TSTP Solution File: NUM541+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM541+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 : n008.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 11:48:30 EDT 2023
% Result : Theorem 38.04s 5.88s
% Output : Proof 48.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM541+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Aug 25 17:54:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.61 ________ _____
% 0.21/0.61 ___ __ \_________(_)________________________________
% 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.61
% 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.61 (2023-06-19)
% 0.21/0.61
% 0.21/0.61 (c) Philipp Rümmer, 2009-2023
% 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.61 Amanda Stjerna.
% 0.21/0.61 Free software under BSD-3-Clause.
% 0.21/0.61
% 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.61
% 0.21/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.42/1.23 Prover 4: Preprocessing ...
% 3.42/1.23 Prover 1: Preprocessing ...
% 3.42/1.27 Prover 0: Preprocessing ...
% 3.42/1.27 Prover 3: Preprocessing ...
% 3.42/1.27 Prover 2: Preprocessing ...
% 3.42/1.27 Prover 6: Preprocessing ...
% 3.42/1.27 Prover 5: Preprocessing ...
% 9.23/2.09 Prover 1: Constructing countermodel ...
% 9.23/2.09 Prover 5: Constructing countermodel ...
% 9.23/2.09 Prover 3: Constructing countermodel ...
% 9.66/2.10 Prover 6: Proving ...
% 10.12/2.17 Prover 2: Proving ...
% 10.76/2.34 Prover 4: Constructing countermodel ...
% 11.99/2.53 Prover 0: Proving ...
% 38.04/5.88 Prover 3: proved (5236ms)
% 38.04/5.88
% 38.04/5.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.04/5.88
% 38.04/5.88 Prover 5: stopped
% 38.04/5.88 Prover 0: stopped
% 38.04/5.88 Prover 2: stopped
% 38.04/5.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 38.04/5.90 Prover 6: stopped
% 38.04/5.90 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 38.04/5.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 38.04/5.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 38.04/5.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 38.83/6.08 Prover 8: Preprocessing ...
% 40.32/6.16 Prover 10: Preprocessing ...
% 40.32/6.17 Prover 7: Preprocessing ...
% 40.32/6.18 Prover 13: Preprocessing ...
% 40.32/6.18 Prover 11: Preprocessing ...
% 41.53/6.30 Prover 7: Constructing countermodel ...
% 41.53/6.31 Prover 8: Warning: ignoring some quantifiers
% 41.53/6.32 Prover 8: Constructing countermodel ...
% 41.53/6.34 Prover 10: Constructing countermodel ...
% 42.12/6.38 Prover 13: Constructing countermodel ...
% 43.88/6.73 Prover 11: Constructing countermodel ...
% 47.83/7.14 Prover 10: Found proof (size 43)
% 48.12/7.14 Prover 10: proved (1241ms)
% 48.12/7.14 Prover 7: stopped
% 48.12/7.14 Prover 8: stopped
% 48.12/7.14 Prover 1: stopped
% 48.12/7.14 Prover 11: stopped
% 48.12/7.14 Prover 13: stopped
% 48.12/7.15 Prover 4: stopped
% 48.12/7.15
% 48.12/7.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.12/7.15
% 48.12/7.15 % SZS output start Proof for theBenchmark
% 48.12/7.15 Assumptions after simplification:
% 48.12/7.15 ---------------------------------
% 48.12/7.15
% 48.12/7.15 (mDefSeg)
% 48.12/7.18 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 48.12/7.18 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 48.12/7.18 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 48.12/7.18 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 48.12/7.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 48.12/7.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 48.12/7.18 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 48.12/7.18 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 48.12/7.18 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 48.12/7.18 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 48.12/7.18 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 48.12/7.18 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 48.12/7.18 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 48.12/7.18 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 48.12/7.18 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 48.12/7.18 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 48.12/7.18 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 48.12/7.18 | aSet0(v1))
