TSTP Solution File: NUM559+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM559+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 : n018.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 11:48:36 EDT 2023
% Result : Theorem 8.89s 1.93s
% Output : Proof 13.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM559+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n018.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 16:04:44 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.55/1.21 Prover 1: Preprocessing ...
% 3.55/1.21 Prover 4: Preprocessing ...
% 3.55/1.25 Prover 2: Preprocessing ...
% 3.55/1.25 Prover 3: Preprocessing ...
% 3.55/1.25 Prover 0: Preprocessing ...
% 3.55/1.26 Prover 5: Preprocessing ...
% 3.55/1.26 Prover 6: Preprocessing ...
% 8.76/1.89 Prover 3: Constructing countermodel ...
% 8.76/1.89 Prover 5: Constructing countermodel ...
% 8.81/1.90 Prover 6: Constructing countermodel ...
% 8.89/1.92 Prover 2: Constructing countermodel ...
% 8.89/1.93 Prover 6: proved (1284ms)
% 8.89/1.93 Prover 2: proved (1295ms)
% 8.89/1.93
% 8.89/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.89/1.93
% 8.89/1.93
% 8.89/1.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.89/1.93
% 8.89/1.94 Prover 3: proved (1286ms)
% 8.89/1.94
% 8.89/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.89/1.94
% 8.89/1.94 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.89/1.94 Prover 5: proved (1285ms)
% 8.89/1.94
% 8.89/1.94 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.89/1.94
% 8.89/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.89/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.89/1.96 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.58/2.07 Prover 7: Preprocessing ...
% 10.22/2.10 Prover 10: Preprocessing ...
% 10.22/2.11 Prover 8: Preprocessing ...
% 10.22/2.12 Prover 11: Preprocessing ...
% 10.22/2.14 Prover 1: Constructing countermodel ...
% 10.22/2.15 Prover 0: Constructing countermodel ...
% 10.22/2.15 Prover 0: stopped
% 10.22/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.98/2.30 Prover 13: Preprocessing ...
% 12.23/2.40 Prover 1: Found proof (size 8)
% 12.23/2.40 Prover 1: proved (1770ms)
% 12.23/2.40 Prover 11: stopped
% 12.47/2.43 Prover 10: Constructing countermodel ...
% 12.63/2.43 Prover 13: stopped
% 12.63/2.43 Prover 7: Constructing countermodel ...
% 12.63/2.45 Prover 10: stopped
% 12.63/2.45 Prover 7: stopped
% 12.63/2.48 Prover 8: Warning: ignoring some quantifiers
% 12.63/2.49 Prover 8: Constructing countermodel ...
% 12.63/2.50 Prover 8: stopped
% 12.63/2.52 Prover 4: Constructing countermodel ...
% 13.23/2.54 Prover 4: stopped
% 13.23/2.54
% 13.23/2.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.23/2.54
% 13.23/2.54 % SZS output start Proof for theBenchmark
% 13.23/2.55 Assumptions after simplification:
% 13.23/2.55 ---------------------------------
% 13.23/2.55
% 13.23/2.55 (m__2323)
% 13.23/2.57 $i(xQ) & $i(xx) & ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xQ) = v0)
% 13.23/2.57
% 13.23/2.57 (m__2338)
% 13.23/2.57 aElementOf0(xx, xQ) = 0 & $i(xQ) & $i(xx)
% 13.23/2.57
% 13.23/2.57 (function-axioms)
% 13.23/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.23/2.58 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0:
% 13.23/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.23/2.58 : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 13.23/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.23/2.58 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 13.23/2.58 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.23/2.58 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 13.23/2.58 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 13.23/2.58 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.23/2.58 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.23/2.58 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 13.23/2.58 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.23/2.58 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 13.23/2.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) |
% 13.23/2.58 ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 13.23/2.58 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : !
% 13.23/2.58 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~
% 13.23/2.58 (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 13.23/2.58 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 13.23/2.58 $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 13.23/2.58 (szszuzczcdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.23/2.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) |
% 13.23/2.58 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.23/2.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~
% 13.23/2.58 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.23/2.58 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 13.23/2.58 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 13.23/2.58 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 13.23/2.58
% 13.23/2.58 Further assumptions not needed in the proof:
% 13.23/2.58 --------------------------------------------
% 13.23/2.58 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 13.23/2.58 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 13.23/2.58 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub,
% 13.23/2.58 mDiffCons, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel,
% 13.23/2.58 mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 13.23/2.58 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 13.23/2.58 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort,
% 13.23/2.58 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 13.23/2.58 mZeroLess, mZeroNum, m__, m__2202, m__2202_02, m__2227, m__2256, m__2270,
% 13.23/2.58 m__2291, m__2304
% 13.23/2.58
% 13.23/2.58 Those formulas are unsatisfiable:
% 13.23/2.58 ---------------------------------
% 13.23/2.58
% 13.23/2.58 Begin of proof
% 13.23/2.58 |
% 13.23/2.58 | ALPHA: (m__2323) implies:
% 13.23/2.58 | (1) ? [v0: int] : ( ~ (v0 = 0) & aElementOf0(xx, xQ) = v0)
% 13.23/2.58 |
% 13.23/2.58 | ALPHA: (m__2338) implies:
% 13.23/2.58 | (2) aElementOf0(xx, xQ) = 0
% 13.23/2.58 |
% 13.23/2.58 | ALPHA: (function-axioms) implies:
% 13.23/2.58 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.23/2.58 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 13.23/2.58 | (aElementOf0(v3, v2) = v0))
% 13.23/2.58 |
% 13.23/2.58 | DELTA: instantiating (1) with fresh symbol all_55_0 gives:
% 13.23/2.59 | (4) ~ (all_55_0 = 0) & aElementOf0(xx, xQ) = all_55_0
% 13.23/2.59 |
% 13.23/2.59 | ALPHA: (4) implies:
% 13.23/2.59 | (5) ~ (all_55_0 = 0)
% 13.23/2.59 | (6) aElementOf0(xx, xQ) = all_55_0
% 13.23/2.59 |
% 13.23/2.59 | GROUND_INST: instantiating (3) with 0, all_55_0, xQ, xx, simplifying with (2),
% 13.23/2.59 | (6) gives:
% 13.23/2.59 | (7) all_55_0 = 0
% 13.23/2.59 |
% 13.23/2.59 | REDUCE: (5), (7) imply:
% 13.23/2.59 | (8) $false
% 13.23/2.59 |
% 13.23/2.59 | CLOSE: (8) is inconsistent.
% 13.23/2.59 |
% 13.23/2.59 End of proof
% 13.23/2.59 % SZS output end Proof for theBenchmark
% 13.23/2.59
% 13.23/2.59 1982ms
%------------------------------------------------------------------------------