TSTP Solution File: NUM536+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : NUM536+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 : n006.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 11:48:27 EDT 2023
% Result : Theorem 27.38s 4.43s
% Output : Proof 27.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM536+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 14:58:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.60 ________ _____
% 0.18/0.60 ___ __ \_________(_)________________________________
% 0.18/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.60
% 0.18/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.60 (2023-06-19)
% 0.18/0.60
% 0.18/0.60 (c) Philipp Rümmer, 2009-2023
% 0.18/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.60 Amanda Stjerna.
% 0.18/0.60 Free software under BSD-3-Clause.
% 0.18/0.60
% 0.18/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.60
% 0.18/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61 Running up to 7 provers in parallel.
% 0.18/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.24/1.08 Prover 4: Preprocessing ...
% 2.24/1.08 Prover 1: Preprocessing ...
% 2.75/1.12 Prover 6: Preprocessing ...
% 2.75/1.12 Prover 2: Preprocessing ...
% 2.75/1.12 Prover 5: Preprocessing ...
% 2.75/1.12 Prover 3: Preprocessing ...
% 2.75/1.12 Prover 0: Preprocessing ...
% 6.08/1.57 Prover 5: Constructing countermodel ...
% 6.08/1.58 Prover 3: Constructing countermodel ...
% 6.08/1.58 Prover 1: Constructing countermodel ...
% 6.26/1.61 Prover 2: Proving ...
% 6.26/1.61 Prover 6: Proving ...
% 7.59/1.86 Prover 4: Constructing countermodel ...
% 8.74/1.93 Prover 0: Proving ...
% 8.74/2.02 Prover 3: gave up
% 8.74/2.02 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.74/2.05 Prover 7: Preprocessing ...
% 9.46/2.18 Prover 1: gave up
% 9.46/2.19 Prover 7: Constructing countermodel ...
% 9.46/2.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 10.56/2.23 Prover 8: Preprocessing ...
% 11.41/2.36 Prover 8: Warning: ignoring some quantifiers
% 11.41/2.37 Prover 8: Constructing countermodel ...
% 15.69/2.95 Prover 8: gave up
% 15.69/2.96 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 16.38/2.98 Prover 9: Preprocessing ...
% 17.48/3.12 Prover 9: Constructing countermodel ...
% 22.08/3.74 Prover 9: gave up
% 22.08/3.74 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.08/3.76 Prover 10: Preprocessing ...
% 22.08/3.78 Prover 10: Constructing countermodel ...
% 27.38/4.42 Prover 10: Found proof (size 65)
% 27.38/4.42 Prover 10: proved (684ms)
% 27.38/4.42 Prover 5: stopped
% 27.38/4.43 Prover 7: stopped
% 27.38/4.43 Prover 2: stopped
% 27.38/4.43 Prover 6: stopped
% 27.38/4.43 Prover 0: stopped
% 27.38/4.43 Prover 4: stopped
% 27.38/4.43
% 27.38/4.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.38/4.43
% 27.54/4.43 % SZS output start Proof for theBenchmark
% 27.54/4.44 Assumptions after simplification:
% 27.54/4.44 ---------------------------------
% 27.54/4.44
% 27.54/4.44 (mDefCons)
% 27.54/4.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 27.54/4.47 (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 27.54/4.47 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & ( ~
% 27.54/4.47 aElementOf0(v4, v3) | ~ aElement0(v4) | ( ~ (v4 = v1) & ~
% 27.54/4.47 aElementOf0(v4, v0))) & (aElementOf0(v4, v3) | (aElement0(v4) & (v4 =
% 27.54/4.47 v1 | aElementOf0(v4, v0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 27.54/4.47 $i] : ! [v3: $i] : (v3 = v1 | ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~
% 27.54/4.47 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) |
% 27.54/4.47 ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 27.54/4.47 $i] : ! [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 27.54/4.47 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~
% 27.54/4.47 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 27.54/4.47 [v3: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 27.54/4.47 ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1) | ~
% 27.54/4.47 aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 27.54/4.47 ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.54/4.47 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v1, v2)) & ! [v0: $i] : ! [v1:
% 27.54/4.47 $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~
% 27.54/4.47 $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 27.54/4.47
% 27.54/4.47 (mDefDiff)
% 27.54/4.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 27.54/4.48 (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 27.54/4.48 aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) & (v4 =
% 27.54/4.48 v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~ aElement0(v4))
% 27.54/4.48 & (aElementOf0(v4, v3) | ( ~ (v4 = v1) & aElementOf0(v4, v0) &
% 27.54/4.48 aElement0(v4))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 27.54/4.48 $i] : (v3 = v1 | ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 27.54/4.48 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~
% 27.54/4.48 aElement0(v1) | ~ aSet0(v0) | aElementOf0(v3, v2)) & ! [v0: $i] : ! [v1:
% 27.54/4.48 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) |
% 27.54/4.48 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1)
% 27.54/4.48 | ~ aSet0(v0) | aElementOf0(v3, v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 27.54/4.48 $i] : ! [v3: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~
% 27.54/4.48 $i(v1) | ~ $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~
% 27.54/4.48 aSet0(v0) | aElement0(v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 27.54/4.48 (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~
% 27.54/4.48 aElementOf0(v1, v2) | ~ aElement0(v1) | ~ aSet0(v0)) & ! [v0: $i] : !
