TSTP Solution File: NUM610+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM610+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 : n023.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 11:48:57 EDT 2023
% Result : Theorem 32.58s 5.16s
% Output : Proof 45.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM610+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n023.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 13:28:57 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.70/0.71 ________ _____
% 0.70/0.71 ___ __ \_________(_)________________________________
% 0.70/0.71 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.70/0.71 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.70/0.71 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.70/0.71
% 0.70/0.71 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.70/0.71 (2023-06-19)
% 0.70/0.71
% 0.70/0.71 (c) Philipp Rümmer, 2009-2023
% 0.70/0.71 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.70/0.71 Amanda Stjerna.
% 0.70/0.71 Free software under BSD-3-Clause.
% 0.70/0.71
% 0.70/0.71 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.70/0.71
% 0.70/0.71 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.82/0.73 Running up to 7 provers in parallel.
% 0.82/0.74 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.82/0.74 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.82/0.74 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.82/0.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.82/0.74 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.82/0.74 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.82/0.75 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.01/1.70 Prover 4: Preprocessing ...
% 6.01/1.74 Prover 1: Preprocessing ...
% 6.01/1.76 Prover 2: Preprocessing ...
% 6.01/1.76 Prover 0: Preprocessing ...
% 6.01/1.76 Prover 3: Preprocessing ...
% 6.01/1.76 Prover 6: Preprocessing ...
% 6.01/1.76 Prover 5: Preprocessing ...
% 20.86/3.69 Prover 1: Constructing countermodel ...
% 21.95/3.79 Prover 3: Constructing countermodel ...
% 21.95/3.79 Prover 6: Proving ...
% 25.58/4.28 Prover 5: Proving ...
% 26.55/4.38 Prover 2: Proving ...
% 31.66/5.08 Prover 4: Constructing countermodel ...
% 32.50/5.16 Prover 3: proved (4419ms)
% 32.50/5.16
% 32.58/5.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 32.58/5.16
% 32.58/5.17 Prover 6: stopped
% 32.58/5.17 Prover 2: stopped
% 32.58/5.17 Prover 5: stopped
% 32.58/5.19 Prover 0: Proving ...
% 32.58/5.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 32.58/5.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 32.58/5.19 Prover 0: stopped
% 32.58/5.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 32.58/5.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 32.58/5.21 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.50/5.58 Prover 10: Preprocessing ...
% 35.50/5.64 Prover 13: Preprocessing ...
% 36.22/5.67 Prover 11: Preprocessing ...
% 36.22/5.68 Prover 7: Preprocessing ...
% 36.65/5.70 Prover 8: Preprocessing ...
% 39.22/6.07 Prover 10: Constructing countermodel ...
% 39.22/6.08 Prover 7: Constructing countermodel ...
% 39.98/6.18 Prover 8: Warning: ignoring some quantifiers
% 39.98/6.19 Prover 8: Constructing countermodel ...
% 40.47/6.23 Prover 13: Warning: ignoring some quantifiers
% 40.47/6.26 Prover 13: Constructing countermodel ...
% 43.72/6.67 Prover 1: Found proof (size 62)
% 43.72/6.67 Prover 1: proved (5935ms)
% 43.72/6.67 Prover 7: stopped
% 43.72/6.67 Prover 10: stopped
% 43.72/6.67 Prover 13: stopped
% 43.72/6.67 Prover 4: stopped
% 43.72/6.68 Prover 8: stopped
% 44.83/6.88 Prover 11: Constructing countermodel ...
