TSTP Solution File: NUM560+2 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM560+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 : n016.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 13.69s 2.69s
% Output : Proof 17.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM560+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 09:35:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.69/1.30 Prover 1: Preprocessing ...
% 3.69/1.30 Prover 4: Preprocessing ...
% 4.11/1.33 Prover 2: Preprocessing ...
% 4.11/1.33 Prover 0: Preprocessing ...
% 4.11/1.33 Prover 6: Preprocessing ...
% 4.11/1.33 Prover 3: Preprocessing ...
% 4.11/1.33 Prover 5: Preprocessing ...
% 11.46/2.38 Prover 6: Proving ...
% 11.46/2.38 Prover 3: Constructing countermodel ...
% 11.46/2.38 Prover 1: Constructing countermodel ...
% 11.46/2.40 Prover 5: Constructing countermodel ...
% 13.16/2.59 Prover 2: Proving ...
% 13.69/2.68 Prover 4: Constructing countermodel ...
% 13.69/2.68 Prover 3: proved (2059ms)
% 13.69/2.68
% 13.69/2.69 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.69/2.69
% 13.69/2.69 Prover 5: stopped
% 13.69/2.71 Prover 6: stopped
% 13.69/2.72 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.69/2.72 Prover 2: stopped
% 14.40/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.40/2.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.40/2.74 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.89/2.82 Prover 8: Preprocessing ...
% 14.89/2.84 Prover 7: Preprocessing ...
% 14.89/2.88 Prover 10: Preprocessing ...
% 14.89/2.88 Prover 1: Found proof (size 11)
% 14.89/2.89 Prover 1: proved (2272ms)
% 14.89/2.91 Prover 7: stopped
% 14.89/2.91 Prover 11: Preprocessing ...
% 14.89/2.93 Prover 0: Proving ...
% 14.89/2.93 Prover 0: stopped
% 14.89/2.95 Prover 4: stopped
% 14.89/2.95 Prover 10: stopped
% 16.40/3.02 Prover 11: stopped
% 16.60/3.06 Prover 8: Warning: ignoring some quantifiers
% 16.60/3.08 Prover 8: Constructing countermodel ...
% 16.60/3.09 Prover 8: stopped
% 16.60/3.09
% 16.60/3.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.60/3.09
% 16.60/3.09 % SZS output start Proof for theBenchmark
% 16.60/3.10 Assumptions after simplification:
% 16.60/3.10 ---------------------------------
% 16.60/3.10
% 16.60/3.10 (m__)
% 16.60/3.12 $i(xy) & $i(xF) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 16.60/3.12 sdtlbdtrb0(xF, xy) = v0 & szDzozmdt0(xF) = v1 & aSubsetOf0(v0, v1) = v2 &
% 16.60/3.12 aSet0(v0) = 0 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~
% 16.60/3.12 (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: $i] :
% 16.60/3.12 (sdtlpdtrp0(xF, v3) = v6 & aElementOf0(v3, v1) = v5 & $i(v6) & ( ~ (v6 =
% 16.60/3.12 xy) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~ (aElementOf0(v3, v0) = 0) |
% 16.60/3.12 ~ $i(v3) | (sdtlpdtrp0(xF, v3) = xy & aElementOf0(v3, v1) = 0)) & ? [v3:
% 16.60/3.12 $i] : ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = v4 &
% 16.60/3.12 aElementOf0(v3, v0) = 0 & $i(v3)))
% 16.60/3.12
% 16.60/3.12 (function-axioms)
% 16.60/3.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.60/3.13 (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2) = v0)) & ! [v0: $i] : !
% 16.60/3.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlpdtrp0(v3, v2) = v1)
% 16.60/3.13 | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 16.60/3.13 ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3,
% 16.60/3.13 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 16.60/3.13 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~
% 16.60/3.13 (iLess0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.60/3.13 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 16.60/3.13 (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 16.60/3.13 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) = v1) |
% 16.60/3.13 ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 16.60/3.13 [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3, v2) = v0))
% 16.60/3.13 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 16.60/3.13 [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) =
% 16.60/3.13 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.60/3.13 $i] : ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 16.60/3.13 (aElementOf0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 16.60/3.13 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~
% 16.60/3.13 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 16.60/3.13 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 16.60/3.13 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 16.60/3.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 16.60/3.13 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 16.60/3.13 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 16.60/3.13 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 16.60/3.13 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 16.60/3.13 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 17.05/3.13 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.05/3.13 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 17.05/3.13 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 17.05/3.13 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 17.05/3.13 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 17.05/3.13 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 17.05/3.13 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 17.05/3.13 ~ (aElement0(v2) = v0))
