TSTP Solution File: SET808+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET808+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n011.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 15:26:32 EDT 2023
% Result : Theorem 283.61s 39.22s
% Output : Proof 284.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET808+4 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n011.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 : Sat Aug 26 12:04:54 EDT 2023
% 0.12/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.84/1.14 Prover 1: Preprocessing ...
% 2.84/1.16 Prover 4: Preprocessing ...
% 2.84/1.18 Prover 3: Preprocessing ...
% 2.84/1.18 Prover 0: Preprocessing ...
% 2.84/1.18 Prover 5: Preprocessing ...
% 2.84/1.18 Prover 2: Preprocessing ...
% 2.84/1.18 Prover 6: Preprocessing ...
% 6.36/1.68 Prover 5: Proving ...
% 6.83/1.70 Prover 2: Proving ...
% 6.83/1.73 Prover 6: Proving ...
% 6.83/1.74 Prover 3: Constructing countermodel ...
% 6.83/1.75 Prover 1: Constructing countermodel ...
% 7.95/1.88 Prover 3: gave up
% 7.95/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.95/1.89 Prover 1: gave up
% 7.95/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.95/1.90 Prover 6: gave up
% 7.95/1.90 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 7.95/1.95 Prover 4: Constructing countermodel ...
% 7.95/1.95 Prover 7: Preprocessing ...
% 7.95/1.96 Prover 9: Preprocessing ...
% 7.95/1.96 Prover 8: Preprocessing ...
% 7.95/2.00 Prover 0: Proving ...
% 9.82/2.11 Prover 7: Warning: ignoring some quantifiers
% 9.82/2.14 Prover 8: Warning: ignoring some quantifiers
% 9.82/2.14 Prover 7: Constructing countermodel ...
% 10.41/2.17 Prover 8: Constructing countermodel ...
% 10.88/2.28 Prover 8: gave up
% 10.88/2.29 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.59/2.33 Prover 10: Preprocessing ...
% 11.59/2.34 Prover 9: Constructing countermodel ...
% 12.13/2.40 Prover 7: gave up
% 12.13/2.40 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.13/2.42 Prover 11: Preprocessing ...
% 12.13/2.44 Prover 10: Warning: ignoring some quantifiers
% 12.13/2.46 Prover 10: Constructing countermodel ...
% 13.04/2.55 Prover 10: gave up
% 13.04/2.55 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 13.04/2.57 Prover 12: Preprocessing ...
% 14.39/2.71 Prover 11: Constructing countermodel ...
% 15.01/2.80 Prover 12: Proving ...
% 35.72/5.51 Prover 12: stopped
% 35.94/5.52 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.94/5.55 Prover 13: Preprocessing ...
% 36.66/5.61 Prover 13: Warning: ignoring some quantifiers
% 36.66/5.63 Prover 13: Constructing countermodel ...
% 57.42/8.31 Prover 2: stopped
% 57.42/8.34 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 58.08/8.37 Prover 14: Preprocessing ...
% 59.68/8.64 Prover 14: Proving ...
% 74.61/10.54 Prover 13: stopped
% 74.61/10.55 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181
% 74.61/10.58 Prover 15: Preprocessing ...
% 75.83/10.70 Prover 15: Proving ...
% 100.77/13.97 Prover 5: stopped
% 100.98/13.99 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 101.35/14.03 Prover 16: Preprocessing ...
% 102.02/14.12 Prover 16: Warning: ignoring some quantifiers
% 102.02/14.12 Prover 16: Constructing countermodel ...
% 138.21/18.97 Prover 16: stopped
% 138.94/19.04 Prover 17: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=642448422
% 138.94/19.08 Prover 17: Preprocessing ...
% 139.35/19.13 Prover 17: Proving ...
% 139.35/19.14 Prover 17: gave up
% 139.35/19.14 Prover 18: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-219651170
% 139.85/19.16 Prover 18: Preprocessing ...
% 140.24/19.22 Prover 18: Warning: ignoring some quantifiers
% 140.24/19.24 Prover 18: Constructing countermodel ...
% 140.24/19.25 Prover 18: gave up
% 140.24/19.30 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 140.24/19.32 Prover 19: Preprocessing ...
% 140.90/19.40 Prover 19: Warning: ignoring some quantifiers
% 140.90/19.41 Prover 19: Constructing countermodel ...
% 141.94/19.47 Prover 19: gave up
% 141.94/19.48 Prover 20: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=2065050644
% 142.32/19.50 Prover 20: Preprocessing ...
% 142.86/19.57 Prover 20: Proving ...
% 204.30/27.99 Prover 4: stopped
% 204.30/28.00 Prover 21: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=201956991
% 204.30/28.01 Prover 21: Preprocessing ...
% 204.74/28.04 Prover 21: Proving ...
% 283.61/39.22 Prover 11: Found proof (size 198)
% 283.61/39.22 Prover 11: proved (36825ms)
% 283.61/39.22 Prover 15: stopped
% 283.61/39.22 Prover 20: stopped
% 283.61/39.22 Prover 9: stopped
% 283.61/39.22 Prover 21: stopped
% 283.61/39.22 Prover 14: stopped
% 283.61/39.22 Prover 0: stopped
% 283.61/39.22
% 283.61/39.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 283.61/39.22
% 283.89/39.23 % SZS output start Proof for theBenchmark
% 283.89/39.23 Assumptions after simplification:
% 283.89/39.23 ---------------------------------
% 283.89/39.23
% 283.89/39.23 (ordinal_number)
% 283.92/39.27 $i(member_predicate) & $i(on) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 283.92/39.27 = 0 | ~ (subset(v1, v0) = v2) | ~ (member(v0, on) = 0) | ~ $i(v1) | ~
% 283.92/39.27 $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3)) & ! [v0: $i] :
% 283.92/39.27 ! [v1: int] : (v1 = 0 | ~ (member(v0, on) = v1) | ~ $i(v0) | ? [v2: int] :
% 283.92/39.27 ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 =
% 283.92/39.27 0 & ~ (v6 = 0) & subset(v4, v0) = v6 & member(v4, v0) = 0) | ( ~ (v3
% 283.92/39.27 = 0) & strict_well_order(member_predicate, v0) = v3) | ( ~ (v2 = 0)
% 283.92/39.27 & set(v0) = v2)))) & ! [v0: $i] : ! [v1: any] : ( ~
% 283.92/39.27 (strict_well_order(member_predicate, v0) = v1) | ~ $i(v0) | ? [v2: int] :
% 283.92/39.27 ? [v3: int] : ((v3 = 0 & v1 = 0 & set(v0) = 0 & ! [v4: $i] : ! [v5: int] :
% 283.92/39.27 (v5 = 0 | ~ (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6
% 283.92/39.27 = 0) & member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0) =
% 283.92/39.27 0) | ~ $i(v4) | subset(v4, v0) = 0)) | ( ~ (v2 = 0) & member(v0,
% 283.92/39.27 on) = v2))) & ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) = v1) | ~
% 283.92/39.27 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 &
% 283.92/39.27 strict_well_order(member_predicate, v0) = 0 & ! [v4: $i] : ! [v5: int]
% 283.92/39.27 : (v5 = 0 | ~ (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~
% 283.92/39.27 (v6 = 0) & member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0)
% 283.92/39.27 = 0) | ~ $i(v4) | subset(v4, v0) = 0)) | ( ~ (v2 = 0) & member(v0,
% 283.92/39.27 on) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v1, v0) = 0) |
% 283.92/39.27 ~ (member(v0, on) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v1, v0) = 0) & !
% 283.92/39.27 [v0: $i] : ( ~ (strict_well_order(member_predicate, v0) = 0) | ~ $i(v0) | ?
% 283.92/39.27 [v1: int] : ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 283.92/39.27 ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & subset(v3, v0) = v5 & member(v3, v0) = 0)
% 283.92/39.27 | (v2 = 0 & member(v0, on) = 0) | ( ~ (v1 = 0) & set(v0) = v1)))) & !
% 283.92/39.27 [v0: $i] : ( ~ (set(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: int] : ?
% 283.92/39.27 [v3: $i] : ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) &
% 283.92/39.27 subset(v3, v0) = v5 & member(v3, v0) = 0) | (v2 = 0 & member(v0, on) =
% 283.92/39.27 0) | ( ~ (v1 = 0) & strict_well_order(member_predicate, v0) = v1)))) &
% 283.92/39.27 ! [v0: $i] : ( ~ (member(v0, on) = 0) | ~ $i(v0) |
% 283.92/39.27 (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 283.92/39.27
% 283.92/39.27 (rel_member)
% 283.92/39.27 $i(member_predicate) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 283.92/39.27 (apply(member_predicate, v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 283.92/39.27 int] : ( ~ (v3 = 0) & member(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] :
% 283.92/39.27 ! [v2: int] : (v2 = 0 | ~ (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 283.92/39.27 [v3: int] : ( ~ (v3 = 0) & apply(member_predicate, v0, v1) = v3)) & ! [v0:
% 283.92/39.27 $i] : ! [v1: $i] : ( ~ (apply(member_predicate, v0, v1) = 0) | ~ $i(v1) |
% 283.92/39.27 ~ $i(v0) | member(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0,
% 283.92/39.27 v1) = 0) | ~ $i(v1) | ~ $i(v0) | apply(member_predicate, v0, v1) = 0)
% 283.92/39.27
% 283.92/39.27 (set_member)
% 283.92/39.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (set(v1) = v2) | ~
% 283.92/39.28 (set(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 283.92/39.28 member(v1, v0) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (set(v0) = 0) | ~
% 283.92/39.28 (member(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | set(v1) = 0)
% 283.92/39.28
% 283.92/39.28 (strict_order)
% 283.92/39.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 283.92/39.29 int] : (v5 = 0 | ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v4) = v5) |
% 283.92/39.29 ~ (strict_order(v0, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 283.92/39.29 | ~ $i(v0) | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ((
% 283.92/39.29 ~ (v9 = 0) & apply(v0, v2, v3) = v9) | ( ~ (v8 = 0) & member(v4, v1) =
% 283.92/39.29 v8) | ( ~ (v7 = 0) & member(v3, v1) = v7) | ( ~ (v6 = 0) & member(v2,
% 283.92/39.29 v1) = v6))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 283.92/39.29 ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v0, v2, v4) = v5) | ~
% 283.92/39.29 (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v4) | ~
% 283.92/39.29 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ? [v7: int] :
% 283.92/39.29 ? [v8: int] : ? [v9: int] : (( ~ (v9 = 0) & apply(v0, v3, v4) = v9) | ( ~
% 283.92/39.29 (v8 = 0) & member(v4, v1) = v8) | ( ~ (v7 = 0) & member(v3, v1) = v7) |
% 283.92/39.29 ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0: $i] : ! [v1: $i] : !
% 283.92/39.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v0,
% 283.92/39.29 v2, v4) = v5) | ~ (strict_order(v0, v1) = 0) | ~ (member(v3, v1) = 0)
% 283.92/39.29 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] :
% 283.92/39.29 ? [v7: int] : ? [v8: int] : ? [v9: int] : (( ~ (v9 = 0) & apply(v0, v3,
% 283.92/39.29 v4) = v9) | ( ~ (v8 = 0) & apply(v0, v2, v3) = v8) | ( ~ (v7 = 0) &
% 283.92/39.29 member(v4, v1) = v7) | ( ~ (v6 = 0) & member(v2, v1) = v6))) & ! [v0:
% 283.92/39.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0,
% 283.92/39.29 v3, v4) = 0) | ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) =
% 283.92/39.29 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 283.92/39.29 int] : ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & apply(v0,
% 283.92/39.29 v2, v4) = 0) | ( ~ (v7 = 0) & member(v4, v1) = v7) | ( ~ (v6 = 0) &
% 283.92/39.29 member(v3, v1) = v6) | ( ~ (v5 = 0) & member(v2, v1) = v5))) & ! [v0:
% 283.92/39.29 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0,
% 283.92/39.29 v3, v4) = 0) | ~ (strict_order(v0, v1) = 0) | ~ (member(v2, v1) = 0) |
% 283.92/39.29 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] :
% 283.92/39.29 ? [v6: int] : ? [v7: int] : ? [v8: int] : ((v8 = 0 & apply(v0, v2, v4) =
% 283.92/39.29 0) | ( ~ (v7 = 0) & apply(v0, v2, v3) = v7) | ( ~ (v6 = 0) & member(v4,
% 283.92/39.29 v1) = v6) | ( ~ (v5 = 0) & member(v3, v1) = v5))) & ! [v0: $i] : !
