TSTP Solution File: NUM491+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM491+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 : n017.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 11:48:07 EDT 2023
% Result : Theorem 12.46s 2.42s
% Output : Proof 18.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM491+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n017.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 13:04:55 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.19/1.21 Prover 1: Preprocessing ...
% 3.19/1.21 Prover 4: Preprocessing ...
% 3.82/1.24 Prover 2: Preprocessing ...
% 3.82/1.24 Prover 0: Preprocessing ...
% 3.82/1.24 Prover 6: Preprocessing ...
% 3.82/1.24 Prover 3: Preprocessing ...
% 3.82/1.24 Prover 5: Preprocessing ...
% 8.43/1.95 Prover 1: Constructing countermodel ...
% 8.43/1.96 Prover 3: Constructing countermodel ...
% 9.75/2.07 Prover 6: Proving ...
% 10.19/2.13 Prover 5: Constructing countermodel ...
% 11.41/2.28 Prover 4: Constructing countermodel ...
% 11.41/2.28 Prover 2: Proving ...
% 12.46/2.41 Prover 3: proved (1770ms)
% 12.46/2.42
% 12.46/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.46/2.42
% 12.46/2.42 Prover 5: stopped
% 12.46/2.43 Prover 6: stopped
% 12.46/2.44 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.46/2.44 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.46/2.44 Prover 2: stopped
% 12.46/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.87/2.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.92/2.45 Prover 0: Proving ...
% 12.92/2.46 Prover 0: stopped
% 12.92/2.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.32/2.58 Prover 10: Preprocessing ...
% 13.32/2.58 Prover 13: Preprocessing ...
% 13.32/2.60 Prover 8: Preprocessing ...
% 13.32/2.61 Prover 11: Preprocessing ...
% 13.32/2.62 Prover 7: Preprocessing ...
% 15.52/2.81 Prover 10: Constructing countermodel ...
% 15.52/2.84 Prover 8: Warning: ignoring some quantifiers
% 15.52/2.84 Prover 13: Constructing countermodel ...
% 15.94/2.85 Prover 8: Constructing countermodel ...
% 15.97/2.86 Prover 7: Constructing countermodel ...
% 17.86/3.13 Prover 11: Constructing countermodel ...
% 18.38/3.18 Prover 10: Found proof (size 23)
% 18.38/3.18 Prover 10: proved (738ms)
% 18.38/3.18 Prover 13: stopped
% 18.38/3.18 Prover 4: stopped
% 18.38/3.18 Prover 8: stopped
% 18.38/3.18 Prover 7: stopped
% 18.38/3.18 Prover 11: stopped
% 18.38/3.18 Prover 1: stopped
% 18.38/3.18
% 18.38/3.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.38/3.18
% 18.38/3.19 % SZS output start Proof for theBenchmark
% 18.38/3.19 Assumptions after simplification:
% 18.38/3.19 ---------------------------------
% 18.38/3.19
% 18.38/3.19 (mDefDiv)
% 18.38/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) | ~
% 18.38/3.22 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 18.38/3.22 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1)) & ! [v0:
% 18.38/3.22 $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ doDivides0(v0, v1) | ~
% 18.38/3.22 aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | ? [v2: $i] : (sdtasdt0(v0,
% 18.38/3.22 v2) = v1 & $i(v2) & aNaturalNumber0(v2)))
% 18.38/3.22
% 18.38/3.22 (mMulComm)
% 18.38/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 18.38/3.22 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 18.38/3.22 (sdtasdt0(v1, v0) = v2 & $i(v2)))
% 18.38/3.22
% 18.38/3.22 (mSortsB_02)
% 18.38/3.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v1) = v2) | ~
% 18.38/3.22 $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) |
% 18.38/3.22 aNaturalNumber0(v2))
% 18.38/3.22
% 18.38/3.22 (m__)
% 18.38/3.23 $i(xp) & $i(xm) & ? [v0: $i] : (sdtasdt0(xp, xm) = v0 & $i(v0) & ~
% 18.38/3.23 doDivides0(xp, v0))
% 18.38/3.23
% 18.38/3.23 (m__1837)
% 18.38/3.23 $i(xp) & $i(xm) & $i(xn) & aNaturalNumber0(xp) & aNaturalNumber0(xm) &
% 18.38/3.23 aNaturalNumber0(xn)
% 18.38/3.23
% 18.38/3.23 (m__1951)
% 18.38/3.23 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 18.38/3.23 (sdtasdt0(xr, xm) = v2 & sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 &
% 18.38/3.23 sdtpldt0(v1, v2) = v0 & $i(v2) & $i(v1) & $i(v0))
% 18.38/3.23
% 18.38/3.23 (m__1978)
% 18.38/3.23 $i(xr) & $i(xp) & $i(xm) & $i(xn) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 18.38/3.23 (sdtmndt0(v1, v2) = v0 & sdtasdt0(xr, xm) = v0 & sdtasdt0(xp, xm) = v2 &
% 18.38/3.23 sdtasdt0(xn, xm) = v1 & $i(v2) & $i(v1) & $i(v0))
% 18.38/3.23
% 18.38/3.23 (function-axioms)
% 18.38/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.38/3.23 (sdtsldt0(v3, v2) = v1) | ~ (sdtsldt0(v3, v2) = v0)) & ! [v0: $i] : !