% 17.05/3.13
% 17.05/3.13 Further assumptions not needed in the proof:
% 17.05/3.13 --------------------------------------------
% 17.05/3.13 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 17.05/3.13 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 17.05/3.13 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefSeg, mDefSel,
% 17.05/3.13 mDefSub, mDiffCons, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet,
% 17.05/3.13 mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgElm, mLessASymm, mLessRefl,
% 17.05/3.13 mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra,
% 17.05/3.13 mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet,
% 17.05/3.13 mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm, mSubFSet, mSubRefl,
% 17.05/3.13 mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__2693
% 17.05/3.13
% 17.05/3.13 Those formulas are unsatisfiable:
% 17.05/3.13 ---------------------------------
% 17.05/3.13
% 17.05/3.13 Begin of proof
% 17.05/3.13 |
% 17.05/3.14 | ALPHA: (m__) implies:
% 17.05/3.14 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 17.05/3.14 | sdtlbdtrb0(xF, xy) = v0 & szDzozmdt0(xF) = v1 & aSubsetOf0(v0, v1) =
% 17.05/3.14 | v2 & aSet0(v0) = 0 & $i(v1) & $i(v0) & ! [v3: $i] : ! [v4: int] :
% 17.05/3.14 | (v4 = 0 | ~ (aElementOf0(v3, v0) = v4) | ~ $i(v3) | ? [v5: any] :
% 17.05/3.14 | ? [v6: $i] : (sdtlpdtrp0(xF, v3) = v6 & aElementOf0(v3, v1) = v5 &
% 17.05/3.14 | $i(v6) & ( ~ (v6 = xy) | ~ (v5 = 0)))) & ! [v3: $i] : ( ~
% 17.05/3.14 | (aElementOf0(v3, v0) = 0) | ~ $i(v3) | (sdtlpdtrp0(xF, v3) = xy &
% 17.05/3.14 | aElementOf0(v3, v1) = 0)) & ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 17.05/3.14 | = 0) & aElementOf0(v3, v1) = v4 & aElementOf0(v3, v0) = 0 &
% 17.05/3.14 | $i(v3)))
% 17.05/3.14 |
% 17.05/3.14 | ALPHA: (function-axioms) implies:
% 17.05/3.14 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 17.05/3.14 | ! [v3: $i] : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~
% 17.05/3.14 | (aElementOf0(v3, v2) = v0))
% 17.05/3.14 |
% 17.05/3.14 | DELTA: instantiating (1) with fresh symbols all_58_0, all_58_1, all_58_2
% 17.05/3.14 | gives:
% 17.05/3.14 | (3) ~ (all_58_0 = 0) & sdtlbdtrb0(xF, xy) = all_58_2 & szDzozmdt0(xF) =
% 17.05/3.14 | all_58_1 & aSubsetOf0(all_58_2, all_58_1) = all_58_0 & aSet0(all_58_2)
% 17.05/3.14 | = 0 & $i(all_58_1) & $i(all_58_2) & ! [v0: $i] : ! [v1: int] : (v1 =
% 17.05/3.14 | 0 | ~ (aElementOf0(v0, all_58_2) = v1) | ~ $i(v0) | ? [v2: any] :
% 17.05/3.14 | ? [v3: $i] : (sdtlpdtrp0(xF, v0) = v3 & aElementOf0(v0, all_58_1) =
% 17.05/3.14 | v2 & $i(v3) & ( ~ (v3 = xy) | ~ (v2 = 0)))) & ! [v0: $i] : ( ~
% 17.05/3.14 | (aElementOf0(v0, all_58_2) = 0) | ~ $i(v0) | (sdtlpdtrp0(xF, v0) =
% 17.05/3.14 | xy & aElementOf0(v0, all_58_1) = 0)) & ? [v0: $i] : ? [v1: int] :
% 17.05/3.14 | ( ~ (v1 = 0) & aElementOf0(v0, all_58_1) = v1 & aElementOf0(v0,
% 17.05/3.14 | all_58_2) = 0 & $i(v0))
% 17.05/3.14 |
% 17.05/3.14 | ALPHA: (3) implies:
% 17.05/3.14 | (4) ! [v0: $i] : ( ~ (aElementOf0(v0, all_58_2) = 0) | ~ $i(v0) |
% 17.05/3.14 | (sdtlpdtrp0(xF, v0) = xy & aElementOf0(v0, all_58_1) = 0))
% 17.05/3.14 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & aElementOf0(v0, all_58_1) =
% 17.05/3.14 | v1 & aElementOf0(v0, all_58_2) = 0 & $i(v0))
% 17.05/3.14 |
% 17.05/3.14 | DELTA: instantiating (5) with fresh symbols all_61_0, all_61_1 gives:
% 17.05/3.14 | (6) ~ (all_61_0 = 0) & aElementOf0(all_61_1, all_58_1) = all_61_0 &
% 17.05/3.14 | aElementOf0(all_61_1, all_58_2) = 0 & $i(all_61_1)
% 17.05/3.14 |
% 17.05/3.14 | ALPHA: (6) implies:
% 17.05/3.15 | (7) ~ (all_61_0 = 0)
% 17.05/3.15 | (8) $i(all_61_1)
% 17.05/3.15 | (9) aElementOf0(all_61_1, all_58_2) = 0
% 17.05/3.15 | (10) aElementOf0(all_61_1, all_58_1) = all_61_0
% 17.05/3.15 |
% 17.05/3.15 | GROUND_INST: instantiating (4) with all_61_1, simplifying with (8), (9) gives:
% 17.05/3.15 | (11) sdtlpdtrp0(xF, all_61_1) = xy & aElementOf0(all_61_1, all_58_1) = 0
% 17.05/3.15 |
% 17.05/3.15 | ALPHA: (11) implies:
% 17.05/3.15 | (12) aElementOf0(all_61_1, all_58_1) = 0
% 17.05/3.15 |
% 17.05/3.15 | GROUND_INST: instantiating (2) with all_61_0, 0, all_58_1, all_61_1,
% 17.05/3.15 | simplifying with (10), (12) gives:
% 17.05/3.15 | (13) all_61_0 = 0
% 17.05/3.15 |
% 17.05/3.15 | REDUCE: (7), (13) imply:
% 17.05/3.15 | (14) $false
% 17.05/3.15 |
% 17.05/3.15 | CLOSE: (14) is inconsistent.
% 17.05/3.15 |
% 17.05/3.15 End of proof
% 17.05/3.15 % SZS output end Proof for theBenchmark
% 17.05/3.15
% 17.05/3.15 2544ms
%------------------------------------------------------------------------------