% 283.92/39.29 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (apply(v0, v2, v3) =
% 283.92/39.29 0) | ~ (strict_order(v0, v1) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v4) |
% 283.92/39.29 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int]
% 283.92/39.29 : ? [v7: int] : ? [v8: int] : ((v8 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v7
% 283.92/39.29 = 0) & apply(v0, v3, v4) = v7) | ( ~ (v6 = 0) & member(v3, v1) = v6) |
% 283.92/39.29 ( ~ (v5 = 0) & member(v2, v1) = v5))) & ! [v0: $i] : ! [v1: $i] : !
% 283.92/39.29 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~ (strict_order(v0, v1) = 0) | ~
% 283.92/39.29 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ (member(v2, v1) = 0) |
% 283.92/39.29 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ?
% 283.92/39.29 [v6: int] : ? [v7: int] : ((v7 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v6 = 0)
% 283.92/39.29 & apply(v0, v3, v4) = v6) | ( ~ (v5 = 0) & apply(v0, v2, v3) = v5))) &
% 283.92/39.29 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v0, v3, v2)
% 283.92/39.29 = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 283.92/39.29 ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : (( ~ (v6 = 0) &
% 283.92/39.29 apply(v0, v2, v3) = v6) | ( ~ (v5 = 0) & member(v3, v1) = v5) | ( ~ (v4
% 283.92/39.29 = 0) & member(v2, v1) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 283.92/39.29 $i] : ! [v3: $i] : ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) =
% 283.92/39.29 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ?
% 283.92/39.29 [v5: int] : ? [v6: int] : (( ~ (v6 = 0) & apply(v0, v3, v2) = v6) | ( ~ (v5
% 283.92/39.29 = 0) & member(v3, v1) = v5) | ( ~ (v4 = 0) & member(v2, v1) = v4))) &
% 283.92/39.29 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (strict_order(v0, v1) =
% 283.92/39.29 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 283.92/39.29 [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ?
% 283.92/39.29 [v11: int] : ? [v12: $i] : ? [v13: $i] : ? [v14: int] : ? [v15: int] :
% 283.92/39.29 ? [v16: int] : ? [v17: int] : ($i(v13) & $i(v12) & $i(v5) & $i(v4) & $i(v3)
% 283.92/39.29 & ((v17 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & apply(v0, v13, v12) = 0 &
% 283.92/39.29 apply(v0, v12, v13) = 0 & member(v13, v1) = 0 & member(v12, v1) = 0) |
% 283.92/39.29 (v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~ (v11 = 0) & apply(v0,
% 283.92/39.29 v4, v5) = 0 & apply(v0, v3, v5) = v11 & apply(v0, v3, v4) = 0 &
% 283.92/39.29 member(v5, v1) = 0 & member(v4, v1) = 0 & member(v3, v1) = 0))))
% 283.92/39.29
% 283.92/39.29 (strict_well_order)
% 283.92/39.30 ! [v0: $i] : ! [v1: $i] : ! [v2: MultipleValueBool] : ! [v3: $i] : ! [v4:
% 283.92/39.30 $i] : ( ~ (strict_order(v0, v1) = v2) | ~ (subset(v3, v1) = 0) | ~
% 283.92/39.30 (member(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) | ?
% 283.92/39.30 [v5: int] : ? [v6: $i] : ? [v7: int] : ($i(v6) & ((v7 = 0 & least(v6, v0,
% 283.92/39.30 v3) = 0) | ( ~ (v5 = 0) & strict_well_order(v0, v1) = v5)))) & !
% 283.92/39.30 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 283.92/39.30 (strict_well_order(v0, v1) = 0) | ~ (subset(v2, v1) = 0) | ~ (member(v3,
% 283.92/39.30 v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 283.92/39.30 (least(v4, v0, v2) = 0 & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: int]
% 283.92/39.30 : (v2 = 0 | ~ (strict_order(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 283.92/39.30 int] : ( ~ (v3 = 0) & strict_well_order(v0, v1) = v3)) & ! [v0: $i] : !
% 283.92/39.30 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (strict_well_order(v0, v1) = v2) | ~
% 283.92/39.30 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ? [v6: $i]
% 283.92/39.30 : ? [v7: int] : ($i(v6) & $i(v4) & ((v7 = 0 & v5 = 0 & subset(v4, v1) = 0 &
% 283.92/39.30 member(v6, v4) = 0 & ! [v8: $i] : ( ~ (least(v8, v0, v4) = 0) | ~
% 283.92/39.30 $i(v8))) | ( ~ (v3 = 0) & strict_order(v0, v1) = v3)))) & ! [v0:
% 283.92/39.30 $i] : ! [v1: $i] : ( ~ (strict_order(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 283.92/39.30 ? [v2: int] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ? [v6: int] :
% 283.92/39.30 ($i(v5) & $i(v3) & ((v6 = 0 & v4 = 0 & subset(v3, v1) = 0 & member(v5, v3) =
% 283.92/39.30 0 & ! [v7: $i] : ( ~ (least(v7, v0, v3) = 0) | ~ $i(v7))) | (v2 = 0
% 283.92/39.30 & strict_well_order(v0, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 283.92/39.30 (strict_well_order(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | strict_order(v0,
% 283.92/39.30 v1) = 0)
% 283.92/39.30
% 283.92/39.30 (subset)
% 283.92/39.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 283.92/39.30 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 283.92/39.30 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 283.92/39.30 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 283.92/39.30 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 283.92/39.30 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 283.92/39.30 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 283.92/39.30 ~ $i(v0) | member(v2, v1) = 0)
% 283.92/39.30
% 283.92/39.30 (thI3)
% 283.92/39.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 283.92/39.30 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 283.92/39.30 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] :
% 283.92/39.30 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3)
% 283.92/39.30 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int]
% 283.92/39.30 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 283.92/39.30 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~
% 283.92/39.30 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0)
% 283.92/39.30
% 283.92/39.30 (thV1)
% 283.92/39.30 $i(on) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, on) = v1 &
% 283.92/39.30 member(v0, on) = 0 & $i(v0))
% 283.92/39.30
% 283.92/39.30 (function-axioms)
% 284.23/39.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 284.23/39.31 | ~ (initial_segment(v4, v3, v2) = v1) | ~ (initial_segment(v4, v3, v2) =
% 284.23/39.31 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 284.23/39.31 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 284.23/39.31 ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 284.23/39.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 284.23/39.31 (least(v4, v3, v2) = v1) | ~ (least(v4, v3, v2) = v0)) & ! [v0:
% 284.23/39.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 284.23/39.31 : (v1 = v0 | ~ (strict_order(v3, v2) = v1) | ~ (strict_order(v3, v2) = v0))
% 284.23/39.31 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 284.23/39.31 [v3: $i] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~
% 284.23/39.31 (strict_well_order(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 284.23/39.31 : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 284.23/39.31 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 284.23/39.31 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2)
% 284.23/39.31 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 284.23/39.31 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 284.23/39.31 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1)
% 284.23/39.31 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 284.23/39.31 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 284.23/39.31 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0:
% 284.23/39.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 284.23/39.31 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 284.23/39.31 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 284.23/39.31 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0:
% 284.23/39.31 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (suc(v2) = v1) | ~ (suc(v2)
% 284.23/39.31 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 284.23/39.31 $i] : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0)) & ! [v0: $i] : !
% 284.23/39.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 284.23/39.31 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 284.23/39.31 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 284.23/39.31 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 284.23/39.31 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 284.23/39.31 (power_set(v2) = v0))
% 284.23/39.31
% 284.23/39.31 Further assumptions not needed in the proof:
% 284.23/39.31 --------------------------------------------
% 284.23/39.31 difference, empty_set, equal_set, initial_segment, intersection, least,
% 284.23/39.31 power_set, product, singleton, successor, sum, union, unordered_pair
% 284.23/39.31
% 284.23/39.31 Those formulas are unsatisfiable:
% 284.23/39.31 ---------------------------------
% 284.23/39.31
% 284.23/39.31 Begin of proof
% 284.23/39.31 |
% 284.23/39.31 | ALPHA: (subset) implies:
% 284.23/39.31 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 284.23/39.31 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 284.23/39.31 | v1) = 0)
% 284.23/39.31 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 284.23/39.31 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 284.23/39.31 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 284.23/39.31 |
% 284.23/39.31 | ALPHA: (ordinal_number) implies:
% 284.23/39.31 | (3) ! [v0: $i] : ( ~ (member(v0, on) = 0) | ~ $i(v0) |
% 284.23/39.31 | (strict_well_order(member_predicate, v0) = 0 & set(v0) = 0))
% 284.23/39.31 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (member(v1, v0) = 0) | ~ (member(v0,
% 284.23/39.31 | on) = 0) | ~ $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 284.23/39.32 | (5) ! [v0: $i] : ! [v1: any] : ( ~ (set(v0) = v1) | ~ $i(v0) | ? [v2:
% 284.23/39.32 | int] : ? [v3: int] : ((v3 = 0 & v1 = 0 &
% 284.23/39.32 | strict_well_order(member_predicate, v0) = 0 & ! [v4: $i] : !
% 284.23/39.32 | [v5: int] : (v5 = 0 | ~ (subset(v4, v0) = v5) | ~ $i(v4) | ?
