TSTP Solution File: NUM538+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM538+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 : 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 22.18s 3.86s
% Output : Proof 30.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : NUM538+2 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Aug 25 14:41:47 EDT 2023
% 0.21/0.36 % CPUTime :
% 0.22/0.60 ________ _____
% 0.22/0.60 ___ __ \_________(_)________________________________
% 0.22/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.60
% 0.22/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.60 (2023-06-19)
% 0.22/0.60
% 0.22/0.60 (c) Philipp Rümmer, 2009-2023
% 0.22/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.60 Amanda Stjerna.
% 0.22/0.60 Free software under BSD-3-Clause.
% 0.22/0.60
% 0.22/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.60
% 0.22/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.62 Running up to 7 provers in parallel.
% 0.22/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.17/1.17 Prover 4: Preprocessing ...
% 3.17/1.17 Prover 1: Preprocessing ...
% 3.17/1.25 Prover 5: Preprocessing ...
% 3.17/1.25 Prover 6: Preprocessing ...
% 3.17/1.25 Prover 0: Preprocessing ...
% 3.17/1.25 Prover 2: Preprocessing ...
% 3.17/1.25 Prover 3: Preprocessing ...
% 8.99/2.05 Prover 5: Constructing countermodel ...
% 9.47/2.06 Prover 3: Constructing countermodel ...
% 9.47/2.08 Prover 1: Constructing countermodel ...
% 9.47/2.08 Prover 2: Proving ...
% 9.77/2.11 Prover 6: Proving ...
% 11.09/2.32 Prover 4: Constructing countermodel ...
% 11.95/2.53 Prover 0: Proving ...
% 22.18/3.84 Prover 0: proved (3218ms)
% 22.18/3.84
% 22.18/3.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.18/3.86
% 22.18/3.86 Prover 5: stopped
% 22.18/3.87 Prover 3: stopped
% 22.81/3.87 Prover 2: stopped
% 22.81/3.87 Prover 6: stopped
% 22.81/3.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.81/3.88 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.81/3.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.81/3.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.81/3.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 23.84/4.00 Prover 10: Preprocessing ...
% 23.84/4.00 Prover 11: Preprocessing ...
% 23.84/4.01 Prover 8: Preprocessing ...
% 23.84/4.02 Prover 7: Preprocessing ...
% 23.84/4.03 Prover 13: Preprocessing ...
% 24.34/4.13 Prover 10: Constructing countermodel ...
% 24.34/4.15 Prover 7: Constructing countermodel ...
% 25.27/4.21 Prover 8: Warning: ignoring some quantifiers
% 25.46/4.22 Prover 8: Constructing countermodel ...
% 25.46/4.22 Prover 13: Constructing countermodel ...
% 27.54/4.50 Prover 11: Constructing countermodel ...
% 29.59/4.78 Prover 7: Found proof (size 38)
% 29.59/4.79 Prover 7: proved (924ms)
% 29.59/4.79 Prover 11: stopped
% 29.59/4.79 Prover 8: stopped
% 29.59/4.79 Prover 13: stopped
% 29.59/4.79 Prover 4: stopped
% 29.59/4.79 Prover 10: stopped
% 29.59/4.79 Prover 1: stopped
% 29.59/4.79
% 29.59/4.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.59/4.79
% 29.59/4.79 % SZS output start Proof for theBenchmark
% 29.59/4.80 Assumptions after simplification:
% 29.59/4.80 ---------------------------------
% 29.59/4.80
% 29.59/4.80 (mCardCons)
% 29.59/4.82 ! [v0: $i] : ! [v1: $i] : ( ~ (sbrdtbr0(v0) = v1) | ~ $i(v0) | ~
% 29.59/4.82 isFinite0(v0) | ~ aSet0(v0) | ? [v2: $i] : (szszuzczcdt0(v1) = v2 & $i(v2)
% 29.59/4.82 & ! [v3: $i] : ! [v4: $i] : ( ~ (sdtpldt0(v0, v3) = v4) | ~ $i(v3) | ~
% 29.59/4.82 aElement0(v3) | sbrdtbr0(v4) = v2 | aElementOf0(v3, v0))))
% 29.59/4.82
% 29.59/4.82 (mCardEmpty)