% 44.83/6.91 Prover 11: stopped
% 44.83/6.91
% 44.83/6.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.83/6.91
% 44.83/6.93 % SZS output start Proof for theBenchmark
% 44.83/6.94 Assumptions after simplification:
% 44.83/6.94 ---------------------------------
% 44.83/6.94
% 44.83/6.94 (mCountNFin)
% 45.25/6.99 ! [v0: $i] : ( ~ (isCountable0(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 45.25/6.99 any] : (isFinite0(v0) = v2 & aSet0(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 =
% 45.25/6.99 0))))
% 45.25/6.99
% 45.25/6.99 (mDefSub)
% 45.38/6.99 ! [v0: $i] : ( ~ (aSet0(v0) = 0) | ~ $i(v0) | ( ! [v1: $i] : ! [v2: int] :
% 45.38/6.99 (v2 = 0 | ~ (aSubsetOf0(v1, v0) = v2) | ~ $i(v1) | ? [v3: $i] : ? [v4:
% 45.38/6.99 int] : ( ~ (v4 = 0) & aElementOf0(v3, v1) = 0 & aElementOf0(v3, v0) =
% 45.38/6.99 v4 & $i(v3)) | ? [v3: int] : ( ~ (v3 = 0) & aSet0(v1) = v3)) & !
% 45.38/6.99 [v1: $i] : ( ~ (aSubsetOf0(v1, v0) = 0) | ~ $i(v1) | (aSet0(v1) = 0 & !
% 45.38/6.99 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (aElementOf0(v2, v0) = v3) | ~
% 45.38/6.99 $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & aElementOf0(v2, v1) =
% 45.38/6.99 v4))))))
% 45.38/6.99
% 45.38/6.99 (mNATSet)
% 45.38/6.99 isCountable0(szNzAzT0) = 0 & aSet0(szNzAzT0) = 0 & $i(szNzAzT0)
% 45.38/6.99
% 45.38/6.99 (mSubTrans)
% 45.38/7.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 45.38/7.00 (aSubsetOf0(v0, v2) = v3) | ~ (aSubsetOf0(v0, v1) = 0) | ~ $i(v2) | ~
% 45.38/7.00 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6: any] : ? [v7:
% 45.38/7.00 any] : (aSubsetOf0(v1, v2) = v7 & aSet0(v2) = v6 & aSet0(v1) = v5 &
% 45.38/7.00 aSet0(v0) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 45.38/7.00
% 45.38/7.00 (m__)
% 45.38/7.00 $i(xP) & $i(xO) & ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xP, xO) = v0)
% 45.38/7.00
% 45.38/7.00 (m__4730)
% 45.38/7.00 aFunction0(xd) = 0 & szDzozmdt0(xd) = szNzAzT0 & $i(xd) & $i(xC) & $i(xN) &
% 45.38/7.00 $i(xk) & $i(szNzAzT0) & ! [v0: $i] : ! [v1: $i] : ( ~ (sdtlpdtrp0(xC, v0) =
% 45.38/7.00 v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 45.38/7.00 ? [v6: $i] : (sdtlpdtrp0(xd, v0) = v6 & sdtlpdtrp0(xN, v3) = v4 &
% 45.38/7.00 slbdtsldtrb0(v4, xk) = v5 & szszuzczcdt0(v0) = v3 & aElementOf0(v0,
% 45.38/7.00 szNzAzT0) = v2 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & ( ~ (v2 = 0) | !
% 45.38/7.00 [v7: $i] : ( ~ (aElementOf0(v7, v5) = 0) | ~ $i(v7) | ? [v8: any] : ?