% 284.23/39.32 | [v6: int] : ( ~ (v6 = 0) & member(v4, v0) = v6)) & ! [v4: $i]
% 284.23/39.32 | : ( ~ (member(v4, v0) = 0) | ~ $i(v4) | subset(v4, v0) = 0)) | (
% 284.23/39.32 | ~ (v2 = 0) & member(v0, on) = v2)))
% 284.23/39.32 | (6) ! [v0: $i] : ! [v1: any] : ( ~ (strict_well_order(member_predicate,
% 284.23/39.32 | v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 &
% 284.23/39.32 | v1 = 0 & set(v0) = 0 & ! [v4: $i] : ! [v5: int] : (v5 = 0 | ~
% 284.23/39.32 | (subset(v4, v0) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0)
% 284.23/39.32 | & member(v4, v0) = v6)) & ! [v4: $i] : ( ~ (member(v4, v0) =
% 284.23/39.32 | 0) | ~ $i(v4) | subset(v4, v0) = 0)) | ( ~ (v2 = 0) &
% 284.23/39.32 | member(v0, on) = v2)))
% 284.23/39.32 | (7) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (member(v0, on) = v1) | ~
% 284.23/39.32 | $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4: $i] : ? [v5: int] :
% 284.23/39.32 | ? [v6: int] : ($i(v4) & ((v5 = 0 & ~ (v6 = 0) & subset(v4, v0) = v6
% 284.23/39.32 | & member(v4, v0) = 0) | ( ~ (v3 = 0) &
% 284.23/39.32 | strict_well_order(member_predicate, v0) = v3) | ( ~ (v2 = 0) &
% 284.23/39.32 | set(v0) = v2))))
% 284.23/39.32 |
% 284.23/39.32 | ALPHA: (strict_well_order) implies:
% 284.23/39.32 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (strict_well_order(v0, v1) = 0) | ~
% 284.23/39.32 | $i(v1) | ~ $i(v0) | strict_order(v0, v1) = 0)
% 284.23/39.32 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 284.23/39.32 | (strict_well_order(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 284.23/39.32 | int] : ? [v4: $i] : ? [v5: int] : ? [v6: $i] : ? [v7: int] :
% 284.23/39.32 | ($i(v6) & $i(v4) & ((v7 = 0 & v5 = 0 & subset(v4, v1) = 0 &
% 284.23/39.32 | member(v6, v4) = 0 & ! [v8: $i] : ( ~ (least(v8, v0, v4) = 0)
% 284.23/39.32 | | ~ $i(v8))) | ( ~ (v3 = 0) & strict_order(v0, v1) = v3))))
% 284.23/39.32 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: MultipleValueBool] : ! [v3: $i] :
% 284.23/39.32 | ! [v4: $i] : ( ~ (strict_order(v0, v1) = v2) | ~ (subset(v3, v1) =
% 284.23/39.32 | 0) | ~ (member(v4, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v1) |
% 284.23/39.32 | ~ $i(v0) | ? [v5: int] : ? [v6: $i] : ? [v7: int] : ($i(v6) &
% 284.23/39.32 | ((v7 = 0 & least(v6, v0, v3) = 0) | ( ~ (v5 = 0) &
% 284.23/39.32 | strict_well_order(v0, v1) = v5))))
% 284.23/39.32 |
% 284.23/39.32 | ALPHA: (rel_member) implies:
% 284.23/39.32 | (11) $i(member_predicate)
% 284.23/39.32 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~ $i(v1) | ~
% 284.23/39.32 | $i(v0) | apply(member_predicate, v0, v1) = 0)
% 284.23/39.32 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (member(v0,
% 284.23/39.32 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0)
% 284.23/39.32 | & apply(member_predicate, v0, v1) = v3))
% 284.23/39.32 |
% 284.23/39.32 | ALPHA: (strict_order) implies:
% 284.23/39.33 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 284.23/39.33 | (strict_order(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 284.23/39.33 | ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ? [v8:
% 284.23/39.33 | int] : ? [v9: int] : ? [v10: int] : ? [v11: int] : ? [v12: $i]
% 284.23/39.33 | : ? [v13: $i] : ? [v14: int] : ? [v15: int] : ? [v16: int] : ?
% 284.23/39.33 | [v17: int] : ($i(v13) & $i(v12) & $i(v5) & $i(v4) & $i(v3) & ((v17 =
% 284.23/39.33 | 0 & v16 = 0 & v15 = 0 & v14 = 0 & apply(v0, v13, v12) = 0 &
% 284.23/39.33 | apply(v0, v12, v13) = 0 & member(v13, v1) = 0 & member(v12,
% 284.23/39.33 | v1) = 0) | (v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & v6 = 0 & ~
% 284.23/39.33 | (v11 = 0) & apply(v0, v4, v5) = 0 & apply(v0, v3, v5) = v11 &
% 284.23/39.33 | apply(v0, v3, v4) = 0 & member(v5, v1) = 0 & member(v4, v1) =
% 284.23/39.33 | 0 & member(v3, v1) = 0))))
% 284.23/39.33 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v0,
% 284.23/39.33 | v3, v2) = 0) | ~ (strict_order(v0, v1) = 0) | ~ $i(v3) | ~
% 284.23/39.33 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 284.23/39.33 | [v6: int] : (( ~ (v6 = 0) & apply(v0, v2, v3) = v6) | ( ~ (v5 = 0) &
% 284.23/39.33 | member(v3, v1) = v5) | ( ~ (v4 = 0) & member(v2, v1) = v4)))
% 284.23/39.33 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 284.23/39.33 | ( ~ (apply(v0, v2, v3) = 0) | ~ (strict_order(v0, v1) = 0) | ~
% 284.23/39.33 | (member(v4, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 284.23/39.33 | | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8:
% 284.23/39.33 | int] : ((v8 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v7 = 0) &
% 284.23/39.33 | apply(v0, v3, v4) = v7) | ( ~ (v6 = 0) & member(v3, v1) = v6) |
% 284.23/39.33 | ( ~ (v5 = 0) & member(v2, v1) = v5)))
% 284.23/39.33 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 284.23/39.33 | ( ~ (apply(v0, v3, v4) = 0) | ~ (apply(v0, v2, v3) = 0) | ~
% 284.23/39.33 | (strict_order(v0, v1) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 284.23/39.33 | $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ? [v7: int] : ?
% 284.23/39.33 | [v8: int] : ((v8 = 0 & apply(v0, v2, v4) = 0) | ( ~ (v7 = 0) &
% 284.23/39.33 | member(v4, v1) = v7) | ( ~ (v6 = 0) & member(v3, v1) = v6) | ( ~
% 284.23/39.33 | (v5 = 0) & member(v2, v1) = v5)))
% 284.23/39.33 |
% 284.23/39.33 | ALPHA: (set_member) implies:
% 284.23/39.33 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (set(v0) = 0) | ~ (member(v1, v0) =
% 284.23/39.33 | 0) | ~ $i(v1) | ~ $i(v0) | set(v1) = 0)
% 284.23/39.33 |
% 284.23/39.33 | ALPHA: (thI3) implies:
% 284.23/39.33 | (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v1, v2) = 0) |
% 284.23/39.33 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 284.23/39.33 | subset(v0, v2) = 0)
% 284.23/39.33 |
% 284.23/39.33 | ALPHA: (thV1) implies:
% 284.23/39.33 | (20) $i(on)
% 284.23/39.34 | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, on) = v1 &
% 284.23/39.34 | member(v0, on) = 0 & $i(v0))
% 284.23/39.34 |
% 284.23/39.34 | ALPHA: (function-axioms) implies:
% 284.23/39.34 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 284.23/39.34 | : (v1 = v0 | ~ (set(v2) = v1) | ~ (set(v2) = v0))
% 284.23/39.34 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 284.23/39.34 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 284.23/39.34 | v2) = v0))
% 284.23/39.34 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 284.23/39.34 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 284.23/39.34 | v2) = v0))
% 284.23/39.34 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 284.23/39.34 | : ! [v3: $i] : (v1 = v0 | ~ (strict_well_order(v3, v2) = v1) | ~
% 284.23/39.34 | (strict_well_order(v3, v2) = v0))
% 284.23/39.34 | (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 284.23/39.34 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 284.23/39.34 | ~ (apply(v4, v3, v2) = v0))
% 284.23/39.34 |
% 284.23/39.34 | DELTA: instantiating (21) with fresh symbols all_24_0, all_24_1 gives:
% 284.23/39.34 | (27) ~ (all_24_0 = 0) & subset(all_24_1, on) = all_24_0 & member(all_24_1,
% 284.23/39.34 | on) = 0 & $i(all_24_1)
% 284.23/39.34 |
% 284.23/39.34 | ALPHA: (27) implies:
% 284.23/39.34 | (28) ~ (all_24_0 = 0)
% 284.23/39.34 | (29) $i(all_24_1)
% 284.23/39.34 | (30) member(all_24_1, on) = 0
% 284.23/39.34 | (31) subset(all_24_1, on) = all_24_0
% 284.23/39.34 |
% 284.23/39.34 | GROUND_INST: instantiating (3) with all_24_1, simplifying with (29), (30)
% 284.23/39.34 | gives:
% 284.23/39.34 | (32) strict_well_order(member_predicate, all_24_1) = 0 & set(all_24_1) = 0
% 284.23/39.34 |
% 284.23/39.34 | ALPHA: (32) implies:
% 284.23/39.34 | (33) set(all_24_1) = 0
% 284.23/39.34 | (34) strict_well_order(member_predicate, all_24_1) = 0
% 284.23/39.34 |
% 284.23/39.34 | GROUND_INST: instantiating (2) with all_24_1, on, all_24_0, simplifying with
% 284.23/39.34 | (20), (29), (31) gives:
% 284.23/39.34 | (35) all_24_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 284.23/39.34 | all_24_1) = 0 & member(v0, on) = v1 & $i(v0))
% 284.23/39.34 |
% 284.23/39.34 | BETA: splitting (35) gives:
% 284.23/39.34 |
% 284.23/39.34 | Case 1:
% 284.23/39.34 | |
% 284.23/39.34 | | (36) all_24_0 = 0
% 284.23/39.34 | |
% 284.23/39.34 | | REDUCE: (28), (36) imply:
% 284.23/39.34 | | (37) $false
% 284.23/39.35 | |
% 284.23/39.35 | | CLOSE: (37) is inconsistent.
% 284.23/39.35 | |
% 284.23/39.35 | Case 2:
% 284.23/39.35 | |
% 284.23/39.35 | | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_24_1) = 0
% 284.23/39.35 | | & member(v0, on) = v1 & $i(v0))
% 284.23/39.35 | |
% 284.23/39.35 | | DELTA: instantiating (38) with fresh symbols all_45_0, all_45_1 gives:
% 284.23/39.35 | | (39) ~ (all_45_0 = 0) & member(all_45_1, all_24_1) = 0 &
% 284.23/39.35 | | member(all_45_1, on) = all_45_0 & $i(all_45_1)
% 284.23/39.35 | |
% 284.23/39.35 | | ALPHA: (39) implies:
% 284.23/39.35 | | (40) ~ (all_45_0 = 0)
% 284.23/39.35 | | (41) $i(all_45_1)
% 284.23/39.35 | | (42) member(all_45_1, on) = all_45_0
% 284.23/39.35 | | (43) member(all_45_1, all_24_1) = 0
% 284.23/39.35 | |
% 284.23/39.35 | | GROUND_INST: instantiating (7) with all_45_1, all_45_0, simplifying with
% 284.23/39.35 | | (41), (42) gives:
% 284.23/39.35 | | (44) all_45_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3:
% 284.23/39.35 | | int] : ? [v4: int] : ($i(v2) & ((v3 = 0 & ~ (v4 = 0) &
% 284.23/39.35 | | subset(v2, all_45_1) = v4 & member(v2, all_45_1) = 0) | ( ~
% 284.23/39.35 | | (v1 = 0) & strict_well_order(member_predicate, all_45_1) = v1)
% 284.23/39.35 | | | ( ~ (v0 = 0) & set(all_45_1) = v0)))
% 284.23/39.35 | |
% 284.23/39.35 | | GROUND_INST: instantiating (4) with all_24_1, all_45_1, simplifying with
% 284.23/39.35 | | (29), (30), (41), (43) gives:
% 284.23/39.35 | | (45) subset(all_45_1, all_24_1) = 0
% 284.23/39.35 | |
% 284.23/39.35 | | GROUND_INST: instantiating (18) with all_24_1, all_45_1, simplifying with
% 284.23/39.35 | | (29), (33), (41), (43) gives:
% 284.23/39.35 | | (46) set(all_45_1) = 0
% 284.23/39.35 | |
% 284.23/39.35 | | GROUND_INST: instantiating (8) with member_predicate, all_24_1, simplifying
% 284.23/39.35 | | with (11), (29), (34) gives:
% 284.23/39.35 | | (47) strict_order(member_predicate, all_24_1) = 0
% 284.23/39.35 | |
% 284.23/39.35 | | GROUND_INST: instantiating (6) with all_24_1, 0, simplifying with (29), (34)
% 284.23/39.35 | | gives:
% 284.23/39.35 | | (48) ? [v0: int] : ? [v1: int] : ((v1 = 0 & set(all_24_1) = 0 & ! [v2:
% 284.23/39.35 | | $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v2, all_24_1) = v3)
% 284.23/39.35 | | | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2,
% 284.23/39.35 | | all_24_1) = v4)) & ! [v2: $i] : ( ~ (member(v2, all_24_1)
% 284.23/39.35 | | = 0) | ~ $i(v2) | subset(v2, all_24_1) = 0)) | ( ~ (v0 = 0)
% 284.23/39.35 | | & member(all_24_1, on) = v0))
% 284.23/39.35 | |
% 284.23/39.35 | | DELTA: instantiating (48) with fresh symbols all_63_0, all_63_1 gives:
% 284.23/39.35 | | (49) (all_63_0 = 0 & set(all_24_1) = 0 & ! [v0: $i] : ! [v1: int] : (v1
% 284.23/39.35 | | = 0 | ~ (subset(v0, all_24_1) = v1) | ~ $i(v0) | ? [v2: int]
% 284.23/39.35 | | : ( ~ (v2 = 0) & member(v0, all_24_1) = v2)) & ! [v0: $i] : ( ~
% 284.23/39.35 | | (member(v0, all_24_1) = 0) | ~ $i(v0) | subset(v0, all_24_1) =
% 284.23/39.35 | | 0)) | ( ~ (all_63_1 = 0) & member(all_24_1, on) = all_63_1)
% 284.23/39.35 | |
% 284.23/39.35 | | BETA: splitting (49) gives:
% 284.23/39.35 | |
% 284.23/39.35 | | Case 1:
% 284.23/39.35 | | |
% 284.23/39.35 | | | (50) all_63_0 = 0 & set(all_24_1) = 0 & ! [v0: $i] : ! [v1: int] :
% 284.23/39.35 | | | (v1 = 0 | ~ (subset(v0, all_24_1) = v1) | ~ $i(v0) | ? [v2:
% 284.23/39.35 | | | int] : ( ~ (v2 = 0) & member(v0, all_24_1) = v2)) & ! [v0:
% 284.23/39.35 | | | $i] : ( ~ (member(v0, all_24_1) = 0) | ~ $i(v0) | subset(v0,
% 284.23/39.35 | | | all_24_1) = 0)
% 284.23/39.35 | | |
% 284.23/39.35 | | | ALPHA: (50) implies:
% 284.23/39.35 | | | (51) ! [v0: $i] : ( ~ (member(v0, all_24_1) = 0) | ~ $i(v0) |
% 284.23/39.35 | | | subset(v0, all_24_1) = 0)
% 284.23/39.35 | | |
% 284.23/39.35 | | | BETA: splitting (44) gives:
% 284.23/39.35 | | |
% 284.23/39.35 | | | Case 1:
% 284.23/39.35 | | | |
% 284.23/39.35 | | | | (52) all_45_0 = 0
% 284.23/39.35 | | | |
% 284.23/39.35 | | | | REDUCE: (40), (52) imply:
% 284.23/39.35 | | | | (53) $false
% 284.23/39.35 | | | |
% 284.23/39.35 | | | | CLOSE: (53) is inconsistent.
