TSTP Solution File: NUM548+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM548+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 : n024.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 11:48:33 EDT 2023
% Result : Theorem 14.32s 2.65s
% Output : Proof 20.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM548+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 14:28:54 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.81/1.25 Prover 1: Preprocessing ...
% 3.81/1.25 Prover 4: Preprocessing ...
% 3.81/1.29 Prover 0: Preprocessing ...
% 3.81/1.29 Prover 6: Preprocessing ...
% 3.81/1.29 Prover 3: Preprocessing ...
% 3.81/1.29 Prover 5: Preprocessing ...
% 3.81/1.29 Prover 2: Preprocessing ...
% 10.56/2.20 Prover 1: Constructing countermodel ...
% 10.56/2.26 Prover 5: Proving ...
% 10.56/2.28 Prover 6: Proving ...
% 10.56/2.29 Prover 3: Constructing countermodel ...
% 11.44/2.33 Prover 2: Proving ...
% 14.32/2.65 Prover 3: proved (2002ms)
% 14.32/2.65
% 14.32/2.65 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.32/2.65
% 14.32/2.66 Prover 5: stopped
% 14.32/2.66 Prover 2: stopped
% 14.32/2.66 Prover 6: stopped
% 14.42/2.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.42/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.42/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.42/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.11/2.77 Prover 4: Constructing countermodel ...
% 15.11/2.80 Prover 0: Proving ...
% 15.11/2.80 Prover 8: Preprocessing ...
% 15.11/2.80 Prover 0: stopped
% 15.11/2.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.11/2.81 Prover 7: Preprocessing ...
% 15.76/2.85 Prover 11: Preprocessing ...
% 15.76/2.85 Prover 10: Preprocessing ...
% 15.76/2.93 Prover 13: Preprocessing ...
% 17.23/3.05 Prover 7: Constructing countermodel ...
% 17.23/3.09 Prover 10: Constructing countermodel ...
% 17.87/3.16 Prover 8: Warning: ignoring some quantifiers
% 17.87/3.17 Prover 8: Constructing countermodel ...
% 19.46/3.33 Prover 13: Constructing countermodel ...
% 19.57/3.35 Prover 10: Found proof (size 9)
% 19.57/3.35 Prover 10: proved (692ms)
% 19.57/3.35 Prover 4: stopped
% 19.57/3.35 Prover 8: stopped
% 19.57/3.35 Prover 7: stopped
% 19.57/3.35 Prover 1: stopped
% 19.57/3.37 Prover 13: stopped
% 19.98/3.47 Prover 11: Constructing countermodel ...
% 20.25/3.49 Prover 11: stopped
% 20.25/3.49
% 20.25/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.25/3.49
% 20.25/3.50 % SZS output start Proof for theBenchmark
% 20.25/3.50 Assumptions after simplification:
% 20.25/3.50 ---------------------------------
% 20.25/3.50
% 20.25/3.50 (mCardNum)
% 20.25/3.52 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0)
% 20.25/3.52 | ~ isFinite0(v0) | ~ aSet0(v0) | aElementOf0(v1, szNzAzT0)) & ! [v0: $i]
% 20.25/3.52 : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 20.25/3.52 szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 20.25/3.52
% 20.25/3.52 (m__)
% 20.25/3.53 $i(xQ) & ~ isFinite0(xQ)
% 20.25/3.53
% 20.25/3.53 (m__2202)
% 20.25/3.53 $i(xk) & $i(szNzAzT0) & aElementOf0(xk, szNzAzT0)
% 20.25/3.53
% 20.25/3.53 (m__2270)
% 20.25/3.53 $i(xQ) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 &
% 20.25/3.53 sbrdtbr0(xQ) = xk & $i(v0) & aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) &
% 20.25/3.53 aSet0(xQ) & ! [v1: $i] : ( ~ $i(v1) | ~ aElementOf0(v1, xQ) |
% 20.25/3.53 aElementOf0(v1, xS)))
% 20.25/3.53
% 20.25/3.53 Further assumptions not needed in the proof:
% 20.25/3.53 --------------------------------------------
% 20.25/3.53 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardS, mCardSeg,
% 20.25/3.53 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 20.25/3.53 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub, mDiffCons,
% 20.25/3.53 mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH,
% 20.25/3.53 mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 20.25/3.53 mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess,
% 20.25/3.53 mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet,
% 20.25/3.53 mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum,
% 20.25/3.53 m__2202_02, m__2227, m__2256
% 20.25/3.53
% 20.25/3.53 Those formulas are unsatisfiable:
% 20.25/3.53 ---------------------------------
% 20.25/3.53
% 20.25/3.53 Begin of proof
% 20.25/3.53 |
% 20.25/3.53 | ALPHA: (mCardNum) implies:
% 20.25/3.53 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 20.25/3.53 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | isFinite0(v0))
% 20.25/3.53 |
% 20.25/3.53 | ALPHA: (m__2202) implies:
% 20.25/3.53 | (2) aElementOf0(xk, szNzAzT0)
% 20.25/3.53 |
% 20.25/3.53 | ALPHA: (m__2270) implies:
% 20.25/3.53 | (3) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & sbrdtbr0(xQ) = xk & $i(v0) &
% 20.25/3.53 | aSubsetOf0(xQ, xS) & aElementOf0(xQ, v0) & aSet0(xQ) & ! [v1: $i] :
% 20.25/3.53 | ( ~ $i(v1) | ~ aElementOf0(v1, xQ) | aElementOf0(v1, xS)))
% 20.25/3.53 |
% 20.25/3.53 | ALPHA: (m__) implies:
% 20.25/3.54 | (4) ~ isFinite0(xQ)
% 20.25/3.54 | (5) $i(xQ)
% 20.25/3.54 |
% 20.25/3.54 | DELTA: instantiating (3) with fresh symbol all_53_0 gives:
% 20.25/3.54 | (6) slbdtsldtrb0(xS, xk) = all_53_0 & sbrdtbr0(xQ) = xk & $i(all_53_0) &
% 20.25/3.54 | aSubsetOf0(xQ, xS) & aElementOf0(xQ, all_53_0) & aSet0(xQ) & ! [v0:
% 20.25/3.54 | $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | aElementOf0(v0, xS))
% 20.25/3.54 |
% 20.25/3.54 | ALPHA: (6) implies:
% 20.25/3.54 | (7) aSet0(xQ)
% 20.25/3.54 | (8) sbrdtbr0(xQ) = xk
% 20.25/3.54 |
% 20.25/3.54 | GROUND_INST: instantiating (1) with xQ, xk, simplifying with (2), (4), (5),
% 20.25/3.54 | (7), (8) gives:
% 20.25/3.54 | (9) $false
% 20.25/3.54 |
% 20.25/3.54 | CLOSE: (9) is inconsistent.
% 20.25/3.54 |
% 20.25/3.54 End of proof
% 20.25/3.54 % SZS output end Proof for theBenchmark
% 20.25/3.54
% 20.25/3.54 2916ms
%------------------------------------------------------------------------------