% 18.38/3.23 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 18.38/3.23 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 18.38/3.23 [v3: $i] : (v1 = v0 | ~ (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 18.38/3.23 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.38/3.23 (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 18.38/3.23
% 18.38/3.23 Further assumptions not needed in the proof:
% 18.38/3.23 --------------------------------------------
% 18.38/3.23 mAMDistr, mAddAsso, mAddCanc, mAddComm, mDefDiff, mDefLE, mDefPrime, mDefQuot,
% 18.38/3.23 mDivAsso, mDivLE, mDivMin, mDivSum, mDivTrans, mIH, mIH_03, mLEAsym, mLENTr,
% 18.38/3.23 mLERefl, mLETotal, mLETran, mMonAdd, mMonMul, mMonMul2, mMulAsso, mMulCanc,
% 18.38/3.23 mNatSort, mPrimDiv, mSortsB, mSortsC, mSortsC_01, mZeroAdd, mZeroMul, m_AddZero,
% 18.38/3.23 m_MulUnit, m_MulZero, m__1799, m__1860, m__1870, m__1883, m__1894, m__1924
% 18.38/3.23
% 18.38/3.23 Those formulas are unsatisfiable:
% 18.38/3.23 ---------------------------------
% 18.38/3.23
% 18.38/3.23 Begin of proof
% 18.38/3.23 |
% 18.38/3.23 | ALPHA: (mDefDiv) implies:
% 18.38/3.23 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtasdt0(v0, v2) = v1) |
% 18.38/3.23 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aNaturalNumber0(v2) | ~
% 18.38/3.23 | aNaturalNumber0(v1) | ~ aNaturalNumber0(v0) | doDivides0(v0, v1))
% 18.38/3.23 |
% 18.38/3.23 | ALPHA: (m__1837) implies:
% 18.38/3.23 | (2) aNaturalNumber0(xm)
% 18.38/3.23 | (3) aNaturalNumber0(xp)
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (m__1951) implies:
% 18.38/3.24 | (4) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtasdt0(xr, xm) = v2 &
% 18.38/3.24 | sdtasdt0(xp, xm) = v1 & sdtasdt0(xn, xm) = v0 & sdtpldt0(v1, v2) = v0
% 18.38/3.24 | & $i(v2) & $i(v1) & $i(v0))
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (m__1978) implies:
% 18.38/3.24 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtmndt0(v1, v2) = v0 &
% 18.38/3.24 | sdtasdt0(xr, xm) = v0 & sdtasdt0(xp, xm) = v2 & sdtasdt0(xn, xm) = v1
% 18.38/3.24 | & $i(v2) & $i(v1) & $i(v0))
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (m__) implies:
% 18.38/3.24 | (6) $i(xm)
% 18.38/3.24 | (7) $i(xp)
% 18.38/3.24 | (8) ? [v0: $i] : (sdtasdt0(xp, xm) = v0 & $i(v0) & ~ doDivides0(xp, v0))
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (function-axioms) implies:
% 18.38/3.24 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 18.38/3.24 | (sdtasdt0(v3, v2) = v1) | ~ (sdtasdt0(v3, v2) = v0))
% 18.38/3.24 |
% 18.38/3.24 | DELTA: instantiating (8) with fresh symbol all_38_0 gives:
% 18.38/3.24 | (10) sdtasdt0(xp, xm) = all_38_0 & $i(all_38_0) & ~ doDivides0(xp,
