TSTP Solution File: SET770+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.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 15:26:22 EDT 2023
% Result : Theorem 9.75s 2.16s
% Output : Proof 14.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET770+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 13:33:17 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.64 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.82/1.08 Prover 4: Preprocessing ...
% 2.82/1.08 Prover 1: Preprocessing ...
% 2.82/1.12 Prover 2: Preprocessing ...
% 2.82/1.12 Prover 5: Preprocessing ...
% 2.82/1.12 Prover 6: Preprocessing ...
% 2.82/1.12 Prover 0: Preprocessing ...
% 2.82/1.12 Prover 3: Preprocessing ...
% 6.66/1.64 Prover 5: Proving ...
% 6.66/1.65 Prover 6: Proving ...
% 6.94/1.67 Prover 2: Proving ...
% 6.94/1.72 Prover 3: Constructing countermodel ...
% 6.94/1.73 Prover 1: Constructing countermodel ...
% 8.29/1.88 Prover 4: Constructing countermodel ...
% 8.29/1.91 Prover 0: Proving ...
% 9.75/2.16 Prover 3: proved (1509ms)
% 9.75/2.16
% 9.75/2.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.75/2.16
% 9.75/2.16 Prover 2: stopped
% 9.75/2.16 Prover 5: stopped
% 9.75/2.17 Prover 0: stopped
% 9.75/2.18 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.75/2.18 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.75/2.18 Prover 6: stopped
% 9.75/2.18 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.75/2.18 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.75/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 9.75/2.21 Prover 7: Preprocessing ...
% 9.75/2.22 Prover 10: Preprocessing ...
% 9.75/2.23 Prover 11: Preprocessing ...
% 9.75/2.24 Prover 8: Preprocessing ...
% 9.75/2.24 Prover 13: Preprocessing ...
% 10.60/2.31 Prover 10: Warning: ignoring some quantifiers
% 11.50/2.33 Prover 7: Warning: ignoring some quantifiers
% 11.50/2.34 Prover 7: Constructing countermodel ...
% 11.50/2.34 Prover 10: Constructing countermodel ...
% 11.50/2.39 Prover 13: Warning: ignoring some quantifiers
% 12.00/2.41 Prover 13: Constructing countermodel ...
% 12.00/2.44 Prover 8: Warning: ignoring some quantifiers
% 12.54/2.47 Prover 10: gave up
% 12.54/2.47 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 12.56/2.47 Prover 8: Constructing countermodel ...
% 12.56/2.49 Prover 16: Preprocessing ...
% 13.03/2.54 Prover 1: Found proof (size 195)
% 13.03/2.54 Prover 1: proved (1900ms)
% 13.03/2.54 Prover 13: stopped
% 13.03/2.54 Prover 4: stopped
% 13.03/2.54 Prover 7: stopped
% 13.03/2.55 Prover 8: stopped
% 13.03/2.57 Prover 16: Warning: ignoring some quantifiers
% 13.03/2.57 Prover 11: Constructing countermodel ...
% 13.03/2.58 Prover 16: Constructing countermodel ...
% 13.03/2.58 Prover 11: stopped
% 13.03/2.59 Prover 16: stopped
% 13.03/2.59
% 13.03/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.03/2.59
% 13.03/2.61 % SZS output start Proof for theBenchmark
% 13.03/2.61 Assumptions after simplification:
% 13.03/2.61 ---------------------------------
% 13.03/2.61
% 13.03/2.61 (disjoint)
% 13.60/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 13.60/2.64 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (member(v3, v1) = 0 &
% 13.60/2.64 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 13.60/2.64 (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~
% 13.60/2.64 (member(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 13.60/2.64 member(v2, v1) = v3)))
% 13.60/2.64
% 13.60/2.64 (equal_set)
% 13.60/2.64 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 13.60/2.64 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 13.60/2.64 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 13.60/2.64 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 13.60/2.64 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 13.60/2.64
% 13.60/2.64 (equivalence)
% 13.60/2.65 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equivalence(v1, v0) =
% 13.60/2.65 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 13.60/2.65 [v6: int] : ( ~ (v6 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v6 &
% 13.60/2.65 apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 &
% 13.60/2.65 member(v3, v0) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i]
% 13.60/2.65 : ? [v5: int] : ( ~ (v5 = 0) & apply(v1, v4, v3) = v5 & apply(v1, v3, v4) =
% 13.60/2.65 0 & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3)) | ? [v3:
% 13.60/2.65 $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v1, v3, v3) = v4 & member(v3,
% 13.60/2.65 v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1,
% 13.60/2.65 v0) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4:
% 13.60/2.65 $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~
% 13.60/2.65 (apply(v1, v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6:
% 13.60/2.65 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4)
% 13.60/2.65 = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6
% 13.60/2.65 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2:
% 13.60/2.65 $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) | ~ $i(v2) |
% 13.60/2.65 ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v2: $i] : !
