TSTP Solution File: NUM551+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM551+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n002.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 11:48:34 EDT 2023
% Result : Theorem 27.14s 4.29s
% Output : Proof 34.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM551+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n002.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 12:18:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.62 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.85/1.20 Prover 4: Preprocessing ...
% 3.85/1.20 Prover 1: Preprocessing ...
% 3.85/1.24 Prover 3: Preprocessing ...
% 3.85/1.24 Prover 0: Preprocessing ...
% 3.85/1.24 Prover 2: Preprocessing ...
% 3.85/1.24 Prover 5: Preprocessing ...
% 3.85/1.24 Prover 6: Preprocessing ...
% 10.00/2.07 Prover 1: Constructing countermodel ...
% 10.20/2.09 Prover 3: Constructing countermodel ...
% 10.64/2.15 Prover 6: Proving ...
% 10.84/2.17 Prover 5: Constructing countermodel ...
% 11.70/2.30 Prover 2: Proving ...
% 13.29/2.58 Prover 4: Constructing countermodel ...
% 14.53/2.67 Prover 0: Proving ...
% 27.14/4.28 Prover 3: proved (3653ms)
% 27.14/4.28
% 27.14/4.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 27.14/4.29
% 27.14/4.30 Prover 5: stopped
% 27.14/4.30 Prover 6: stopped
% 27.14/4.30 Prover 0: stopped
% 27.14/4.30 Prover 2: stopped
% 27.14/4.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 27.14/4.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.14/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.14/4.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.14/4.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 28.86/4.53 Prover 7: Preprocessing ...
% 28.86/4.58 Prover 8: Preprocessing ...
% 28.86/4.60 Prover 11: Preprocessing ...
% 29.64/4.61 Prover 13: Preprocessing ...
% 29.64/4.61 Prover 10: Preprocessing ...
% 30.35/4.71 Prover 7: Constructing countermodel ...
% 30.35/4.76 Prover 8: Warning: ignoring some quantifiers
% 30.35/4.77 Prover 8: Constructing countermodel ...
% 31.09/4.79 Prover 10: Constructing countermodel ...
% 31.98/4.91 Prover 13: Constructing countermodel ...
% 32.68/5.10 Prover 11: Constructing countermodel ...
% 34.03/5.17 Prover 10: Found proof (size 23)
% 34.03/5.17 Prover 10: proved (873ms)
% 34.03/5.17 Prover 11: stopped
% 34.03/5.17 Prover 13: stopped
% 34.03/5.17 Prover 7: stopped
% 34.03/5.17 Prover 8: stopped
% 34.03/5.17 Prover 1: stopped
% 34.03/5.18 Prover 4: stopped
% 34.03/5.18
% 34.03/5.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.03/5.18
% 34.03/5.18 % SZS output start Proof for theBenchmark
% 34.08/5.18 Assumptions after simplification:
% 34.08/5.18 ---------------------------------
% 34.08/5.18
% 34.08/5.18 (mDefEmp)
% 34.08/5.19 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 34.08/5.19 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 34.08/5.19 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 34.08/5.19
% 34.08/5.19 (mDefSeg)
% 34.20/5.22 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 34.20/5.22 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 34.20/5.22 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 34.20/5.22 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 34.20/5.22 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 34.20/5.22 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 34.20/5.22 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 34.20/5.22 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 34.20/5.22 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 34.20/5.22 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 34.20/5.22 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 34.20/5.22 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 34.20/5.22 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 34.20/5.22 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 34.20/5.22 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 34.20/5.22 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 34.20/5.22 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 34.20/5.22 | aSet0(v1))
% 34.20/5.22
% 34.20/5.22 (mEOfElem)
% 34.20/5.22 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 34.20/5.22 ~ aSet0(v0) | aElement0(v1))
% 34.20/5.22
% 34.20/5.22 (mSegZero)
% 34.20/5.22 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 34.20/5.22
% 34.20/5.22 (mZeroNum)
% 34.20/5.22 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 34.20/5.22
% 34.20/5.22 (m__)
% 34.20/5.22 $i(xQ) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0))
% 34.20/5.22
% 34.20/5.22 (m__2202_02)
% 34.20/5.22 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS)
% 34.20/5.22
% 34.20/5.22 (m__2291)
% 34.20/5.22 sbrdtbr0(xQ) = xk & $i(xQ) & $i(xk) & isFinite0(xQ) & aSet0(xQ)
% 34.20/5.22