% 48.12/7.18
% 48.12/7.18 (mLessASymm)
% 48.12/7.18 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) |
% 48.12/7.18 ~ sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1, szNzAzT0)
% 48.12/7.18 | ~ aElementOf0(v0, szNzAzT0))
% 48.12/7.18
% 48.12/7.18 (mLessRefl)
% 48.12/7.18 $i(szNzAzT0) & ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 48.12/7.18 sdtlseqdt0(v0, v0))
% 48.12/7.18
% 48.12/7.18 (mLessSucc)
% 48.12/7.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~
% 48.12/7.19 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v0, v1))
% 48.12/7.19
% 48.12/7.19 (mLessTotal)
% 48.12/7.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1)
% 48.12/7.19 = v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 48.12/7.19 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1))
% 48.12/7.19
% 48.12/7.19 (mLessTrans)
% 48.12/7.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~
% 48.12/7.19 $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~
% 48.12/7.19 aElementOf0(v2, szNzAzT0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 48.12/7.19 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v0, v2))
% 48.12/7.19
% 48.12/7.19 (mSuccEquSucc)
% 48.12/7.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.12/7.19 (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 48.12/7.19 | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 48.12/7.19
% 48.12/7.19 (mSuccLess)
% 48.12/7.19 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 48.12/7.19 (szszuzczcdt0(v1) = v3) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~ $i(v0)
% 48.12/7.19 | ~ sdtlseqdt0(v2, v3) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0,
% 48.12/7.19 szNzAzT0) | sdtlseqdt0(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 48.12/7.19 : ! [v3: $i] : ( ~ (szszuzczcdt0(v1) = v3) | ~ (szszuzczcdt0(v0) = v2) | ~
% 48.12/7.19 $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1, szNzAzT0) |
% 48.12/7.19 ~ aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v3))
% 48.12/7.19
% 48.12/7.19 (mSuccNum)
% 48.12/7.19 $i(sz00) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) =
% 48.12/7.19 v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1,
% 48.12/7.19 szNzAzT0)) & ! [v0: $i] : ( ~ (szszuzczcdt0(v0) = sz00) | ~ $i(v0) | ~
% 48.12/7.19 aElementOf0(v0, szNzAzT0))
% 48.12/7.19
% 48.12/7.19 (m__)
% 48.12/7.19 $i(xn) & $i(xm) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 48.12/7.19 (slbdtrb0(v1) = v2 & szszuzczcdt0(xn) = v1 & szszuzczcdt0(xm) = v0 & $i(v2) &
% 48.12/7.19 $i(v1) & $i(v0) & (( ~ (xn = xm) & slbdtrb0(xn) = v3 & $i(v3) &
% 48.12/7.19 sdtlseqdt0(v0, v1) & aElementOf0(xm, v2) & ~ sdtlseqdt0(v0, xn) & ~
% 48.12/7.19 aElementOf0(xm, v3)) | ( ~ sdtlseqdt0(v0, v1) & ~ aElementOf0(xm, v2) &
% 48.12/7.19 (xn = xm | (slbdtrb0(xn) = v3 & $i(v3) & sdtlseqdt0(v0, xn) &
% 48.12/7.19 aElementOf0(xm, v3))))))
% 48.12/7.19
% 48.12/7.19 (m__1936)
% 48.12/7.19 $i(xn) & $i(xm) & $i(szNzAzT0) & aElementOf0(xn, szNzAzT0) & aElementOf0(xm,
% 48.12/7.19 szNzAzT0)
% 48.12/7.19
% 48.12/7.19 Further assumptions not needed in the proof:
% 48.12/7.19 --------------------------------------------
% 48.12/7.19 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 48.12/7.19 mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefCons,
% 48.12/7.19 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort,
% 48.12/7.19 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mIH, mIHSort, mLessRel, mMinMin,
% 48.12/7.19 mNATSet, mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegZero, mSetSort,