% 284.23/39.35 | | | |
% 284.23/39.35 | | | Case 2:
% 284.23/39.35 | | | |
% 284.23/39.36 | | | | (54) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: int] : ?
% 284.23/39.36 | | | | [v4: int] : ($i(v2) & ((v3 = 0 & ~ (v4 = 0) & subset(v2,
% 284.23/39.36 | | | | all_45_1) = v4 & member(v2, all_45_1) = 0) | ( ~ (v1 =
% 284.23/39.36 | | | | 0) & strict_well_order(member_predicate, all_45_1) = v1)
% 284.23/39.36 | | | | | ( ~ (v0 = 0) & set(all_45_1) = v0)))
% 284.23/39.36 | | | |
% 284.23/39.36 | | | | DELTA: instantiating (54) with fresh symbols all_95_0, all_95_1,
% 284.23/39.36 | | | | all_95_2, all_95_3, all_95_4 gives:
% 284.23/39.36 | | | | (55) $i(all_95_2) & ((all_95_1 = 0 & ~ (all_95_0 = 0) &
% 284.23/39.36 | | | | subset(all_95_2, all_45_1) = all_95_0 & member(all_95_2,
% 284.23/39.36 | | | | all_45_1) = 0) | ( ~ (all_95_3 = 0) &
% 284.23/39.36 | | | | strict_well_order(member_predicate, all_45_1) = all_95_3) |
% 284.23/39.36 | | | | ( ~ (all_95_4 = 0) & set(all_45_1) = all_95_4))
% 284.23/39.36 | | | |
% 284.23/39.36 | | | | ALPHA: (55) implies:
% 284.23/39.36 | | | | (56) $i(all_95_2)
% 284.23/39.36 | | | | (57) (all_95_1 = 0 & ~ (all_95_0 = 0) & subset(all_95_2, all_45_1) =
% 284.23/39.36 | | | | all_95_0 & member(all_95_2, all_45_1) = 0) | ( ~ (all_95_3 =
% 284.23/39.36 | | | | 0) & strict_well_order(member_predicate, all_45_1) =
% 284.23/39.36 | | | | all_95_3) | ( ~ (all_95_4 = 0) & set(all_45_1) = all_95_4)
% 284.23/39.36 | | | |
% 284.23/39.36 | | | | GROUND_INST: instantiating (5) with all_45_1, 0, simplifying with (41),
% 284.23/39.36 | | | | (46) gives:
% 284.23/39.36 | | | | (58) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 284.23/39.36 | | | | strict_well_order(member_predicate, all_45_1) = 0 & ! [v2:
% 284.23/39.36 | | | | $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v2, all_45_1) =
% 284.23/39.36 | | | | v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) &
% 284.23/39.36 | | | | member(v2, all_45_1) = v4)) & ! [v2: $i] : ( ~
% 284.23/39.36 | | | | (member(v2, all_45_1) = 0) | ~ $i(v2) | subset(v2,
% 284.23/39.36 | | | | all_45_1) = 0)) | ( ~ (v0 = 0) & member(all_45_1, on) =
% 284.23/39.36 | | | | v0))
% 284.23/39.36 | | | |
% 284.23/39.36 | | | | DELTA: instantiating (58) with fresh symbols all_122_0, all_122_1 gives:
% 284.23/39.36 | | | | (59) (all_122_0 = 0 & strict_well_order(member_predicate, all_45_1) =
% 284.23/39.36 | | | | 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subset(v0,
% 284.23/39.36 | | | | all_45_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 284.23/39.36 | | | | 0) & member(v0, all_45_1) = v2)) & ! [v0: $i] : ( ~
% 284.23/39.36 | | | | (member(v0, all_45_1) = 0) | ~ $i(v0) | subset(v0,
% 284.23/39.36 | | | | all_45_1) = 0)) | ( ~ (all_122_1 = 0) & member(all_45_1,
% 284.23/39.36 | | | | on) = all_122_1)
% 284.23/39.36 | | | |
% 284.23/39.36 | | | | BETA: splitting (57) gives:
% 284.23/39.36 | | | |
% 284.23/39.36 | | | | Case 1:
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | (60) all_95_1 = 0 & ~ (all_95_0 = 0) & subset(all_95_2, all_45_1)
% 284.23/39.36 | | | | | = all_95_0 & member(all_95_2, all_45_1) = 0
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | ALPHA: (60) implies:
% 284.23/39.36 | | | | | (61) ~ (all_95_0 = 0)
% 284.23/39.36 | | | | | (62) member(all_95_2, all_45_1) = 0
% 284.23/39.36 | | | | | (63) subset(all_95_2, all_45_1) = all_95_0
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | GROUND_INST: instantiating (1) with all_45_1, all_24_1, all_95_2,
% 284.23/39.36 | | | | | simplifying with (29), (41), (45), (56), (62) gives:
% 284.23/39.36 | | | | | (64) member(all_95_2, all_24_1) = 0
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | GROUND_INST: instantiating (12) with all_95_2, all_45_1, simplifying
% 284.23/39.36 | | | | | with (41), (56), (62) gives:
% 284.23/39.36 | | | | | (65) apply(member_predicate, all_95_2, all_45_1) = 0
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | GROUND_INST: instantiating (2) with all_95_2, all_45_1, all_95_0,
% 284.23/39.36 | | | | | simplifying with (41), (56), (63) gives:
% 284.23/39.36 | | | | | (66) all_95_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 284.23/39.36 | | | | | member(v0, all_95_2) = 0 & member(v0, all_45_1) = v1 &
% 284.23/39.36 | | | | | $i(v0))
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | BETA: splitting (66) gives:
% 284.23/39.36 | | | | |
% 284.23/39.36 | | | | | Case 1:
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | (67) all_95_0 = 0
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | REDUCE: (61), (67) imply:
% 284.23/39.36 | | | | | | (68) $false
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | CLOSE: (68) is inconsistent.
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | Case 2:
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | (69) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 284.23/39.36 | | | | | | all_95_2) = 0 & member(v0, all_45_1) = v1 & $i(v0))
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | DELTA: instantiating (69) with fresh symbols all_233_0, all_233_1
% 284.23/39.36 | | | | | | gives:
% 284.23/39.36 | | | | | | (70) ~ (all_233_0 = 0) & member(all_233_1, all_95_2) = 0 &
% 284.23/39.36 | | | | | | member(all_233_1, all_45_1) = all_233_0 & $i(all_233_1)
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | ALPHA: (70) implies:
% 284.23/39.36 | | | | | | (71) ~ (all_233_0 = 0)
% 284.23/39.36 | | | | | | (72) $i(all_233_1)
% 284.23/39.36 | | | | | | (73) member(all_233_1, all_45_1) = all_233_0
% 284.23/39.36 | | | | | | (74) member(all_233_1, all_95_2) = 0
% 284.23/39.36 | | | | | |
% 284.23/39.36 | | | | | | GROUND_INST: instantiating (51) with all_95_2, simplifying with
% 284.23/39.36 | | | | | | (56), (64) gives:
% 284.23/39.37 | | | | | | (75) subset(all_95_2, all_24_1) = 0
% 284.23/39.37 | | | | | |
% 284.23/39.37 | | | | | | GROUND_INST: instantiating (13) with all_233_1, all_45_1, all_233_0,
% 284.23/39.37 | | | | | | simplifying with (41), (72), (73) gives:
% 284.23/39.37 | | | | | | (76) all_233_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 284.23/39.37 | | | | | | apply(member_predicate, all_233_1, all_45_1) = v0)
% 284.23/39.37 | | | | | |
% 284.23/39.37 | | | | | | GROUND_INST: instantiating (12) with all_233_1, all_95_2,
% 284.23/39.37 | | | | | | simplifying with (56), (72), (74) gives:
% 284.23/39.37 | | | | | | (77) apply(member_predicate, all_233_1, all_95_2) = 0
% 284.52/39.37 | | | | | |
% 284.52/39.37 | | | | | | BETA: splitting (76) gives:
% 284.52/39.37 | | | | | |
% 284.52/39.37 | | | | | | Case 1:
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | (78) all_233_0 = 0
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | REDUCE: (71), (78) imply:
% 284.52/39.37 | | | | | | | (79) $false
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | CLOSE: (79) is inconsistent.