% 34.20/5.22 (m__2313)
% 34.27/5.22 ~ (xQ = slcrc0) & $i(xQ) & $i(slcrc0)
% 34.27/5.22
% 34.27/5.22 Further assumptions not needed in the proof:
% 34.27/5.22 --------------------------------------------
% 34.27/5.22 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 34.27/5.22 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 34.27/5.22 mDefCons, mDefDiff, mDefMax, mDefMin, mDefSel, mDefSub, mDiffCons, mElmSort,
% 34.27/5.22 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, mLessASymm,
% 34.27/5.22 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet,
% 34.27/5.22 mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSelCSet,
% 34.27/5.22 mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 34.27/5.22 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, m__2202, m__2227, m__2256, m__2270
% 34.27/5.22
% 34.27/5.22 Those formulas are unsatisfiable:
% 34.27/5.22 ---------------------------------
% 34.27/5.22
% 34.27/5.22 Begin of proof
% 34.27/5.22 |
% 34.27/5.22 | ALPHA: (mDefEmp) implies:
% 34.27/5.22 | (1) ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] :
% 34.27/5.22 | ($i(v1) & aElementOf0(v1, v0)))
% 34.27/5.22 |
% 34.27/5.22 | ALPHA: (mZeroNum) implies:
% 34.27/5.22 | (2) aElementOf0(sz00, szNzAzT0)
% 34.27/5.22 |
% 34.27/5.22 | ALPHA: (mDefSeg) implies:
% 34.27/5.23 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) =
% 34.27/5.23 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~
% 34.27/5.23 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 34.27/5.23 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 34.27/5.23 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 34.27/5.23 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 34.27/5.23 | aElementOf0(v3, szNzAzT0)))))
% 34.27/5.23 |
% 34.27/5.23 | ALPHA: (mSegZero) implies:
% 34.27/5.23 | (4) slbdtrb0(sz00) = slcrc0
% 34.27/5.23 |
% 34.27/5.23 | ALPHA: (m__2202_02) implies:
% 34.27/5.23 | (5) $i(sz00)
% 34.27/5.23 |
% 34.27/5.23 | ALPHA: (m__2291) implies:
% 34.27/5.23 | (6) aSet0(xQ)
% 34.27/5.23 |
% 34.27/5.23 | ALPHA: (m__2313) implies:
% 34.27/5.23 | (7) ~ (xQ = slcrc0)
% 34.27/5.23 |
% 34.27/5.23 | ALPHA: (m__) implies:
% 34.27/5.23 | (8) $i(xQ)
% 34.27/5.23 | (9) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, xQ) | ~ aElement0(v0))
% 34.27/5.23 |
% 34.27/5.23 | GROUND_INST: instantiating (1) with xQ, simplifying with (6), (8) gives:
% 34.27/5.23 | (10) xQ = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ))
% 34.27/5.23 |
% 34.27/5.23 | GROUND_INST: instantiating (3) with sz00, slcrc0, xQ, simplifying with (2),
% 34.27/5.23 | (4), (5), (6), (8) gives:
% 34.27/5.23 | (11) xQ = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~
% 34.27/5.23 | aElementOf0(v0, xQ) | ~ aElementOf0(v0, szNzAzT0) |
% 34.27/5.23 | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) &
% 34.27/5.23 | (aElementOf0(v0, xQ) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 34.27/5.23 | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 34.27/5.23 |
% 34.27/5.23 | BETA: splitting (10) gives:
% 34.27/5.23 |
% 34.27/5.23 | Case 1:
% 34.27/5.23 | |
% 34.27/5.23 | | (12) xQ = slcrc0
% 34.27/5.23 | |
% 34.27/5.23 | | REDUCE: (7), (12) imply:
% 34.27/5.23 | | (13) $false
% 34.27/5.23 | |
% 34.27/5.23 | | CLOSE: (13) is inconsistent.
% 34.27/5.23 | |
% 34.27/5.23 | Case 2:
% 34.27/5.23 | |
% 34.27/5.23 | | (14) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xQ))
% 34.27/5.23 | |
% 34.27/5.23 | | DELTA: instantiating (14) with fresh symbol all_87_0 gives:
% 34.27/5.23 | | (15) $i(all_87_0) & aElementOf0(all_87_0, xQ)
% 34.27/5.23 | |
% 34.27/5.23 | | ALPHA: (15) implies:
% 34.27/5.23 | | (16) aElementOf0(all_87_0, xQ)
% 34.27/5.23 | | (17) $i(all_87_0)
% 34.27/5.23 | |
% 34.27/5.23 | | BETA: splitting (11) gives:
% 34.27/5.23 | |
% 34.27/5.23 | | Case 1:
% 34.27/5.23 | | |
% 34.27/5.23 | | | (18) xQ = slcrc0
% 34.27/5.23 | | |
% 34.27/5.23 | | | REDUCE: (7), (18) imply:
% 34.27/5.23 | | | (19) $false
% 34.27/5.23 | | |
% 34.27/5.23 | | | CLOSE: (19) is inconsistent.
% 34.27/5.24 | | |
% 34.27/5.24 | | Case 2:
% 34.27/5.24 | | |
% 34.27/5.24 | | |
% 34.27/5.24 | | | GROUND_INST: instantiating (mEOfElem) with xQ, all_87_0, simplifying with
% 34.27/5.24 | | | (6), (8), (16), (17) gives:
% 34.27/5.24 | | | (20) aElement0(all_87_0)
% 34.27/5.24 | | |
% 34.27/5.24 | | | GROUND_INST: instantiating (9) with all_87_0, simplifying with (16), (17),
% 34.27/5.24 | | | (20) gives:
% 34.27/5.24 | | | (21) $false
% 34.27/5.24 | | |
% 34.27/5.24 | | | CLOSE: (21) is inconsistent.
% 34.27/5.24 | | |
% 34.27/5.24 | | End of split
% 34.27/5.24 | |
% 34.27/5.24 | End of split
% 34.27/5.24 |
% 34.27/5.24 End of proof
% 34.27/5.24 % SZS output end Proof for theBenchmark
% 34.27/5.24
% 34.27/5.24 4630ms
%------------------------------------------------------------------------------