% 27.54/4.48 [v1: $i] : ! [v2: $i] : ( ~ (sdtmndt0(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) |
% 27.54/4.48 ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) | aSet0(v2))
% 27.54/4.48
% 27.54/4.48 (mDefSub)
% 27.54/4.48 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 27.54/4.48 ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~ aSet0(v0) |
% 27.54/4.48 aElementOf0(v2, v0)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) |
% 27.54/4.48 ~ aSubsetOf0(v1, v0) | ~ aSet0(v0) | aSet0(v1)) & ! [v0: $i] : ! [v1: $i]
% 27.54/4.48 : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~ aSet0(v0) | aSubsetOf0(v1, v0) |
% 27.54/4.48 ? [v2: $i] : ($i(v2) & aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 27.54/4.48
% 27.54/4.48 (mEOfElem)
% 27.54/4.48 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aElementOf0(v1, v0) |
% 27.54/4.48 ~ aSet0(v0) | aElement0(v1))
% 27.54/4.48
% 27.54/4.48 (m__)
% 27.54/4.48 $i(xS) & $i(xx) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(v0, xx)
% 27.54/4.48 = v1 & sdtpldt0(xS, xx) = v0 & $i(v1) & $i(v0))
% 27.54/4.48
% 27.54/4.48 (m__679)
% 27.54/4.48 $i(xS) & $i(xx) & aElement0(xx) & aSet0(xS)
% 27.54/4.48
% 27.54/4.48 (m__679_02)
% 27.54/4.48 $i(xS) & $i(xx) & ~ aElementOf0(xx, xS)
% 27.54/4.48
% 27.54/4.48 Further assumptions not needed in the proof:
% 27.54/4.48 --------------------------------------------
% 27.54/4.48 mCntRel, mConsDiff, mCountNFin, mCountNFin_01, mDefEmp, mElmSort, mEmpFin,
% 27.54/4.48 mFinRel, mSetSort, mSubASymm, mSubFSet, mSubRefl, mSubTrans
% 27.54/4.48
% 27.54/4.48 Those formulas are unsatisfiable:
% 27.54/4.48 ---------------------------------
% 27.54/4.48
% 27.54/4.48 Begin of proof
% 27.54/4.48 |
% 27.54/4.48 | ALPHA: (mDefSub) implies:
% 27.54/4.48 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ aSet0(v1) | ~
% 27.54/4.48 | aSet0(v0) | aSubsetOf0(v1, v0) | ? [v2: $i] : ($i(v2) &
% 27.54/4.48 | aElementOf0(v2, v1) & ~ aElementOf0(v2, v0)))
% 27.54/4.48 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~
% 27.54/4.48 | $i(v0) | ~ aSubsetOf0(v1, v0) | ~ aElementOf0(v2, v1) | ~
% 27.54/4.48 | aSet0(v0) | aElementOf0(v2, v0))
% 27.54/4.48 |
% 27.54/4.48 | ALPHA: (mDefCons) implies:
% 27.54/4.48 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 27.54/4.48 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) |
% 27.54/4.48 | aSet0(v2))
% 27.54/4.48 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (sdtpldt0(v0, v1) = v2) |
% 27.54/4.48 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ aElement0(v1) | ~ aSet0(v0) |
% 27.54/4.48 | aElementOf0(v1, v2))
% 27.54/4.49 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 27.54/4.49 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 27.54/4.49 | $i(v0) | ~ aElementOf0(v3, v0) | ~ aElement0(v3) | ~ aElement0(v1)
% 27.54/4.49 | | ~ aSet0(v0) | aElementOf0(v3, v2))
% 27.54/4.49 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | ~
% 27.54/4.49 | (sdtpldt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 27.54/4.49 | $i(v0) | ~ aElementOf0(v3, v2) | ~ aElement0(v1) | ~ aSet0(v0) |
% 27.54/4.49 | aElementOf0(v3, v0))
% 27.54/4.49 |