% 45.38/7.00 [v9: $i] : (sdtlpdtrp0(v1, v7) = v9 & aSet0(v7) = v8 & $i(v9) & ( ~
% 45.38/7.00 (v8 = 0) | v9 = v6))))))
% 45.38/7.00
% 45.38/7.00 (m__4758)
% 45.38/7.00 $i(xd) & $i(xT) & ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 &
% 45.38/7.00 szDzozmdt0(xd) = v0 & aSubsetOf0(v1, xT) = 0 & $i(v1) & $i(v0))
% 45.38/7.00
% 45.38/7.00 (m__4891)
% 45.38/7.01 $i(xO) & $i(xd) & $i(xe) & ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 &
% 45.38/7.01 sdtlcdtrc0(xe, v1) = xO & sdtlbdtrb0(xd, v0) = v1 & aSet0(xO) = 0 & $i(v1) &
% 45.38/7.01 $i(v0))
% 45.38/7.01
% 45.38/7.01 (m__4908)
% 45.38/7.01 isCountable0(xO) = 0 & aSet0(xO) = 0 & $i(xO)
% 45.38/7.01
% 45.38/7.01 (m__5093)
% 45.38/7.01 ~ (xQ = slcrc0) & aSubsetOf0(xQ, xO) = 0 & $i(xQ) & $i(xO) & $i(slcrc0)
% 45.38/7.01
% 45.38/7.01 (m__5106)
% 45.38/7.01 aSubsetOf0(xQ, szNzAzT0) = 0 & $i(xQ) & $i(szNzAzT0)
% 45.38/7.01
% 45.38/7.01 (m__5164)
% 45.38/7.01 $i(xP) & $i(xQ) & ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP &
% 45.38/7.01 aSet0(xP) = 0 & $i(v0))
% 45.38/7.01
% 45.38/7.01 (m__5195)
% 45.38/7.01 aSubsetOf0(xP, xQ) = 0 & $i(xP) & $i(xQ)
% 45.38/7.01
% 45.38/7.01 (function-axioms)
% 45.38/7.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.38/7.02 (sdtexdt0(v3, v2) = v1) | ~ (sdtexdt0(v3, v2) = v0)) & ! [v0: $i] : !
% 45.38/7.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtlcdtrc0(v3, v2) = v1)
% 45.38/7.02 | ~ (sdtlcdtrc0(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 45.38/7.02 ! [v3: $i] : (v1 = v0 | ~ (sdtlbdtrb0(v3, v2) = v1) | ~ (sdtlbdtrb0(v3, v2)
% 45.38/7.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 45.38/7.02 | ~ (sdtlpdtrp0(v3, v2) = v1) | ~ (sdtlpdtrp0(v3, v2) = v0)) & ! [v0: $i]
% 45.38/7.02 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (slbdtsldtrb0(v3,
% 45.38/7.02 v2) = v1) | ~ (slbdtsldtrb0(v3, v2) = v0)) & ! [v0: MultipleValueBool]
% 45.38/7.02 : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.38/7.02 (iLess0(v3, v2) = v1) | ~ (iLess0(v3, v2) = v0)) & ! [v0:
% 45.38/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 45.38/7.02 : (v1 = v0 | ~ (sdtlseqdt0(v3, v2) = v1) | ~ (sdtlseqdt0(v3, v2) = v0)) & !
% 45.38/7.02 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.38/7.02 (sdtmndt0(v3, v2) = v1) | ~ (sdtmndt0(v3, v2) = v0)) & ! [v0: $i] : !
% 45.38/7.02 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (sdtpldt0(v3, v2) = v1) |
% 45.38/7.02 ~ (sdtpldt0(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.38/7.02 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 45.38/7.02 (aSubsetOf0(v3, v2) = v1) | ~ (aSubsetOf0(v3, v2) = v0)) & ! [v0:
% 45.38/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 45.38/7.02 : (v1 = v0 | ~ (aElementOf0(v3, v2) = v1) | ~ (aElementOf0(v3, v2) = v0)) &
% 45.38/7.02 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (szDzizrdt0(v2) = v1) |
% 45.38/7.02 ~ (szDzizrdt0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 45.38/7.02 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aFunction0(v2) = v1) | ~
% 45.38/7.02 (aFunction0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 45.38/7.02 | ~ (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0)) & ! [v0: $i] : !