% 48.12/7.19 mSubASymm, mSubFSet, mSubRefl, mSubTrans, mZeroLess, mZeroNum
% 48.12/7.19
% 48.12/7.19 Those formulas are unsatisfiable:
% 48.12/7.19 ---------------------------------
% 48.12/7.19
% 48.12/7.19 Begin of proof
% 48.12/7.19 |
% 48.12/7.20 | ALPHA: (mSuccNum) implies:
% 48.12/7.20 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 48.12/7.20 | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v1, szNzAzT0))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mSuccEquSucc) implies:
% 48.12/7.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 48.12/7.20 | (szszuzczcdt0(v1) = v2) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~
% 48.12/7.20 | $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mSuccLess) implies:
% 48.12/7.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 48.12/7.20 | (szszuzczcdt0(v1) = v3) | ~ (szszuzczcdt0(v0) = v2) | ~ $i(v1) | ~
% 48.12/7.20 | $i(v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1, szNzAzT0) | ~
% 48.12/7.20 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v3))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mLessSucc) implies:
% 48.12/7.20 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (szszuzczcdt0(v0) = v1) | ~ $i(v0) |
% 48.12/7.20 | ~ aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v0, v1))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mLessRefl) implies:
% 48.12/7.20 | (5) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) |
% 48.12/7.20 | sdtlseqdt0(v0, v0))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mLessASymm) implies:
% 48.12/7.20 | (6) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~
% 48.12/7.20 | sdtlseqdt0(v1, v0) | ~ sdtlseqdt0(v0, v1) | ~ aElementOf0(v1,
% 48.12/7.20 | szNzAzT0) | ~ aElementOf0(v0, szNzAzT0))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mLessTrans) implies:
% 48.12/7.20 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 48.12/7.20 | $i(v0) | ~ sdtlseqdt0(v1, v2) | ~ sdtlseqdt0(v0, v1) | ~
% 48.12/7.20 | aElementOf0(v2, szNzAzT0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 48.12/7.20 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v0, v2))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mLessTotal) implies:
% 48.12/7.20 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (szszuzczcdt0(v1) = v2) |
% 48.12/7.20 | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~
% 48.12/7.20 | aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v2, v0) | sdtlseqdt0(v0, v1))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (mDefSeg) implies:
% 48.12/7.20 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 48.12/7.20 | (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~
% 48.12/7.20 | $i(v1) | ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2,
% 48.12/7.20 | szNzAzT0) | ~ aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1))
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (m__1936) implies:
% 48.12/7.20 | (10) aElementOf0(xm, szNzAzT0)
% 48.12/7.20 | (11) aElementOf0(xn, szNzAzT0)
% 48.12/7.20 |
% 48.12/7.20 | ALPHA: (m__) implies:
% 48.12/7.20 | (12) $i(xm)
% 48.12/7.20 | (13) $i(xn)
% 48.12/7.21 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : (slbdtrb0(v1)
% 48.12/7.21 | = v2 & szszuzczcdt0(xn) = v1 & szszuzczcdt0(xm) = v0 & $i(v2) &
% 48.12/7.21 | $i(v1) & $i(v0) & (( ~ (xn = xm) & slbdtrb0(xn) = v3 & $i(v3) &
% 48.12/7.21 | sdtlseqdt0(v0, v1) & aElementOf0(xm, v2) & ~ sdtlseqdt0(v0, xn)
% 48.12/7.21 | & ~ aElementOf0(xm, v3)) | ( ~ sdtlseqdt0(v0, v1) & ~
% 48.12/7.21 | aElementOf0(xm, v2) & (xn = xm | (slbdtrb0(xn) = v3 & $i(v3) &
% 48.12/7.21 | sdtlseqdt0(v0, xn) & aElementOf0(xm, v3))))))
% 48.12/7.21 |
% 48.12/7.21 | DELTA: instantiating (14) with fresh symbols all_45_0, all_45_1, all_45_2,
% 48.12/7.21 | all_45_3 gives:
% 48.12/7.21 | (15) slbdtrb0(all_45_2) = all_45_1 & szszuzczcdt0(xn) = all_45_2 &
% 48.12/7.21 | szszuzczcdt0(xm) = all_45_3 & $i(all_45_1) & $i(all_45_2) &
