TSTP Solution File: NUM547+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM547+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 : n005.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 11:48:32 EDT 2023
% Result : Theorem 84.05s 11.86s
% Output : Proof 84.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 17:02:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.62 ________ _____
% 0.19/0.62 ___ __ \_________(_)________________________________
% 0.19/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.62
% 0.19/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.62 (2023-06-19)
% 0.19/0.62
% 0.19/0.62 (c) Philipp Rümmer, 2009-2023
% 0.19/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.62 Amanda Stjerna.
% 0.19/0.62 Free software under BSD-3-Clause.
% 0.19/0.62
% 0.19/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.62
% 0.19/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.58/1.26 Prover 1: Preprocessing ...
% 3.58/1.27 Prover 4: Preprocessing ...
% 3.58/1.31 Prover 6: Preprocessing ...
% 3.58/1.31 Prover 3: Preprocessing ...
% 3.58/1.31 Prover 5: Preprocessing ...
% 3.58/1.31 Prover 0: Preprocessing ...
% 3.58/1.31 Prover 2: Preprocessing ...
% 10.82/2.26 Prover 1: Constructing countermodel ...
% 10.82/2.26 Prover 3: Constructing countermodel ...
% 11.50/2.37 Prover 6: Proving ...
% 11.98/2.42 Prover 5: Constructing countermodel ...
% 11.98/2.43 Prover 2: Proving ...
% 15.74/2.91 Prover 4: Constructing countermodel ...
% 16.55/3.06 Prover 0: Proving ...
% 72.06/10.36 Prover 2: stopped
% 72.06/10.38 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.74/10.51 Prover 7: Preprocessing ...
% 74.46/10.67 Prover 7: Constructing countermodel ...
% 84.05/11.84 Prover 7: Found proof (size 47)
% 84.05/11.84 Prover 7: proved (1464ms)
% 84.05/11.84 Prover 6: stopped
% 84.05/11.85 Prover 3: stopped
% 84.05/11.85 Prover 0: stopped
% 84.05/11.85 Prover 1: stopped
% 84.05/11.85 Prover 4: stopped
% 84.05/11.86 Prover 5: stopped
% 84.05/11.86
% 84.05/11.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 84.05/11.86
% 84.05/11.87 % SZS output start Proof for theBenchmark
% 84.05/11.87 Assumptions after simplification:
% 84.05/11.87 ---------------------------------
% 84.05/11.87
% 84.05/11.87 (mCountNFin_01)
% 84.21/11.88 $i(slcrc0) & ( ~ isCountable0(slcrc0) | ~ aSet0(slcrc0))
% 84.21/11.88
% 84.21/11.88 (mDefEmp)
% 84.21/11.88 $i(slcrc0) & aSet0(slcrc0) & ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~
% 84.21/11.88 aSet0(v0) | ? [v1: $i] : ($i(v1) & aElementOf0(v1, v0))) & ! [v0: $i] : (
% 84.21/11.88 ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 84.21/11.88
% 84.21/11.88 (mDefSeg)
% 84.21/11.90 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 84.21/11.90 (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 84.21/11.90 ~ $i(v0) | ~ sdtlseqdt0(v3, v0) | ~ aElementOf0(v2, szNzAzT0) | ~
% 84.21/11.90 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, v1)) & ! [v0: $i] : ! [v1: $i]
% 84.21/11.90 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 84.21/11.91 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 84.21/11.91 aElementOf0(v0, szNzAzT0) | sdtlseqdt0(v3, v0)) & ! [v0: $i] : ! [v1: $i]
% 84.21/11.91 : ! [v2: $i] : ! [v3: $i] : ( ~ (slbdtrb0(v0) = v1) | ~ (szszuzczcdt0(v2) =
% 84.21/11.91 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v2, v1) | ~
% 84.21/11.91 aElementOf0(v0, szNzAzT0) | aElementOf0(v2, szNzAzT0)) & ! [v0: $i] : !