% 13.60/2.65 [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4:
% 13.60/2.65 any] : ? [v5: any] : ? [v6: any] : (apply(v1, v3, v2) = v6 &
% 13.60/2.65 member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)
% 13.60/2.65 | v6 = 0)))))
% 13.60/2.65
% 13.60/2.65 (equivalence_class)
% 13.60/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 13.60/2.66 int] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3,
% 13.60/2.66 v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any]
% 13.60/2.66 : ? [v7: any] : (apply(v0, v2, v3) = v7 & member(v3, v1) = v6 & ( ~ (v7 =
% 13.60/2.66 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 13.60/2.66 [v3: $i] : ! [v4: $i] : ( ~ (equivalence_class(v2, v1, v0) = v4) | ~
% 13.60/2.66 (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 13.60/2.66 (apply(v0, v2, v3) = 0 & member(v3, v1) = 0))
% 13.60/2.66
% 13.60/2.66 (subset)
% 13.60/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 13.60/2.66 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.60/2.66 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.60/2.66 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 13.60/2.66 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.60/2.66
% 13.60/2.66 (thIII06)
% 13.60/2.66 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 13.60/2.66 $i] : ? [v6: int] : ? [v7: int] : ( ~ (v7 = 0) & ~ (v6 = 0) &
% 13.60/2.66 equivalence_class(v3, v0, v1) = v5 & equivalence_class(v2, v0, v1) = v4 &
% 13.60/2.66 equivalence(v1, v0) = 0 & disjoint(v4, v5) = v7 & equal_set(v4, v5) = v6 &
% 13.60/2.66 member(v3, v0) = 0 & member(v2, v0) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2)
% 13.60/2.66 & $i(v1) & $i(v0))
% 13.60/2.66
% 13.60/2.66 (function-axioms)
% 13.60/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 13.60/2.67 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3,
% 13.60/2.67 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 13.60/2.67 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) =
% 13.60/2.67 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.60/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.60/2.67 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0:
% 13.60/2.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 13.60/2.67 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) &
% 13.60/2.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 13.60/2.67 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 13.60/2.67 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 13.60/2.67 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 13.60/2.67 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.60/2.67 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 13.60/2.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.60/2.67 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 13.60/2.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 13.60/2.67 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 13.60/2.67 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 13.60/2.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 13.60/2.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 13.60/2.67 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 13.60/2.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 13.60/2.67 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 13.60/2.67 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 13.60/2.67 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 13.60/2.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 13.60/2.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 13.60/2.67 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 13.60/2.67 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 13.60/2.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 13.60/2.67 (power_set(v2) = v0))
% 13.60/2.67
% 13.60/2.67 Further assumptions not needed in the proof:
% 13.60/2.67 --------------------------------------------
% 13.60/2.67 difference, empty_set, intersection, partition, power_set, pre_order, product,
% 13.60/2.67 singleton, sum, union, unordered_pair
% 13.60/2.67
% 13.60/2.67 Those formulas are unsatisfiable:
% 13.60/2.67 ---------------------------------
% 13.60/2.67
% 13.60/2.67 Begin of proof
% 13.60/2.68 |
% 13.60/2.68 | ALPHA: (subset) implies:
% 13.60/2.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 13.60/2.68 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 13.60/2.68 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.60/2.68 |
% 13.60/2.68 | ALPHA: (equal_set) implies:
% 13.60/2.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 13.60/2.68 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 13.60/2.68 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 13.60/2.68 | 0))))
% 13.60/2.68 |
% 13.60/2.68 | ALPHA: (disjoint) implies:
% 13.60/2.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 13.60/2.68 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (member(v3, v1)
% 13.60/2.68 | = 0 & member(v3, v0) = 0 & $i(v3)))
% 13.60/2.68 |
% 13.60/2.68 | ALPHA: (equivalence) implies:
% 13.60/2.68 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1, v0) = 0) | ~ $i(v1) |
% 13.60/2.68 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] :
% 13.60/2.68 | (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0)
% 13.60/2.68 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 13.60/2.68 | : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4) = v9 &
% 13.60/2.68 | member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6
% 13.60/2.68 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) &
% 13.60/2.68 | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) |
% 13.60/2.68 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &
% 13.60/2.68 | ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3)
% 13.60/2.68 | | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 13.60/2.68 | (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) =
% 13.60/2.68 | v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))))
% 13.60/2.68 |
% 13.60/2.68 | ALPHA: (equivalence_class) implies:
% 13.60/2.69 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 13.60/2.69 | ~ (equivalence_class(v2, v1, v0) = v4) | ~ (member(v3, v4) = 0) | ~
