25 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0:
% 10.73/2.25 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.73/2.25 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 10.73/2.25 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.73/2.25 (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 10.73/2.25 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 10.73/2.25 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.73/2.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isPrime0(v2) = v1) | ~
% 10.73/2.25 (isPrime0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.73/2.25 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aNaturalNumber0(v2) = v1)
% 10.73/2.25 | ~ (aNaturalNumber0(v2) = v0))
% 10.73/2.25
% 10.73/2.25 Further assumptions not needed in the proof:
% 10.73/2.25 --------------------------------------------
% 10.73/2.25 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime,
% 10.73/2.25 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym,
% 10.73/2.25 mLENTr, mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso,
% 10.73/2.25 mMulCanc, mMulComm, mNatSort, mSortsB, mSortsB_02, mSortsC, mSortsC_01,
% 10.73/2.25 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__, m__1700, m__1716,
% 10.73/2.25 m__1716_04
% 10.73/2.25
% 10.73/2.25 Those formulas are unsatisfiable:
% 10.73/2.25 ---------------------------------
% 10.73/2.25
% 10.73/2.25 Begin of proof
% 10.73/2.25 |
% 10.93/2.25 | ALPHA: (m__1725) implies:
% 10.93/2.25 | (1) ? [v0: int] : ( ~ (v0 = 0) & isPrime0(xk) = v0)
% 10.93/2.25 |
% 10.93/2.25 | ALPHA: (m__1737) implies:
% 10.93/2.25 | (2) isPrime0(xk) = 0
% 10.93/2.25 |
% 10.93/2.25 | ALPHA: (function-axioms) implies:
% 10.93/2.25 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.93/2.25 | (v1 = v0 | ~ (isPrime0(v2) = v1) | ~ (isPrime0(v2) = v0))
% 10.93/2.25 |
% 10.93/2.25 | DELTA: instantiating (1) with fresh symbol all_39_0 gives:
% 10.95/2.25 | (4) ~ (all_39_0 = 0) & isPrime0(xk) = all_39_0
% 10.95/2.25 |
% 10.95/2.25 | ALPHA: (4) implies:
% 10.95/2.25 | (5) ~ (all_39_0 = 0)
% 10.95/2.25 | (6) isPrime0(xk) = all_39_0
% 10.95/2.25 |
% 10.95/2.26 | GROUND_INST: instantiating (3) with 0, all_39_0, xk, simplifying with (2), (6)
% 10.95/2.26 | gives:
% 10.95/2.26 | (7) all_39_0 = 0
% 10.95/2.26 |
% 10.95/2.26 | REDUCE: (5), (7) imply:
% 10.95/2.26 | (8) $false
% 10.95/2.26 |
% 10.95/2.26 | CLOSE: (8) is inconsistent.
% 10.95/2.26 |
% 10.95/2.26 End of proof
% 10.95/2.26 % SZS output end Proof for theBenchmark
% 10.95/2.26
% 10.95/2.26 1654ms
%------------------------------------------------------------------------------