% 84.21/11.91 [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) = v1) | ~ $i(v2) | ~
% 84.21/11.91 $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~ aSet0(v2) | ? [v3: $i] : ? [v4:
% 84.21/11.91 $i] : ($i(v3) & ( ~ aElementOf0(v3, v2) | ~ aElementOf0(v3, szNzAzT0) |
% 84.21/11.91 (szszuzczcdt0(v3) = v4 & $i(v4) & ~ sdtlseqdt0(v4, v0))) &
% 84.21/11.91 (aElementOf0(v3, v2) | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4,
% 84.21/11.91 v0) & aElementOf0(v3, szNzAzT0))))) & ! [v0: $i] : ! [v1: $i] : (
% 84.21/11.91 ~ (slbdtrb0(v0) = v1) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0)
% 84.21/11.91 | aSet0(v1))
% 84.21/11.91
% 84.21/11.91 (mDefSel)
% 84.21/11.91 $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 84.21/11.91 $i] : (v4 = v1 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v4) |
% 84.21/11.91 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~
% 84.21/11.91 aElementOf0(v1, szNzAzT0) | ~ aSet0(v0)) & ! [v0: $i] : ! [v1: $i] : !
% 84.21/11.91 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~
% 84.21/11.91 (sbrdtbr0(v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 84.21/11.91 aElementOf0(v3, v2) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) |
% 84.21/11.91 aSubsetOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 84.21/11.91 : (v3 = v2 | ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~
% 84.21/11.91 $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v3) | ~ aSet0(v0) | ?
% 84.21/11.91 [v4: $i] : ? [v5: $i] : ($i(v4) & ( ~ aSubsetOf0(v4, v0) | ~
% 84.21/11.91 aElementOf0(v4, v3) | ( ~ (v5 = v1) & sbrdtbr0(v4) = v5 & $i(v5))) &
% 84.21/11.91 (aElementOf0(v4, v3) | (v5 = v1 & sbrdtbr0(v4) = v1 & aSubsetOf0(v4,
% 84.21/11.91 v0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (
% 84.21/11.91 ~ (slbdtsldtrb0(v0, v1) = v2) | ~ (sbrdtbr0(v3) = v1) | ~ $i(v3) | ~
% 84.21/11.91 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aSubsetOf0(v3, v0) | ~ aElementOf0(v1,
% 84.21/11.91 szNzAzT0) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 84.21/11.91 $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1)
% 84.21/11.91 | ~ $i(v0) | ~ aElementOf0(v1, szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 84.21/11.91
% 84.21/11.91 (mNATSet)
% 84.21/11.91 $i(szNzAzT0) & isCountable0(szNzAzT0) & aSet0(szNzAzT0)
% 84.21/11.91
% 84.21/11.91 (mSegZero)
% 84.21/11.91 slbdtrb0(sz00) = slcrc0 & $i(sz00) & $i(slcrc0)
% 84.21/11.91
% 84.21/11.91 (mZeroNum)
% 84.21/11.91 $i(sz00) & $i(szNzAzT0) & aElementOf0(sz00, szNzAzT0)
% 84.21/11.91
% 84.21/11.91 (m__)
% 84.21/11.92 $i(xS) & $i(xk) & ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & ! [v1:
% 84.21/11.92 $i] : ( ~ $i(v1) | ~ aElementOf0(v1, v0)))
% 84.21/11.92
% 84.21/11.92 (m__2202)
% 84.21/11.92 $i(xk) & $i(szNzAzT0) & aElementOf0(xk, szNzAzT0)
% 84.21/11.92
% 84.21/11.92 (m__2202_02)
% 84.21/11.92 ~ (xk = sz00) & $i(xT) & $i(xS) & $i(xk) & $i(sz00) & aSet0(xT) & aSet0(xS)
% 84.21/11.92
% 84.21/11.92 (m__2227)
% 84.21/11.92 $i(xT) & $i(xS) & $i(xk) & $i(slcrc0) & ? [v0: $i] : ? [v1: $i] : ( ~ (v0 =
% 84.21/11.92 slcrc0) & slbdtsldtrb0(xT, xk) = v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) &
% 84.21/11.92 $i(v0) & aSubsetOf0(v0, v1))
% 84.21/11.92
% 84.21/11.92 (m__2256)
% 84.21/11.92 $i(xx) & $i(xS) & aElementOf0(xx, xS)
% 84.21/11.92
% 84.21/11.92 (function-axioms)
% 84.21/11.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 84.21/11.92 (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: $i]
% 84.21/11.92 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtmndt0(v3, v2) =
% 84.21/11.92 v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 84.21/11.92 $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) | ~ (sdtpldt0(v3,
% 84.21/11.92 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 84.21/11.92 (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 84.21/11.92 ! [v2: $i] : (v1 = v0 | ~ (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) &
% 84.21/11.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1)
% 84.21/11.92 | ~ (szmzizndt0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1
% 84.21/11.92 = v0 | ~ (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : !
% 84.21/11.92 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~
% 84.21/11.92 (szszuzczcdt0(v2) = v0))
% 84.21/11.92
% 84.21/11.92 Further assumptions not needed in the proof:
% 84.21/11.92 --------------------------------------------
% 84.21/11.92 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 84.21/11.92 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin, mDefCons,
% 84.21/11.92 mDefDiff, mDefMax, mDefMin, mDefSub, mDiffCons, mEOfElem, mElmSort, mEmpFin,
% 84.21/11.92 mFConsSet, mFDiffSet, mFinRel, mFinSubSeg, mIH, mIHSort, mLessASymm, mLessRefl,
% 84.21/11.92 mLessRel, mLessSucc, mLessTotal, mLessTrans, mMinMin, mNatExtra, mNatNSucc,
% 84.21/11.92 mNoScLessZr, mSegFin, mSegLess, mSegSucc, mSelCSet, mSelFSet, mSelNSet,
% 84.21/11.92 mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans, mSuccEquSucc, mSuccLess,
% 84.21/11.92 mSuccNum, mZeroLess
% 84.21/11.92
% 84.21/11.92 Those formulas are unsatisfiable:
% 84.21/11.92 ---------------------------------
% 84.21/11.92
% 84.21/11.92 Begin of proof
% 84.21/11.92 |
% 84.21/11.92 | ALPHA: (mDefEmp) implies:
% 84.21/11.92 | (1) aSet0(slcrc0)
% 84.21/11.92 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, slcrc0))
% 84.21/11.92 | (3) ! [v0: $i] : (v0 = slcrc0 | ~ $i(v0) | ~ aSet0(v0) | ? [v1: $i] :
% 84.21/11.92 | ($i(v1) & aElementOf0(v1, v0)))
% 84.21/11.92 |
% 84.21/11.92 | ALPHA: (mCountNFin_01) implies:
% 84.21/11.92 | (4) ~ isCountable0(slcrc0) | ~ aSet0(slcrc0)
% 84.21/11.92 |
% 84.21/11.92 | ALPHA: (mNATSet) implies:
% 84.21/11.92 | (5) aSet0(szNzAzT0)
% 84.21/11.92 | (6) isCountable0(szNzAzT0)
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (mZeroNum) implies:
% 84.21/11.93 | (7) aElementOf0(sz00, szNzAzT0)
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (mDefSeg) implies:
% 84.21/11.93 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (slbdtrb0(v0) =
% 84.21/11.93 | v1) | ~ $i(v2) | ~ $i(v0) | ~ aElementOf0(v0, szNzAzT0) | ~
% 84.21/11.93 | aSet0(v2) | ? [v3: $i] : ? [v4: $i] : ($i(v3) & ( ~ aElementOf0(v3,
% 84.21/11.93 | v2) | ~ aElementOf0(v3, szNzAzT0) | (szszuzczcdt0(v3) = v4 &
% 84.21/11.93 | $i(v4) & ~ sdtlseqdt0(v4, v0))) & (aElementOf0(v3, v2) |
% 84.21/11.93 | (szszuzczcdt0(v3) = v4 & $i(v4) & sdtlseqdt0(v4, v0) &
% 84.21/11.93 | aElementOf0(v3, szNzAzT0)))))
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (mSegZero) implies:
% 84.21/11.93 | (9) slbdtrb0(sz00) = slcrc0
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (mDefSel) implies:
% 84.21/11.93 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (slbdtsldtrb0(v0, v1) =
% 84.21/11.93 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1,
% 84.21/11.93 | szNzAzT0) | ~ aSet0(v0) | aSet0(v2))
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (m__2202) implies:
% 84.21/11.93 | (11) aElementOf0(xk, szNzAzT0)
% 84.21/11.93 | (12) $i(szNzAzT0)
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (m__2202_02) implies:
% 84.21/11.93 | (13) aSet0(xS)
% 84.21/11.93 | (14) $i(sz00)
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (m__2227) implies:
% 84.21/11.93 | (15) ? [v0: $i] : ? [v1: $i] : ( ~ (v0 = slcrc0) & slbdtsldtrb0(xT, xk) =
% 84.21/11.93 | v1 & slbdtsldtrb0(xS, xk) = v0 & $i(v1) & $i(v0) & aSubsetOf0(v0,
% 84.21/11.93 | v1))
% 84.21/11.93 |
% 84.21/11.93 | ALPHA: (m__2256) implies:
% 84.21/11.93 | (16) aElementOf0(xx, xS)
% 84.49/11.93 | (17) $i(xx)
% 84.49/11.93 |
% 84.49/11.93 | ALPHA: (m__) implies:
% 84.49/11.93 | (18) $i(xk)