% 27.54/4.49 | ALPHA: (mDefDiff) implies:
% 27.54/4.49 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v2 | ~
% 27.54/4.49 | (sdtmndt0(v0, v1) = v2) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ~
% 27.54/4.49 | aElement0(v1) | ~ aSet0(v3) | ~ aSet0(v0) | ? [v4: $i] : ($i(v4) &
% 27.54/4.49 | (v4 = v1 | ~ aElementOf0(v4, v3) | ~ aElementOf0(v4, v0) | ~
% 27.54/4.49 | aElement0(v4)) & (aElementOf0(v4, v3) | ( ~ (v4 = v1) &
% 27.54/4.49 | aElementOf0(v4, v0) & aElement0(v4)))))
% 27.54/4.49 |
% 27.54/4.49 | ALPHA: (m__679) implies:
% 27.54/4.49 | (8) aSet0(xS)
% 27.54/4.49 | (9) aElement0(xx)
% 27.54/4.49 |
% 27.54/4.49 | ALPHA: (m__679_02) implies:
% 27.54/4.49 | (10) ~ aElementOf0(xx, xS)
% 27.54/4.49 |
% 27.54/4.49 | ALPHA: (m__) implies:
% 27.54/4.49 | (11) $i(xx)
% 27.54/4.49 | (12) $i(xS)
% 27.54/4.49 | (13) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = xS) & sdtmndt0(v0, xx) = v1 &
% 27.54/4.49 | sdtpldt0(xS, xx) = v0 & $i(v1) & $i(v0))
% 27.54/4.49 |
% 27.54/4.49 | DELTA: instantiating (13) with fresh symbols all_15_0, all_15_1 gives:
% 27.54/4.49 | (14) ~ (all_15_0 = xS) & sdtmndt0(all_15_1, xx) = all_15_0 & sdtpldt0(xS,
% 27.54/4.49 | xx) = all_15_1 & $i(all_15_0) & $i(all_15_1)
% 27.54/4.49 |
% 27.54/4.49 | ALPHA: (14) implies:
% 27.54/4.49 | (15) ~ (all_15_0 = xS)
% 27.54/4.49 | (16) $i(all_15_1)
% 27.54/4.49 | (17) sdtpldt0(xS, xx) = all_15_1
% 27.54/4.49 | (18) sdtmndt0(all_15_1, xx) = all_15_0
% 27.54/4.49 |
% 27.54/4.49 | GROUND_INST: instantiating (4) with xS, xx, all_15_1, simplifying with (8),
% 27.54/4.49 | (9), (11), (12), (16), (17) gives:
% 27.54/4.49 | (19) aElementOf0(xx, all_15_1)
% 27.54/4.49 |
% 27.54/4.49 | GROUND_INST: instantiating (3) with xS, xx, all_15_1, simplifying with (8),
% 27.54/4.49 | (9), (11), (12), (16), (17) gives:
% 27.54/4.49 | (20) aSet0(all_15_1)
% 27.54/4.49 |
% 27.54/4.49 | GROUND_INST: instantiating (7) with all_15_1, xx, all_15_0, xS, simplifying
% 27.54/4.49 | with (8), (9), (11), (12), (16), (18), (20) gives:
% 27.54/4.49 | (21) all_15_0 = xS | ? [v0: $i] : ($i(v0) & (v0 = xx | ~ aElementOf0(v0,
% 27.54/4.49 | all_15_1) | ~ aElementOf0(v0, xS) | ~ aElement0(v0)) &
% 27.54/4.49 | (aElementOf0(v0, xS) | ( ~ (v0 = xx) & aElementOf0(v0, all_15_1) &
% 27.54/4.49 | aElement0(v0))))
% 27.54/4.49 |
% 27.54/4.49 | GROUND_INST: instantiating (1) with xS, all_15_1, simplifying with (8), (12),
% 27.54/4.49 | (16), (20) gives:
% 27.54/4.49 | (22) aSubsetOf0(all_15_1, xS) | ? [v0: $i] : ($i(v0) & aElementOf0(v0,
% 27.54/4.49 | all_15_1) & ~ aElementOf0(v0, xS))
% 27.54/4.49 |
% 27.54/4.49 | GROUND_INST: instantiating (1) with all_15_1, xS, simplifying with (8), (12),
% 27.54/4.49 | (16), (20) gives:
% 27.54/4.49 | (23) aSubsetOf0(xS, all_15_1) | ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS)
% 27.54/4.49 | & ~ aElementOf0(v0, all_15_1))
% 27.54/4.49 |
% 27.54/4.49 | BETA: splitting (21) gives:
% 27.54/4.49 |
% 27.54/4.50 | Case 1:
% 27.54/4.50 | |
% 27.54/4.50 | | (24) all_15_0 = xS
% 27.54/4.50 | |
% 27.54/4.50 | | REDUCE: (15), (24) imply:
% 27.54/4.50 | | (25) $false
% 27.54/4.50 | |
% 27.54/4.50 | | CLOSE: (25) is inconsistent.