% 13.60/2.69 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (apply(v0, v2, v3) = 0 &
% 13.60/2.69 | member(v3, v1) = 0))
% 13.60/2.69 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 13.60/2.69 | ! [v5: int] : (v5 = 0 | ~ (equivalence_class(v2, v1, v0) = v4) | ~
% 13.60/2.69 | (member(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 13.60/2.69 | | ? [v6: any] : ? [v7: any] : (apply(v0, v2, v3) = v7 & member(v3,
% 13.60/2.69 | v1) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 13.60/2.69 |
% 13.60/2.69 | ALPHA: (function-axioms) implies:
% 13.60/2.69 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.60/2.69 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 13.60/2.69 | = v0))
% 13.60/2.69 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 13.60/2.69 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 13.60/2.69 | (apply(v4, v3, v2) = v0))
% 13.60/2.69 |
% 13.60/2.69 | DELTA: instantiating (thIII06) with fresh symbols all_20_0, all_20_1,
% 13.60/2.69 | all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 gives:
% 13.60/2.69 | (9) ~ (all_20_0 = 0) & ~ (all_20_1 = 0) & equivalence_class(all_20_4,
% 13.60/2.69 | all_20_7, all_20_6) = all_20_2 & equivalence_class(all_20_5,
% 13.60/2.69 | all_20_7, all_20_6) = all_20_3 & equivalence(all_20_6, all_20_7) = 0
% 13.60/2.69 | & disjoint(all_20_3, all_20_2) = all_20_0 & equal_set(all_20_3,
% 13.60/2.69 | all_20_2) = all_20_1 & member(all_20_4, all_20_7) = 0 &
% 13.60/2.69 | member(all_20_5, all_20_7) = 0 & $i(all_20_2) & $i(all_20_3) &
% 13.60/2.69 | $i(all_20_4) & $i(all_20_5) & $i(all_20_6) & $i(all_20_7)
% 13.60/2.69 |
% 13.60/2.69 | ALPHA: (9) implies:
% 13.60/2.69 | (10) ~ (all_20_1 = 0)
% 13.60/2.69 | (11) ~ (all_20_0 = 0)
% 13.60/2.69 | (12) $i(all_20_7)
% 13.60/2.69 | (13) $i(all_20_6)
% 13.60/2.69 | (14) $i(all_20_5)
% 13.60/2.69 | (15) $i(all_20_4)
% 13.60/2.69 | (16) $i(all_20_3)
% 13.60/2.69 | (17) $i(all_20_2)
% 13.60/2.69 | (18) member(all_20_5, all_20_7) = 0
% 13.94/2.69 | (19) member(all_20_4, all_20_7) = 0
% 13.94/2.69 | (20) equal_set(all_20_3, all_20_2) = all_20_1
% 13.94/2.69 | (21) disjoint(all_20_3, all_20_2) = all_20_0
% 13.94/2.69 | (22) equivalence(all_20_6, all_20_7) = 0
% 13.94/2.69 | (23) equivalence_class(all_20_5, all_20_7, all_20_6) = all_20_3
% 13.94/2.69 | (24) equivalence_class(all_20_4, all_20_7, all_20_6) = all_20_2
% 13.94/2.69 |
% 13.94/2.69 | GROUND_INST: instantiating (2) with all_20_3, all_20_2, all_20_1, simplifying
% 13.94/2.69 | with (16), (17), (20) gives:
% 13.94/2.70 | (25) all_20_1 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_20_2,
% 13.94/2.70 | all_20_3) = v1 & subset(all_20_3, all_20_2) = v0 & ( ~ (v1 = 0) |
% 13.94/2.70 | ~ (v0 = 0)))
% 13.94/2.70 |
% 13.94/2.70 | GROUND_INST: instantiating (3) with all_20_3, all_20_2, all_20_0, simplifying
% 13.94/2.70 | with (16), (17), (21) gives:
% 13.94/2.70 | (26) all_20_0 = 0 | ? [v0: $i] : (member(v0, all_20_2) = 0 & member(v0,
% 13.94/2.70 | all_20_3) = 0 & $i(v0))
% 13.94/2.70 |
% 13.94/2.70 | GROUND_INST: instantiating (4) with all_20_7, all_20_6, simplifying with (12),
% 13.94/2.70 | (13), (22) gives:
% 13.94/2.70 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.94/2.70 | (apply(all_20_6, v0, v2) = v3) | ~ (apply(all_20_6, v0, v1) = 0) |
% 13.94/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 13.94/2.70 | [v6: any] : ? [v7: any] : (apply(all_20_6, v1, v2) = v7 &
% 13.94/2.70 | member(v2, all_20_7) = v6 & member(v1, all_20_7) = v5 & member(v0,
% 13.94/2.70 | all_20_7) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 13.94/2.70 | (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 13.94/2.70 | (apply(all_20_6, v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 13.94/2.70 | = 0) & member(v0, all_20_7) = v2)) & ! [v0: $i] : ! [v1: $i] :
% 13.94/2.70 | ( ~ (apply(all_20_6, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 13.94/2.70 | any] : ? [v3: any] : ? [v4: any] : (apply(all_20_6, v1, v0) = v4
% 13.94/2.70 | & member(v1, all_20_7) = v3 & member(v0, all_20_7) = v2 & ( ~ (v3
% 13.94/2.70 | = 0) | ~ (v2 = 0) | v4 = 0)))
% 13.94/2.70 |
% 13.94/2.70 | ALPHA: (27) implies:
% 13.94/2.70 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_20_6, v0, v1) = 0) | ~
% 13.94/2.70 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 13.94/2.70 | (apply(all_20_6, v1, v0) = v4 & member(v1, all_20_7) = v3 &
% 13.94/2.70 | member(v0, all_20_7) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 13.94/2.70 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 13.94/2.70 | (apply(all_20_6, v0, v2) = v3) | ~ (apply(all_20_6, v0, v1) = 0) |
% 13.94/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 13.94/2.70 | [v6: any] : ? [v7: any] : (apply(all_20_6, v1, v2) = v7 &
% 13.94/2.70 | member(v2, all_20_7) = v6 & member(v1, all_20_7) = v5 & member(v0,
% 13.94/2.70 | all_20_7) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 13.94/2.70 | (v4 = 0))))
% 13.94/2.70 |
% 13.94/2.70 | BETA: splitting (26) gives:
% 13.94/2.70 |
% 13.94/2.70 | Case 1:
% 13.94/2.70 | |
% 13.94/2.70 | | (30) all_20_0 = 0
% 13.94/2.70 | |
% 13.94/2.70 | | REDUCE: (11), (30) imply:
% 13.94/2.70 | | (31) $false
% 13.94/2.70 | |
% 13.94/2.70 | | CLOSE: (31) is inconsistent.
% 13.94/2.70 | |
% 13.94/2.70 | Case 2:
% 13.94/2.70 | |
% 13.94/2.71 | | (32) ? [v0: $i] : (member(v0, all_20_2) = 0 & member(v0, all_20_3) = 0 &
% 13.94/2.71 | | $i(v0))
% 13.94/2.71 | |
% 13.94/2.71 | | DELTA: instantiating (32) with fresh symbol all_32_0 gives:
% 13.94/2.71 | | (33) member(all_32_0, all_20_2) = 0 & member(all_32_0, all_20_3) = 0 &
% 13.94/2.71 | | $i(all_32_0)
% 13.94/2.71 | |
% 13.94/2.71 | | ALPHA: (33) implies:
% 13.94/2.71 | | (34) $i(all_32_0)
% 13.94/2.71 | | (35) member(all_32_0, all_20_3) = 0
% 13.94/2.71 | | (36) member(all_32_0, all_20_2) = 0
% 13.94/2.71 | |
% 13.94/2.71 | | BETA: splitting (25) gives:
% 13.94/2.71 | |
% 13.94/2.71 | | Case 1:
% 13.94/2.71 | | |
% 13.94/2.71 | | | (37) all_20_1 = 0
% 13.94/2.71 | | |
% 13.94/2.71 | | | REDUCE: (10), (37) imply:
% 13.94/2.71 | | | (38) $false
% 13.94/2.71 | | |
% 13.94/2.71 | | | CLOSE: (38) is inconsistent.