% 84.49/11.93 | (19) $i(xS)
% 84.49/11.93 | (20) ? [v0: $i] : (slbdtsldtrb0(xS, xk) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 84.49/11.93 | $i(v1) | ~ aElementOf0(v1, v0)))
% 84.49/11.93 |
% 84.49/11.93 | ALPHA: (function-axioms) implies:
% 84.49/11.93 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 84.49/11.93 | (slbdtsldtrb0(v3, v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0))
% 84.49/11.93 |
% 84.49/11.93 | DELTA: instantiating (20) with fresh symbol all_53_0 gives:
% 84.49/11.93 | (22) slbdtsldtrb0(xS, xk) = all_53_0 & $i(all_53_0) & ! [v0: $i] : ( ~
% 84.49/11.93 | $i(v0) | ~ aElementOf0(v0, all_53_0))
% 84.49/11.93 |
% 84.49/11.93 | ALPHA: (22) implies:
% 84.49/11.93 | (23) slbdtsldtrb0(xS, xk) = all_53_0
% 84.49/11.93 | (24) ! [v0: $i] : ( ~ $i(v0) | ~ aElementOf0(v0, all_53_0))
% 84.49/11.93 |
% 84.49/11.93 | DELTA: instantiating (15) with fresh symbols all_56_0, all_56_1 gives:
% 84.49/11.93 | (25) ~ (all_56_1 = slcrc0) & slbdtsldtrb0(xT, xk) = all_56_0 &
% 84.49/11.93 | slbdtsldtrb0(xS, xk) = all_56_1 & $i(all_56_0) & $i(all_56_1) &
% 84.49/11.93 | aSubsetOf0(all_56_1, all_56_0)
% 84.49/11.93 |
% 84.49/11.93 | ALPHA: (25) implies:
% 84.49/11.93 | (26) ~ (all_56_1 = slcrc0)
% 84.49/11.93 | (27) $i(all_56_1)
% 84.49/11.93 | (28) slbdtsldtrb0(xS, xk) = all_56_1
% 84.49/11.93 |
% 84.49/11.93 | BETA: splitting (4) gives:
% 84.49/11.93 |
% 84.49/11.93 | Case 1:
% 84.49/11.93 | |
% 84.49/11.93 | | (29) ~ isCountable0(slcrc0)
% 84.49/11.93 | |
% 84.49/11.94 | | GROUND_INST: instantiating (21) with all_53_0, all_56_1, xk, xS, simplifying
% 84.49/11.94 | | with (23), (28) gives:
% 84.49/11.94 | | (30) all_56_1 = all_53_0
% 84.49/11.94 | |
% 84.49/11.94 | | PRED_UNIFY: (6), (29) imply:
% 84.49/11.94 | | (31) ~ (szNzAzT0 = slcrc0)
% 84.49/11.94 | |
% 84.49/11.94 | | REDUCE: (26), (30) imply:
% 84.49/11.94 | | (32) ~ (all_53_0 = slcrc0)
% 84.49/11.94 | |
% 84.49/11.94 | | REDUCE: (27), (30) imply:
% 84.49/11.94 | | (33) $i(all_53_0)
% 84.49/11.94 | |
% 84.49/11.94 | | GROUND_INST: instantiating (3) with szNzAzT0, simplifying with (5), (12)
% 84.49/11.94 | | gives:
% 84.49/11.94 | | (34) szNzAzT0 = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0,
% 84.49/11.94 | | szNzAzT0))
% 84.49/11.94 | |
% 84.49/11.94 | | GROUND_INST: instantiating (2) with xx, simplifying with (17) gives:
% 84.49/11.94 | | (35) ~ aElementOf0(xx, slcrc0)
% 84.49/11.94 | |
% 84.49/11.94 | | GROUND_INST: instantiating (8) with sz00, slcrc0, xS, simplifying with (7),
% 84.49/11.94 | | (9), (13), (14), (19) gives:
% 84.49/11.94 | | (36) xS = slcrc0 | ? [v0: $i] : ? [v1: $i] : ($i(v0) & ( ~
% 84.49/11.94 | | aElementOf0(v0, xS) | ~ aElementOf0(v0, szNzAzT0) |
% 84.49/11.94 | | (szszuzczcdt0(v0) = v1 & $i(v1) & ~ sdtlseqdt0(v1, sz00))) &
% 84.49/11.94 | | (aElementOf0(v0, xS) | (szszuzczcdt0(v0) = v1 & $i(v1) &
% 84.49/11.94 | | sdtlseqdt0(v1, sz00) & aElementOf0(v0, szNzAzT0))))
% 84.49/11.94 | |
% 84.49/11.94 | | GROUND_INST: instantiating (10) with xS, xk, all_53_0, simplifying with
% 84.49/11.94 | | (11), (13), (18), (19), (23), (33) gives:
% 84.49/11.94 | | (37) aSet0(all_53_0)
% 84.49/11.94 | |
% 84.49/11.94 | | BETA: splitting (34) gives:
% 84.49/11.94 | |
% 84.49/11.94 | | Case 1:
% 84.49/11.94 | | |
% 84.49/11.94 | | | (38) szNzAzT0 = slcrc0
% 84.49/11.94 | | |
% 84.49/11.94 | | | REDUCE: (31), (38) imply:
% 84.49/11.94 | | | (39) $false
% 84.49/11.94 | | |
% 84.49/11.94 | | | CLOSE: (39) is inconsistent.