% 45.38/7.02 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (slbdtrb0(v2) = v1) | ~ (slbdtrb0(v2)
% 45.38/7.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 45.38/7.02 (szmzazxdt0(v2) = v1) | ~ (szmzazxdt0(v2) = v0)) & ! [v0: $i] : ! [v1:
% 45.38/7.02 $i] : ! [v2: $i] : (v1 = v0 | ~ (szmzizndt0(v2) = v1) | ~ (szmzizndt0(v2)
% 45.38/7.02 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 45.38/7.02 (sbrdtbr0(v2) = v1) | ~ (sbrdtbr0(v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 45.38/7.02 ! [v2: $i] : (v1 = v0 | ~ (szszuzczcdt0(v2) = v1) | ~ (szszuzczcdt0(v2) =
% 45.38/7.02 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 45.38/7.02 $i] : (v1 = v0 | ~ (isCountable0(v2) = v1) | ~ (isCountable0(v2) = v0)) &
% 45.38/7.02 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 45.38/7.02 v0 | ~ (isFinite0(v2) = v1) | ~ (isFinite0(v2) = v0)) & ! [v0:
% 45.38/7.02 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 45.38/7.02 ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 45.38/7.02 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (aElement0(v2) = v1) |
% 45.38/7.02 ~ (aElement0(v2) = v0))
% 45.38/7.02
% 45.38/7.02 Further assumptions not needed in the proof:
% 45.38/7.02 --------------------------------------------
% 45.38/7.02 mCConsSet, mCDiffSet, mCardCons, mCardDiff, mCardEmpty, mCardNum, mCardS,
% 45.38/7.02 mCardSeg, mCardSub, mCardSubEx, mCntRel, mConsDiff, mCountNFin_01, mDefCons,
% 45.38/7.02 mDefDiff, mDefEmp, mDefMax, mDefMin, mDefPtt, mDefRst, mDefSImg, mDefSeg,
% 45.38/7.02 mDefSel, mDiffCons, mDirichlet, mDomSet, mEOfElem, mElmSort, mEmpFin, mFConsSet,
% 45.38/7.02 mFDiffSet, mFinRel, mFinSubSeg, mFunSort, mIH, mIHSort, mImgCount, mImgElm,
% 45.38/7.02 mImgRng, mLessASymm, mLessRefl, mLessRel, mLessSucc, mLessTotal, mLessTrans,
% 45.38/7.02 mMinMin, mNatExtra, mNatNSucc, mNoScLessZr, mPttSet, mSegFin, mSegLess,
% 45.38/7.02 mSegSucc, mSegZero, mSelCSet, mSelExtra, mSelFSet, mSelNSet, mSelSub, mSetSort,
% 45.38/7.02 mSubASymm, mSubFSet, mSubRefl, mSuccEquSucc, mSuccLess, mSuccNum, mZeroLess,
% 45.38/7.02 mZeroNum, m__3291, m__3398, m__3418, m__3435, m__3453, m__3462, m__3520,
% 45.38/7.02 m__3533, m__3623, m__3671, m__3754, m__3821, m__3965, m__4151, m__4182, m__4331,
% 45.38/7.02 m__4411, m__4618, m__4660, m__4854, m__4982, m__4998, m__5078, m__5116, m__5147,
% 45.38/7.02 m__5173, m__5182
% 45.38/7.02
% 45.38/7.02 Those formulas are unsatisfiable:
% 45.38/7.02 ---------------------------------
% 45.38/7.02
% 45.38/7.02 Begin of proof
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (mNATSet) implies:
% 45.38/7.02 | (1) aSet0(szNzAzT0) = 0
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__4730) implies:
% 45.38/7.02 | (2) szDzozmdt0(xd) = szNzAzT0
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__4758) implies:
% 45.38/7.02 | (3) ? [v0: $i] : ? [v1: $i] : (sdtlcdtrc0(xd, v0) = v1 & szDzozmdt0(xd) =
% 45.38/7.02 | v0 & aSubsetOf0(v1, xT) = 0 & $i(v1) & $i(v0))
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__4891) implies:
% 45.38/7.02 | (4) ? [v0: $i] : ? [v1: $i] : (szDzizrdt0(xd) = v0 & sdtlcdtrc0(xe, v1) =
% 45.38/7.02 | xO & sdtlbdtrb0(xd, v0) = v1 & aSet0(xO) = 0 & $i(v1) & $i(v0))
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__4908) implies:
% 45.38/7.02 | (5) isCountable0(xO) = 0
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__5093) implies:
% 45.38/7.02 | (6) aSubsetOf0(xQ, xO) = 0
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__5106) implies:
% 45.38/7.02 | (7) aSubsetOf0(xQ, szNzAzT0) = 0
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__5164) implies:
% 45.38/7.02 | (8) ? [v0: $i] : (szmzizndt0(xQ) = v0 & sdtmndt0(xQ, v0) = xP & aSet0(xP)
% 45.38/7.02 | = 0 & $i(v0))
% 45.38/7.02 |
% 45.38/7.02 | ALPHA: (m__5195) implies:
% 45.54/7.02 | (9) $i(xQ)
% 45.54/7.02 | (10) aSubsetOf0(xP, xQ) = 0
% 45.54/7.02 |
% 45.54/7.02 | ALPHA: (m__) implies:
% 45.54/7.02 | (11) $i(xO)
% 45.54/7.02 | (12) $i(xP)
% 45.54/7.02 | (13) ? [v0: int] : ( ~ (v0 = 0) & aSubsetOf0(xP, xO) = v0)
% 45.54/7.02 |
% 45.54/7.02 | ALPHA: (function-axioms) implies:
% 45.54/7.02 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 45.54/7.02 | : (v1 = v0 | ~ (aSet0(v2) = v1) | ~ (aSet0(v2) = v0))
% 45.54/7.03 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 45.54/7.03 | (szDzozmdt0(v2) = v1) | ~ (szDzozmdt0(v2) = v0))
% 45.54/7.03 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 45.54/7.03 | : ! [v3: $i] : (v1 = v0 | ~ (aSubsetOf0(v3, v2) = v1) | ~
% 45.54/7.03 | (aSubsetOf0(v3, v2) = v0))
% 45.54/7.03 |
% 45.54/7.03 | DELTA: instantiating (13) with fresh symbol all_76_0 gives:
% 45.54/7.03 | (17) ~ (all_76_0 = 0) & aSubsetOf0(xP, xO) = all_76_0
% 45.54/7.03 |
% 45.54/7.03 | ALPHA: (17) implies:
% 45.54/7.03 | (18) ~ (all_76_0 = 0)
% 45.54/7.03 | (19) aSubsetOf0(xP, xO) = all_76_0
% 45.54/7.03 |
% 45.54/7.03 | DELTA: instantiating (8) with fresh symbol all_82_0 gives:
% 45.56/7.03 | (20) szmzizndt0(xQ) = all_82_0 & sdtmndt0(xQ, all_82_0) = xP & aSet0(xP) =
% 45.56/7.03 | 0 & $i(all_82_0)
% 45.56/7.03 |
% 45.56/7.03 | ALPHA: (20) implies:
% 45.56/7.03 | (21) aSet0(xP) = 0
% 45.56/7.03 |
% 45.56/7.03 | DELTA: instantiating (3) with fresh symbols all_84_0, all_84_1 gives:
% 45.56/7.03 | (22) sdtlcdtrc0(xd, all_84_1) = all_84_0 & szDzozmdt0(xd) = all_84_1 &
% 45.56/7.03 | aSubsetOf0(all_84_0, xT) = 0 & $i(all_84_0) & $i(all_84_1)
% 45.56/7.03 |
% 45.56/7.03 | ALPHA: (22) implies:
% 45.56/7.03 | (23) $i(all_84_1)
% 45.56/7.03 | (24) szDzozmdt0(xd) = all_84_1
% 45.56/7.03 |
% 45.56/7.03 | DELTA: instantiating (4) with fresh symbols all_88_0, all_88_1 gives:
% 45.56/7.03 | (25) szDzizrdt0(xd) = all_88_1 & sdtlcdtrc0(xe, all_88_0) = xO &
% 45.56/7.03 | sdtlbdtrb0(xd, all_88_1) = all_88_0 & aSet0(xO) = 0 & $i(all_88_0) &
% 45.56/7.03 | $i(all_88_1)
% 45.56/7.03 |
% 45.56/7.03 | ALPHA: (25) implies:
% 45.56/7.03 | (26) aSet0(xO) = 0
% 45.56/7.03 |
% 45.56/7.03 | GROUND_INST: instantiating (15) with szNzAzT0, all_84_1, xd, simplifying with
% 45.56/7.03 | (2), (24) gives:
% 45.56/7.03 | (27) all_84_1 = szNzAzT0
% 45.56/7.03 |
% 45.56/7.03 | REDUCE: (23), (27) imply:
% 45.56/7.03 | (28) $i(szNzAzT0)
% 45.56/7.03 |
% 45.56/7.03 | GROUND_INST: instantiating (mDefSub) with szNzAzT0, simplifying with (1), (28)
% 45.56/7.03 | gives:
% 45.56/7.03 | (29) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, szNzAzT0) =
% 45.56/7.03 | v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 45.56/7.03 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, szNzAzT0) = v3 & $i(v2))
% 45.56/7.03 | | ? [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 45.56/7.03 | (aSubsetOf0(v0, szNzAzT0) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & !
% 45.56/7.03 | [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, szNzAzT0)
% 45.56/7.03 | = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 45.56/7.03 | aElementOf0(v1, v0) = v3))))
% 45.56/7.03 |
% 45.56/7.03 | ALPHA: (29) implies:
% 45.56/7.03 | (30) ! [v0: $i] : ( ~ (aSubsetOf0(v0, szNzAzT0) = 0) | ~ $i(v0) |
% 45.56/7.03 | (aSet0(v0) = 0 & ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 45.56/7.03 | (aElementOf0(v1, szNzAzT0) = v2) | ~ $i(v1) | ? [v3: int] : (
% 45.56/7.03 | ~ (v3 = 0) & aElementOf0(v1, v0) = v3))))
% 45.56/7.03 |
% 45.56/7.03 | GROUND_INST: instantiating (mDefSub) with xO, simplifying with (11), (26)
% 45.56/7.03 | gives:
% 45.56/7.03 | (31) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xO) = v1) |
% 45.56/7.03 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 45.56/7.03 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xO) = v3 & $i(v2)) | ?
% 45.56/7.03 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2)) & ! [v0: $i] : ( ~
% 45.56/7.03 | (aSubsetOf0(v0, xO) = 0) | ~ $i(v0) | (aSet0(v0) = 0 & ! [v1: $i]
% 45.56/7.03 | : ! [v2: int] : (v2 = 0 | ~ (aElementOf0(v1, xO) = v2) | ~
% 45.56/7.03 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & aElementOf0(v1, v0) =
% 45.56/7.03 | v3))))
% 45.56/7.03 |
% 45.56/7.03 | ALPHA: (31) implies:
% 45.56/7.03 | (32) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (aSubsetOf0(v0, xO) = v1) |
% 45.56/7.03 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 45.56/7.03 | aElementOf0(v2, v0) = 0 & aElementOf0(v2, xO) = v3 & $i(v2)) | ?
% 45.56/7.03 | [v2: int] : ( ~ (v2 = 0) & aSet0(v0) = v2))
% 45.56/7.04 |
% 45.56/7.04 | GROUND_INST: instantiating (mCountNFin) with xO, simplifying with (5), (11)
% 45.56/7.04 | gives:
% 45.56/7.04 | (33) ? [v0: any] : ? [v1: any] : (isFinite0(xO) = v1 & aSet0(xO) = v0 & (
% 45.56/7.04 | ~ (v1 = 0) | ~ (v0 = 0)))
% 45.56/7.04 |
% 45.56/7.04 | GROUND_INST: instantiating (mSubTrans) with xP, xQ, xO, all_76_0, simplifying
% 45.56/7.04 | with (9), (10), (11), (12), (19) gives:
% 45.56/7.04 | (34) all_76_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3:
% 45.56/7.04 | any] : (aSubsetOf0(xQ, xO) = v3 & aSet0(xP) = v0 & aSet0(xQ) = v1 &
% 45.56/7.04 | aSet0(xO) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 45.56/7.04 | 0)))
% 45.56/7.04 |
% 45.56/7.04 | GROUND_INST: instantiating (32) with xP, all_76_0, simplifying with (12), (19)
% 45.56/7.04 | gives:
% 45.56/7.04 | (35) all_76_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 45.56/7.04 | aElementOf0(v0, xP) = 0 & aElementOf0(v0, xO) = v1 & $i(v0)) | ?
