TSTP Solution File: NUM489+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM489+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 : n009.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 11.32s 2.31s
% Output : Proof 16.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : NUM489+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 16:21:21 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.41/0.64 ________ _____
% 0.41/0.64 ___ __ \_________(_)________________________________
% 0.41/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.41/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.41/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.41/0.64
% 0.41/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.41/0.64 (2023-06-19)
% 0.41/0.64
% 0.41/0.64 (c) Philipp Rümmer, 2009-2023
% 0.41/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.41/0.64 Amanda Stjerna.
% 0.41/0.64 Free software under BSD-3-Clause.
% 0.41/0.64
% 0.41/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.41/0.64
% 0.41/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.41/0.65 Running up to 7 provers in parallel.
% 0.71/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.71/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.71/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.71/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.71/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.71/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.71/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.86/1.29 Prover 4: Preprocessing ...
% 3.86/1.29 Prover 1: Preprocessing ...
% 3.86/1.32 Prover 3: Preprocessing ...
% 3.86/1.32 Prover 0: Preprocessing ...
% 3.86/1.32 Prover 2: Preprocessing ...
% 3.86/1.32 Prover 5: Preprocessing ...
% 3.86/1.32 Prover 6: Preprocessing ...
% 8.63/2.00 Prover 3: Constructing countermodel ...
% 8.63/2.00 Prover 1: Constructing countermodel ...
% 9.38/2.08 Prover 6: Proving ...
% 10.24/2.17 Prover 5: Constructing countermodel ...
% 11.32/2.31 Prover 3: proved (1655ms)
% 11.32/2.31
% 11.32/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.32/2.31
% 11.32/2.32 Prover 5: stopped
% 11.32/2.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.32/2.33 Prover 6: stopped
% 11.65/2.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.65/2.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.65/2.40 Prover 2: Proving ...
% 11.65/2.40 Prover 2: stopped
% 11.65/2.41 Prover 7: Preprocessing ...
% 11.65/2.41 Prover 10: Preprocessing ...
% 11.65/2.41 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.65/2.42 Prover 8: Preprocessing ...
% 12.83/2.50 Prover 4: Constructing countermodel ...
% 12.83/2.50 Prover 11: Preprocessing ...
% 13.53/2.65 Prover 10: Constructing countermodel ...
% 13.53/2.68 Prover 8: Warning: ignoring some quantifiers
% 13.53/2.69 Prover 7: Constructing countermodel ...
% 13.53/2.69 Prover 0: Proving ...
% 13.53/2.71 Prover 8: Constructing countermodel ...
% 14.60/2.74 Prover 0: stopped
% 14.60/2.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.94/2.80 Prover 13: Preprocessing ...
% 14.94/2.82 Prover 10: Found proof (size 11)
% 14.94/2.82 Prover 10: proved (463ms)
% 14.94/2.82 Prover 4: stopped
% 14.94/2.82 Prover 7: stopped
% 14.94/2.82 Prover 8: stopped
% 14.94/2.82 Prover 1: stopped
% 15.46/2.86 Prover 13: stopped
% 15.90/3.01 Prover 11: Constructing countermodel ...
% 15.90/3.02 Prover 11: stopped
% 15.90/3.03
% 15.90/3.03 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.90/3.03
% 15.90/3.03 % SZS output start Proof for theBenchmark
% 16.29/3.04 Assumptions after simplification:
% 16.29/3.04 ---------------------------------
% 16.29/3.04
% 16.29/3.04 (mDefDiff)
% 16.49/3.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 16.49/3.09 (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v3) = v1) | ~ $i(v3) | ~ $i(v1)
% 16.49/3.09 | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v3) | ~
% 16.49/3.09 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.49/3.09 ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtmndt0(v1, v0) = v2) | ~
% 16.49/3.09 (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 16.49/3.09 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0)) & !