% 29.59/4.83 $i(sz00) & $i(slcrc0) & ! [v0: $i] : (v0 = sz00 | ~ (sbrdtbr0(slcrc0) = v0)
% 29.59/4.83 | ~ aSet0(slcrc0)) & ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00)
% 29.59/4.83 | ~ $i(v0) | ~ aSet0(v0))
% 29.59/4.83
% 29.59/4.83 (mConsDiff)
% 29.59/4.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~
% 29.59/4.83 $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) | ~ aSet0(v0) | sdtpldt0(v2,
% 29.59/4.83 v1) = v0)
% 29.59/4.83
% 29.59/4.83 (mCountNFin_01)
% 29.59/4.83 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 29.59/4.83
% 29.59/4.83 (mDefCons)
% 29.59/4.83 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 29.59/4.83 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 29.59/4.83 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 29.59/4.83 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~
% 29.59/4.83 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 =
% 29.59/4.83 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.59/4.83 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~
% 29.59/4.83 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) |
% 29.59/4.83 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 29.59/4.83 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 29.59/4.83 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~
% 29.59/4.83 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 29.59/4.83 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 29.59/4.83 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~
% 29.59/4.83 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 29.59/4.83 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 29.59/4.84 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1:
% 29.59/4.84 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~
% 29.59/4.84 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 29.59/4.84
% 29.59/4.84 (mDefEmp)
% 29.59/4.84 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 29.59/4.84 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 29.59/4.84 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 29.59/4.84
% 29.59/4.84 (mEOfElem)
% 29.59/4.84 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 29.59/4.84 ~ aSet0(v0) | aElement0(v1))
% 29.59/4.84
% 29.59/4.84 (mFDiffSet)
% 29.59/4.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v1, v0) = v2) | ~
% 29.59/4.84 $i(v1) | ~ $i(v0) | ~ isFinite0(v1) | ~ aElement0(v0) | ~ aSet0(v1) |
% 29.59/4.84 isFinite0(v2))
% 29.59/4.84
% 29.59/4.84 (m__)
% 29.59/4.84 $i(xx) & $i(xS) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~
% 29.59/4.84 (v3 = v2) & sbrdtbr0(v0) = v1 & sbrdtbr0(xS) = v3 & szszuzczcdt0(v1) = v2 &
% 29.59/4.84 sdtmndt0(xS, xx) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & aSet0(v0) & ~
% 29.59/4.84 aElementOf0(xx, v0) & ! [v4: $i] : (v4 = xx | ~ $i(v4) | ~
% 29.59/4.84 aElementOf0(v4, xS) | ~ aElement0(v4) | aElementOf0(v4, v0)) & ! [v4:
% 29.59/4.84 $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) | aElementOf0(v4, xS)) & ! [v4:
% 29.59/4.84 $i] : ( ~ $i(v4) | ~ aElementOf0(v4, v0) | aElement0(v4)))
% 29.59/4.84
% 29.59/4.84 (m__1522)
% 29.59/4.84 $i(xS) & aSet0(xS)
% 29.59/4.84
% 29.59/4.84 (m__1522_02)
% 29.59/4.84 $i(xx) & $i(xS) & isFinite0(xS) & aElementOf0(xx, xS)
% 29.59/4.84
% 29.59/4.84 (function-axioms)
% 29.59/4.84 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 29.59/4.84 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 29.59/4.84 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 29.59/4.84 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 29.59/4.84 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : !
% 29.59/4.84 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 29.59/4.84 (szszuzczcdt0(v2) = v0))
% 29.59/4.84
% 29.59/4.84 Further assumptions not needed in the proof:
% 29.59/4.84 --------------------------------------------
% 29.59/4.84 mCConsSet, mCDiffSet, mCardNum, mCardS, mCntRel, mCountNFin, mDefDiff, mDefSub,
% 29.59/4.84 mDiffCons, mElmSort, mEmpFin, mFConsSet, mFinRel, mIH, mIHSort, mLessASymm,
% 29.59/4.84 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mNATSet, mNatExtra,
% 29.59/4.84 mNatNSucc, mNoScLessZr, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans,
% 29.59/4.84 mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum
% 29.59/4.84
% 29.59/4.84 Those formulas are unsatisfiable:
% 29.59/4.84 ---------------------------------
% 29.59/4.84
% 29.59/4.84 Begin of proof
% 29.59/4.84 |
% 29.59/4.84 | ALPHA: (mDefEmp) implies:
% 29.59/4.85 | (1) aSet0(slcrc0)
% 29.59/4.85 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (mCountNFin_01) implies:
% 29.59/4.85 | (3) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (mDefCons) implies:
% 29.59/4.85 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 29.59/4.85 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 29.59/4.85 | aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) &
% 29.59/4.85 | ( ~ aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~
% 29.59/4.85 | aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) &
% 29.59/4.85 | (v4 = v1 | aElementOf0(v4, v0))))))
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (mCardEmpty) implies:
% 29.59/4.85 | (5) $i(slcrc0)
% 29.59/4.85 | (6) ! [v0: $i] : (v0 = slcrc0 | ~ (sbrdtbr0(v0) = sz00) | ~ $i(v0) | ~
% 29.59/4.85 | aSet0(v0))
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (m__1522) implies:
% 29.59/4.85 | (7) aSet0(xS)
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (m__1522_02) implies:
% 29.59/4.85 | (8) aElementOf0(xx, xS)
% 29.59/4.85 | (9) isFinite0(xS)
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (m__) implies:
% 29.59/4.85 | (10) $i(xS)
% 29.59/4.85 | (11) $i(xx)
% 29.59/4.85 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v3 = v2)
% 29.59/4.85 | & sbrdtbr0(v0) = v1 & sbrdtbr0(xS) = v3 & szszuzczcdt0(v1) = v2 &
% 29.59/4.85 | sdtmndt0(xS, xx) = v0 & $i(v3) & $i(v2) & $i(v1) & $i(v0) &
% 29.59/4.85 | aSet0(v0) & ~ aElementOf0(xx, v0) & ! [v4: $i] : (v4 = xx | ~
% 29.59/4.85 | $i(v4) | ~ aElementOf0(v4, xS) | ~ aElement0(v4) |
% 29.59/4.85 | aElementOf0(v4, v0)) & ! [v4: $i] : ( ~ $i(v4) | ~
% 29.59/4.85 | aElementOf0(v4, v0) | aElementOf0(v4, xS)) & ! [v4: $i] : ( ~
% 29.59/4.85 | $i(v4) | ~ aElementOf0(v4, v0) | aElement0(v4)))
% 29.59/4.85 |
% 29.59/4.85 | ALPHA: (function-axioms) implies:
% 29.59/4.85 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 29.59/4.85 | (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) = v0))
% 29.59/4.85 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sbrdtbr0(v2)
% 29.59/4.85 | = v1) | ~ (sbrdtbr0(v2) = v0))
% 29.59/4.85 |
% 29.59/4.86 | DELTA: instantiating (12) with fresh symbols all_37_0, all_37_1, all_37_2,
% 29.59/4.86 | all_37_3 gives:
% 29.59/4.86 | (15) ~ (all_37_0 = all_37_1) & sbrdtbr0(all_37_3) = all_37_2 &
% 29.59/4.86 | sbrdtbr0(xS) = all_37_0 & szszuzczcdt0(all_37_2) = all_37_1 &
% 29.59/4.86 | sdtmndt0(xS, xx) = all_37_3 & $i(all_37_0) & $i(all_37_1) &
% 29.59/4.86 | $i(all_37_2) & $i(all_37_3) & aSet0(all_37_3) & ~ aElementOf0(xx,
% 29.59/4.86 | all_37_3) & ! [v0: $i] : (v0 = xx | ~ $i(v0) | ~ aElementOf0(v0,
% 29.59/4.86 | xS) | ~ aElement0(v0) | aElementOf0(v0, all_37_3)) & ! [v0: $i]
% 29.59/4.86 | : ( ~ $i(v0) | ~ aElementOf0(v0, all_37_3) | aElementOf0(v0, xS)) &
% 29.59/4.86 | ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_37_3) |
% 29.59/4.86 | aElement0(v0))
% 29.59/4.86 |
% 29.59/4.86 | ALPHA: (15) implies:
% 29.59/4.86 | (16) ~ (all_37_0 = all_37_1)
% 29.59/4.86 | (17) ~ aElementOf0(xx, all_37_3)
% 29.59/4.86 | (18) aSet0(all_37_3)
% 29.59/4.86 | (19) $i(all_37_3)
% 29.59/4.86 | (20) sdtmndt0(xS, xx) = all_37_3
% 29.59/4.86 | (21) szszuzczcdt0(all_37_2) = all_37_1
% 29.59/4.86 | (22) sbrdtbr0(xS) = all_37_0
% 29.59/4.86 | (23) sbrdtbr0(all_37_3) = all_37_2
% 29.59/4.86 |
% 29.59/4.86 | BETA: splitting (3) gives:
% 29.59/4.86 |
% 29.59/4.86 | Case 1:
% 29.59/4.86 | |
% 29.59/4.86 | | (24) ~ aSet0(slcrc0)
% 29.59/4.86 | |
% 29.59/4.86 | | PRED_UNIFY: (1), (24) imply:
% 29.59/4.86 | | (25) $false
% 29.59/4.86 | |
% 29.59/4.86 | | CLOSE: (25) is inconsistent.