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | Case 2:
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & apply(member_predicate,
% 284.52/39.37 | | | | | | | all_233_1, all_45_1) = v0)
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | DELTA: instantiating (80) with fresh symbol all_272_0 gives:
% 284.52/39.37 | | | | | | | (81) ~ (all_272_0 = 0) & apply(member_predicate, all_233_1,
% 284.52/39.37 | | | | | | | all_45_1) = all_272_0
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | ALPHA: (81) implies:
% 284.52/39.37 | | | | | | | (82) ~ (all_272_0 = 0)
% 284.52/39.37 | | | | | | | (83) apply(member_predicate, all_233_1, all_45_1) = all_272_0
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | BETA: splitting (59) gives:
% 284.52/39.37 | | | | | | |
% 284.52/39.37 | | | | | | | Case 1:
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | (84) all_122_0 = 0 & strict_well_order(member_predicate,
% 284.52/39.37 | | | | | | | | all_45_1) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 284.52/39.37 | | | | | | | | ~ (subset(v0, all_45_1) = v1) | ~ $i(v0) | ? [v2:
% 284.52/39.37 | | | | | | | | int] : ( ~ (v2 = 0) & member(v0, all_45_1) = v2)) &
% 284.52/39.37 | | | | | | | | ! [v0: $i] : ( ~ (member(v0, all_45_1) = 0) | ~ $i(v0)
% 284.52/39.37 | | | | | | | | | subset(v0, all_45_1) = 0)
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | ALPHA: (84) implies:
% 284.52/39.37 | | | | | | | | (85) ! [v0: $i] : ( ~ (member(v0, all_45_1) = 0) | ~ $i(v0)
% 284.52/39.37 | | | | | | | | | subset(v0, all_45_1) = 0)
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | GROUND_INST: instantiating (85) with all_95_2, simplifying with
% 284.52/39.37 | | | | | | | | (56), (62) gives:
% 284.52/39.37 | | | | | | | | (86) subset(all_95_2, all_45_1) = 0
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | GROUND_INST: instantiating (24) with all_95_0, 0, all_45_1,
% 284.52/39.37 | | | | | | | | all_95_2, simplifying with (63), (86) gives:
% 284.52/39.37 | | | | | | | | (87) all_95_0 = 0
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | REDUCE: (61), (87) imply:
% 284.52/39.37 | | | | | | | | (88) $false
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | CLOSE: (88) is inconsistent.
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | Case 2:
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | GROUND_INST: instantiating (1) with all_95_2, all_24_1,
% 284.52/39.37 | | | | | | | | all_233_1, simplifying with (29), (56), (72), (74),
% 284.52/39.37 | | | | | | | | (75) gives:
% 284.52/39.37 | | | | | | | | (89) member(all_233_1, all_24_1) = 0
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | GROUND_INST: instantiating (16) with member_predicate, all_24_1,
% 284.52/39.37 | | | | | | | | all_233_1, all_95_2, all_45_1, simplifying with
% 284.52/39.37 | | | | | | | | (11), (29), (41), (43), (47), (56), (72), (77)
% 284.52/39.37 | | | | | | | | gives:
% 284.52/39.37 | | | | | | | | (90) ? [v0: int] : ? [v1: int] : ? [v2: int] : ? [v3:
% 284.52/39.37 | | | | | | | | int] : ((v3 = 0 & apply(member_predicate, all_233_1,
% 284.52/39.37 | | | | | | | | all_45_1) = 0) | ( ~ (v2 = 0) &
% 284.52/39.37 | | | | | | | | apply(member_predicate, all_95_2, all_45_1) = v2) |
% 284.52/39.37 | | | | | | | | ( ~ (v1 = 0) & member(all_95_2, all_24_1) = v1) | ( ~
% 284.52/39.37 | | | | | | | | (v0 = 0) & member(all_233_1, all_24_1) = v0))
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | DELTA: instantiating (90) with fresh symbols all_491_0,
% 284.52/39.37 | | | | | | | | all_491_1, all_491_2, all_491_3 gives:
% 284.52/39.37 | | | | | | | | (91) (all_491_0 = 0 & apply(member_predicate, all_233_1,
% 284.52/39.37 | | | | | | | | all_45_1) = 0) | ( ~ (all_491_1 = 0) &
% 284.52/39.37 | | | | | | | | apply(member_predicate, all_95_2, all_45_1) =
% 284.52/39.37 | | | | | | | | all_491_1) | ( ~ (all_491_2 = 0) & member(all_95_2,
% 284.52/39.37 | | | | | | | | all_24_1) = all_491_2) | ( ~ (all_491_3 = 0) &
% 284.52/39.37 | | | | | | | | member(all_233_1, all_24_1) = all_491_3)
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | BETA: splitting (91) gives:
% 284.52/39.37 | | | | | | | |
% 284.52/39.37 | | | | | | | | Case 1:
% 284.52/39.37 | | | | | | | | |
% 284.52/39.37 | | | | | | | | | (92) (all_491_0 = 0 & apply(member_predicate, all_233_1,
% 284.52/39.37 | | | | | | | | | all_45_1) = 0) | ( ~ (all_491_1 = 0) &
% 284.52/39.37 | | | | | | | | | apply(member_predicate, all_95_2, all_45_1) =
% 284.52/39.37 | | | | | | | | | all_491_1)
% 284.52/39.37 | | | | | | | | |
% 284.52/39.37 | | | | | | | | | BETA: splitting (92) gives:
% 284.52/39.37 | | | | | | | | |
% 284.52/39.37 | | | | | | | | | Case 1:
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | (93) all_491_0 = 0 & apply(member_predicate, all_233_1,
% 284.52/39.37 | | | | | | | | | | all_45_1) = 0
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | ALPHA: (93) implies:
% 284.52/39.37 | | | | | | | | | | (94) apply(member_predicate, all_233_1, all_45_1) = 0
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | GROUND_INST: instantiating (26) with all_272_0, 0, all_45_1,
% 284.52/39.37 | | | | | | | | | | all_233_1, member_predicate, simplifying with
% 284.52/39.37 | | | | | | | | | | (83), (94) gives:
% 284.52/39.37 | | | | | | | | | | (95) all_272_0 = 0
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | REDUCE: (82), (95) imply:
% 284.52/39.37 | | | | | | | | | | (96) $false
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | CLOSE: (96) is inconsistent.
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | Case 2:
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | (97) ~ (all_491_1 = 0) & apply(member_predicate,
% 284.52/39.37 | | | | | | | | | | all_95_2, all_45_1) = all_491_1
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.37 | | | | | | | | | | ALPHA: (97) implies:
% 284.52/39.37 | | | | | | | | | | (98) ~ (all_491_1 = 0)
% 284.52/39.37 | | | | | | | | | | (99) apply(member_predicate, all_95_2, all_45_1) =
% 284.52/39.37 | | | | | | | | | | all_491_1
% 284.52/39.37 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_491_1, all_45_1,
% 284.52/39.38 | | | | | | | | | | all_95_2, member_predicate, simplifying with (65),
% 284.52/39.38 | | | | | | | | | | (99) gives:
% 284.52/39.38 | | | | | | | | | | (100) all_491_1 = 0
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | REDUCE: (98), (100) imply:
% 284.52/39.38 | | | | | | | | | | (101) $false
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | CLOSE: (101) is inconsistent.
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | End of split
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | Case 2:
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | | (102) ( ~ (all_491_2 = 0) & member(all_95_2, all_24_1) =
% 284.52/39.38 | | | | | | | | | all_491_2) | ( ~ (all_491_3 = 0) &
% 284.52/39.38 | | | | | | | | | member(all_233_1, all_24_1) = all_491_3)
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | | BETA: splitting (102) gives:
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | | Case 1:
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | (103) ~ (all_491_2 = 0) & member(all_95_2, all_24_1) =
% 284.52/39.38 | | | | | | | | | | all_491_2
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | ALPHA: (103) implies:
% 284.52/39.38 | | | | | | | | | | (104) ~ (all_491_2 = 0)
% 284.52/39.38 | | | | | | | | | | (105) member(all_95_2, all_24_1) = all_491_2
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_491_2, all_24_1,
% 284.52/39.38 | | | | | | | | | | all_95_2, simplifying with (64), (105) gives:
% 284.52/39.38 | | | | | | | | | | (106) all_491_2 = 0
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | REDUCE: (104), (106) imply:
% 284.52/39.38 | | | | | | | | | | (107) $false
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | CLOSE: (107) is inconsistent.
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | Case 2:
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | (108) ~ (all_491_3 = 0) & member(all_233_1, all_24_1) =
% 284.52/39.38 | | | | | | | | | | all_491_3
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | ALPHA: (108) implies:
% 284.52/39.38 | | | | | | | | | | (109) ~ (all_491_3 = 0)
% 284.52/39.38 | | | | | | | | | | (110) member(all_233_1, all_24_1) = all_491_3
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_491_3, all_24_1,
% 284.52/39.38 | | | | | | | | | | all_233_1, simplifying with (89), (110) gives:
% 284.52/39.38 | | | | | | | | | | (111) all_491_3 = 0
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | REDUCE: (109), (111) imply:
% 284.52/39.38 | | | | | | | | | | (112) $false
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | | CLOSE: (112) is inconsistent.
% 284.52/39.38 | | | | | | | | | |
% 284.52/39.38 | | | | | | | | | End of split
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | End of split
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | End of split
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | End of split
% 284.52/39.38 | | | | | |
% 284.52/39.38 | | | | | End of split
% 284.52/39.38 | | | | |
% 284.52/39.38 | | | | Case 2:
% 284.52/39.38 | | | | |
% 284.52/39.38 | | | | | (113) ( ~ (all_95_3 = 0) & strict_well_order(member_predicate,
% 284.52/39.38 | | | | | all_45_1) = all_95_3) | ( ~ (all_95_4 = 0) &
% 284.52/39.38 | | | | | set(all_45_1) = all_95_4)
% 284.52/39.38 | | | | |
% 284.52/39.38 | | | | | BETA: splitting (113) gives:
% 284.52/39.38 | | | | |
% 284.52/39.38 | | | | | Case 1:
% 284.52/39.38 | | | | | |
% 284.52/39.38 | | | | | | (114) ~ (all_95_3 = 0) & strict_well_order(member_predicate,
% 284.52/39.38 | | | | | | all_45_1) = all_95_3
% 284.52/39.38 | | | | | |
% 284.52/39.38 | | | | | | ALPHA: (114) implies:
% 284.52/39.38 | | | | | | (115) ~ (all_95_3 = 0)
% 284.52/39.38 | | | | | | (116) strict_well_order(member_predicate, all_45_1) = all_95_3
% 284.52/39.38 | | | | | |
% 284.52/39.38 | | | | | | BETA: splitting (59) gives:
% 284.52/39.38 | | | | | |
% 284.52/39.38 | | | | | | Case 1:
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | (117) all_122_0 = 0 & strict_well_order(member_predicate,
% 284.52/39.38 | | | | | | | all_45_1) = 0 & ! [v0: $i] : ! [v1: int] : (v1 = 0 |
% 284.52/39.38 | | | | | | | ~ (subset(v0, all_45_1) = v1) | ~ $i(v0) | ? [v2:
% 284.52/39.38 | | | | | | | int] : ( ~ (v2 = 0) & member(v0, all_45_1) = v2)) &
% 284.52/39.38 | | | | | | | ! [v0: $i] : ( ~ (member(v0, all_45_1) = 0) | ~ $i(v0) |
% 284.52/39.38 | | | | | | | subset(v0, all_45_1) = 0)
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | ALPHA: (117) implies:
% 284.52/39.38 | | | | | | | (118) strict_well_order(member_predicate, all_45_1) = 0
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | GROUND_INST: instantiating (25) with 0, all_95_3, all_45_1,
% 284.52/39.38 | | | | | | | member_predicate, simplifying with (116), (118)
% 284.52/39.38 | | | | | | | gives:
% 284.52/39.38 | | | | | | | (119) all_95_3 = 0
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | REDUCE: (115), (119) imply:
% 284.52/39.38 | | | | | | | (120) $false
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | CLOSE: (120) is inconsistent.
