TSTP Solution File: NUM552+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM552+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 : n004.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 135.23s 18.54s
% Output : Proof 135.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM552+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 15:50:37 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.58 ________ _____
% 0.19/0.58 ___ __ \_________(_)________________________________
% 0.19/0.58 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.58 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.58 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.58 (2023-06-19)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2023
% 0.19/0.58 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.58 Amanda Stjerna.
% 0.19/0.58 Free software under BSD-3-Clause.
% 0.19/0.58
% 0.19/0.58 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.58
% 0.19/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.59 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.61 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.61 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.61 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.61 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.54/1.17 Prover 4: Preprocessing ...
% 3.54/1.17 Prover 1: Preprocessing ...
% 3.86/1.21 Prover 5: Preprocessing ...
% 3.86/1.21 Prover 2: Preprocessing ...
% 3.86/1.21 Prover 0: Preprocessing ...
% 3.86/1.21 Prover 6: Preprocessing ...
% 3.86/1.21 Prover 3: Preprocessing ...
% 9.67/2.14 Prover 1: Constructing countermodel ...
% 10.84/2.15 Prover 6: Proving ...
% 10.84/2.15 Prover 3: Constructing countermodel ...
% 10.84/2.17 Prover 5: Constructing countermodel ...
% 11.14/2.23 Prover 2: Proving ...
% 13.99/2.58 Prover 4: Constructing countermodel ...
% 13.99/2.63 Prover 0: Proving ...
% 72.86/10.28 Prover 2: stopped
% 72.86/10.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 74.08/10.43 Prover 7: Preprocessing ...
% 75.91/10.70 Prover 7: Constructing countermodel ...
% 100.87/13.93 Prover 5: stopped
% 100.87/13.94 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 101.80/14.00 Prover 8: Preprocessing ...
% 102.77/14.18 Prover 8: Warning: ignoring some quantifiers
% 103.30/14.18 Prover 8: Constructing countermodel ...
% 116.51/15.96 Prover 1: stopped
% 116.51/15.97 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 117.19/16.06 Prover 9: Preprocessing ...
% 120.03/16.45 Prover 9: Constructing countermodel ...
% 130.06/17.85 Prover 6: stopped
% 130.06/17.85 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 130.55/17.98 Prover 10: Preprocessing ...
% 132.94/18.11 Prover 10: Constructing countermodel ...
% 135.23/18.46 Prover 10: Found proof (size 31)
% 135.23/18.47 Prover 10: proved (612ms)
% 135.23/18.47 Prover 9: stopped
% 135.23/18.47 Prover 0: stopped
% 135.23/18.47 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 135.23/18.47 Prover 8: stopped
% 135.23/18.47 Prover 7: stopped
% 135.23/18.48 Prover 3: stopped
% 135.23/18.50 Prover 4: stopped
% 135.23/18.50 Prover 11: Preprocessing ...
% 135.23/18.54 Prover 11: stopped
% 135.23/18.54
% 135.23/18.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 135.23/18.54
% 135.23/18.54 % SZS output start Proof for theBenchmark
% 135.23/18.55 Assumptions after simplification:
% 135.23/18.55 ---------------------------------
% 135.23/18.55
% 135.23/18.55 (mDefEmp)
% 135.23/18.55 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 135.23/18.55 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 135.23/18.55 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 135.23/18.55
% 135.23/18.55 (mDefSel)
% 135.90/18.58 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 135.90/18.58 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) |
% 135.90/18.58 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 135.90/18.58 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 135.90/18.58 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~
% 135.90/18.58 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 135.90/18.58 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 135.90/18.58 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 135.90/18.58 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 135.90/18.58 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ?
% 135.90/18.58 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 135.90/18.58 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 135.90/18.58 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 135.90/18.58 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 135.90/18.58 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 135.90/18.59 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1,
% 135.90/18.59 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 135.90/18.59 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1)
% 135.90/18.59 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 135.90/18.59
% 135.90/18.59 (mDefSub)
% 135.90/18.59 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 135.90/18.59 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 135.90/18.59 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 135.90/18.59 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 135.90/18.59 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 135.90/18.59 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 135.90/18.59
% 135.90/18.59 (m__)
% 135.90/18.59 $i(xQ) & $i(xx) & $i(xT) & aElementOf0(xx, xQ) & ~ aElementOf0(xx, xT)
% 135.90/18.59
% 135.90/18.59 (m__2202)
% 135.90/18.59 $i(xk) & $i(szNzAzT0) & aElementOf0(xk, szNzAzT0)
% 135.90/18.59
% 135.90/18.59 (m__2202_02)
% 135.90/18.59 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS)
% 135.90/18.59
% 135.90/18.59 (m__2227)
% 135.90/18.59 $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 =
% 135.90/18.59 slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) &
% 135.90/18.59 $i(v0) & aSubsetOf0(v0, v1))
% 135.90/18.59
% 135.90/18.59 (m__2270)
% 135.90/18.59 $i(xQ) & $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) &
% 135.90/18.59 aElementOf0(xQ, v0))
% 135.90/18.59
% 135.90/18.59 (m__2291)
% 135.90/18.59 sbrdtbr0(xQ) = xk & $i(xQ) & $i(xk) & isFinite0(xQ) & aSet0(xQ)
% 135.90/18.59
% 135.90/18.59 (function-axioms)
% 135.90/18.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.90/18.60 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i]
% 135.90/18.60 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) =
% 135.90/18.60 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 135.90/18.60 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3,
% 135.90/18.60 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 135.90/18.60 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 135.90/18.60 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) &
% 135.90/18.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1)
% 135.90/18.60 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 135.90/18.60 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : !
% 135.90/18.60 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 135.90/18.60 (szszuzczcdt0(v2) = v0))
% 135.90/18.60
% 135.90/18.60 Further assumptions not needed in the proof:
% 135.90/18.60 --------------------------------------------
% 135.90/18.60 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 135.90/18.60 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mCountNFin_01,
% 135.90/18.60 mDefCons, mDefDiff, mDefMax, mDefMin, mDefSeg, mDiffCons, mEOfElem, mElmSort,
% 135.90/18.60 mEmpFin, mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, mLessASymm,
% 135.90/18.60 mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNATSet,
% 135.90/18.60 mNatExtra, mNatNSucc, mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSegZero,
% 135.90/18.60 mSelCSet, mSelFSet, mSelNSet, mSetSort, mSubASymm, mSubFSet, mSubRefl,
% 135.90/18.60 mSubTrans, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess, mZeroNum, m__2256,
% 135.90/18.60 m__2304
% 135.90/18.60
% 135.90/18.60 Those formulas are unsatisfiable:
% 135.90/18.60 ---------------------------------
% 135.90/18.60
% 135.90/18.60 Begin of proof
% 135.90/18.60 |
% 135.90/18.60 | ALPHA: (mDefEmp) implies:
% 135.90/18.60 | (1) ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] :
% 135.90/18.60 | ($i(v1) & aElementOf0(v1, v0)))
% 135.90/18.60 |
% 135.90/18.60 | ALPHA: (mDefSub) implies:
% 135.90/18.60 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 135.90/18.60 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 135.90/18.60 | aSet0(v0) | aElementOf0(v2, v0))
% 135.90/18.60 |
% 135.90/18.60 | ALPHA: (mDefSel) implies:
% 135.90/18.61 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) =
% 135.90/18.61 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 135.90/18.61 | szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 135.90/18.61 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 135.90/18.61 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) | ~ $i(v3) |
% 135.90/18.61 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 135.90/18.61 | aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSubsetOf0(v3, v0))
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (m__2202) implies:
% 135.90/18.61 | (5) aElementOf0(xk, szNzAzT0)
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (m__2202_02) implies:
% 135.90/18.61 | (6) aSet0(xS)
% 135.90/18.61 | (7) aSet0(xT)
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (m__2227) implies:
% 135.90/18.61 | (8) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) =
% 135.90/18.61 | v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0,
% 135.90/18.61 | v1))
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (m__2270) implies:
% 135.90/18.61 | (9) $i(xS)
% 135.90/18.61 | (10) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & aElementOf0(xQ,
% 135.90/18.61 | v0))
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (m__2291) implies:
% 135.90/18.61 | (11) $i(xk)
% 135.90/18.61 | (12) sbrdtbr0(xQ) = xk
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (m__) implies:
% 135.90/18.61 | (13) ~ aElementOf0(xx, xT)
% 135.90/18.61 | (14) aElementOf0(xx, xQ)
% 135.90/18.61 | (15) $i(xT)
% 135.90/18.61 | (16) $i(xx)
% 135.90/18.61 | (17) $i(xQ)
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (function-axioms) implies:
% 135.90/18.61 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 135.90/18.61 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0))
% 135.90/18.61 |
