TSTP Solution File: NUM540+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM540+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 11:48:29 EDT 2023
% Result : Theorem 78.52s 11.04s
% Output : Proof 79.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM540+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 10:45:47 EDT 2023
% 0.14/0.34 % 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/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.34/1.19 Prover 1: Preprocessing ...
% 3.34/1.19 Prover 4: Preprocessing ...
% 3.66/1.22 Prover 0: Preprocessing ...
% 3.66/1.22 Prover 6: Preprocessing ...
% 3.66/1.22 Prover 3: Preprocessing ...
% 3.66/1.22 Prover 2: Preprocessing ...
% 3.66/1.23 Prover 5: Preprocessing ...
% 8.97/2.06 Prover 1: Constructing countermodel ...
% 8.97/2.07 Prover 5: Constructing countermodel ...
% 8.97/2.08 Prover 3: Constructing countermodel ...
% 9.52/2.13 Prover 2: Proving ...
% 10.55/2.18 Prover 6: Proving ...
% 12.27/2.44 Prover 4: Constructing countermodel ...
% 13.53/2.61 Prover 0: Proving ...
% 73.85/10.36 Prover 2: stopped
% 73.85/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.25/10.45 Prover 7: Preprocessing ...
% 74.80/10.56 Prover 7: Constructing countermodel ...
% 78.16/10.96 Prover 7: Found proof (size 21)
% 78.52/11.02 Prover 7: proved (626ms)
% 78.52/11.02 Prover 0: stopped
% 78.52/11.02 Prover 3: stopped
% 78.52/11.02 Prover 5: stopped
% 78.52/11.03 Prover 1: stopped
% 78.52/11.03 Prover 4: stopped
% 78.52/11.03 Prover 6: stopped
% 78.52/11.03
% 78.52/11.04 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 78.52/11.04
% 78.52/11.04 % SZS output start Proof for theBenchmark
% 78.52/11.04 Assumptions after simplification:
% 78.52/11.04 ---------------------------------
% 79.02/11.04
% 79.02/11.04 (mDefEmp)
% 79.02/11.05 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 79.02/11.05 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 79.02/11.05 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 79.02/11.05
% 79.02/11.05 (mDefSeg)
% 79.14/11.08 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 79.14/11.08 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 79.14/11.08 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 79.14/11.08 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 79.14/11.08 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 79.14/11.08 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 79.14/11.08 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 79.14/11.08 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 79.14/11.08 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 79.14/11.08 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 79.14/11.08 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 79.14/11.08 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 79.14/11.08 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 79.14/11.08 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 79.14/11.08 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 79.14/11.08 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 79.14/11.08 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 79.14/11.08 | aSet0(v1))
% 79.14/11.08
% 79.14/11.08 (mNoScLessZr)
% 79.14/11.08 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 79.14/11.08 v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0))
% 79.14/11.08
% 79.14/11.08 (mZeroNum)
% 79.14/11.08 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 79.14/11.08
% 79.14/11.08 (m__)
% 79.14/11.08 $i(sz00) & $i(slcrc0) & ? [v0: $i] : ( ~ (v0 = slcrc0) & slbdtrb0(sz00) = v0
% 79.14/11.08 & $i(v0))
% 79.14/11.08
% 79.14/11.08 Further assumptions not needed in the proof:
% 79.14/11.08 --------------------------------------------
% 79.14/11.08 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 79.14/11.08 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 79.14/11.08 mDefDiff, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort, mEmpFin,
% 79.14/11.08 mFConsSet, mFDiffSet, mFinRel, mIH, mIHSort, mLessASymm, mLessRefl, mLessRel,
% 79.14/11.08 mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet, mNatExtra, mNatNSucc,
% 79.14/11.08 mSegFin, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc,
% 79.14/11.08 mSuccLess, mSuccNum, mZeroLess
% 79.14/11.08
% 79.14/11.08 Those formulas are unsatisfiable:
% 79.14/11.08 ---------------------------------
% 79.14/11.08
% 79.14/11.08 Begin of proof
% 79.14/11.08 |
% 79.14/11.08 | ALPHA: (mDefEmp) implies:
% 79.14/11.08 | (1) aSet0(slcrc0)
% 79.14/11.08 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 79.14/11.08 |
% 79.14/11.08 | ALPHA: (mZeroNum) implies:
% 79.14/11.08 | (3) aElementOf0(sz00, szNzAzT0)
% 79.14/11.08 |
% 79.14/11.08 | ALPHA: (mNoScLessZr) implies:
% 79.14/11.08 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 79.14/11.08 | ~ sdtlseqdt0(v1, sz00) | ~ aElementOf0(v0, szNzAzT0))
% 79.14/11.08 |
% 79.14/11.08 | ALPHA: (mDefSeg) implies:
% 79.14/11.09 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) =
% 79.14/11.09 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~
% 79.14/11.09 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 79.14/11.09 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 79.14/11.09 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 79.14/11.09 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 79.14/11.09 | aElementOf0(v3, szNzAzT0)))))
% 79.14/11.09 |
% 79.14/11.09 | ALPHA: (m__) implies:
% 79.14/11.09 | (6) $i(slcrc0)
% 79.14/11.09 | (7) $i(sz00)
% 79.14/11.09 | (8) ? [v0: $i] : ( ~ (v0 = slcrc0) & slbdtrb0(sz00) = v0 & $i(v0))
% 79.14/11.09 |
% 79.14/11.09 | DELTA: instantiating (8) with fresh symbol all_45_0 gives:
% 79.14/11.09 | (9) ~ (all_45_0 = slcrc0) & slbdtrb0(sz00) = all_45_0 & $i(all_45_0)
% 79.14/11.09 |
% 79.14/11.09 | ALPHA: (9) implies:
% 79.14/11.09 | (10) ~ (all_45_0 = slcrc0)
% 79.14/11.09 | (11) slbdtrb0(sz00) = all_45_0
% 79.14/11.09 |
% 79.14/11.09 | GROUND_INST: instantiating (5) with sz00, all_45_0, slcrc0, simplifying with
% 79.14/11.09 | (1), (3), (6), (7), (11) gives:
% 79.14/11.09 | (12) all_45_0 = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~
% 79.14/11.09 | aElementOf0(v0, szNzAzT0) | ~ aElementOf0(v0, slcrc0) |
% 79.14/11.09 | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) &
% 79.14/11.09 | (aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 79.14/11.09 | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 79.14/11.09 |
% 79.14/11.09 | BETA: splitting (12) gives:
% 79.14/11.09 |
% 79.14/11.09 | Case 1:
% 79.14/11.09 | |
% 79.14/11.09 | | (13) all_45_0 = slcrc0
% 79.14/11.09 | |
% 79.14/11.09 | | REDUCE: (10), (13) imply:
% 79.14/11.09 | | (14) $false
% 79.14/11.10 | |
% 79.14/11.10 | | CLOSE: (14) is inconsistent.