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | Case 2:
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | GROUND_INST: instantiating (9) with member_predicate, all_45_1,
% 284.52/39.38 | | | | | | | all_95_3, simplifying with (11), (41), (116) gives:
% 284.52/39.38 | | | | | | | (121) all_95_3 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int]
% 284.52/39.38 | | | | | | | : ? [v3: $i] : ? [v4: int] : ($i(v3) & $i(v1) & ((v4 =
% 284.52/39.38 | | | | | | | 0 & v2 = 0 & subset(v1, all_45_1) = 0 & member(v3,
% 284.52/39.38 | | | | | | | v1) = 0 & ! [v5: $i] : ( ~ (least(v5,
% 284.52/39.38 | | | | | | | member_predicate, v1) = 0) | ~ $i(v5))) | (
% 284.52/39.38 | | | | | | | ~ (v0 = 0) & strict_order(member_predicate,
% 284.52/39.38 | | | | | | | all_45_1) = v0)))
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | BETA: splitting (121) gives:
% 284.52/39.38 | | | | | | |
% 284.52/39.38 | | | | | | | Case 1:
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | (122) all_95_3 = 0
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | REDUCE: (115), (122) imply:
% 284.52/39.38 | | | | | | | | (123) $false
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | CLOSE: (123) is inconsistent.
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | Case 2:
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | (124) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ? [v3: $i]
% 284.52/39.38 | | | | | | | | : ? [v4: int] : ($i(v3) & $i(v1) & ((v4 = 0 & v2 = 0 &
% 284.52/39.38 | | | | | | | | subset(v1, all_45_1) = 0 & member(v3, v1) = 0 &
% 284.52/39.38 | | | | | | | | ! [v5: $i] : ( ~ (least(v5, member_predicate, v1)
% 284.52/39.38 | | | | | | | | = 0) | ~ $i(v5))) | ( ~ (v0 = 0) &
% 284.52/39.38 | | | | | | | | strict_order(member_predicate, all_45_1) = v0)))
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | DELTA: instantiating (124) with fresh symbols all_232_0,
% 284.52/39.38 | | | | | | | | all_232_1, all_232_2, all_232_3, all_232_4 gives:
% 284.52/39.38 | | | | | | | | (125) $i(all_232_1) & $i(all_232_3) & ((all_232_0 = 0 &
% 284.52/39.38 | | | | | | | | all_232_2 = 0 & subset(all_232_3, all_45_1) = 0 &
% 284.52/39.38 | | | | | | | | member(all_232_1, all_232_3) = 0 & ! [v0: $i] : (
% 284.52/39.38 | | | | | | | | ~ (least(v0, member_predicate, all_232_3) = 0) |
% 284.52/39.38 | | | | | | | | ~ $i(v0))) | ( ~ (all_232_4 = 0) &
% 284.52/39.38 | | | | | | | | strict_order(member_predicate, all_45_1) =
% 284.52/39.38 | | | | | | | | all_232_4))
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | ALPHA: (125) implies:
% 284.52/39.38 | | | | | | | | (126) $i(all_232_3)
% 284.52/39.38 | | | | | | | | (127) $i(all_232_1)
% 284.52/39.38 | | | | | | | | (128) (all_232_0 = 0 & all_232_2 = 0 & subset(all_232_3,
% 284.52/39.38 | | | | | | | | all_45_1) = 0 & member(all_232_1, all_232_3) = 0 &
% 284.52/39.38 | | | | | | | | ! [v0: $i] : ( ~ (least(v0, member_predicate,
% 284.52/39.38 | | | | | | | | all_232_3) = 0) | ~ $i(v0))) | ( ~ (all_232_4
% 284.52/39.38 | | | | | | | | = 0) & strict_order(member_predicate, all_45_1) =
% 284.52/39.38 | | | | | | | | all_232_4)
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | BETA: splitting (128) gives:
% 284.52/39.38 | | | | | | | |
% 284.52/39.38 | | | | | | | | Case 1:
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | | (129) all_232_0 = 0 & all_232_2 = 0 & subset(all_232_3,
% 284.52/39.38 | | | | | | | | | all_45_1) = 0 & member(all_232_1, all_232_3) = 0 &
% 284.52/39.38 | | | | | | | | | ! [v0: $i] : ( ~ (least(v0, member_predicate,
% 284.52/39.38 | | | | | | | | | all_232_3) = 0) | ~ $i(v0))
% 284.52/39.38 | | | | | | | | |
% 284.52/39.38 | | | | | | | | | ALPHA: (129) implies:
% 284.52/39.38 | | | | | | | | | (130) member(all_232_1, all_232_3) = 0
% 284.52/39.38 | | | | | | | | | (131) subset(all_232_3, all_45_1) = 0
% 284.52/39.39 | | | | | | | | | (132) ! [v0: $i] : ( ~ (least(v0, member_predicate,
% 284.52/39.39 | | | | | | | | | all_232_3) = 0) | ~ $i(v0))
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | GROUND_INST: instantiating (19) with all_232_3, all_45_1,
% 284.52/39.39 | | | | | | | | | all_24_1, simplifying with (29), (41), (45),
% 284.52/39.39 | | | | | | | | | (126), (131) gives:
% 284.52/39.39 | | | | | | | | | (133) subset(all_232_3, all_24_1) = 0
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | GROUND_INST: instantiating (10) with member_predicate,
% 284.52/39.39 | | | | | | | | | all_24_1, 0, all_232_3, all_232_1, simplifying
% 284.52/39.39 | | | | | | | | | with (11), (29), (47), (126), (127), (130), (133)
% 284.52/39.39 | | | | | | | | | gives:
% 284.52/39.39 | | | | | | | | | (134) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ($i(v1) &
% 284.52/39.39 | | | | | | | | | ((v2 = 0 & least(v1, member_predicate, all_232_3) =
% 284.52/39.39 | | | | | | | | | 0) | ( ~ (v0 = 0) &
% 284.52/39.39 | | | | | | | | | strict_well_order(member_predicate, all_24_1) =
% 284.52/39.39 | | | | | | | | | v0)))
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | DELTA: instantiating (134) with fresh symbols all_990_0,
% 284.52/39.39 | | | | | | | | | all_990_1, all_990_2 gives:
% 284.52/39.39 | | | | | | | | | (135) $i(all_990_1) & ((all_990_0 = 0 & least(all_990_1,
% 284.52/39.39 | | | | | | | | | member_predicate, all_232_3) = 0) | ( ~
% 284.52/39.39 | | | | | | | | | (all_990_2 = 0) &
% 284.52/39.39 | | | | | | | | | strict_well_order(member_predicate, all_24_1) =
% 284.52/39.39 | | | | | | | | | all_990_2))
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | ALPHA: (135) implies:
% 284.52/39.39 | | | | | | | | | (136) $i(all_990_1)
% 284.52/39.39 | | | | | | | | | (137) (all_990_0 = 0 & least(all_990_1, member_predicate,
% 284.52/39.39 | | | | | | | | | all_232_3) = 0) | ( ~ (all_990_2 = 0) &
% 284.52/39.39 | | | | | | | | | strict_well_order(member_predicate, all_24_1) =
% 284.52/39.39 | | | | | | | | | all_990_2)
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | BETA: splitting (137) gives:
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | Case 1:
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | (138) all_990_0 = 0 & least(all_990_1, member_predicate,
% 284.52/39.39 | | | | | | | | | | all_232_3) = 0
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | ALPHA: (138) implies:
% 284.52/39.39 | | | | | | | | | | (139) least(all_990_1, member_predicate, all_232_3) = 0
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | GROUND_INST: instantiating (132) with all_990_1, simplifying
% 284.52/39.39 | | | | | | | | | | with (136), (139) gives:
% 284.52/39.39 | | | | | | | | | | (140) $false
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | CLOSE: (140) is inconsistent.
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | Case 2:
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | (141) ~ (all_990_2 = 0) &
% 284.52/39.39 | | | | | | | | | | strict_well_order(member_predicate, all_24_1) =
% 284.52/39.39 | | | | | | | | | | all_990_2
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | ALPHA: (141) implies:
% 284.52/39.39 | | | | | | | | | | (142) ~ (all_990_2 = 0)
% 284.52/39.39 | | | | | | | | | | (143) strict_well_order(member_predicate, all_24_1) =
% 284.52/39.39 | | | | | | | | | | all_990_2
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_990_2, all_24_1,
% 284.52/39.39 | | | | | | | | | | member_predicate, simplifying with (34), (143)
% 284.52/39.39 | | | | | | | | | | gives:
% 284.52/39.39 | | | | | | | | | | (144) all_990_2 = 0
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | REDUCE: (142), (144) imply:
% 284.52/39.39 | | | | | | | | | | (145) $false
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | CLOSE: (145) is inconsistent.
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | End of split
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | Case 2:
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | (146) ~ (all_232_4 = 0) & strict_order(member_predicate,
% 284.52/39.39 | | | | | | | | | all_45_1) = all_232_4
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | ALPHA: (146) implies:
% 284.52/39.39 | | | | | | | | | (147) ~ (all_232_4 = 0)
% 284.52/39.39 | | | | | | | | | (148) strict_order(member_predicate, all_45_1) = all_232_4
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | GROUND_INST: instantiating (14) with member_predicate,
% 284.52/39.39 | | | | | | | | | all_45_1, all_232_4, simplifying with (11), (41),
% 284.52/39.39 | | | | | | | | | (148) gives:
% 284.52/39.39 | | | | | | | | | (149) all_232_4 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2:
% 284.52/39.39 | | | | | | | | | $i] : ? [v3: int] : ? [v4: int] : ? [v5: int] :
% 284.52/39.39 | | | | | | | | | ? [v6: int] : ? [v7: int] : ? [v8: int] : ? [v9:
% 284.52/39.39 | | | | | | | | | $i] : ? [v10: $i] : ? [v11: int] : ? [v12: int]
% 284.52/39.39 | | | | | | | | | : ? [v13: int] : ? [v14: int] : ($i(v10) & $i(v9) &
% 284.52/39.39 | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ((v14 = 0 & v13 = 0 &
% 284.52/39.39 | | | | | | | | | v12 = 0 & v11 = 0 & apply(member_predicate,
% 284.52/39.39 | | | | | | | | | v10, v9) = 0 & apply(member_predicate, v9,
% 284.52/39.39 | | | | | | | | | v10) = 0 & member(v10, all_45_1) = 0 &
% 284.52/39.39 | | | | | | | | | member(v9, all_45_1) = 0) | (v7 = 0 & v6 = 0 &
% 284.52/39.39 | | | | | | | | | v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) &
% 284.52/39.39 | | | | | | | | | apply(member_predicate, v1, v2) = 0 &
% 284.52/39.39 | | | | | | | | | apply(member_predicate, v0, v2) = v8 &
% 284.52/39.39 | | | | | | | | | apply(member_predicate, v0, v1) = 0 &
% 284.52/39.39 | | | | | | | | | member(v2, all_45_1) = 0 & member(v1, all_45_1)
% 284.52/39.39 | | | | | | | | | = 0 & member(v0, all_45_1) = 0)))
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | BETA: splitting (149) gives:
% 284.52/39.39 | | | | | | | | |
% 284.52/39.39 | | | | | | | | | Case 1:
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | (150) all_232_4 = 0
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | REDUCE: (147), (150) imply:
% 284.52/39.39 | | | | | | | | | | (151) $false
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | CLOSE: (151) is inconsistent.
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | Case 2:
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | (152) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3:
% 284.52/39.39 | | | | | | | | | | int] : ? [v4: int] : ? [v5: int] : ? [v6: int]
% 284.52/39.39 | | | | | | | | | | : ? [v7: int] : ? [v8: int] : ? [v9: $i] : ?
% 284.52/39.39 | | | | | | | | | | [v10: $i] : ? [v11: int] : ? [v12: int] : ?
