TSTP Solution File: NUM505+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM505+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 : n015.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 11:48:14 EDT 2023
% Result : Theorem 14.45s 2.86s
% Output : Proof 21.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM505+3 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n015.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 16:29:07 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.75/1.36 Prover 1: Preprocessing ...
% 3.75/1.36 Prover 4: Preprocessing ...
% 3.75/1.42 Prover 0: Preprocessing ...
% 3.75/1.42 Prover 3: Preprocessing ...
% 3.75/1.42 Prover 6: Preprocessing ...
% 3.75/1.42 Prover 2: Preprocessing ...
% 3.75/1.42 Prover 5: Preprocessing ...
% 11.58/2.40 Prover 1: Constructing countermodel ...
% 11.58/2.40 Prover 6: Proving ...
% 11.58/2.43 Prover 3: Constructing countermodel ...
% 12.12/2.48 Prover 5: Constructing countermodel ...
% 13.52/2.72 Prover 2: Proving ...
% 13.52/2.81 Prover 4: Constructing countermodel ...
% 14.45/2.86 Prover 3: proved (2216ms)
% 14.45/2.86
% 14.45/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.45/2.86
% 14.45/2.86 Prover 5: stopped
% 15.04/2.87 Prover 6: stopped
% 15.04/2.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 15.04/2.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 15.04/2.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 15.20/2.92 Prover 0: Proving ...
% 15.47/2.93 Prover 0: stopped
% 15.47/2.93 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.47/2.94 Prover 2: stopped
% 15.47/2.94 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.47/2.94 Prover 8: Preprocessing ...
% 15.47/2.95 Prover 7: Preprocessing ...
% 15.99/3.04 Prover 10: Preprocessing ...
% 16.48/3.07 Prover 11: Preprocessing ...
% 16.48/3.13 Prover 13: Preprocessing ...
% 17.48/3.22 Prover 8: Warning: ignoring some quantifiers
% 17.51/3.24 Prover 8: Constructing countermodel ...
% 17.51/3.28 Prover 10: Constructing countermodel ...
% 17.51/3.32 Prover 7: Constructing countermodel ...
% 19.65/3.55 Prover 13: Constructing countermodel ...
% 20.32/3.67 Prover 11: Constructing countermodel ...
% 20.74/3.70 Prover 10: Found proof (size 16)
% 20.74/3.70 Prover 10: proved (817ms)
% 20.74/3.70 Prover 4: stopped
% 20.74/3.70 Prover 7: stopped
% 20.74/3.70 Prover 13: stopped
% 20.74/3.70 Prover 1: stopped
% 20.74/3.70 Prover 11: stopped
% 20.74/3.71 Prover 8: stopped
% 20.74/3.71
% 20.74/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 20.74/3.71
% 20.74/3.71 % SZS output start Proof for theBenchmark
% 20.74/3.71 Assumptions after simplification:
% 20.74/3.71 ---------------------------------
% 20.74/3.71
% 20.74/3.72 (mLETotal)
% 20.74/3.72 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) |
% 20.74/3.72 ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) | sdtlseqdt0(v0, v1)) & ! [v0:
% 20.74/3.72 $i] : ( ~ $i(v0) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v0, v0))
% 20.74/3.72
% 20.74/3.72 (m__)
% 20.74/3.74 $i(xk) & $i(xp) & ~ sdtlseqdt0(xp, xk) & ! [v0: $i] : ( ~ (sdtpldt0(xp, v0)
% 20.74/3.74 = xk) | ~ $i(v0) | ~ aNaturalNumber0(v0)) & (xk = xp | ( ~
% 20.74/3.74 sdtlseqdt0(xk, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xk, v0) = xp) | ~ $i(v0)
% 20.74/3.74 | ~ aNaturalNumber0(v0))))
% 20.74/3.74
% 20.74/3.74 (m__1837)
% 20.74/3.74 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 20.74/3.74 aNaturalNumber0(xn)
% 20.74/3.74
% 20.74/3.74 (m__2306)