% 13.94/2.71 | | |
% 13.94/2.71 | | Case 2:
% 13.94/2.71 | | |
% 13.94/2.71 | | | (39) ? [v0: any] : ? [v1: any] : (subset(all_20_2, all_20_3) = v1 &
% 13.94/2.71 | | | subset(all_20_3, all_20_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.94/2.71 | | |
% 13.94/2.71 | | | DELTA: instantiating (39) with fresh symbols all_38_0, all_38_1 gives:
% 13.94/2.71 | | | (40) subset(all_20_2, all_20_3) = all_38_0 & subset(all_20_3, all_20_2)
% 13.94/2.71 | | | = all_38_1 & ( ~ (all_38_0 = 0) | ~ (all_38_1 = 0))
% 13.94/2.71 | | |
% 13.94/2.71 | | | ALPHA: (40) implies:
% 13.94/2.71 | | | (41) subset(all_20_3, all_20_2) = all_38_1
% 13.94/2.71 | | | (42) subset(all_20_2, all_20_3) = all_38_0
% 13.94/2.71 | | | (43) ~ (all_38_0 = 0) | ~ (all_38_1 = 0)
% 13.94/2.71 | | |
% 13.94/2.71 | | | GROUND_INST: instantiating (5) with all_20_6, all_20_7, all_20_5,
% 13.94/2.71 | | | all_32_0, all_20_3, simplifying with (12), (13), (14), (23),
% 13.94/2.71 | | | (34), (35) gives:
% 13.94/2.71 | | | (44) apply(all_20_6, all_20_5, all_32_0) = 0 & member(all_32_0,
% 13.94/2.71 | | | all_20_7) = 0
% 13.94/2.71 | | |
% 13.94/2.71 | | | ALPHA: (44) implies:
% 13.94/2.71 | | | (45) apply(all_20_6, all_20_5, all_32_0) = 0
% 13.94/2.71 | | |
% 13.94/2.71 | | | GROUND_INST: instantiating (5) with all_20_6, all_20_7, all_20_4,
% 13.94/2.71 | | | all_32_0, all_20_2, simplifying with (12), (13), (15), (24),
% 13.94/2.71 | | | (34), (36) gives:
% 13.94/2.71 | | | (46) apply(all_20_6, all_20_4, all_32_0) = 0 & member(all_32_0,
% 13.94/2.71 | | | all_20_7) = 0
% 13.94/2.71 | | |
% 13.94/2.71 | | | ALPHA: (46) implies:
% 13.94/2.71 | | | (47) member(all_32_0, all_20_7) = 0
% 13.94/2.71 | | | (48) apply(all_20_6, all_20_4, all_32_0) = 0
% 13.94/2.71 | | |
% 13.94/2.71 | | | GROUND_INST: instantiating (1) with all_20_3, all_20_2, all_38_1,
% 13.94/2.71 | | | simplifying with (16), (17), (41) gives:
% 13.94/2.71 | | | (49) all_38_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.94/2.71 | | | member(v0, all_20_2) = v1 & member(v0, all_20_3) = 0 & $i(v0))
% 13.94/2.71 | | |
% 13.94/2.71 | | | GROUND_INST: instantiating (1) with all_20_2, all_20_3, all_38_0,
% 13.94/2.71 | | | simplifying with (16), (17), (42) gives:
% 13.94/2.71 | | | (50) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.94/2.71 | | | member(v0, all_20_2) = 0 & member(v0, all_20_3) = v1 & $i(v0))
% 13.94/2.71 | | |
% 13.94/2.72 | | | GROUND_INST: instantiating (28) with all_20_5, all_32_0, simplifying with
% 13.94/2.72 | | | (14), (34), (45) gives:
% 13.94/2.72 | | | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_20_6,
% 13.94/2.72 | | | all_32_0, all_20_5) = v2 & member(all_32_0, all_20_7) = v1 &
% 13.94/2.72 | | | member(all_20_5, all_20_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 13.94/2.72 | | | v2 = 0))
% 13.94/2.72 | | |
% 13.94/2.72 | | | GROUND_INST: instantiating (28) with all_20_4, all_32_0, simplifying with
% 13.94/2.72 | | | (15), (34), (48) gives:
% 13.94/2.72 | | | (52) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_20_6,
% 13.94/2.72 | | | all_32_0, all_20_4) = v2 & member(all_32_0, all_20_7) = v1 &
% 13.94/2.72 | | | member(all_20_4, all_20_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 13.94/2.72 | | | v2 = 0))
% 13.94/2.72 | | |
% 13.94/2.72 | | | DELTA: instantiating (52) with fresh symbols all_51_0, all_51_1, all_51_2
% 13.94/2.72 | | | gives:
% 13.94/2.72 | | | (53) apply(all_20_6, all_32_0, all_20_4) = all_51_0 & member(all_32_0,
% 13.94/2.72 | | | all_20_7) = all_51_1 & member(all_20_4, all_20_7) = all_51_2 & (
% 13.94/2.72 | | | ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | all_51_0 = 0)
% 13.94/2.72 | | |
% 13.94/2.72 | | | ALPHA: (53) implies:
% 13.94/2.72 | | | (54) member(all_20_4, all_20_7) = all_51_2
% 13.94/2.72 | | | (55) member(all_32_0, all_20_7) = all_51_1
% 13.94/2.72 | | | (56) apply(all_20_6, all_32_0, all_20_4) = all_51_0
% 13.94/2.72 | | | (57) ~ (all_51_1 = 0) | ~ (all_51_2 = 0) | all_51_0 = 0
% 13.94/2.72 | | |
% 13.94/2.72 | | | DELTA: instantiating (51) with fresh symbols all_53_0, all_53_1, all_53_2
% 13.94/2.72 | | | gives:
% 13.94/2.72 | | | (58) apply(all_20_6, all_32_0, all_20_5) = all_53_0 & member(all_32_0,
% 13.94/2.72 | | | all_20_7) = all_53_1 & member(all_20_5, all_20_7) = all_53_2 & (
% 13.94/2.72 | | | ~ (all_53_1 = 0) | ~ (all_53_2 = 0) | all_53_0 = 0)
% 13.94/2.72 | | |
% 13.94/2.72 | | | ALPHA: (58) implies:
% 13.94/2.72 | | | (59) member(all_20_5, all_20_7) = all_53_2
% 13.94/2.72 | | | (60) member(all_32_0, all_20_7) = all_53_1
% 13.94/2.72 | | | (61) apply(all_20_6, all_32_0, all_20_5) = all_53_0
% 13.94/2.72 | | | (62) ~ (all_53_1 = 0) | ~ (all_53_2 = 0) | all_53_0 = 0
% 13.94/2.72 | | |
% 13.94/2.72 | | | GROUND_INST: instantiating (7) with 0, all_53_2, all_20_7, all_20_5,
% 13.94/2.72 | | | simplifying with (18), (59) gives:
% 13.94/2.72 | | | (63) all_53_2 = 0
% 13.94/2.72 | | |
% 13.94/2.72 | | | GROUND_INST: instantiating (7) with 0, all_51_2, all_20_7, all_20_4,
% 13.94/2.72 | | | simplifying with (19), (54) gives:
% 13.94/2.72 | | | (64) all_51_2 = 0
% 13.94/2.72 | | |
% 13.94/2.72 | | | GROUND_INST: instantiating (7) with 0, all_53_1, all_20_7, all_32_0,
% 13.94/2.72 | | | simplifying with (47), (60) gives:
% 13.94/2.72 | | | (65) all_53_1 = 0
% 13.94/2.72 | | |
% 13.94/2.72 | | | GROUND_INST: instantiating (7) with all_51_1, all_53_1, all_20_7,
% 13.94/2.72 | | | all_32_0, simplifying with (55), (60) gives:
% 13.94/2.72 | | | (66) all_53_1 = all_51_1
% 13.94/2.72 | | |
% 13.94/2.72 | | | COMBINE_EQS: (65), (66) imply:
% 13.94/2.72 | | | (67) all_51_1 = 0
% 13.94/2.72 | | |
% 13.94/2.72 | | | BETA: splitting (62) gives:
% 13.94/2.72 | | |
% 13.94/2.72 | | | Case 1:
% 13.94/2.72 | | | |
% 13.94/2.72 | | | | (68) ~ (all_53_1 = 0)
% 13.94/2.72 | | | |
% 13.94/2.72 | | | | REDUCE: (65), (68) imply:
% 13.94/2.72 | | | | (69) $false
% 13.94/2.72 | | | |
% 13.94/2.72 | | | | CLOSE: (69) is inconsistent.