% 27.54/4.50 | |
% 27.54/4.50 | Case 2:
% 27.54/4.50 | |
% 27.54/4.50 | | (26) ? [v0: $i] : ($i(v0) & (v0 = xx | ~ aElementOf0(v0, all_15_1) | ~
% 27.54/4.50 | | aElementOf0(v0, xS) | ~ aElement0(v0)) & (aElementOf0(v0, xS) |
% 27.54/4.50 | | ( ~ (v0 = xx) & aElementOf0(v0, all_15_1) & aElement0(v0))))
% 27.54/4.50 | |
% 27.54/4.50 | | DELTA: instantiating (26) with fresh symbol all_37_0 gives:
% 27.54/4.50 | | (27) $i(all_37_0) & (all_37_0 = xx | ~ aElementOf0(all_37_0, all_15_1) |
% 27.54/4.50 | | ~ aElementOf0(all_37_0, xS) | ~ aElement0(all_37_0)) &
% 27.54/4.50 | | (aElementOf0(all_37_0, xS) | ( ~ (all_37_0 = xx) &
% 27.54/4.50 | | aElementOf0(all_37_0, all_15_1) & aElement0(all_37_0)))
% 27.54/4.50 | |
% 27.54/4.50 | | ALPHA: (27) implies:
% 27.54/4.50 | | (28) $i(all_37_0)
% 27.54/4.50 | | (29) aElementOf0(all_37_0, xS) | ( ~ (all_37_0 = xx) &
% 27.54/4.50 | | aElementOf0(all_37_0, all_15_1) & aElement0(all_37_0))
% 27.54/4.50 | | (30) all_37_0 = xx | ~ aElementOf0(all_37_0, all_15_1) | ~
% 27.54/4.50 | | aElementOf0(all_37_0, xS) | ~ aElement0(all_37_0)
% 27.54/4.50 | |
% 27.54/4.50 | | BETA: splitting (22) gives:
% 27.54/4.50 | |
% 27.54/4.50 | | Case 1:
% 27.54/4.50 | | |
% 27.54/4.50 | | | (31) aSubsetOf0(all_15_1, xS)
% 27.54/4.50 | | |
% 27.54/4.50 | | | GROUND_INST: instantiating (2) with xS, all_15_1, xx, simplifying with
% 27.54/4.50 | | | (8), (10), (11), (12), (16), (19), (31) gives:
% 27.54/4.50 | | | (32) $false
% 27.54/4.50 | | |
% 27.54/4.50 | | | CLOSE: (32) is inconsistent.