% 284.52/39.39 | | | | | | | | | | [v13: int] : ? [v14: int] : ($i(v10) & $i(v9) &
% 284.52/39.39 | | | | | | | | | | $i(v2) & $i(v1) & $i(v0) & ((v14 = 0 & v13 = 0 &
% 284.52/39.39 | | | | | | | | | | v12 = 0 & v11 = 0 & apply(member_predicate,
% 284.52/39.39 | | | | | | | | | | v10, v9) = 0 & apply(member_predicate, v9,
% 284.52/39.39 | | | | | | | | | | v10) = 0 & member(v10, all_45_1) = 0 &
% 284.52/39.39 | | | | | | | | | | member(v9, all_45_1) = 0) | (v7 = 0 & v6 = 0
% 284.52/39.39 | | | | | | | | | | & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v8 = 0) &
% 284.52/39.39 | | | | | | | | | | apply(member_predicate, v1, v2) = 0 &
% 284.52/39.39 | | | | | | | | | | apply(member_predicate, v0, v2) = v8 &
% 284.52/39.39 | | | | | | | | | | apply(member_predicate, v0, v1) = 0 &
% 284.52/39.39 | | | | | | | | | | member(v2, all_45_1) = 0 & member(v1,
% 284.52/39.39 | | | | | | | | | | all_45_1) = 0 & member(v0, all_45_1) = 0)))
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | DELTA: instantiating (152) with fresh symbols all_731_0,
% 284.52/39.39 | | | | | | | | | | all_731_1, all_731_2, all_731_3, all_731_4,
% 284.52/39.39 | | | | | | | | | | all_731_5, all_731_6, all_731_7, all_731_8,
% 284.52/39.39 | | | | | | | | | | all_731_9, all_731_10, all_731_11, all_731_12,
% 284.52/39.39 | | | | | | | | | | all_731_13, all_731_14 gives:
% 284.52/39.39 | | | | | | | | | | (153) $i(all_731_4) & $i(all_731_5) & $i(all_731_12) &
% 284.52/39.39 | | | | | | | | | | $i(all_731_13) & $i(all_731_14) & ((all_731_0 = 0 &
% 284.52/39.39 | | | | | | | | | | all_731_1 = 0 & all_731_2 = 0 & all_731_3 = 0 &
% 284.52/39.39 | | | | | | | | | | apply(member_predicate, all_731_4, all_731_5) =
% 284.52/39.39 | | | | | | | | | | 0 & apply(member_predicate, all_731_5,
% 284.52/39.39 | | | | | | | | | | all_731_4) = 0 & member(all_731_4, all_45_1)
% 284.52/39.39 | | | | | | | | | | = 0 & member(all_731_5, all_45_1) = 0) |
% 284.52/39.39 | | | | | | | | | | (all_731_7 = 0 & all_731_8 = 0 & all_731_9 = 0 &
% 284.52/39.39 | | | | | | | | | | all_731_10 = 0 & all_731_11 = 0 & ~ (all_731_6
% 284.52/39.39 | | | | | | | | | | = 0) & apply(member_predicate, all_731_13,
% 284.52/39.39 | | | | | | | | | | all_731_12) = 0 & apply(member_predicate,
% 284.52/39.39 | | | | | | | | | | all_731_14, all_731_12) = all_731_6 &
% 284.52/39.39 | | | | | | | | | | apply(member_predicate, all_731_14, all_731_13)
% 284.52/39.39 | | | | | | | | | | = 0 & member(all_731_12, all_45_1) = 0 &
% 284.52/39.39 | | | | | | | | | | member(all_731_13, all_45_1) = 0 &
% 284.52/39.39 | | | | | | | | | | member(all_731_14, all_45_1) = 0))
% 284.52/39.39 | | | | | | | | | |
% 284.52/39.39 | | | | | | | | | | ALPHA: (153) implies:
% 284.52/39.39 | | | | | | | | | | (154) $i(all_731_14)
% 284.52/39.39 | | | | | | | | | | (155) $i(all_731_13)
% 284.52/39.39 | | | | | | | | | | (156) $i(all_731_12)
% 284.52/39.39 | | | | | | | | | | (157) $i(all_731_5)
% 284.52/39.39 | | | | | | | | | | (158) $i(all_731_4)
% 284.52/39.40 | | | | | | | | | | (159) (all_731_0 = 0 & all_731_1 = 0 & all_731_2 = 0 &
% 284.52/39.40 | | | | | | | | | | all_731_3 = 0 & apply(member_predicate,
% 284.52/39.40 | | | | | | | | | | all_731_4, all_731_5) = 0 &
% 284.52/39.40 | | | | | | | | | | apply(member_predicate, all_731_5, all_731_4) = 0
% 284.52/39.40 | | | | | | | | | | & member(all_731_4, all_45_1) = 0 &
% 284.52/39.40 | | | | | | | | | | member(all_731_5, all_45_1) = 0) | (all_731_7 = 0
% 284.52/39.40 | | | | | | | | | | & all_731_8 = 0 & all_731_9 = 0 & all_731_10 = 0
% 284.52/39.40 | | | | | | | | | | & all_731_11 = 0 & ~ (all_731_6 = 0) &
% 284.52/39.40 | | | | | | | | | | apply(member_predicate, all_731_13, all_731_12) =
% 284.52/39.40 | | | | | | | | | | 0 & apply(member_predicate, all_731_14,
% 284.52/39.40 | | | | | | | | | | all_731_12) = all_731_6 &
% 284.52/39.40 | | | | | | | | | | apply(member_predicate, all_731_14, all_731_13) =
% 284.52/39.40 | | | | | | | | | | 0 & member(all_731_12, all_45_1) = 0 &
% 284.52/39.40 | | | | | | | | | | member(all_731_13, all_45_1) = 0 &
% 284.52/39.40 | | | | | | | | | | member(all_731_14, all_45_1) = 0)
% 284.52/39.40 | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | BETA: splitting (159) gives:
% 284.52/39.40 | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | Case 1:
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | (160) all_731_0 = 0 & all_731_1 = 0 & all_731_2 = 0 &
% 284.52/39.40 | | | | | | | | | | | all_731_3 = 0 & apply(member_predicate, all_731_4,
% 284.52/39.40 | | | | | | | | | | | all_731_5) = 0 & apply(member_predicate,
% 284.52/39.40 | | | | | | | | | | | all_731_5, all_731_4) = 0 & member(all_731_4,
% 284.52/39.40 | | | | | | | | | | | all_45_1) = 0 & member(all_731_5, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | ALPHA: (160) implies:
% 284.52/39.40 | | | | | | | | | | | (161) member(all_731_5, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | | (162) member(all_731_4, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | | (163) apply(member_predicate, all_731_5, all_731_4) = 0
% 284.52/39.40 | | | | | | | | | | | (164) apply(member_predicate, all_731_4, all_731_5) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_45_1, all_24_1,
% 284.52/39.40 | | | | | | | | | | | all_731_5, simplifying with (29), (41), (45),
% 284.52/39.40 | | | | | | | | | | | (157), (161) gives:
% 284.52/39.40 | | | | | | | | | | | (165) member(all_731_5, all_24_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_45_1, all_24_1,
% 284.52/39.40 | | | | | | | | | | | all_731_4, simplifying with (29), (41), (45),
% 284.52/39.40 | | | | | | | | | | | (158), (162) gives:
% 284.52/39.40 | | | | | | | | | | | (166) member(all_731_4, all_24_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (15) with member_predicate,
% 284.52/39.40 | | | | | | | | | | | all_24_1, all_731_4, all_731_5, simplifying with
% 284.52/39.40 | | | | | | | | | | | (11), (29), (47), (157), (158), (163) gives:
% 284.52/39.40 | | | | | | | | | | | (167) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~
% 284.52/39.40 | | | | | | | | | | | (v2 = 0) & apply(member_predicate, all_731_4,
% 284.52/39.40 | | | | | | | | | | | all_731_5) = v2) | ( ~ (v1 = 0) &
% 284.52/39.40 | | | | | | | | | | | member(all_731_5, all_24_1) = v1) | ( ~ (v0 =
% 284.52/39.40 | | | | | | | | | | | 0) & member(all_731_4, all_24_1) = v0))
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | DELTA: instantiating (167) with fresh symbols all_1402_0,
% 284.52/39.40 | | | | | | | | | | | all_1402_1, all_1402_2 gives:
% 284.52/39.40 | | | | | | | | | | | (168) ( ~ (all_1402_0 = 0) & apply(member_predicate,
% 284.52/39.40 | | | | | | | | | | | all_731_4, all_731_5) = all_1402_0) | ( ~
% 284.52/39.40 | | | | | | | | | | | (all_1402_1 = 0) & member(all_731_5, all_24_1) =
% 284.52/39.40 | | | | | | | | | | | all_1402_1) | ( ~ (all_1402_2 = 0) &
% 284.52/39.40 | | | | | | | | | | | member(all_731_4, all_24_1) = all_1402_2)
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | BETA: splitting (168) gives:
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | Case 1:
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | (169) ~ (all_1402_0 = 0) & apply(member_predicate,
% 284.52/39.40 | | | | | | | | | | | | all_731_4, all_731_5) = all_1402_0
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | ALPHA: (169) implies:
% 284.52/39.40 | | | | | | | | | | | | (170) ~ (all_1402_0 = 0)
% 284.52/39.40 | | | | | | | | | | | | (171) apply(member_predicate, all_731_4, all_731_5) =
% 284.52/39.40 | | | | | | | | | | | | all_1402_0
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_1402_0, all_731_5,
% 284.52/39.40 | | | | | | | | | | | | all_731_4, member_predicate, simplifying with
% 284.52/39.40 | | | | | | | | | | | | (164), (171) gives:
% 284.52/39.40 | | | | | | | | | | | | (172) all_1402_0 = 0
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | REDUCE: (170), (172) imply:
% 284.52/39.40 | | | | | | | | | | | | (173) $false
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | Case 2:
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | (174) ( ~ (all_1402_1 = 0) & member(all_731_5, all_24_1)
% 284.52/39.40 | | | | | | | | | | | | = all_1402_1) | ( ~ (all_1402_2 = 0) &
% 284.52/39.40 | | | | | | | | | | | | member(all_731_4, all_24_1) = all_1402_2)
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | BETA: splitting (174) gives:
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | Case 1:
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | (175) ~ (all_1402_1 = 0) & member(all_731_5, all_24_1)
% 284.52/39.40 | | | | | | | | | | | | | = all_1402_1
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | ALPHA: (175) implies:
% 284.52/39.40 | | | | | | | | | | | | | (176) ~ (all_1402_1 = 0)
% 284.52/39.40 | | | | | | | | | | | | | (177) member(all_731_5, all_24_1) = all_1402_1
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1402_1, all_24_1,
% 284.52/39.40 | | | | | | | | | | | | | all_731_5, simplifying with (165), (177) gives:
% 284.52/39.40 | | | | | | | | | | | | | (178) all_1402_1 = 0
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | REDUCE: (176), (178) imply:
% 284.52/39.40 | | | | | | | | | | | | | (179) $false
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | CLOSE: (179) is inconsistent.