% 135.90/18.61 | DELTA: instantiating (10) with fresh symbol all_53_0 gives:
% 135.90/18.61 | (19) slbdtsldtrb0(xS, xk) = all_53_0 & $i(all_53_0) & aElementOf0(xQ,
% 135.90/18.61 | all_53_0)
% 135.90/18.61 |
% 135.90/18.61 | ALPHA: (19) implies:
% 135.90/18.61 | (20) aElementOf0(xQ, all_53_0)
% 135.90/18.62 | (21) slbdtsldtrb0(xS, xk) = all_53_0
% 135.90/18.62 |
% 135.90/18.62 | DELTA: instantiating (8) with fresh symbols all_55_0, all_55_1 gives:
% 135.90/18.62 | (22) ~ (all_55_1 = slcrc0) & slbdtsldtrb0(xT, xk) = all_55_0 &
% 135.90/18.62 | slbdtsldtrb0(xS, xk) = all_55_1 & $i(all_55_0) & $i(all_55_1) &
% 135.90/18.62 | aSubsetOf0(all_55_1, all_55_0)
% 135.90/18.62 |
% 135.90/18.62 | ALPHA: (22) implies:
% 135.90/18.62 | (23) ~ (all_55_1 = slcrc0)
% 135.90/18.62 | (24) aSubsetOf0(all_55_1, all_55_0)
% 135.90/18.62 | (25) $i(all_55_1)
% 135.90/18.62 | (26) $i(all_55_0)
% 135.90/18.62 | (27) slbdtsldtrb0(xS, xk) = all_55_1
% 135.90/18.62 | (28) slbdtsldtrb0(xT, xk) = all_55_0
% 135.90/18.62 |
% 135.90/18.62 | GROUND_INST: instantiating (18) with all_53_0, all_55_1, xk, xS, simplifying
% 135.90/18.62 | with (21), (27) gives:
% 135.90/18.62 | (29) all_55_1 = all_53_0
% 135.90/18.62 |
% 135.90/18.62 | REDUCE: (23), (29) imply:
% 135.90/18.62 | (30) ~ (all_53_0 = slcrc0)
% 135.90/18.62 |
% 135.90/18.62 | REDUCE: (25), (29) imply:
% 135.90/18.62 | (31) $i(all_53_0)
% 135.90/18.62 |
% 135.90/18.62 | REDUCE: (24), (29) imply:
% 135.90/18.62 | (32) aSubsetOf0(all_53_0, all_55_0)
% 135.90/18.62 |
% 135.90/18.62 | GROUND_INST: instantiating (3) with xS, xk, all_53_0, simplifying with (5),
% 135.90/18.62 | (6), (9), (11), (21), (31) gives:
% 135.90/18.62 | (33) aSet0(all_53_0)
% 135.90/18.62 |
% 135.90/18.62 | GROUND_INST: instantiating (3) with xT, xk, all_55_0, simplifying with (5),
% 135.90/18.62 | (7), (11), (15), (26), (28) gives:
% 135.90/18.62 | (34) aSet0(all_55_0)
% 135.90/18.62 |
% 135.90/18.62 | GROUND_INST: instantiating (1) with all_53_0, simplifying with (31), (33)
% 135.90/18.62 | gives:
% 135.90/18.62 | (35) all_53_0 = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_53_0))
% 135.90/18.62 |
% 135.90/18.62 | GROUND_INST: instantiating (2) with all_55_0, all_53_0, xQ, simplifying with
% 135.90/18.62 | (17), (20), (26), (31), (32), (34) gives:
% 135.90/18.62 | (36) aElementOf0(xQ, all_55_0)
% 135.90/18.62 |
% 135.90/18.62 | BETA: splitting (35) gives:
% 135.90/18.62 |
% 135.90/18.62 | Case 1:
% 135.90/18.62 | |
% 135.90/18.62 | | (37) all_53_0 = slcrc0
% 135.90/18.62 | |
% 135.90/18.62 | | REDUCE: (30), (37) imply:
% 135.90/18.62 | | (38) $false
% 135.90/18.62 | |
% 135.90/18.62 | | CLOSE: (38) is inconsistent.
% 135.90/18.62 | |
% 135.90/18.62 | Case 2:
% 135.90/18.63 | |
% 135.90/18.63 | |
% 135.90/18.63 | | GROUND_INST: instantiating (4) with xT, xk, all_55_0, xQ, xk, simplifying
% 135.90/18.63 | | with (5), (7), (11), (12), (15), (17), (26), (28), (36) gives:
% 135.90/18.63 | | (39) aSubsetOf0(xQ, xT)
% 135.90/18.63 | |
% 135.90/18.63 | | GROUND_INST: instantiating (2) with xT, xQ, xx, simplifying with (7), (13),
% 135.90/18.63 | | (14), (15), (16), (17), (39) gives:
% 135.90/18.63 | | (40) $false
% 135.90/18.63 | |
% 135.90/18.63 | | CLOSE: (40) is inconsistent.
% 135.90/18.63 | |
% 135.90/18.63 | End of split
% 135.90/18.63 |
% 135.90/18.63 End of proof
% 135.90/18.63 % SZS output end Proof for theBenchmark
% 135.90/18.63
% 135.90/18.63 18047ms
%------------------------------------------------------------------------------