TSTP Solution File: NUM557+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM557+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 : n007.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 10.79s 2.25s
% Output : Proof 15.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM557+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n007.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 15:02:25 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.62/0.67 ________ _____
% 0.62/0.67 ___ __ \_________(_)________________________________
% 0.62/0.67 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.62/0.67 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.62/0.67 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.62/0.67
% 0.62/0.67 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.62/0.67 (2023-06-19)
% 0.62/0.67
% 0.62/0.67 (c) Philipp Rümmer, 2009-2023
% 0.62/0.67 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.62/0.67 Amanda Stjerna.
% 0.62/0.67 Free software under BSD-3-Clause.
% 0.62/0.67
% 0.62/0.67 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.62/0.67
% 0.62/0.67 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.69 Running up to 7 provers in parallel.
% 0.62/0.70 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.62/0.70 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.62/0.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.62/0.70 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.62/0.70 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.62/0.70 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.62/0.70 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.23/1.36 Prover 4: Preprocessing ...
% 4.23/1.36 Prover 1: Preprocessing ...
% 4.64/1.40 Prover 6: Preprocessing ...
% 4.64/1.40 Prover 0: Preprocessing ...
% 4.64/1.40 Prover 5: Preprocessing ...
% 4.64/1.40 Prover 2: Preprocessing ...
% 4.64/1.40 Prover 3: Preprocessing ...
% 10.79/2.22 Prover 5: Constructing countermodel ...
% 10.79/2.25 Prover 5: proved (1547ms)
% 10.79/2.25
% 10.79/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.79/2.25
% 10.79/2.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.53/2.32 Prover 3: Constructing countermodel ...
% 11.53/2.34 Prover 3: stopped
% 11.53/2.35 Prover 1: Constructing countermodel ...
% 11.53/2.36 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.53/2.38 Prover 7: Preprocessing ...
% 12.21/2.42 Prover 6: Proving ...
% 12.21/2.43 Prover 6: stopped
% 12.21/2.43 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.21/2.46 Prover 2: Proving ...
% 12.21/2.46 Prover 8: Preprocessing ...
% 12.21/2.46 Prover 2: stopped
% 12.21/2.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.94/2.53 Prover 10: Preprocessing ...
% 13.81/2.62 Prover 7: Constructing countermodel ...
% 13.81/2.62 Prover 11: Preprocessing ...
% 13.81/2.68 Prover 1: Found proof (size 13)
% 13.81/2.69 Prover 1: proved (1989ms)
% 13.81/2.69 Prover 7: stopped
% 14.54/2.76 Prover 10: Constructing countermodel ...
% 14.54/2.77 Prover 11: stopped
% 14.54/2.77 Prover 4: Constructing countermodel ...
% 14.54/2.78 Prover 8: Warning: ignoring some quantifiers
% 15.12/2.79 Prover 10: stopped
% 15.12/2.80 Prover 8: Constructing countermodel ...
% 15.12/2.81 Prover 4: stopped
% 15.12/2.81 Prover 8: stopped
% 15.12/2.85 Prover 0: Proving ...
% 15.12/2.85 Prover 0: stopped
% 15.12/2.85
% 15.12/2.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.12/2.85
% 15.12/2.85 % SZS output start Proof for theBenchmark
% 15.12/2.86 Assumptions after simplification:
% 15.12/2.86 ---------------------------------
% 15.12/2.86
% 15.12/2.86 (m__)
% 15.56/2.88 $i(xP) & $i(xS) & $i(xk) & ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 15.56/2.88 int] : ( ~ (v3 = 0) & slbdtsldtrb0(xS, xk) = v2 & sbrdtbr0(xP) = v1 &
% 15.56/2.88 aSubsetOf0(xP, xS) = v0 & aElementOf0(xP, v2) = v3 & $i(v2) & $i(v1) & ( ~
% 15.56/2.88 (v1 = xk) | ( ~ (v0 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 15.56/2.88 aElementOf0(v4, xP) = 0 & aElementOf0(v4, xS) = v5 & $i(v4)))))
% 15.56/2.88
% 15.56/2.88 (m__2431)
% 15.57/2.88 sbrdtbr0(xP) = xk & aSubsetOf0(xP, xS) = 0 & $i(xP) & $i(xS) & $i(xk) & !
% 15.57/2.88 [v0: $i] : ( ~ (aElementOf0(v0, xP) = 0) | ~ $i(v0) | aElementOf0(v0, xS) =
% 15.57/2.88 0)
% 15.57/2.88
% 15.57/2.88 (function-axioms)
% 15.57/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.57/2.89 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0:
% 15.57/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.57/2.89 : (v1 = v0 | ~ (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 15.57/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.57/2.89 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 15.57/2.89 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.57/2.89 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 15.57/2.89 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 15.57/2.89 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.57/2.89 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 15.57/2.89 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 15.57/2.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 15.57/2.89 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 15.57/2.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) |
% 15.57/2.89 ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.57/2.89 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : !
% 15.57/2.89 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~
% 15.57/2.89 (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 15.57/2.89 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 15.57/2.89 $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 15.57/2.89 (szszuzczcdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.57/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) |
% 15.57/2.89 ~ (isCountable0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.57/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (isFinite0(v2) = v1) | ~
% 15.57/2.89 (isFinite0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 15.57/2.89 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aSet0(v2) = v1) | ~
% 15.57/2.89 (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 15.57/2.89 : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) | ~ (aElement0(v2) = v0))
% 15.57/2.89
% 15.57/2.89 Further assumptions not needed in the proof:
% 15.57/2.89 --------------------------------------------
% 15.57/2.89 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 15.57/2.89 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 15.57/2.89 mDefCons, mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSeg, mDefSel, mDefSub,
% 15.57/2.89 mDiffCons, mEOfElem, mElmSort, mEmpFin, mFConsSet, mFDiffSet, mFinRel,
% 15.57/2.89 mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel, mLessSucc,
% 15.57/2.89 mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc, mNoScLessZr,
% 15.57/2.89 mSegFin, mSegLess, mSegSucc, mSegZero, mSelCSet, mSelFSet, mSelNSet, mSetSort,
% 15.57/2.89 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum,
% 15.57/2.89 mZeroLess, mZeroNum, m__2202, m__2202_02, m__2227, m__2256, m__2270, m__2291,
% 15.57/2.89 m__2304, m__2323, m__2338, m__2357, m__2411
% 15.57/2.89
% 15.57/2.89 Those formulas are unsatisfiable:
% 15.57/2.89 ---------------------------------
% 15.57/2.89
% 15.57/2.89 Begin of proof
% 15.57/2.90 |
% 15.57/2.90 | ALPHA: (m__2431) implies:
% 15.57/2.90 | (1) aSubsetOf0(xP, xS) = 0
% 15.57/2.90 | (2) sbrdtbr0(xP) = xk
% 15.57/2.90 |
% 15.57/2.90 | ALPHA: (m__) implies:
% 15.65/2.90 | (3) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0)
% 15.65/2.90 | & slbdtsldtrb0(xS, xk) = v2 & sbrdtbr0(xP) = v1 & aSubsetOf0(xP, xS)
% 15.65/2.90 | = v0 & aElementOf0(xP, v2) = v3 & $i(v2) & $i(v1) & ( ~ (v1 = xk) | (
% 15.65/2.90 | ~ (v0 = 0) & ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 15.65/2.90 | aElementOf0(v4, xP) = 0 & aElementOf0(v4, xS) = v5 & $i(v4)))))
% 15.65/2.90 |
% 15.65/2.90 | ALPHA: (function-axioms) implies:
% 15.65/2.90 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2) =
% 15.65/2.90 | v1) | ~ (sbrdtbr0(v2) = v0))
% 15.65/2.90 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 15.65/2.90 | ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~
% 15.65/2.90 | (aSubsetOf0(v3, v2) = v0))
% 15.65/2.90 |
% 15.65/2.90 | DELTA: instantiating (3) with fresh symbols all_61_0, all_61_1, all_61_2,
% 15.65/2.90 | all_61_3 gives:
% 15.65/2.90 | (6) ~ (all_61_0 = 0) & slbdtsldtrb0(xS, xk) = all_61_1 & sbrdtbr0(xP) =
% 15.65/2.90 | all_61_2 & aSubsetOf0(xP, xS) = all_61_3 & aElementOf0(xP, all_61_1) =
% 15.65/2.90 | all_61_0 & $i(all_61_1) & $i(all_61_2) & ( ~ (all_61_2 = xk) | ( ~
% 15.65/2.90 | (all_61_3 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.65/2.90 | aElementOf0(v0, xP) = 0 & aElementOf0(v0, xS) = v1 & $i(v0))))
% 15.65/2.90 |
% 15.65/2.90 | ALPHA: (6) implies:
% 15.65/2.90 | (7) aSubsetOf0(xP, xS) = all_61_3
% 15.65/2.90 | (8) sbrdtbr0(xP) = all_61_2
% 15.65/2.90 | (9) ~ (all_61_2 = xk) | ( ~ (all_61_3 = 0) & ? [v0: $i] : ? [v1: int] :
% 15.65/2.91 | ( ~ (v1 = 0) & aElementOf0(v0, xP) = 0 & aElementOf0(v0, xS) = v1 &
% 15.65/2.91 | $i(v0)))
% 15.65/2.91 |
% 15.65/2.91 | GROUND_INST: instantiating (5) with 0, all_61_3, xS, xP, simplifying with (1),
% 15.65/2.91 | (7) gives:
% 15.65/2.91 | (10) all_61_3 = 0
% 15.65/2.91 |
% 15.65/2.91 | GROUND_INST: instantiating (4) with xk, all_61_2, xP, simplifying with (2),
% 15.65/2.91 | (8) gives:
% 15.65/2.91 | (11) all_61_2 = xk
% 15.65/2.91 |
% 15.65/2.91 | BETA: splitting (9) gives:
% 15.65/2.91 |
% 15.65/2.91 | Case 1:
% 15.65/2.91 | |
% 15.65/2.91 | | (12) ~ (all_61_2 = xk)
% 15.65/2.91 | |
% 15.65/2.91 | | REDUCE: (11), (12) imply:
% 15.65/2.91 | | (13) $false
% 15.65/2.91 | |
% 15.65/2.91 | | CLOSE: (13) is inconsistent.
% 15.65/2.91 | |
% 15.65/2.91 | Case 2:
% 15.65/2.91 | |
% 15.65/2.91 | | (14) ~ (all_61_3 = 0) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 15.65/2.91 | | aElementOf0(v0, xP) = 0 & aElementOf0(v0, xS) = v1 & $i(v0))
% 15.65/2.91 | |
% 15.65/2.91 | | ALPHA: (14) implies:
% 15.65/2.91 | | (15) ~ (all_61_3 = 0)
% 15.65/2.91 | |
% 15.65/2.91 | | REDUCE: (10), (15) imply:
% 15.65/2.91 | | (16) $false
% 15.65/2.91 | |
% 15.65/2.91 | | CLOSE: (16) is inconsistent.
% 15.65/2.91 | |
% 15.65/2.91 | End of split
% 15.65/2.91 |
% 15.65/2.91 End of proof
% 15.65/2.91 % SZS output end Proof for theBenchmark
% 15.65/2.91
% 15.65/2.91 2239ms
%------------------------------------------------------------------------------