TSTP Solution File: NUM576+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM576+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 11:48:43 EDT 2023
% Result : Theorem 21.85s 3.74s
% Output : Proof 36.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM576+3 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 08:51:39 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.65/1.42 Prover 4: Preprocessing ...
% 4.65/1.44 Prover 1: Preprocessing ...
% 5.31/1.46 Prover 6: Preprocessing ...
% 5.31/1.46 Prover 0: Preprocessing ...
% 5.31/1.46 Prover 3: Preprocessing ...
% 5.31/1.46 Prover 5: Preprocessing ...
% 5.31/1.46 Prover 2: Preprocessing ...
% 13.96/2.61 Prover 6: Proving ...
% 14.13/2.69 Prover 1: Constructing countermodel ...
% 14.89/2.76 Prover 3: Constructing countermodel ...
% 16.28/2.91 Prover 5: Proving ...
% 21.85/3.64 Prover 2: Proving ...
% 21.85/3.73 Prover 3: proved (3109ms)
% 21.85/3.74
% 21.85/3.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.85/3.74
% 21.85/3.74 Prover 6: stopped
% 21.85/3.74 Prover 5: stopped
% 21.85/3.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.85/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.85/3.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.85/3.76 Prover 2: stopped
% 21.85/3.76 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.96/3.94 Prover 11: Preprocessing ...
% 24.38/3.98 Prover 8: Preprocessing ...
% 24.38/3.98 Prover 10: Preprocessing ...
% 24.38/4.00 Prover 7: Preprocessing ...
% 28.29/4.49 Prover 7: Constructing countermodel ...
% 28.29/4.49 Prover 8: Warning: ignoring some quantifiers
% 28.56/4.53 Prover 8: Constructing countermodel ...
% 29.21/4.61 Prover 10: Constructing countermodel ...
% 29.79/4.72 Prover 4: Constructing countermodel ...
% 33.52/5.19 Prover 10: Found proof (size 17)
% 33.52/5.19 Prover 10: proved (1436ms)
% 33.52/5.19 Prover 4: stopped
% 33.52/5.19 Prover 8: stopped
% 33.52/5.19 Prover 7: stopped
% 33.52/5.19 Prover 1: stopped
% 34.00/5.28 Prover 0: Proving ...
% 34.00/5.29 Prover 0: stopped
% 35.78/5.70 Prover 11: Constructing countermodel ...
% 35.78/5.73 Prover 11: stopped
% 35.78/5.73
% 35.78/5.73 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 35.78/5.73
% 35.78/5.73 % SZS output start Proof for theBenchmark
% 35.78/5.74 Assumptions after simplification:
% 35.78/5.74 ---------------------------------
% 35.78/5.74
% 35.78/5.74 (mCountNFin_01)
% 35.78/5.74 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 35.78/5.74
% 35.78/5.74 (mDefEmp)
% 35.78/5.74 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 35.78/5.74 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 35.78/5.74 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 35.78/5.74
% 35.78/5.74 (mLessASymm)
% 35.78/5.74 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) |
% 35.78/5.74 ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1, szNzAzT0)
% 35.78/5.74 | ~ aElementOf0(v0, szNzAzT0))
% 35.78/5.74
% 35.78/5.74 (mLessTotal)
% 36.16/5.77 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1)
% 36.16/5.77 = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 36.16/5.77 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1))
% 36.16/5.77
% 36.16/5.77 (m__)
% 36.16/5.77 $i(xj) & $i(xi) & ? [v0: $i] : ? [v1: $i] : ( ~ (xj = xi) & szszuzczcdt0(xj)
% 36.16/5.77 = v0 & szszuzczcdt0(xi) = v1 & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, xj) & ~
% 36.16/5.77 sdtlseqdt0(v0, xi))
% 36.16/5.77
% 36.16/5.77 (m__3856)
% 36.16/5.77 $i(xj) & $i(xi) & $i(szNzAzT0) & aElementOf0(xj, szNzAzT0) & aElementOf0(xi,
% 36.16/5.77 szNzAzT0)
% 36.16/5.77
% 36.16/5.77 Further assumptions not needed in the proof:
% 36.16/5.77 --------------------------------------------
% 36.16/5.77 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 36.16/5.77 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 36.16/5.77 mDefDiff, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg, mDefSel,