% 84.49/11.94 | | |
% 84.49/11.94 | | Case 2:
% 84.49/11.94 | | |
% 84.49/11.94 | | |
% 84.49/11.94 | | | PRED_UNIFY: (16), (35) imply:
% 84.49/11.94 | | | (40) ~ (xS = slcrc0)
% 84.49/11.94 | | |
% 84.49/11.94 | | | BETA: splitting (36) gives:
% 84.49/11.94 | | |
% 84.49/11.94 | | | Case 1:
% 84.49/11.94 | | | |
% 84.49/11.94 | | | | (41) xS = slcrc0
% 84.49/11.94 | | | |
% 84.49/11.94 | | | | REDUCE: (40), (41) imply:
% 84.49/11.94 | | | | (42) $false
% 84.49/11.94 | | | |
% 84.49/11.94 | | | | CLOSE: (42) is inconsistent.
% 84.49/11.94 | | | |
% 84.49/11.94 | | | Case 2:
% 84.49/11.94 | | | |
% 84.49/11.94 | | | |
% 84.49/11.94 | | | | GROUND_INST: instantiating (3) with all_53_0, simplifying with (33),
% 84.49/11.94 | | | | (37) gives:
% 84.49/11.94 | | | | (43) all_53_0 = slcrc0 | ? [v0: $i] : ($i(v0) & aElementOf0(v0,
% 84.49/11.94 | | | | all_53_0))
% 84.49/11.94 | | | |
% 84.49/11.94 | | | | BETA: splitting (43) gives:
% 84.49/11.94 | | | |
% 84.49/11.94 | | | | Case 1:
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | (44) all_53_0 = slcrc0
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | REDUCE: (32), (44) imply:
% 84.49/11.94 | | | | | (45) $false
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | CLOSE: (45) is inconsistent.
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | Case 2:
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | (46) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_53_0))
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | DELTA: instantiating (46) with fresh symbol all_146_0 gives:
% 84.49/11.94 | | | | | (47) $i(all_146_0) & aElementOf0(all_146_0, all_53_0)
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | ALPHA: (47) implies:
% 84.49/11.94 | | | | | (48) aElementOf0(all_146_0, all_53_0)
% 84.49/11.94 | | | | | (49) $i(all_146_0)
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | GROUND_INST: instantiating (24) with all_146_0, simplifying with (48),
% 84.49/11.94 | | | | | (49) gives:
% 84.49/11.94 | | | | | (50) $false
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | | CLOSE: (50) is inconsistent.
% 84.49/11.94 | | | | |
% 84.49/11.94 | | | | End of split
% 84.49/11.94 | | | |
% 84.49/11.94 | | | End of split
% 84.49/11.94 | | |
% 84.49/11.94 | | End of split
% 84.49/11.94 | |
% 84.49/11.94 | Case 2:
% 84.49/11.94 | |
% 84.49/11.95 | | (51) ~ aSet0(slcrc0)
% 84.49/11.95 | |
% 84.49/11.95 | | PRED_UNIFY: (1), (51) imply:
% 84.49/11.95 | | (52) $false
% 84.49/11.95 | |
% 84.49/11.95 | | CLOSE: (52) is inconsistent.
% 84.49/11.95 | |
% 84.49/11.95 | End of split
% 84.49/11.95 |
% 84.49/11.95 End of proof
% 84.49/11.95 % SZS output end Proof for theBenchmark
% 84.49/11.95
% 84.49/11.95 11328ms
%------------------------------------------------------------------------------