% 45.56/7.04 | [v0: int] : ( ~ (v0 = 0) & aSet0(xP) = v0)
% 45.56/7.04 |
% 45.56/7.04 | GROUND_INST: instantiating (30) with xQ, simplifying with (7), (9) gives:
% 45.56/7.04 | (36) aSet0(xQ) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 45.56/7.04 | (aElementOf0(v0, szNzAzT0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~
% 45.56/7.04 | (v2 = 0) & aElementOf0(v0, xQ) = v2))
% 45.56/7.04 |
% 45.56/7.04 | ALPHA: (36) implies:
% 45.56/7.04 | (37) aSet0(xQ) = 0
% 45.56/7.04 |
% 45.56/7.04 | DELTA: instantiating (33) with fresh symbols all_166_0, all_166_1 gives:
% 45.56/7.04 | (38) isFinite0(xO) = all_166_0 & aSet0(xO) = all_166_1 & ( ~ (all_166_0 =
% 45.56/7.04 | 0) | ~ (all_166_1 = 0))
% 45.56/7.04 |
% 45.56/7.04 | ALPHA: (38) implies:
% 45.56/7.04 | (39) aSet0(xO) = all_166_1
% 45.56/7.04 |
% 45.56/7.04 | BETA: splitting (34) gives:
% 45.56/7.04 |
% 45.56/7.04 | Case 1:
% 45.56/7.04 | |
% 45.56/7.04 | | (40) all_76_0 = 0
% 45.56/7.04 | |
% 45.56/7.04 | | REDUCE: (18), (40) imply:
% 45.56/7.04 | | (41) $false
% 45.56/7.04 | |
% 45.56/7.04 | | CLOSE: (41) is inconsistent.
% 45.56/7.04 | |
% 45.56/7.04 | Case 2:
% 45.56/7.04 | |
% 45.56/7.04 | | (42) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 45.56/7.04 | | (aSubsetOf0(xQ, xO) = v3 & aSet0(xP) = v0 & aSet0(xQ) = v1 &
% 45.56/7.04 | | aSet0(xO) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 45.56/7.04 | | = 0)))
% 45.56/7.04 | |
% 45.56/7.04 | | DELTA: instantiating (42) with fresh symbols all_394_0, all_394_1,
% 45.56/7.04 | | all_394_2, all_394_3 gives:
% 45.56/7.04 | | (43) aSubsetOf0(xQ, xO) = all_394_0 & aSet0(xP) = all_394_3 & aSet0(xQ) =
% 45.56/7.04 | | all_394_2 & aSet0(xO) = all_394_1 & ( ~ (all_394_0 = 0) | ~
% 45.56/7.04 | | (all_394_1 = 0) | ~ (all_394_2 = 0) | ~ (all_394_3 = 0))
% 45.56/7.04 | |
% 45.56/7.04 | | ALPHA: (43) implies:
% 45.56/7.04 | | (44) aSet0(xO) = all_394_1
% 45.56/7.04 | | (45) aSet0(xQ) = all_394_2
% 45.56/7.04 | | (46) aSet0(xP) = all_394_3
% 45.56/7.04 | | (47) aSubsetOf0(xQ, xO) = all_394_0
% 45.56/7.04 | | (48) ~ (all_394_0 = 0) | ~ (all_394_1 = 0) | ~ (all_394_2 = 0) | ~
% 45.56/7.04 | | (all_394_3 = 0)
% 45.56/7.04 | |
% 45.56/7.04 | | BETA: splitting (35) gives:
% 45.56/7.04 | |
% 45.56/7.04 | | Case 1:
% 45.56/7.04 | | |
% 45.56/7.04 | | | (49) all_76_0 = 0
% 45.56/7.04 | | |
% 45.56/7.04 | | | REDUCE: (18), (49) imply:
% 45.56/7.04 | | | (50) $false
% 45.56/7.04 | | |
% 45.56/7.04 | | | CLOSE: (50) is inconsistent.