% 27.54/4.50 | | |
% 27.54/4.50 | | Case 2:
% 27.54/4.50 | | |
% 27.54/4.50 | | | (33) ? [v0: $i] : ($i(v0) & aElementOf0(v0, all_15_1) & ~
% 27.54/4.50 | | | aElementOf0(v0, xS))
% 27.54/4.50 | | |
% 27.54/4.50 | | | DELTA: instantiating (33) with fresh symbol all_131_0 gives:
% 27.54/4.50 | | | (34) $i(all_131_0) & aElementOf0(all_131_0, all_15_1) & ~
% 27.54/4.50 | | | aElementOf0(all_131_0, xS)
% 27.54/4.50 | | |
% 27.54/4.50 | | | ALPHA: (34) implies:
% 27.54/4.50 | | | (35) ~ aElementOf0(all_131_0, xS)
% 27.54/4.50 | | | (36) aElementOf0(all_131_0, all_15_1)
% 27.54/4.50 | | | (37) $i(all_131_0)
% 27.54/4.50 | | |
% 27.54/4.50 | | | BETA: splitting (23) gives:
% 27.54/4.50 | | |
% 27.54/4.50 | | | Case 1:
% 27.54/4.50 | | | |
% 27.54/4.50 | | | | (38) aSubsetOf0(xS, all_15_1)
% 27.54/4.50 | | | |
% 27.54/4.50 | | | | GROUND_INST: instantiating (6) with xS, xx, all_15_1, all_131_0,
% 27.54/4.50 | | | | simplifying with (8), (9), (11), (12), (16), (17), (35),
% 27.54/4.50 | | | | (36), (37) gives:
% 27.54/4.50 | | | | (39) all_131_0 = xx
% 27.54/4.50 | | | |
% 27.54/4.50 | | | | GROUND_INST: instantiating (mEOfElem) with all_15_1, all_131_0,
% 27.54/4.50 | | | | simplifying with (16), (20), (36), (37) gives:
% 27.54/4.50 | | | | (40) aElement0(all_131_0)
% 27.54/4.50 | | | |
% 27.54/4.50 | | | | BETA: splitting (29) gives:
% 27.54/4.50 | | | |
% 27.54/4.50 | | | | Case 1:
% 27.54/4.50 | | | | |
% 27.54/4.50 | | | | | (41) aElementOf0(all_37_0, xS)
% 27.54/4.50 | | | | |
% 27.54/4.50 | | | | | BETA: splitting (30) gives:
% 27.54/4.50 | | | | |
% 27.54/4.50 | | | | | Case 1:
% 27.54/4.50 | | | | | |
% 27.54/4.50 | | | | | | (42) ~ aElementOf0(all_37_0, xS)
% 27.54/4.50 | | | | | |
% 27.54/4.50 | | | | | | PRED_UNIFY: (41), (42) imply:
% 27.54/4.50 | | | | | | (43) $false
% 27.54/4.50 | | | | | |
% 27.54/4.50 | | | | | | CLOSE: (43) is inconsistent.
% 27.54/4.50 | | | | | |
% 27.54/4.50 | | | | | Case 2:
% 27.54/4.50 | | | | | |
% 27.54/4.50 | | | | | | (44) all_37_0 = xx | ~ aElementOf0(all_37_0, all_15_1) | ~
% 27.54/4.50 | | | | | | aElement0(all_37_0)
% 27.54/4.50 | | | | | |
% 27.54/4.50 | | | | | | GROUND_INST: instantiating (2) with all_15_1, xS, all_37_0,
% 27.54/4.50 | | | | | | simplifying with (12), (16), (20), (28), (38), (41)
% 27.54/4.50 | | | | | | gives:
% 27.54/4.50 | | | | | | (45) aElementOf0(all_37_0, all_15_1)
% 27.54/4.50 | | | | | |
% 27.54/4.51 | | | | | | GROUND_INST: instantiating (mEOfElem) with xS, all_37_0, simplifying
% 27.54/4.51 | | | | | | with (8), (12), (28), (41) gives:
% 27.54/4.51 | | | | | | (46) aElement0(all_37_0)
% 27.54/4.51 | | | | | |
% 27.54/4.51 | | | | | | BETA: splitting (44) gives:
% 27.54/4.51 | | | | | |
% 27.54/4.51 | | | | | | Case 1:
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | | (47) ~ aElementOf0(all_37_0, all_15_1)
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | | PRED_UNIFY: (45), (47) imply:
% 27.54/4.51 | | | | | | | (48) $false
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | | CLOSE: (48) is inconsistent.
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | Case 2:
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | | (49) all_37_0 = xx | ~ aElement0(all_37_0)
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | | BETA: splitting (49) gives:
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | | Case 1:
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | (50) ~ aElement0(all_37_0)
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | PRED_UNIFY: (46), (50) imply:
% 27.54/4.51 | | | | | | | | (51) $false
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | CLOSE: (51) is inconsistent.