% 16.49/3.09 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v1, v0) =
% 16.49/3.09 v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 16.49/3.09 sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 16.49/3.09 aNaturalNumber0(v2))
% 16.49/3.09
% 16.49/3.09 (m__)
% 16.49/3.09 $i(xr) & $i(xp) & $i(xn) & ? [v0: $i] : ( ~ (v0 = xn) & sdtpldt0(xp, xr) = v0
% 16.49/3.09 & $i(v0))
% 16.49/3.09
% 16.49/3.09 (m__1837)
% 16.49/3.09 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 16.49/3.09 aNaturalNumber0(xn)
% 16.49/3.09
% 16.49/3.09 (m__1870)
% 16.49/3.09 $i(xp) & $i(xn) & sdtlseqdt0(xp, xn)
% 16.49/3.09
% 16.49/3.09 (m__1883)
% 16.49/3.09 sdtmndt0(xn, xp) = xr & $i(xr) & $i(xp) & $i(xn)
% 16.49/3.09
% 16.49/3.09 Further assumptions not needed in the proof:
% 16.49/3.09 --------------------------------------------
% 16.49/3.09 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiv, mDefLE, mDefPrime, mDefQuot,
% 16.49/3.09 mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr,
% 16.49/3.09 mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc,
% 16.49/3.09 mMulComm, mNatSort, mPrimDiv, mSortsB, mSortsB_02, mSortsC, mSortsC_01,
% 16.49/3.09 mZeroAdd, mZeroMul, m_AddZero, m_MulUnit, m_MulZero, m__1799, m__1860, m__1894
% 16.49/3.09
% 16.49/3.09 Those formulas are unsatisfiable:
% 16.49/3.09 ---------------------------------
% 16.49/3.09
% 16.49/3.09 Begin of proof
% 16.49/3.09 |
% 16.49/3.09 | ALPHA: (mDefDiff) implies:
% 16.49/3.10 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 16.49/3.10 | (sdtmndt0(v1, v0) = v2) | ~ (sdtpldt0(v0, v2) = v3) | ~ $i(v2) | ~
% 16.49/3.10 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aNaturalNumber0(v1) |
% 16.49/3.10 | ~ aNaturalNumber0(v0))
% 16.49/3.10 |
% 16.49/3.10 | ALPHA: (m__1837) implies:
% 16.49/3.10 | (2) aNaturalNumber0(xn)
% 16.49/3.10 | (3) aNaturalNumber0(xp)
% 16.49/3.10 |
% 16.49/3.10 | ALPHA: (m__1870) implies:
% 16.49/3.10 | (4) sdtlseqdt0(xp, xn)
% 16.49/3.10 |
% 16.49/3.10 | ALPHA: (m__1883) implies:
% 16.49/3.10 | (5) sdtmndt0(xn, xp) = xr
% 16.49/3.10 |
% 16.49/3.10 | ALPHA: (m__) implies:
% 16.49/3.10 | (6) $i(xn)
% 16.49/3.10 | (7) $i(xp)
% 16.49/3.10 | (8) $i(xr)
% 16.49/3.10 | (9) ? [v0: $i] : ( ~ (v0 = xn) & sdtpldt0(xp, xr) = v0 & $i(v0))
% 16.49/3.10 |
% 16.49/3.10 | DELTA: instantiating (9) with fresh symbol all_38_0 gives:
% 16.49/3.10 | (10) ~ (all_38_0 = xn) & sdtpldt0(xp, xr) = all_38_0 & $i(all_38_0)
% 16.49/3.10 |
% 16.49/3.10 | ALPHA: (10) implies:
% 16.49/3.10 | (11) ~ (all_38_0 = xn)
% 16.49/3.10 | (12) sdtpldt0(xp, xr) = all_38_0
% 16.49/3.10 |
% 16.49/3.10 | GROUND_INST: instantiating (1) with xp, xn, xr, all_38_0, simplifying with
% 16.49/3.10 | (2), (3), (4), (5), (6), (7), (8), (12) gives:
% 16.49/3.10 | (13) all_38_0 = xn
% 16.49/3.10 |
% 16.49/3.10 | REDUCE: (11), (13) imply:
% 16.49/3.10 | (14) $false
% 16.49/3.10 |
% 16.49/3.10 | CLOSE: (14) is inconsistent.
% 16.49/3.10 |
% 16.49/3.10 End of proof
% 16.49/3.10 % SZS output end Proof for theBenchmark
% 16.49/3.10
% 16.49/3.10 2465ms
%------------------------------------------------------------------------------