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | Case 2:
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | (180) ~ (all_1402_2 = 0) & member(all_731_4, all_24_1)
% 284.52/39.40 | | | | | | | | | | | | | = all_1402_2
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | ALPHA: (180) implies:
% 284.52/39.40 | | | | | | | | | | | | | (181) ~ (all_1402_2 = 0)
% 284.52/39.40 | | | | | | | | | | | | | (182) member(all_731_4, all_24_1) = all_1402_2
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1402_2, all_24_1,
% 284.52/39.40 | | | | | | | | | | | | | all_731_4, simplifying with (166), (182) gives:
% 284.52/39.40 | | | | | | | | | | | | | (183) all_1402_2 = 0
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | REDUCE: (181), (183) imply:
% 284.52/39.40 | | | | | | | | | | | | | (184) $false
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 284.52/39.40 | | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | | End of split
% 284.52/39.40 | | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | End of split
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | Case 2:
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | (185) all_731_7 = 0 & all_731_8 = 0 & all_731_9 = 0 &
% 284.52/39.40 | | | | | | | | | | | all_731_10 = 0 & all_731_11 = 0 & ~ (all_731_6 =
% 284.52/39.40 | | | | | | | | | | | 0) & apply(member_predicate, all_731_13,
% 284.52/39.40 | | | | | | | | | | | all_731_12) = 0 & apply(member_predicate,
% 284.52/39.40 | | | | | | | | | | | all_731_14, all_731_12) = all_731_6 &
% 284.52/39.40 | | | | | | | | | | | apply(member_predicate, all_731_14, all_731_13) =
% 284.52/39.40 | | | | | | | | | | | 0 & member(all_731_12, all_45_1) = 0 &
% 284.52/39.40 | | | | | | | | | | | member(all_731_13, all_45_1) = 0 &
% 284.52/39.40 | | | | | | | | | | | member(all_731_14, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | ALPHA: (185) implies:
% 284.52/39.40 | | | | | | | | | | | (186) ~ (all_731_6 = 0)
% 284.52/39.40 | | | | | | | | | | | (187) member(all_731_14, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | | (188) member(all_731_13, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | | (189) member(all_731_12, all_45_1) = 0
% 284.52/39.40 | | | | | | | | | | | (190) apply(member_predicate, all_731_14, all_731_13) =
% 284.52/39.40 | | | | | | | | | | | 0
% 284.52/39.40 | | | | | | | | | | | (191) apply(member_predicate, all_731_14, all_731_12) =
% 284.52/39.40 | | | | | | | | | | | all_731_6
% 284.52/39.40 | | | | | | | | | | | (192) apply(member_predicate, all_731_13, all_731_12) =
% 284.52/39.40 | | | | | | | | | | | 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_45_1, all_24_1,
% 284.52/39.40 | | | | | | | | | | | all_731_14, simplifying with (29), (41), (45),
% 284.52/39.40 | | | | | | | | | | | (154), (187) gives:
% 284.52/39.40 | | | | | | | | | | | (193) member(all_731_14, all_24_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_45_1, all_24_1,
% 284.52/39.40 | | | | | | | | | | | all_731_13, simplifying with (29), (41), (45),
% 284.52/39.40 | | | | | | | | | | | (155), (188) gives:
% 284.52/39.40 | | | | | | | | | | | (194) member(all_731_13, all_24_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (1) with all_45_1, all_24_1,
% 284.52/39.40 | | | | | | | | | | | all_731_12, simplifying with (29), (41), (45),
% 284.52/39.40 | | | | | | | | | | | (156), (189) gives:
% 284.52/39.40 | | | | | | | | | | | (195) member(all_731_12, all_24_1) = 0
% 284.52/39.40 | | | | | | | | | | |
% 284.52/39.40 | | | | | | | | | | | GROUND_INST: instantiating (17) with member_predicate,
% 284.52/39.40 | | | | | | | | | | | all_24_1, all_731_14, all_731_13, all_731_12,
% 284.52/39.40 | | | | | | | | | | | simplifying with (11), (29), (47), (154), (155),
% 284.52/39.40 | | | | | | | | | | | (156), (190), (192) gives:
% 284.52/39.41 | | | | | | | | | | | (196) ? [v0: int] : ? [v1: int] : ? [v2: int] : ?
% 284.52/39.41 | | | | | | | | | | | [v3: int] : ((v3 = 0 & apply(member_predicate,
% 284.52/39.41 | | | | | | | | | | | all_731_14, all_731_12) = 0) | ( ~ (v2 = 0)
% 284.52/39.41 | | | | | | | | | | | & member(all_731_12, all_24_1) = v2) | ( ~ (v1
% 284.52/39.41 | | | | | | | | | | | = 0) & member(all_731_13, all_24_1) = v1) |
% 284.52/39.41 | | | | | | | | | | | ( ~ (v0 = 0) & member(all_731_14, all_24_1) =
% 284.52/39.41 | | | | | | | | | | | v0))
% 284.52/39.41 | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | DELTA: instantiating (196) with fresh symbols all_1414_0,
% 284.52/39.41 | | | | | | | | | | | all_1414_1, all_1414_2, all_1414_3 gives:
% 284.52/39.41 | | | | | | | | | | | (197) (all_1414_0 = 0 & apply(member_predicate,
% 284.52/39.41 | | | | | | | | | | | all_731_14, all_731_12) = 0) | ( ~ (all_1414_1
% 284.52/39.41 | | | | | | | | | | | = 0) & member(all_731_12, all_24_1) =
% 284.52/39.41 | | | | | | | | | | | all_1414_1) | ( ~ (all_1414_2 = 0) &
% 284.52/39.41 | | | | | | | | | | | member(all_731_13, all_24_1) = all_1414_2) | ( ~
% 284.52/39.41 | | | | | | | | | | | (all_1414_3 = 0) & member(all_731_14, all_24_1)
% 284.52/39.41 | | | | | | | | | | | = all_1414_3)
% 284.52/39.41 | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | BETA: splitting (197) gives:
% 284.52/39.41 | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | Case 1:
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | (198) (all_1414_0 = 0 & apply(member_predicate,
% 284.52/39.41 | | | | | | | | | | | | all_731_14, all_731_12) = 0) | ( ~ (all_1414_1
% 284.52/39.41 | | | | | | | | | | | | = 0) & member(all_731_12, all_24_1) =
% 284.52/39.41 | | | | | | | | | | | | all_1414_1)
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | BETA: splitting (198) gives:
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | Case 1:
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | (199) all_1414_0 = 0 & apply(member_predicate,
% 284.52/39.41 | | | | | | | | | | | | | all_731_14, all_731_12) = 0
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | ALPHA: (199) implies:
% 284.52/39.41 | | | | | | | | | | | | | (200) apply(member_predicate, all_731_14, all_731_12) =
% 284.52/39.41 | | | | | | | | | | | | | 0
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | GROUND_INST: instantiating (26) with all_731_6, 0, all_731_12,
% 284.52/39.41 | | | | | | | | | | | | | all_731_14, member_predicate, simplifying with
% 284.52/39.41 | | | | | | | | | | | | | (191), (200) gives:
% 284.52/39.41 | | | | | | | | | | | | | (201) all_731_6 = 0
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | REDUCE: (186), (201) imply:
% 284.52/39.41 | | | | | | | | | | | | | (202) $false
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | CLOSE: (202) is inconsistent.
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | Case 2:
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | (203) ~ (all_1414_1 = 0) & member(all_731_12, all_24_1)
% 284.52/39.41 | | | | | | | | | | | | | = all_1414_1
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | ALPHA: (203) implies:
% 284.52/39.41 | | | | | | | | | | | | | (204) ~ (all_1414_1 = 0)
% 284.52/39.41 | | | | | | | | | | | | | (205) member(all_731_12, all_24_1) = all_1414_1
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1414_1, all_24_1,
% 284.52/39.41 | | | | | | | | | | | | | all_731_12, simplifying with (195), (205) gives:
% 284.52/39.41 | | | | | | | | | | | | | (206) all_1414_1 = 0
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | REDUCE: (204), (206) imply:
% 284.52/39.41 | | | | | | | | | | | | | (207) $false
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | CLOSE: (207) is inconsistent.
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | End of split
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | Case 2:
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | (208) ( ~ (all_1414_2 = 0) & member(all_731_13,
% 284.52/39.41 | | | | | | | | | | | | all_24_1) = all_1414_2) | ( ~ (all_1414_3 = 0)
% 284.52/39.41 | | | | | | | | | | | | & member(all_731_14, all_24_1) = all_1414_3)
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | BETA: splitting (208) gives:
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | Case 1:
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | (209) ~ (all_1414_2 = 0) & member(all_731_13, all_24_1)
% 284.52/39.41 | | | | | | | | | | | | | = all_1414_2
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | ALPHA: (209) implies:
% 284.52/39.41 | | | | | | | | | | | | | (210) ~ (all_1414_2 = 0)
% 284.52/39.41 | | | | | | | | | | | | | (211) member(all_731_13, all_24_1) = all_1414_2
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1414_2, all_24_1,
% 284.52/39.41 | | | | | | | | | | | | | all_731_13, simplifying with (194), (211) gives:
% 284.52/39.41 | | | | | | | | | | | | | (212) all_1414_2 = 0
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | REDUCE: (210), (212) imply:
% 284.52/39.41 | | | | | | | | | | | | | (213) $false
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | CLOSE: (213) is inconsistent.
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | Case 2:
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | (214) ~ (all_1414_3 = 0) & member(all_731_14, all_24_1)
% 284.52/39.41 | | | | | | | | | | | | | = all_1414_3
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | ALPHA: (214) implies:
% 284.52/39.41 | | | | | | | | | | | | | (215) ~ (all_1414_3 = 0)
% 284.52/39.41 | | | | | | | | | | | | | (216) member(all_731_14, all_24_1) = all_1414_3
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_1414_3, all_24_1,
% 284.52/39.41 | | | | | | | | | | | | | all_731_14, simplifying with (193), (216) gives:
% 284.52/39.41 | | | | | | | | | | | | | (217) all_1414_3 = 0
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | REDUCE: (215), (217) imply:
% 284.52/39.41 | | | | | | | | | | | | | (218) $false
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 284.52/39.41 | | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | | End of split
% 284.52/39.41 | | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | | End of split
% 284.52/39.41 | | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | | End of split
% 284.52/39.41 | | | | | | | | | |
% 284.52/39.41 | | | | | | | | | End of split
% 284.52/39.41 | | | | | | | | |
% 284.52/39.41 | | | | | | | | End of split
% 284.52/39.41 | | | | | | | |
% 284.52/39.41 | | | | | | | End of split
% 284.52/39.41 | | | | | | |
% 284.52/39.41 | | | | | | End of split
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | Case 2:
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | | (219) ~ (all_95_4 = 0) & set(all_45_1) = all_95_4
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | | ALPHA: (219) implies:
% 284.52/39.41 | | | | | | (220) ~ (all_95_4 = 0)
% 284.52/39.41 | | | | | | (221) set(all_45_1) = all_95_4
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | | GROUND_INST: instantiating (22) with 0, all_95_4, all_45_1,
% 284.52/39.41 | | | | | | simplifying with (46), (221) gives:
% 284.52/39.41 | | | | | | (222) all_95_4 = 0
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | | REDUCE: (220), (222) imply:
% 284.52/39.41 | | | | | | (223) $false
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | | CLOSE: (223) is inconsistent.
% 284.52/39.41 | | | | | |
% 284.52/39.41 | | | | | End of split
% 284.52/39.41 | | | | |
% 284.52/39.41 | | | | End of split
% 284.52/39.41 | | | |
% 284.52/39.41 | | | End of split
% 284.52/39.41 | | |
% 284.52/39.41 | | Case 2:
% 284.52/39.41 | | |
% 284.52/39.41 | | | (224) ~ (all_63_1 = 0) & member(all_24_1, on) = all_63_1
% 284.52/39.41 | | |
% 284.52/39.41 | | | ALPHA: (224) implies:
% 284.52/39.41 | | | (225) ~ (all_63_1 = 0)
% 284.52/39.41 | | | (226) member(all_24_1, on) = all_63_1
% 284.52/39.41 | | |
% 284.52/39.41 | | | GROUND_INST: instantiating (23) with 0, all_63_1, on, all_24_1,
% 284.52/39.41 | | | simplifying with (30), (226) gives:
% 284.52/39.41 | | | (227) all_63_1 = 0
% 284.52/39.41 | | |
% 284.52/39.41 | | | REDUCE: (225), (227) imply:
% 284.52/39.41 | | | (228) $false
% 284.52/39.41 | | |
% 284.52/39.41 | | | CLOSE: (228) is inconsistent.
% 284.52/39.41 | | |
% 284.52/39.41 | | End of split
% 284.52/39.41 | |
% 284.52/39.41 | End of split
% 284.52/39.41 |
% 284.52/39.41 End of proof
% 284.52/39.41 % SZS output end Proof for theBenchmark
% 284.52/39.41
% 284.52/39.41 38793ms
%------------------------------------------------------------------------------