% 29.59/4.86 | |
% 29.59/4.86 | Case 2:
% 29.59/4.86 | |
% 29.59/4.86 | |
% 30.11/4.86 | | GROUND_INST: instantiating (mEOfElem) with xS, xx, simplifying with (7),
% 30.11/4.86 | | (8), (10), (11) gives:
% 30.11/4.86 | | (26) aElement0(xx)
% 30.11/4.86 | |
% 30.11/4.86 | | GROUND_INST: instantiating (2) with xx, simplifying with (11) gives:
% 30.11/4.86 | | (27) ~ aElementOf0(xx, slcrc0)
% 30.11/4.86 | |
% 30.11/4.87 | | GROUND_INST: instantiating (mConsDiff) with xS, xx, all_37_3, simplifying
% 30.11/4.87 | | with (7), (8), (10), (11), (20) gives:
% 30.11/4.87 | | (28) sdtpldt0(all_37_3, xx) = xS
% 30.11/4.87 | |
% 30.11/4.87 | | GROUND_INST: instantiating (6) with xS, simplifying with (7), (10) gives:
% 30.11/4.87 | | (29) xS = slcrc0 | ~ (sbrdtbr0(xS) = sz00)
% 30.11/4.87 | |
% 30.11/4.87 | | PRED_UNIFY: (8), (27) imply:
% 30.11/4.87 | | (30) ~ (xS = slcrc0)
% 30.11/4.87 | |
% 30.11/4.87 | | BETA: splitting (29) gives:
% 30.11/4.87 | |
% 30.11/4.87 | | Case 1:
% 30.11/4.87 | | |
% 30.11/4.87 | | |
% 30.11/4.87 | | | GROUND_INST: instantiating (mFDiffSet) with xx, xS, all_37_3, simplifying
% 30.11/4.87 | | | with (7), (9), (10), (11), (20), (26) gives:
% 30.11/4.87 | | | (31) isFinite0(all_37_3)
% 30.11/4.87 | | |
% 30.11/4.87 | | | GROUND_INST: instantiating (4) with all_37_3, xx, xS, slcrc0, simplifying
% 30.11/4.87 | | | with (1), (5), (11), (18), (19), (26), (28) gives:
% 30.11/4.87 | | | (32) xS = slcrc0 | ? [v0: $i] : ($i(v0) & ( ~ aElementOf0(v0, slcrc0)
% 30.11/4.87 | | | | ~ aElement0(v0) | ( ~ (v0 = xx) & ~ aElementOf0(v0,
% 30.11/4.87 | | | all_37_3))) & (aElementOf0(v0, slcrc0) | (aElement0(v0) &
% 30.11/4.87 | | | (v0 = xx | aElementOf0(v0, all_37_3)))))
% 30.11/4.87 | | |
% 30.11/4.87 | | | BETA: splitting (32) gives:
% 30.11/4.87 | | |
% 30.11/4.87 | | | Case 1:
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | (33) xS = slcrc0
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | REDUCE: (30), (33) imply:
% 30.11/4.87 | | | | (34) $false
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | CLOSE: (34) is inconsistent.