% 79.14/11.10 | |
% 79.14/11.10 | Case 2:
% 79.14/11.10 | |
% 79.14/11.10 | | (15) ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~ aElementOf0(v0, szNzAzT0)
% 79.14/11.10 | | | ~ aElementOf0(v0, slcrc0) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 79.14/11.10 | | ~ sdtlseqdt0(v1, sz00))) & (aElementOf0(v0, slcrc0) |
% 79.14/11.10 | | (szszuzczcdt0(v0) = v1 & $i(v1) & sdtlseqdt0(v1, sz00) &
% 79.14/11.10 | | aElementOf0(v0, szNzAzT0))))
% 79.14/11.10 | |
% 79.14/11.10 | | DELTA: instantiating (15) with fresh symbols all_70_0, all_70_1 gives:
% 79.14/11.10 | | (16) $i(all_70_1) & ( ~ aElementOf0(all_70_1, szNzAzT0) | ~
% 79.14/11.10 | | aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0
% 79.14/11.10 | | & $i(all_70_0) & ~ sdtlseqdt0(all_70_0, sz00))) &
% 79.14/11.10 | | (aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0
% 79.14/11.10 | | & $i(all_70_0) & sdtlseqdt0(all_70_0, sz00) &
% 79.14/11.10 | | aElementOf0(all_70_1, szNzAzT0)))
% 79.14/11.10 | |
% 79.14/11.10 | | ALPHA: (16) implies:
% 79.14/11.10 | | (17) $i(all_70_1)
% 79.14/11.10 | | (18) aElementOf0(all_70_1, slcrc0) | (szszuzczcdt0(all_70_1) = all_70_0 &
% 79.14/11.10 | | $i(all_70_0) & sdtlseqdt0(all_70_0, sz00) & aElementOf0(all_70_1,
% 79.14/11.10 | | szNzAzT0))
% 79.14/11.10 | |
% 79.14/11.10 | | BETA: splitting (18) gives:
% 79.14/11.10 | |
% 79.14/11.10 | | Case 1:
% 79.14/11.10 | | |
% 79.14/11.10 | | | (19) aElementOf0(all_70_1, slcrc0)
% 79.14/11.10 | | |
% 79.14/11.10 | | | GROUND_INST: instantiating (2) with all_70_1, simplifying with (17), (19)
% 79.14/11.10 | | | gives:
% 79.14/11.10 | | | (20) $false
% 79.14/11.10 | | |
% 79.14/11.10 | | | CLOSE: (20) is inconsistent.
% 79.14/11.10 | | |
% 79.14/11.10 | | Case 2:
% 79.14/11.10 | | |
% 79.14/11.10 | | | (21) szszuzczcdt0(all_70_1) = all_70_0 & $i(all_70_0) &
% 79.14/11.10 | | | sdtlseqdt0(all_70_0, sz00) & aElementOf0(all_70_1, szNzAzT0)
% 79.14/11.10 | | |
% 79.14/11.10 | | | ALPHA: (21) implies:
% 79.14/11.10 | | | (22) aElementOf0(all_70_1, szNzAzT0)
% 79.14/11.10 | | | (23) sdtlseqdt0(all_70_0, sz00)
% 79.14/11.10 | | | (24) szszuzczcdt0(all_70_1) = all_70_0
% 79.14/11.10 | | |
% 79.14/11.10 | | | GROUND_INST: instantiating (4) with all_70_1, all_70_0, simplifying with
% 79.14/11.10 | | | (17), (22), (23), (24) gives:
% 79.14/11.10 | | | (25) $false
% 79.14/11.10 | | |
% 79.14/11.10 | | | CLOSE: (25) is inconsistent.
% 79.14/11.10 | | |
% 79.14/11.10 | | End of split
% 79.14/11.10 | |
% 79.14/11.10 | End of split
% 79.14/11.10 |
% 79.14/11.10 End of proof
% 79.14/11.10 % SZS output end Proof for theBenchmark
% 79.14/11.10
% 79.14/11.10 10505ms
%------------------------------------------------------------------------------