% 18.38/3.24 | all_38_0)
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (10) implies:
% 18.38/3.24 | (11) ~ doDivides0(xp, all_38_0)
% 18.38/3.24 | (12) sdtasdt0(xp, xm) = all_38_0
% 18.38/3.24 |
% 18.38/3.24 | DELTA: instantiating (4) with fresh symbols all_42_0, all_42_1, all_42_2
% 18.38/3.24 | gives:
% 18.38/3.24 | (13) sdtasdt0(xr, xm) = all_42_0 & sdtasdt0(xp, xm) = all_42_1 &
% 18.38/3.24 | sdtasdt0(xn, xm) = all_42_2 & sdtpldt0(all_42_1, all_42_0) = all_42_2
% 18.38/3.24 | & $i(all_42_0) & $i(all_42_1) & $i(all_42_2)
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (13) implies:
% 18.38/3.24 | (14) sdtasdt0(xp, xm) = all_42_1
% 18.38/3.24 |
% 18.38/3.24 | DELTA: instantiating (5) with fresh symbols all_44_0, all_44_1, all_44_2
% 18.38/3.24 | gives:
% 18.38/3.24 | (15) sdtmndt0(all_44_1, all_44_0) = all_44_2 & sdtasdt0(xr, xm) = all_44_2
% 18.38/3.24 | & sdtasdt0(xp, xm) = all_44_0 & sdtasdt0(xn, xm) = all_44_1 &
% 18.38/3.24 | $i(all_44_0) & $i(all_44_1) & $i(all_44_2)
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (15) implies:
% 18.38/3.24 | (16) sdtasdt0(xp, xm) = all_44_0
% 18.38/3.24 |
% 18.38/3.24 | GROUND_INST: instantiating (9) with all_42_1, all_44_0, xm, xp, simplifying
% 18.38/3.24 | with (14), (16) gives:
% 18.38/3.24 | (17) all_44_0 = all_42_1
% 18.38/3.24 |
% 18.38/3.24 | GROUND_INST: instantiating (9) with all_38_0, all_44_0, xm, xp, simplifying
% 18.38/3.24 | with (12), (16) gives:
% 18.38/3.24 | (18) all_44_0 = all_38_0
% 18.38/3.24 |
% 18.38/3.24 | COMBINE_EQS: (17), (18) imply:
% 18.38/3.24 | (19) all_42_1 = all_38_0
% 18.38/3.24 |
% 18.38/3.24 | SIMP: (19) implies:
% 18.38/3.24 | (20) all_42_1 = all_38_0
% 18.38/3.24 |
% 18.38/3.24 | GROUND_INST: instantiating (mSortsB_02) with xp, xm, all_38_0, simplifying
% 18.38/3.24 | with (2), (3), (6), (7), (12) gives:
% 18.38/3.24 | (21) aNaturalNumber0(all_38_0)
% 18.38/3.24 |
% 18.38/3.24 | GROUND_INST: instantiating (mMulComm) with xp, xm, all_38_0, simplifying with
% 18.38/3.24 | (2), (3), (6), (7), (12) gives:
% 18.38/3.24 | (22) sdtasdt0(xm, xp) = all_38_0 & $i(all_38_0)
% 18.38/3.24 |
% 18.38/3.24 | ALPHA: (22) implies:
% 18.38/3.24 | (23) $i(all_38_0)
% 18.38/3.24 |
% 18.38/3.25 | GROUND_INST: instantiating (1) with xp, all_38_0, xm, simplifying with (2),
% 18.38/3.25 | (3), (6), (7), (11), (12), (21), (23) gives:
% 18.38/3.25 | (24) $false
% 18.38/3.25 |
% 18.38/3.25 | CLOSE: (24) is inconsistent.
% 18.38/3.25 |
% 18.38/3.25 End of proof
% 18.38/3.25 % SZS output end Proof for theBenchmark
% 18.38/3.25
% 18.38/3.25 2637ms
%------------------------------------------------------------------------------