% 30.11/4.87 | | | |
% 30.11/4.87 | | | Case 2:
% 30.11/4.87 | | | |
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | GROUND_INST: instantiating (mCardCons) with all_37_3, all_37_2,
% 30.11/4.87 | | | | simplifying with (18), (19), (23), (31) gives:
% 30.11/4.87 | | | | (35) ? [v0: $i] : (szszuzczcdt0(all_37_2) = v0 & $i(v0) & ! [v1:
% 30.11/4.87 | | | | $i] : ! [v2: $i] : ( ~ (sdtpldt0(all_37_3, v1) = v2) | ~
% 30.11/4.87 | | | | $i(v1) | ~ aElement0(v1) | sbrdtbr0(v2) = v0 |
% 30.11/4.87 | | | | aElementOf0(v1, all_37_3)))
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | DELTA: instantiating (35) with fresh symbol all_117_0 gives:
% 30.11/4.87 | | | | (36) szszuzczcdt0(all_37_2) = all_117_0 & $i(all_117_0) & ! [v0: $i]
% 30.11/4.87 | | | | : ! [v1: $i] : ( ~ (sdtpldt0(all_37_3, v0) = v1) | ~ $i(v0) |
% 30.11/4.87 | | | | ~ aElement0(v0) | sbrdtbr0(v1) = all_117_0 | aElementOf0(v0,
% 30.11/4.87 | | | | all_37_3))
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | ALPHA: (36) implies:
% 30.11/4.87 | | | | (37) szszuzczcdt0(all_37_2) = all_117_0
% 30.11/4.87 | | | | (38) ! [v0: $i] : ! [v1: $i] : ( ~ (sdtpldt0(all_37_3, v0) = v1) |
% 30.11/4.87 | | | | ~ $i(v0) | ~ aElement0(v0) | sbrdtbr0(v1) = all_117_0 |
% 30.11/4.87 | | | | aElementOf0(v0, all_37_3))
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | GROUND_INST: instantiating (38) with xx, xS, simplifying with (11),
% 30.11/4.87 | | | | (17), (26), (28) gives:
% 30.11/4.87 | | | | (39) sbrdtbr0(xS) = all_117_0
% 30.11/4.87 | | | |
% 30.11/4.87 | | | | GROUND_INST: instantiating (13) with all_37_1, all_117_0, all_37_2,
% 30.11/4.88 | | | | simplifying with (21), (37) gives:
% 30.11/4.88 | | | | (40) all_117_0 = all_37_1
% 30.11/4.88 | | | |
% 30.11/4.88 | | | | GROUND_INST: instantiating (14) with all_37_0, all_117_0, xS,
% 30.11/4.88 | | | | simplifying with (22), (39) gives:
% 30.11/4.88 | | | | (41) all_117_0 = all_37_0
% 30.11/4.88 | | | |
% 30.11/4.88 | | | | COMBINE_EQS: (40), (41) imply:
% 30.11/4.88 | | | | (42) all_37_0 = all_37_1
% 30.11/4.88 | | | |
% 30.11/4.88 | | | | REDUCE: (16), (42) imply:
% 30.11/4.88 | | | | (43) $false
% 30.11/4.88 | | | |
% 30.11/4.88 | | | | CLOSE: (43) is inconsistent.
% 30.11/4.88 | | | |
% 30.11/4.88 | | | End of split
% 30.11/4.88 | | |
% 30.11/4.88 | | Case 2:
% 30.11/4.88 | | |
% 30.11/4.88 | | | (44) xS = slcrc0
% 30.11/4.88 | | |
% 30.11/4.88 | | | REDUCE: (30), (44) imply:
% 30.11/4.88 | | | (45) $false
% 30.11/4.88 | | |
% 30.11/4.88 | | | CLOSE: (45) is inconsistent.
% 30.11/4.88 | | |
% 30.11/4.88 | | End of split
% 30.11/4.88 | |
% 30.11/4.88 | End of split
% 30.11/4.88 |
% 30.11/4.88 End of proof
% 30.11/4.88 % SZS output end Proof for theBenchmark
% 30.11/4.88
% 30.11/4.88 4272ms
%------------------------------------------------------------------------------