% 36.16/5.77 mDefSub, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 36.16/5.77 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 36.16/5.77 mImgRng, mLessRefl, mLessRel, mLessSucc, mLessTrans, mMinMin, mNATSet,
% 36.16/5.77 mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess, mSegSucc,
% 36.16/5.77 mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort, mSubASymm,
% 36.16/5.77 mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess,
% 36.16/5.77 mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520,
% 36.16/5.77 m__3533, m__3623, m__3671, m__3754
% 36.16/5.77
% 36.16/5.77 Those formulas are unsatisfiable:
% 36.16/5.77 ---------------------------------
% 36.16/5.77
% 36.16/5.77 Begin of proof
% 36.16/5.77 |
% 36.16/5.77 | ALPHA: (mDefEmp) implies:
% 36.16/5.77 | (1) aSet0(slcrc0)
% 36.16/5.77 |
% 36.16/5.77 | ALPHA: (mCountNFin_01) implies:
% 36.16/5.77 | (2) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 36.16/5.77 |
% 36.16/5.77 | ALPHA: (mLessASymm) implies:
% 36.16/5.77 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 36.16/5.77 | sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1,
% 36.16/5.77 | szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 36.16/5.77 |
% 36.16/5.77 | ALPHA: (mLessTotal) implies:
% 36.16/5.77 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) = v2) |
% 36.16/5.77 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 36.16/5.77 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1))
% 36.16/5.77 |
% 36.16/5.77 | ALPHA: (m__3856) implies:
% 36.16/5.78 | (5) aElementOf0(xi, szNzAzT0)
% 36.16/5.78 | (6) aElementOf0(xj, szNzAzT0)
% 36.16/5.78 |
% 36.16/5.78 | ALPHA: (m__) implies:
% 36.16/5.78 | (7) $i(xi)
% 36.16/5.78 | (8) $i(xj)
% 36.16/5.78 | (9) ? [v0: $i] : ? [v1: $i] : ( ~ (xj = xi) & szszuzczcdt0(xj) = v0 &
% 36.16/5.78 | szszuzczcdt0(xi) = v1 & $i(v1) & $i(v0) & ~ sdtlseqdt0(v1, xj) & ~
% 36.16/5.78 | sdtlseqdt0(v0, xi))
% 36.16/5.78 |
% 36.16/5.78 | DELTA: instantiating (9) with fresh symbols all_69_0, all_69_1 gives:
% 36.16/5.78 | (10) ~ (xj = xi) & szszuzczcdt0(xj) = all_69_1 & szszuzczcdt0(xi) =
% 36.16/5.78 | all_69_0 & $i(all_69_0) & $i(all_69_1) & ~ sdtlseqdt0(all_69_0, xj) &
% 36.16/5.78 | ~ sdtlseqdt0(all_69_1, xi)
% 36.16/5.78 |
% 36.16/5.78 | ALPHA: (10) implies:
% 36.16/5.78 | (11) ~ (xj = xi)
% 36.16/5.78 | (12) ~ sdtlseqdt0(all_69_1, xi)
% 36.16/5.78 | (13) ~ sdtlseqdt0(all_69_0, xj)
% 36.16/5.78 | (14) szszuzczcdt0(xi) = all_69_0
% 36.16/5.78 | (15) szszuzczcdt0(xj) = all_69_1
% 36.16/5.78 |
% 36.16/5.78 | BETA: splitting (2) gives:
% 36.16/5.78 |
% 36.16/5.78 | Case 1:
% 36.16/5.78 | |
% 36.16/5.78 | | (16) ~ aSet0(slcrc0)
% 36.16/5.78 | |
% 36.16/5.78 | | PRED_UNIFY: (1), (16) imply:
% 36.16/5.78 | | (17) $false
% 36.16/5.78 | |
% 36.16/5.78 | | CLOSE: (17) is inconsistent.
% 36.16/5.78 | |
% 36.16/5.78 | Case 2:
% 36.16/5.78 | |
% 36.16/5.78 | |
% 36.16/5.78 | | GROUND_INST: instantiating (4) with xj, xi, all_69_0, simplifying with (5),
% 36.16/5.78 | | (6), (7), (8), (13), (14) gives:
% 36.16/5.78 | | (18) sdtlseqdt0(xj, xi)
% 36.16/5.78 | |
% 36.16/5.78 | | GROUND_INST: instantiating (4) with xi, xj, all_69_1, simplifying with (5),
% 36.16/5.78 | | (6), (7), (8), (12), (15) gives:
% 36.16/5.78 | | (19) sdtlseqdt0(xi, xj)
% 36.16/5.78 | |
% 36.16/5.78 | | GROUND_INST: instantiating (3) with xi, xj, simplifying with (5), (6), (7),
% 36.16/5.78 | | (8), (18), (19) gives:
% 36.16/5.78 | | (20) xj = xi
% 36.16/5.78 | |
% 36.16/5.78 | | REDUCE: (11), (20) imply:
% 36.16/5.78 | | (21) $false
% 36.16/5.78 | |
% 36.16/5.78 | | CLOSE: (21) is inconsistent.
% 36.16/5.78 | |
% 36.16/5.78 | End of split
% 36.16/5.78 |
% 36.16/5.78 End of proof
% 36.16/5.78 % SZS output end Proof for theBenchmark
% 36.16/5.79
% 36.16/5.79 5192ms
%------------------------------------------------------------------------------