% 48.12/7.21 | $i(all_45_3) & (( ~ (xn = xm) & slbdtrb0(xn) = all_45_0 & $i(all_45_0)
% 48.12/7.21 | & sdtlseqdt0(all_45_3, all_45_2) & aElementOf0(xm, all_45_1) & ~
% 48.12/7.21 | sdtlseqdt0(all_45_3, xn) & ~ aElementOf0(xm, all_45_0)) | ( ~
% 48.12/7.21 | sdtlseqdt0(all_45_3, all_45_2) & ~ aElementOf0(xm, all_45_1) &
% 48.12/7.21 | (xn = xm | (slbdtrb0(xn) = all_45_0 & $i(all_45_0) &
% 48.12/7.21 | sdtlseqdt0(all_45_3, xn) & aElementOf0(xm, all_45_0)))))
% 48.12/7.21 |
% 48.12/7.21 | ALPHA: (15) implies:
% 48.12/7.21 | (16) $i(all_45_3)
% 48.12/7.21 | (17) $i(all_45_2)
% 48.12/7.21 | (18) $i(all_45_1)
% 48.12/7.21 | (19) szszuzczcdt0(xm) = all_45_3
% 48.12/7.21 | (20) szszuzczcdt0(xn) = all_45_2
% 48.12/7.21 | (21) slbdtrb0(all_45_2) = all_45_1
% 48.12/7.21 | (22) ( ~ (xn = xm) & slbdtrb0(xn) = all_45_0 & $i(all_45_0) &
% 48.12/7.21 | sdtlseqdt0(all_45_3, all_45_2) & aElementOf0(xm, all_45_1) & ~
% 48.12/7.21 | sdtlseqdt0(all_45_3, xn) & ~ aElementOf0(xm, all_45_0)) | ( ~
% 48.12/7.21 | sdtlseqdt0(all_45_3, all_45_2) & ~ aElementOf0(xm, all_45_1) & (xn
% 48.12/7.21 | = xm | (slbdtrb0(xn) = all_45_0 & $i(all_45_0) &
% 48.12/7.21 | sdtlseqdt0(all_45_3, xn) & aElementOf0(xm, all_45_0))))
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (5) with xn, simplifying with (11), (13) gives:
% 48.12/7.21 | (23) sdtlseqdt0(xn, xn)
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (1) with xm, all_45_3, simplifying with (10), (12),
% 48.12/7.21 | (19) gives:
% 48.12/7.21 | (24) aElementOf0(all_45_3, szNzAzT0)
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (4) with xn, all_45_2, simplifying with (11), (13),
% 48.12/7.21 | (20) gives:
% 48.12/7.21 | (25) sdtlseqdt0(xn, all_45_2)
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (1) with xn, all_45_2, simplifying with (11), (13),
% 48.12/7.21 | (20) gives:
% 48.12/7.21 | (26) aElementOf0(all_45_2, szNzAzT0)
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (8) with all_45_3, xn, all_45_2, simplifying with
% 48.12/7.21 | (11), (13), (16), (20), (24) gives:
% 48.12/7.21 | (27) sdtlseqdt0(all_45_2, all_45_3) | sdtlseqdt0(all_45_3, xn)
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (3) with xn, xn, all_45_2, all_45_2, simplifying
% 48.12/7.21 | with (11), (13), (20), (23) gives:
% 48.12/7.21 | (28) sdtlseqdt0(all_45_2, all_45_2)
% 48.12/7.21 |
% 48.12/7.21 | GROUND_INST: instantiating (9) with all_45_2, all_45_1, xn, all_45_2,
% 48.12/7.21 | simplifying with (11), (13), (17), (18), (20), (21), (26), (28)
% 48.12/7.21 | gives:
% 48.12/7.22 | (29) aElementOf0(xn, all_45_1)
% 48.12/7.22 |
% 48.12/7.22 | BETA: splitting (22) gives:
% 48.12/7.22 |
% 48.12/7.22 | Case 1:
% 48.12/7.22 | |
% 48.12/7.22 | | (30) ~ (xn = xm) & slbdtrb0(xn) = all_45_0 & $i(all_45_0) &
% 48.12/7.22 | | sdtlseqdt0(all_45_3, all_45_2) & aElementOf0(xm, all_45_1) & ~
% 48.12/7.22 | | sdtlseqdt0(all_45_3, xn) & ~ aElementOf0(xm, all_45_0)
% 48.12/7.22 | |
% 48.12/7.22 | | ALPHA: (30) implies:
% 48.12/7.22 | | (31) ~ (xn = xm)
% 48.12/7.22 | | (32) ~ sdtlseqdt0(all_45_3, xn)
% 48.12/7.22 | | (33) sdtlseqdt0(all_45_3, all_45_2)
% 48.12/7.22 | |
% 48.12/7.22 | | BETA: splitting (27) gives:
% 48.12/7.22 | |
% 48.12/7.22 | | Case 1:
% 48.12/7.22 | | |
% 48.12/7.22 | | | (34) sdtlseqdt0(all_45_2, all_45_3)
% 48.12/7.22 | | |
% 48.12/7.22 | | | GROUND_INST: instantiating (6) with all_45_3, all_45_2, simplifying with
% 48.12/7.22 | | | (16), (17), (24), (26), (33), (34) gives:
% 48.12/7.22 | | | (35) all_45_2 = all_45_3
% 48.12/7.22 | | |
% 48.12/7.22 | | | REDUCE: (20), (35) imply:
% 48.12/7.22 | | | (36) szszuzczcdt0(xn) = all_45_3
% 48.12/7.22 | | |
% 48.12/7.22 | | | GROUND_INST: instantiating (2) with xm, xn, all_45_3, simplifying with
% 48.12/7.22 | | | (10), (11), (12), (13), (19), (36) gives:
% 48.12/7.22 | | | (37) xn = xm
% 48.12/7.22 | | |
% 48.12/7.22 | | | REDUCE: (31), (37) imply:
% 48.12/7.22 | | | (38) $false
% 48.12/7.22 | | |
% 48.12/7.22 | | | CLOSE: (38) is inconsistent.