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | Case 2:
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | (52) all_37_0 = xx
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | REDUCE: (41), (52) imply:
% 27.54/4.51 | | | | | | | | (53) aElementOf0(xx, xS)
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | PRED_UNIFY: (10), (53) imply:
% 27.54/4.51 | | | | | | | | (54) $false
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | | CLOSE: (54) is inconsistent.
% 27.54/4.51 | | | | | | | |
% 27.54/4.51 | | | | | | | End of split
% 27.54/4.51 | | | | | | |
% 27.54/4.51 | | | | | | End of split
% 27.54/4.51 | | | | | |
% 27.54/4.51 | | | | | End of split
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | Case 2:
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | | (55) ~ aElementOf0(all_37_0, xS)
% 27.54/4.51 | | | | | (56) ~ (all_37_0 = xx) & aElementOf0(all_37_0, all_15_1) &
% 27.54/4.51 | | | | | aElement0(all_37_0)
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | | ALPHA: (56) implies:
% 27.54/4.51 | | | | | (57) ~ (all_37_0 = xx)
% 27.54/4.51 | | | | | (58) aElementOf0(all_37_0, all_15_1)
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | | GROUND_INST: instantiating (6) with xS, xx, all_15_1, all_37_0,
% 27.54/4.51 | | | | | simplifying with (8), (9), (11), (12), (16), (17), (28),
% 27.54/4.51 | | | | | (55), (58) gives:
% 27.54/4.51 | | | | | (59) all_37_0 = xx
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | | REDUCE: (57), (59) imply:
% 27.54/4.51 | | | | | (60) $false
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | | CLOSE: (60) is inconsistent.
% 27.54/4.51 | | | | |
% 27.54/4.51 | | | | End of split
% 27.54/4.51 | | | |
% 27.54/4.51 | | | Case 2:
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | (61) ? [v0: $i] : ($i(v0) & aElementOf0(v0, xS) & ~ aElementOf0(v0,
% 27.54/4.51 | | | | all_15_1))
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | DELTA: instantiating (61) with fresh symbol all_153_0 gives:
% 27.54/4.51 | | | | (62) $i(all_153_0) & aElementOf0(all_153_0, xS) & ~
% 27.54/4.51 | | | | aElementOf0(all_153_0, all_15_1)
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | ALPHA: (62) implies:
% 27.54/4.51 | | | | (63) ~ aElementOf0(all_153_0, all_15_1)
% 27.54/4.51 | | | | (64) aElementOf0(all_153_0, xS)
% 27.54/4.51 | | | | (65) $i(all_153_0)
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | GROUND_INST: instantiating (6) with xS, xx, all_15_1, all_131_0,
% 27.54/4.51 | | | | simplifying with (8), (9), (11), (12), (16), (17), (35),
% 27.54/4.51 | | | | (36), (37) gives:
% 27.54/4.51 | | | | (66) all_131_0 = xx
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | GROUND_INST: instantiating (mEOfElem) with all_15_1, all_131_0,
% 27.54/4.51 | | | | simplifying with (16), (20), (36), (37) gives:
% 27.54/4.51 | | | | (67) aElement0(all_131_0)
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | GROUND_INST: instantiating (mEOfElem) with xS, all_153_0, simplifying
% 27.54/4.51 | | | | with (8), (12), (64), (65) gives:
% 27.54/4.51 | | | | (68) aElement0(all_153_0)
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | GROUND_INST: instantiating (5) with xS, xx, all_15_1, all_153_0,
% 27.54/4.51 | | | | simplifying with (8), (9), (11), (12), (16), (17), (63),
% 27.54/4.51 | | | | (64), (65), (68) gives:
% 27.54/4.51 | | | | (69) $false
% 27.54/4.51 | | | |
% 27.54/4.51 | | | | CLOSE: (69) is inconsistent.
% 27.54/4.51 | | | |
% 27.54/4.51 | | | End of split
% 27.54/4.51 | | |
% 27.54/4.51 | | End of split
% 27.54/4.51 | |
% 27.54/4.51 | End of split
% 27.54/4.51 |
% 27.54/4.51 End of proof
% 27.54/4.51 % SZS output end Proof for theBenchmark
% 27.54/4.51
% 27.54/4.51 3913ms
%------------------------------------------------------------------------------