% 13.94/2.72 | | | |
% 13.94/2.72 | | | Case 2:
% 13.94/2.72 | | | |
% 13.94/2.72 | | | | (70) ~ (all_53_2 = 0) | all_53_0 = 0
% 13.94/2.72 | | | |
% 13.94/2.72 | | | | BETA: splitting (57) gives:
% 13.94/2.72 | | | |
% 13.94/2.72 | | | | Case 1:
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | | (71) ~ (all_51_1 = 0)
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | | REDUCE: (67), (71) imply:
% 13.94/2.72 | | | | | (72) $false
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | | CLOSE: (72) is inconsistent.
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | Case 2:
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | | (73) ~ (all_51_2 = 0) | all_51_0 = 0
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | | BETA: splitting (70) gives:
% 13.94/2.72 | | | | |
% 13.94/2.72 | | | | | Case 1:
% 13.94/2.72 | | | | | |
% 13.94/2.72 | | | | | | (74) ~ (all_53_2 = 0)
% 13.94/2.72 | | | | | |
% 13.94/2.72 | | | | | | REDUCE: (63), (74) imply:
% 13.94/2.72 | | | | | | (75) $false
% 13.94/2.72 | | | | | |
% 13.94/2.72 | | | | | | CLOSE: (75) is inconsistent.
% 13.94/2.72 | | | | | |
% 13.94/2.72 | | | | | Case 2:
% 13.94/2.72 | | | | | |
% 13.94/2.73 | | | | | | (76) all_53_0 = 0
% 13.94/2.73 | | | | | |
% 13.94/2.73 | | | | | | REDUCE: (61), (76) imply:
% 13.94/2.73 | | | | | | (77) apply(all_20_6, all_32_0, all_20_5) = 0
% 13.94/2.73 | | | | | |
% 13.94/2.73 | | | | | | BETA: splitting (73) gives:
% 13.94/2.73 | | | | | |
% 13.94/2.73 | | | | | | Case 1:
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | (78) ~ (all_51_2 = 0)
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | REDUCE: (64), (78) imply:
% 13.94/2.73 | | | | | | | (79) $false
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | CLOSE: (79) is inconsistent.
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | Case 2:
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | (80) all_51_0 = 0
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | REDUCE: (56), (80) imply:
% 13.94/2.73 | | | | | | | (81) apply(all_20_6, all_32_0, all_20_4) = 0
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | BETA: splitting (43) gives:
% 13.94/2.73 | | | | | | |
% 13.94/2.73 | | | | | | | Case 1:
% 13.94/2.73 | | | | | | | |
% 13.94/2.73 | | | | | | | | (82) ~ (all_38_0 = 0)
% 13.94/2.73 | | | | | | | |
% 13.94/2.73 | | | | | | | | BETA: splitting (50) gives:
% 13.94/2.73 | | | | | | | |
% 13.94/2.73 | | | | | | | | Case 1:
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | (83) all_38_0 = 0
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | REDUCE: (82), (83) imply:
% 13.94/2.73 | | | | | | | | | (84) $false
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | CLOSE: (84) is inconsistent.
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | Case 2:
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | (85) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 13.94/2.73 | | | | | | | | | all_20_2) = 0 & member(v0, all_20_3) = v1 &
% 13.94/2.73 | | | | | | | | | $i(v0))
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | DELTA: instantiating (85) with fresh symbols all_86_0,
% 13.94/2.73 | | | | | | | | | all_86_1 gives:
% 13.94/2.73 | | | | | | | | | (86) ~ (all_86_0 = 0) & member(all_86_1, all_20_2) = 0 &
% 13.94/2.73 | | | | | | | | | member(all_86_1, all_20_3) = all_86_0 & $i(all_86_1)
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | ALPHA: (86) implies:
% 13.94/2.73 | | | | | | | | | (87) ~ (all_86_0 = 0)
% 13.94/2.73 | | | | | | | | | (88) $i(all_86_1)
% 13.94/2.73 | | | | | | | | | (89) member(all_86_1, all_20_3) = all_86_0
% 13.94/2.73 | | | | | | | | | (90) member(all_86_1, all_20_2) = 0
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | GROUND_INST: instantiating (6) with all_20_6, all_20_7,
% 13.94/2.73 | | | | | | | | | all_20_5, all_86_1, all_20_3, all_86_0,
% 13.94/2.73 | | | | | | | | | simplifying with (12), (13), (14), (23), (88),
% 13.94/2.73 | | | | | | | | | (89) gives:
% 13.94/2.73 | | | | | | | | | (91) all_86_0 = 0 | ? [v0: any] : ? [v1: any] :
% 13.94/2.73 | | | | | | | | | (apply(all_20_6, all_20_5, all_86_1) = v1 &
% 13.94/2.73 | | | | | | | | | member(all_86_1, all_20_7) = v0 & ( ~ (v1 = 0) | ~
% 13.94/2.73 | | | | | | | | | (v0 = 0)))
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | GROUND_INST: instantiating (5) with all_20_6, all_20_7,
% 13.94/2.73 | | | | | | | | | all_20_4, all_86_1, all_20_2, simplifying with
% 13.94/2.73 | | | | | | | | | (12), (13), (15), (24), (88), (90) gives:
% 13.94/2.73 | | | | | | | | | (92) apply(all_20_6, all_20_4, all_86_1) = 0 &
% 13.94/2.73 | | | | | | | | | member(all_86_1, all_20_7) = 0
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | ALPHA: (92) implies:
% 13.94/2.73 | | | | | | | | | (93) member(all_86_1, all_20_7) = 0
% 13.94/2.73 | | | | | | | | | (94) apply(all_20_6, all_20_4, all_86_1) = 0
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | BETA: splitting (91) gives:
% 13.94/2.73 | | | | | | | | |
% 13.94/2.73 | | | | | | | | | Case 1:
% 13.94/2.73 | | | | | | | | | |
% 13.94/2.73 | | | | | | | | | | (95) all_86_0 = 0
% 13.94/2.73 | | | | | | | | | |
% 13.94/2.73 | | | | | | | | | | REDUCE: (87), (95) imply:
% 13.94/2.73 | | | | | | | | | | (96) $false
% 13.94/2.73 | | | | | | | | | |
% 13.94/2.73 | | | | | | | | | | CLOSE: (96) is inconsistent.