% 45.56/7.04 | | |
% 45.56/7.04 | | Case 2:
% 45.56/7.04 | | |
% 45.56/7.04 | | |
% 45.56/7.04 | | | GROUND_INST: instantiating (14) with 0, all_394_1, xO, simplifying with
% 45.56/7.04 | | | (26), (44) gives:
% 45.56/7.04 | | | (51) all_394_1 = 0
% 45.56/7.04 | | |
% 45.56/7.04 | | | GROUND_INST: instantiating (14) with all_166_1, all_394_1, xO, simplifying
% 45.56/7.04 | | | with (39), (44) gives:
% 45.56/7.04 | | | (52) all_394_1 = all_166_1
% 45.56/7.04 | | |
% 45.56/7.05 | | | GROUND_INST: instantiating (14) with 0, all_394_2, xQ, simplifying with
% 45.56/7.05 | | | (37), (45) gives:
% 45.56/7.05 | | | (53) all_394_2 = 0
% 45.56/7.05 | | |
% 45.56/7.05 | | | GROUND_INST: instantiating (14) with 0, all_394_3, xP, simplifying with
% 45.56/7.05 | | | (21), (46) gives:
% 45.56/7.05 | | | (54) all_394_3 = 0
% 45.56/7.05 | | |
% 45.56/7.05 | | | GROUND_INST: instantiating (16) with 0, all_394_0, xO, xQ, simplifying
% 45.56/7.05 | | | with (6), (47) gives:
% 45.56/7.05 | | | (55) all_394_0 = 0
% 45.56/7.05 | | |
% 45.56/7.05 | | | COMBINE_EQS: (51), (52) imply:
% 45.56/7.05 | | | (56) all_166_1 = 0
% 45.56/7.05 | | |
% 45.56/7.05 | | | BETA: splitting (48) gives:
% 45.56/7.05 | | |
% 45.56/7.05 | | | Case 1:
% 45.56/7.05 | | | |
% 45.56/7.05 | | | | (57) ~ (all_394_0 = 0)
% 45.56/7.05 | | | |
% 45.56/7.05 | | | | REDUCE: (55), (57) imply:
% 45.56/7.05 | | | | (58) $false
% 45.56/7.05 | | | |
% 45.56/7.05 | | | | CLOSE: (58) is inconsistent.
% 45.56/7.05 | | | |
% 45.56/7.05 | | | Case 2:
% 45.56/7.05 | | | |
% 45.56/7.05 | | | | (59) ~ (all_394_1 = 0) | ~ (all_394_2 = 0) | ~ (all_394_3 = 0)
% 45.56/7.05 | | | |
% 45.56/7.05 | | | | BETA: splitting (59) gives:
% 45.56/7.05 | | | |
% 45.56/7.05 | | | | Case 1:
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | | (60) ~ (all_394_1 = 0)
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | | REDUCE: (51), (60) imply:
% 45.56/7.05 | | | | | (61) $false
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | | CLOSE: (61) is inconsistent.
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | Case 2:
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | | (62) ~ (all_394_2 = 0) | ~ (all_394_3 = 0)
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | | BETA: splitting (62) gives:
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | | Case 1:
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | | (63) ~ (all_394_2 = 0)
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | | REDUCE: (53), (63) imply:
% 45.56/7.05 | | | | | | (64) $false
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | | CLOSE: (64) is inconsistent.
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | Case 2:
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | | (65) ~ (all_394_3 = 0)
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | | REDUCE: (54), (65) imply:
% 45.56/7.05 | | | | | | (66) $false
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | | CLOSE: (66) is inconsistent.
% 45.56/7.05 | | | | | |
% 45.56/7.05 | | | | | End of split
% 45.56/7.05 | | | | |
% 45.56/7.05 | | | | End of split
% 45.56/7.05 | | | |
% 45.56/7.05 | | | End of split
% 45.56/7.05 | | |
% 45.56/7.05 | | End of split
% 45.56/7.05 | |
% 45.56/7.05 | End of split
% 45.56/7.05 |
% 45.56/7.05 End of proof
% 45.56/7.05 % SZS output end Proof for theBenchmark
% 45.56/7.05
% 45.56/7.05 6334ms
%------------------------------------------------------------------------------