% 48.12/7.22 | | |
% 48.12/7.22 | | Case 2:
% 48.12/7.22 | | |
% 48.12/7.22 | | | (39) sdtlseqdt0(all_45_3, xn)
% 48.12/7.22 | | |
% 48.12/7.22 | | | PRED_UNIFY: (32), (39) imply:
% 48.12/7.22 | | | (40) $false
% 48.12/7.22 | | |
% 48.12/7.22 | | | CLOSE: (40) is inconsistent.
% 48.12/7.22 | | |
% 48.12/7.22 | | End of split
% 48.12/7.22 | |
% 48.12/7.22 | Case 2:
% 48.12/7.22 | |
% 48.12/7.22 | | (41) ~ sdtlseqdt0(all_45_3, all_45_2) & ~ aElementOf0(xm, all_45_1) &
% 48.12/7.22 | | (xn = xm | (slbdtrb0(xn) = all_45_0 & $i(all_45_0) &
% 48.12/7.22 | | sdtlseqdt0(all_45_3, xn) & aElementOf0(xm, all_45_0)))
% 48.12/7.22 | |
% 48.12/7.22 | | ALPHA: (41) implies:
% 48.12/7.22 | | (42) ~ aElementOf0(xm, all_45_1)
% 48.12/7.22 | | (43) ~ sdtlseqdt0(all_45_3, all_45_2)
% 48.12/7.22 | | (44) xn = xm | (slbdtrb0(xn) = all_45_0 & $i(all_45_0) &
% 48.12/7.22 | | sdtlseqdt0(all_45_3, xn) & aElementOf0(xm, all_45_0))
% 48.12/7.22 | |
% 48.12/7.22 | | BETA: splitting (44) gives:
% 48.12/7.22 | |
% 48.12/7.22 | | Case 1:
% 48.12/7.22 | | |
% 48.12/7.22 | | | (45) xn = xm
% 48.12/7.22 | | |
% 48.12/7.22 | | | REDUCE: (29), (45) imply:
% 48.12/7.22 | | | (46) aElementOf0(xm, all_45_1)
% 48.12/7.22 | | |
% 48.12/7.22 | | | PRED_UNIFY: (42), (46) imply:
% 48.12/7.22 | | | (47) $false
% 48.12/7.22 | | |
% 48.12/7.22 | | | CLOSE: (47) is inconsistent.
% 48.12/7.22 | | |
% 48.12/7.22 | | Case 2:
% 48.12/7.22 | | |
% 48.12/7.22 | | | (48) slbdtrb0(xn) = all_45_0 & $i(all_45_0) & sdtlseqdt0(all_45_3, xn)
% 48.12/7.22 | | | & aElementOf0(xm, all_45_0)
% 48.12/7.22 | | |
% 48.12/7.22 | | | ALPHA: (48) implies:
% 48.12/7.22 | | | (49) sdtlseqdt0(all_45_3, xn)
% 48.12/7.22 | | |
% 48.12/7.22 | | | GROUND_INST: instantiating (7) with all_45_3, xn, all_45_2, simplifying
% 48.12/7.22 | | | with (11), (13), (16), (17), (24), (25), (26), (43), (49)
% 48.12/7.22 | | | gives:
% 48.12/7.22 | | | (50) $false
% 48.12/7.22 | | |
% 48.12/7.22 | | | CLOSE: (50) is inconsistent.
% 48.12/7.22 | | |
% 48.12/7.22 | | End of split
% 48.12/7.22 | |
% 48.12/7.22 | End of split
% 48.12/7.22 |
% 48.12/7.22 End of proof
% 48.12/7.23 % SZS output end Proof for theBenchmark
% 48.12/7.23
% 48.12/7.23 6609ms
%------------------------------------------------------------------------------