% 13.94/2.73 | | | | | | | | | |
% 13.94/2.73 | | | | | | | | | Case 2:
% 13.94/2.73 | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | (97) ? [v0: any] : ? [v1: any] : (apply(all_20_6,
% 13.94/2.74 | | | | | | | | | | all_20_5, all_86_1) = v1 & member(all_86_1,
% 13.94/2.74 | | | | | | | | | | all_20_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.94/2.74 | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | DELTA: instantiating (97) with fresh symbols all_98_0,
% 13.94/2.74 | | | | | | | | | | all_98_1 gives:
% 13.94/2.74 | | | | | | | | | | (98) apply(all_20_6, all_20_5, all_86_1) = all_98_0 &
% 13.94/2.74 | | | | | | | | | | member(all_86_1, all_20_7) = all_98_1 & ( ~
% 13.94/2.74 | | | | | | | | | | (all_98_0 = 0) | ~ (all_98_1 = 0))
% 13.94/2.74 | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | ALPHA: (98) implies:
% 13.94/2.74 | | | | | | | | | | (99) member(all_86_1, all_20_7) = all_98_1
% 13.94/2.74 | | | | | | | | | | (100) apply(all_20_6, all_20_5, all_86_1) = all_98_0
% 13.94/2.74 | | | | | | | | | | (101) ~ (all_98_0 = 0) | ~ (all_98_1 = 0)
% 13.94/2.74 | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_98_1, all_20_7,
% 13.94/2.74 | | | | | | | | | | all_86_1, simplifying with (93), (99) gives:
% 13.94/2.74 | | | | | | | | | | (102) all_98_1 = 0
% 13.94/2.74 | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | BETA: splitting (101) gives:
% 13.94/2.74 | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | Case 1:
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | (103) ~ (all_98_0 = 0)
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | GROUND_INST: instantiating (29) with all_20_5, all_32_0,
% 13.94/2.74 | | | | | | | | | | | all_86_1, all_98_0, simplifying with (14), (34),
% 13.94/2.74 | | | | | | | | | | | (45), (88), (100) gives:
% 13.94/2.74 | | | | | | | | | | | (104) all_98_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 13.94/2.74 | | | | | | | | | | | [v2: any] : ? [v3: any] : (apply(all_20_6,
% 13.94/2.74 | | | | | | | | | | | all_32_0, all_86_1) = v3 & member(all_86_1,
% 13.94/2.74 | | | | | | | | | | | all_20_7) = v2 & member(all_32_0, all_20_7) =
% 13.94/2.74 | | | | | | | | | | | v1 & member(all_20_5, all_20_7) = v0 & ( ~ (v3 =
% 13.94/2.74 | | | | | | | | | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 13.94/2.74 | | | | | | | | | | | 0)))
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | GROUND_INST: instantiating (28) with all_20_4, all_86_1,
% 13.94/2.74 | | | | | | | | | | | simplifying with (15), (88), (94) gives:
% 13.94/2.74 | | | | | | | | | | | (105) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 13.94/2.74 | | | | | | | | | | | (apply(all_20_6, all_86_1, all_20_4) = v2 &
% 13.94/2.74 | | | | | | | | | | | member(all_86_1, all_20_7) = v1 &
% 13.94/2.74 | | | | | | | | | | | member(all_20_4, all_20_7) = v0 & ( ~ (v1 = 0) |
% 13.94/2.74 | | | | | | | | | | | ~ (v0 = 0) | v2 = 0))
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | DELTA: instantiating (105) with fresh symbols all_113_0,
% 13.94/2.74 | | | | | | | | | | | all_113_1, all_113_2 gives:
% 13.94/2.74 | | | | | | | | | | | (106) apply(all_20_6, all_86_1, all_20_4) = all_113_0 &
% 13.94/2.74 | | | | | | | | | | | member(all_86_1, all_20_7) = all_113_1 &
% 13.94/2.74 | | | | | | | | | | | member(all_20_4, all_20_7) = all_113_2 & ( ~
% 13.94/2.74 | | | | | | | | | | | (all_113_1 = 0) | ~ (all_113_2 = 0) | all_113_0
% 13.94/2.74 | | | | | | | | | | | = 0)
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | ALPHA: (106) implies:
% 13.94/2.74 | | | | | | | | | | | (107) member(all_20_4, all_20_7) = all_113_2
% 13.94/2.74 | | | | | | | | | | | (108) member(all_86_1, all_20_7) = all_113_1
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | BETA: splitting (104) gives:
% 13.94/2.74 | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | Case 1:
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | | (109) all_98_0 = 0
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | | REDUCE: (103), (109) imply:
% 13.94/2.74 | | | | | | | | | | | | (110) $false
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | | CLOSE: (110) is inconsistent.