% 20.74/3.75 $i(xk) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : (sdtsldt0(v0, xp) = xk &
% 20.74/3.75 sdtasdt0(xp, xk) = v0 & sdtasdt0(xn, xm) = v0 & $i(v0) &
% 20.74/3.75 aNaturalNumber0(xk))
% 20.74/3.75
% 20.74/3.75 Further assumptions not needed in the proof:
% 20.74/3.75 --------------------------------------------
% 20.74/3.75 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefDiv, mDefLE, mDefPrime,
% 20.74/3.75 mDefQuot, mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym,
% 20.74/3.75 mLENTr, mLERefl, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc,
% 20.74/3.75 mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, mSortsC_01,
% 20.74/3.75 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, m__1860, m__1870,
% 20.74/3.75 m__2075, m__2287, m__2315, m__2327, m__2342, m__2362
% 20.74/3.75
% 20.74/3.75 Those formulas are unsatisfiable:
% 20.74/3.75 ---------------------------------
% 20.74/3.75
% 20.74/3.75 Begin of proof
% 20.74/3.75 |
% 20.74/3.75 | ALPHA: (mLETotal) implies:
% 20.74/3.75 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~
% 20.74/3.75 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | sdtlseqdt0(v1, v0) |
% 20.74/3.75 | sdtlseqdt0(v0, v1))
% 20.74/3.75 |
% 20.74/3.75 | ALPHA: (m__1837) implies:
% 20.74/3.75 | (2) aNaturalNumber0(xp)
% 20.74/3.75 |
% 20.74/3.75 | ALPHA: (m__2306) implies:
% 20.74/3.75 | (3) ? [v0: $i] : (sdtsldt0(v0, xp) = xk & sdtasdt0(xp, xk) = v0 &
% 20.74/3.75 | sdtasdt0(xn, xm) = v0 & $i(v0) & aNaturalNumber0(xk))
% 20.74/3.75 |
% 20.74/3.75 | ALPHA: (m__) implies:
% 20.74/3.75 | (4) ~ sdtlseqdt0(xp, xk)
% 20.74/3.75 | (5) $i(xp)
% 20.74/3.75 | (6) $i(xk)
% 20.74/3.75 | (7) xk = xp | ( ~ sdtlseqdt0(xk, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xk, v0)
% 20.74/3.75 | = xp) | ~ $i(v0) | ~ aNaturalNumber0(v0)))
% 20.74/3.75 |
% 20.74/3.75 | DELTA: instantiating (3) with fresh symbol all_41_0 gives:
% 20.74/3.75 | (8) sdtsldt0(all_41_0, xp) = xk & sdtasdt0(xp, xk) = all_41_0 &
% 20.74/3.75 | sdtasdt0(xn, xm) = all_41_0 & $i(all_41_0) & aNaturalNumber0(xk)
% 20.74/3.75 |
% 20.74/3.75 | ALPHA: (8) implies:
% 20.74/3.75 | (9) aNaturalNumber0(xk)
% 20.74/3.75 |
% 21.11/3.76 | GROUND_INST: instantiating (1) with xp, xk, simplifying with (2), (4), (5),
% 21.11/3.76 | (6), (9) gives:
% 21.11/3.76 | (10) sdtlseqdt0(xk, xp)
% 21.11/3.76 |
% 21.11/3.76 | BETA: splitting (7) gives:
% 21.11/3.76 |
% 21.11/3.76 | Case 1:
% 21.11/3.76 | |
% 21.11/3.76 | | (11) xk = xp
% 21.11/3.76 | |
% 21.11/3.76 | | REDUCE: (10), (11) imply:
% 21.11/3.76 | | (12) sdtlseqdt0(xp, xp)
% 21.11/3.76 | |
% 21.11/3.76 | | REDUCE: (4), (11) imply:
% 21.11/3.76 | | (13) ~ sdtlseqdt0(xp, xp)
% 21.11/3.76 | |
% 21.11/3.76 | | PRED_UNIFY: (12), (13) imply:
% 21.11/3.76 | | (14) $false
% 21.11/3.76 | |
% 21.11/3.76 | | CLOSE: (14) is inconsistent.
% 21.11/3.76 | |
% 21.11/3.76 | Case 2:
% 21.11/3.76 | |
% 21.11/3.76 | | (15) ~ sdtlseqdt0(xk, xp) & ! [v0: $i] : ( ~ (sdtpldt0(xk, v0) = xp) |
% 21.11/3.76 | | ~ $i(v0) | ~ aNaturalNumber0(v0))
% 21.11/3.76 | |
% 21.11/3.76 | | ALPHA: (15) implies:
% 21.11/3.76 | | (16) ~ sdtlseqdt0(xk, xp)
% 21.11/3.76 | |
% 21.11/3.76 | | PRED_UNIFY: (10), (16) imply:
% 21.11/3.76 | | (17) $false
% 21.11/3.76 | |
% 21.11/3.76 | | CLOSE: (17) is inconsistent.
% 21.11/3.76 | |
% 21.11/3.76 | End of split
% 21.11/3.76 |
% 21.11/3.76 End of proof
% 21.11/3.76 % SZS output end Proof for theBenchmark
% 21.11/3.76
% 21.11/3.76 3143ms
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