TSTP Solution File: NUM561+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM561+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n004.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 11:48:37 EDT 2023
% Result : Theorem 13.80s 2.66s
% Output : Proof 20.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM561+2 : 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 : n004.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 13:59:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.94/1.25 Prover 1: Preprocessing ...
% 3.94/1.25 Prover 4: Preprocessing ...
% 3.94/1.29 Prover 0: Preprocessing ...
% 3.94/1.29 Prover 2: Preprocessing ...
% 3.94/1.29 Prover 6: Preprocessing ...
% 3.94/1.29 Prover 5: Preprocessing ...
% 3.94/1.30 Prover 3: Preprocessing ...
% 11.86/2.34 Prover 1: Constructing countermodel ...
% 11.86/2.39 Prover 3: Constructing countermodel ...
% 12.48/2.43 Prover 6: Proving ...
% 12.48/2.44 Prover 5: Proving ...
% 13.80/2.61 Prover 2: Proving ...
% 13.80/2.65 Prover 3: proved (2028ms)
% 13.80/2.65
% 13.80/2.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.80/2.66
% 13.80/2.66 Prover 6: stopped
% 13.80/2.66 Prover 5: stopped
% 13.80/2.66 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.80/2.66 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.80/2.66 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.80/2.67 Prover 2: stopped
% 13.80/2.67 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.71/2.78 Prover 10: Preprocessing ...
% 14.71/2.78 Prover 8: Preprocessing ...
% 14.71/2.79 Prover 11: Preprocessing ...
% 15.31/2.81 Prover 7: Preprocessing ...
% 16.24/2.96 Prover 4: Constructing countermodel ...
% 16.98/3.03 Prover 0: Proving ...
% 16.98/3.05 Prover 0: stopped
% 16.98/3.05 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.98/3.06 Prover 7: Constructing countermodel ...
% 16.98/3.06 Prover 10: Constructing countermodel ...
% 17.58/3.14 Prover 13: Preprocessing ...
% 18.22/3.18 Prover 8: Warning: ignoring some quantifiers
% 18.23/3.20 Prover 8: Constructing countermodel ...
% 18.23/3.21 Prover 7: Found proof (size 13)
% 18.23/3.21 Prover 7: proved (557ms)
% 18.23/3.21 Prover 4: stopped
% 18.23/3.21 Prover 1: stopped
% 18.23/3.22 Prover 10: stopped
% 18.23/3.22 Prover 8: stopped
% 18.23/3.23 Prover 13: stopped
% 19.69/3.51 Prover 11: Constructing countermodel ...
% 19.69/3.53 Prover 11: stopped
% 19.69/3.53
% 19.69/3.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.69/3.53
% 19.69/3.54 % SZS output start Proof for theBenchmark
% 19.69/3.55 Assumptions after simplification:
% 19.69/3.55 ---------------------------------
% 19.69/3.55
% 19.69/3.55 (m__)
% 20.14/3.60 $i(xx) & $i(xF) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlcdtrc0(xF,
% 20.14/3.60 v0) = v2 & sdtlpdtrp0(xF, xx) = v1 & szDzozmdt0(xF) = v0 & $i(v2) & $i(v1)
% 20.14/3.60 & $i(v0) & ~ aElementOf0(v1, v2) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xF, v3) =
% 20.14/3.60 v1) | ~ $i(v3) | ~ aElementOf0(v3, v0)))
% 20.14/3.60
% 20.14/3.60 (m__2911_02)
% 20.14/3.60 $i(xx) & $i(xF) & ? [v0: $i] : (szDzozmdt0(xF) = v0 & $i(v0) &
% 20.14/3.60 aElementOf0(xx, v0))
% 20.14/3.60
% 20.14/3.60 (function-axioms)
% 20.14/3.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 20.14/3.61 (sdtlcdtrc0(v3, v2) = v1) | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : !
% 20.14/3.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1)
% 20.14/3.61 | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 20.14/3.61 ! [v3: $i] : (v1 = v0 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2)
% 20.14/3.61 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 20.14/3.61 | ~ (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0:
% 20.14/3.61 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3,
% 20.14/3.61 v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 20.14/3.61 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~
% 20.14/3.61 (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 20.14/3.61 v0 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 20.14/3.61 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 20.14/3.61 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.14/3.61 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 20.14/3.61 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 20.14/3.61 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 20.14/3.61 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 20.14/3.61 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 20.14/3.61 v0))
% 20.14/3.61
% 20.14/3.61 Further assumptions not needed in the proof:
% 20.14/3.61 --------------------------------------------
% 20.14/3.62 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 20.14/3.62 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 20.14/3.62 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefSImg, mDefSeg,
% 20.14/3.62 mDefSel, mDefSub, mDiffCons, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 20.14/3.62 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgElm, mLessASymm,
% 20.14/3.62 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet,
% 20.14/3.62 mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc,
% 20.14/3.62 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 20.14/3.62 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess,
% 20.14/3.62 mZeroNum, m__2911
% 20.14/3.62
% 20.14/3.62 Those formulas are unsatisfiable:
% 20.14/3.62 ---------------------------------
% 20.14/3.62
% 20.14/3.62 Begin of proof
% 20.14/3.62 |
% 20.14/3.62 | ALPHA: (m__2911_02) implies:
% 20.14/3.62 | (1) ? [v0: $i] : (szDzozmdt0(xF) = v0 & $i(v0) & aElementOf0(xx, v0))
% 20.14/3.62 |
% 20.14/3.62 | ALPHA: (m__) implies:
% 20.14/3.62 | (2) $i(xx)
% 20.14/3.62 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (sdtlcdtrc0(xF, v0) = v2 &
% 20.14/3.62 | sdtlpdtrp0(xF, xx) = v1 & szDzozmdt0(xF) = v0 & $i(v2) & $i(v1) &
% 20.14/3.62 | $i(v0) & ~ aElementOf0(v1, v2) & ! [v3: $i] : ( ~ (sdtlpdtrp0(xF,
% 20.14/3.62 | v3) = v1) | ~ $i(v3) | ~ aElementOf0(v3, v0)))
% 20.14/3.62 |
% 20.14/3.62 | ALPHA: (function-axioms) implies:
% 20.14/3.62 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzozmdt0(v2)
% 20.14/3.62 | = v1) | ~ (szDzozmdt0(v2) = v0))
% 20.14/3.62 |
% 20.14/3.63 | DELTA: instantiating (1) with fresh symbol all_60_0 gives:
% 20.14/3.63 | (5) szDzozmdt0(xF) = all_60_0 & $i(all_60_0) & aElementOf0(xx, all_60_0)
% 20.14/3.63 |
% 20.14/3.63 | ALPHA: (5) implies:
% 20.14/3.63 | (6) aElementOf0(xx, all_60_0)
% 20.14/3.63 | (7) szDzozmdt0(xF) = all_60_0
% 20.14/3.63 |
% 20.14/3.63 | DELTA: instantiating (3) with fresh symbols all_62_0, all_62_1, all_62_2
% 20.14/3.63 | gives:
% 20.14/3.63 | (8) sdtlcdtrc0(xF, all_62_2) = all_62_0 & sdtlpdtrp0(xF, xx) = all_62_1 &
% 20.14/3.63 | szDzozmdt0(xF) = all_62_2 & $i(all_62_0) & $i(all_62_1) & $i(all_62_2)
% 20.14/3.63 | & ~ aElementOf0(all_62_1, all_62_0) & ! [v0: $i] : ( ~
% 20.14/3.63 | (sdtlpdtrp0(xF, v0) = all_62_1) | ~ $i(v0) | ~ aElementOf0(v0,
% 20.14/3.63 | all_62_2))
% 20.14/3.63 |
% 20.14/3.63 | ALPHA: (8) implies:
% 20.14/3.63 | (9) szDzozmdt0(xF) = all_62_2
% 20.14/3.63 | (10) sdtlpdtrp0(xF, xx) = all_62_1
% 20.14/3.63 | (11) ! [v0: $i] : ( ~ (sdtlpdtrp0(xF, v0) = all_62_1) | ~ $i(v0) | ~
% 20.14/3.63 | aElementOf0(v0, all_62_2))
% 20.14/3.63 |
% 20.14/3.63 | GROUND_INST: instantiating (4) with all_60_0, all_62_2, xF, simplifying with
% 20.14/3.63 | (7), (9) gives:
% 20.14/3.63 | (12) all_62_2 = all_60_0
% 20.14/3.63 |
% 20.14/3.63 | GROUND_INST: instantiating (11) with xx, simplifying with (2), (10) gives:
% 20.14/3.63 | (13) ~ aElementOf0(xx, all_62_2)
% 20.14/3.63 |
% 20.14/3.63 | REDUCE: (12), (13) imply:
% 20.14/3.63 | (14) ~ aElementOf0(xx, all_60_0)
% 20.14/3.63 |
% 20.14/3.63 | PRED_UNIFY: (6), (14) imply:
% 20.14/3.63 | (15) $false
% 20.14/3.64 |
% 20.14/3.64 | CLOSE: (15) is inconsistent.
% 20.14/3.64 |
% 20.14/3.64 End of proof
% 20.14/3.64 % SZS output end Proof for theBenchmark
% 20.14/3.64
% 20.14/3.64 3033ms
%------------------------------------------------------------------------------