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | Case 2:
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | | (111) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 13.94/2.74 | | | | | | | | | | | | [v3: any] : (apply(all_20_6, all_32_0, all_86_1) =
% 13.94/2.74 | | | | | | | | | | | | v3 & member(all_86_1, all_20_7) = v2 &
% 13.94/2.74 | | | | | | | | | | | | member(all_32_0, all_20_7) = v1 &
% 13.94/2.74 | | | | | | | | | | | | member(all_20_5, all_20_7) = v0 & ( ~ (v3 = 0) |
% 13.94/2.74 | | | | | | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | | DELTA: instantiating (111) with fresh symbols all_119_0,
% 13.94/2.74 | | | | | | | | | | | | all_119_1, all_119_2, all_119_3 gives:
% 13.94/2.74 | | | | | | | | | | | | (112) apply(all_20_6, all_32_0, all_86_1) = all_119_0 &
% 13.94/2.74 | | | | | | | | | | | | member(all_86_1, all_20_7) = all_119_1 &
% 13.94/2.74 | | | | | | | | | | | | member(all_32_0, all_20_7) = all_119_2 &
% 13.94/2.74 | | | | | | | | | | | | member(all_20_5, all_20_7) = all_119_3 & ( ~
% 13.94/2.74 | | | | | | | | | | | | (all_119_0 = 0) | ~ (all_119_1 = 0) | ~
% 13.94/2.74 | | | | | | | | | | | | (all_119_2 = 0) | ~ (all_119_3 = 0))
% 13.94/2.74 | | | | | | | | | | | |
% 13.94/2.74 | | | | | | | | | | | | ALPHA: (112) implies:
% 13.94/2.74 | | | | | | | | | | | | (113) member(all_20_5, all_20_7) = all_119_3
% 13.94/2.74 | | | | | | | | | | | | (114) member(all_32_0, all_20_7) = all_119_2
% 13.94/2.74 | | | | | | | | | | | | (115) member(all_86_1, all_20_7) = all_119_1
% 13.94/2.74 | | | | | | | | | | | | (116) apply(all_20_6, all_32_0, all_86_1) = all_119_0
% 13.94/2.75 | | | | | | | | | | | | (117) ~ (all_119_0 = 0) | ~ (all_119_1 = 0) | ~
% 13.94/2.75 | | | | | | | | | | | | (all_119_2 = 0) | ~ (all_119_3 = 0)
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_119_3, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | all_20_5, simplifying with (18), (113) gives:
% 13.94/2.75 | | | | | | | | | | | | (118) all_119_3 = 0
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_113_2, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | all_20_4, simplifying with (19), (107) gives:
% 13.94/2.75 | | | | | | | | | | | | (119) all_113_2 = 0
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_119_2, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | all_32_0, simplifying with (47), (114) gives:
% 13.94/2.75 | | | | | | | | | | | | (120) all_119_2 = 0
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_119_1, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | all_86_1, simplifying with (93), (115) gives:
% 13.94/2.75 | | | | | | | | | | | | (121) all_119_1 = 0
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_113_1, all_119_1,
% 13.94/2.75 | | | | | | | | | | | | all_20_7, all_86_1, simplifying with (108), (115)
% 13.94/2.75 | | | | | | | | | | | | gives:
% 13.94/2.75 | | | | | | | | | | | | (122) all_119_1 = all_113_1
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | COMBINE_EQS: (121), (122) imply:
% 13.94/2.75 | | | | | | | | | | | | (123) all_113_1 = 0
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | BETA: splitting (117) gives:
% 13.94/2.75 | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | Case 1:
% 13.94/2.75 | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | (124) ~ (all_119_0 = 0)
% 13.94/2.75 | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_32_0, all_20_4,
% 13.94/2.75 | | | | | | | | | | | | | all_86_1, all_119_0, simplifying with (15), (34),
% 13.94/2.75 | | | | | | | | | | | | | (81), (88), (116) gives:
% 13.94/2.75 | | | | | | | | | | | | | (125) all_119_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 13.94/2.75 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : (apply(all_20_6,
% 13.94/2.75 | | | | | | | | | | | | | all_20_4, all_86_1) = v3 & member(all_86_1,
% 13.94/2.75 | | | | | | | | | | | | | all_20_7) = v2 & member(all_32_0, all_20_7) =
% 13.94/2.75 | | | | | | | | | | | | | v0 & member(all_20_4, all_20_7) = v1 & ( ~ (v3 =
% 13.94/2.75 | | | | | | | | | | | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 13.94/2.75 | | | | | | | | | | | | | 0)))
% 13.94/2.75 | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | BETA: splitting (125) gives:
% 13.94/2.75 | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | Case 1:
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | (126) all_119_0 = 0
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | REDUCE: (124), (126) imply:
% 13.94/2.75 | | | | | | | | | | | | | | (127) $false
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | Case 2:
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | (128) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 13.94/2.75 | | | | | | | | | | | | | | [v3: any] : (apply(all_20_6, all_20_4, all_86_1) =
% 13.94/2.75 | | | | | | | | | | | | | | v3 & member(all_86_1, all_20_7) = v2 &
% 13.94/2.75 | | | | | | | | | | | | | | member(all_32_0, all_20_7) = v0 &
% 13.94/2.75 | | | | | | | | | | | | | | member(all_20_4, all_20_7) = v1 & ( ~ (v3 = 0) |
% 13.94/2.75 | | | | | | | | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | DELTA: instantiating (128) with fresh symbols all_148_0,
% 13.94/2.75 | | | | | | | | | | | | | | all_148_1, all_148_2, all_148_3 gives:
% 13.94/2.75 | | | | | | | | | | | | | | (129) apply(all_20_6, all_20_4, all_86_1) = all_148_0 &
% 13.94/2.75 | | | | | | | | | | | | | | member(all_86_1, all_20_7) = all_148_1 &
% 13.94/2.75 | | | | | | | | | | | | | | member(all_32_0, all_20_7) = all_148_3 &
% 13.94/2.75 | | | | | | | | | | | | | | member(all_20_4, all_20_7) = all_148_2 & ( ~
% 13.94/2.75 | | | | | | | | | | | | | | (all_148_0 = 0) | ~ (all_148_1 = 0) | ~
% 13.94/2.75 | | | | | | | | | | | | | | (all_148_2 = 0) | ~ (all_148_3 = 0))
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | ALPHA: (129) implies:
% 13.94/2.75 | | | | | | | | | | | | | | (130) member(all_20_4, all_20_7) = all_148_2
% 13.94/2.75 | | | | | | | | | | | | | | (131) member(all_32_0, all_20_7) = all_148_3
% 13.94/2.75 | | | | | | | | | | | | | | (132) member(all_86_1, all_20_7) = all_148_1
% 13.94/2.75 | | | | | | | | | | | | | | (133) apply(all_20_6, all_20_4, all_86_1) = all_148_0
% 13.94/2.75 | | | | | | | | | | | | | | (134) ~ (all_148_0 = 0) | ~ (all_148_1 = 0) | ~
% 13.94/2.75 | | | | | | | | | | | | | | (all_148_2 = 0) | ~ (all_148_3 = 0)
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_148_2, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | | | all_20_4, simplifying with (19), (130) gives:
% 13.94/2.75 | | | | | | | | | | | | | | (135) all_148_2 = 0
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_148_3, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | | | all_32_0, simplifying with (47), (131) gives:
% 13.94/2.75 | | | | | | | | | | | | | | (136) all_148_3 = 0
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_148_1, all_20_7,
% 13.94/2.75 | | | | | | | | | | | | | | all_86_1, simplifying with (93), (132) gives:
% 13.94/2.75 | | | | | | | | | | | | | | (137) all_148_1 = 0
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_148_0, all_86_1,
% 13.94/2.75 | | | | | | | | | | | | | | all_20_4, all_20_6, simplifying with (94), (133)
% 13.94/2.75 | | | | | | | | | | | | | | gives:
% 13.94/2.75 | | | | | | | | | | | | | | (138) all_148_0 = 0
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 13.94/2.75 | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | Case 1:
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | (139) ~ (all_148_0 = 0)
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | REDUCE: (138), (139) imply:
% 13.94/2.75 | | | | | | | | | | | | | | | (140) $false
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | Case 2:
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | (141) ~ (all_148_1 = 0) | ~ (all_148_2 = 0) | ~
% 13.94/2.75 | | | | | | | | | | | | | | | (all_148_3 = 0)
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 13.94/2.75 | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | Case 1:
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | (142) ~ (all_148_1 = 0)
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | REDUCE: (137), (142) imply:
% 13.94/2.75 | | | | | | | | | | | | | | | | (143) $false
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | CLOSE: (143) is inconsistent.
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | Case 2:
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | (144) ~ (all_148_2 = 0) | ~ (all_148_3 = 0)
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 13.94/2.75 | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | Case 1:
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | | (145) ~ (all_148_2 = 0)
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | | REDUCE: (135), (145) imply:
% 13.94/2.75 | | | | | | | | | | | | | | | | | (146) $false
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | Case 2:
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | | (147) ~ (all_148_3 = 0)
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.75 | | | | | | | | | | | | | | | | | REDUCE: (136), (147) imply:
% 13.94/2.75 | | | | | | | | | | | | | | | | | (148) $false
% 13.94/2.75 | | | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | | | CLOSE: (148) is inconsistent.
% 13.94/2.76 | | | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | (149) ~ (all_119_1 = 0) | ~ (all_119_2 = 0) | ~
% 13.94/2.76 | | | | | | | | | | | | | (all_119_3 = 0)
% 13.94/2.76 | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | BETA: splitting (149) gives:
% 13.94/2.76 | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | Case 1:
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | (150) ~ (all_119_1 = 0)
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | REDUCE: (121), (150) imply:
% 13.94/2.76 | | | | | | | | | | | | | | (151) $false
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | CLOSE: (151) is inconsistent.
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | (152) ~ (all_119_2 = 0) | ~ (all_119_3 = 0)
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | Case 1:
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | (153) ~ (all_119_2 = 0)
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | REDUCE: (120), (153) imply:
% 13.94/2.76 | | | | | | | | | | | | | | | (154) $false
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | (155) ~ (all_119_3 = 0)
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | REDUCE: (118), (155) imply:
% 13.94/2.76 | | | | | | | | | | | | | | | (156) $false
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 13.94/2.76 | | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | (157) ~ (all_98_1 = 0)
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | REDUCE: (102), (157) imply:
% 13.94/2.76 | | | | | | | | | | | (158) $false
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | CLOSE: (158) is inconsistent.
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | End of split
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | End of split
% 13.94/2.76 | | | | | | | |
% 13.94/2.76 | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | |
% 13.94/2.76 | | | | | | | | (159) ~ (all_38_1 = 0)
% 13.94/2.76 | | | | | | | |
% 13.94/2.76 | | | | | | | | BETA: splitting (49) gives:
% 13.94/2.76 | | | | | | | |
% 13.94/2.76 | | | | | | | | Case 1:
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | (160) all_38_1 = 0
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | REDUCE: (159), (160) imply:
% 13.94/2.76 | | | | | | | | | (161) $false
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | CLOSE: (161) is inconsistent.
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | (162) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.94/2.76 | | | | | | | | | member(v0, all_20_2) = v1 & member(v0, all_20_3) =
% 13.94/2.76 | | | | | | | | | 0 & $i(v0))
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | DELTA: instantiating (162) with fresh symbols all_86_0,
% 13.94/2.76 | | | | | | | | | all_86_1 gives:
% 13.94/2.76 | | | | | | | | | (163) ~ (all_86_0 = 0) & member(all_86_1, all_20_2) =
% 13.94/2.76 | | | | | | | | | all_86_0 & member(all_86_1, all_20_3) = 0 &
% 13.94/2.76 | | | | | | | | | $i(all_86_1)
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | ALPHA: (163) implies:
% 13.94/2.76 | | | | | | | | | (164) ~ (all_86_0 = 0)
% 13.94/2.76 | | | | | | | | | (165) $i(all_86_1)
% 13.94/2.76 | | | | | | | | | (166) member(all_86_1, all_20_3) = 0
% 13.94/2.76 | | | | | | | | | (167) member(all_86_1, all_20_2) = all_86_0
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | GROUND_INST: instantiating (5) with all_20_6, all_20_7,
% 13.94/2.76 | | | | | | | | | all_20_5, all_86_1, all_20_3, simplifying with
% 13.94/2.76 | | | | | | | | | (12), (13), (14), (23), (165), (166) gives:
% 13.94/2.76 | | | | | | | | | (168) apply(all_20_6, all_20_5, all_86_1) = 0 &
% 13.94/2.76 | | | | | | | | | member(all_86_1, all_20_7) = 0
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | ALPHA: (168) implies:
% 13.94/2.76 | | | | | | | | | (169) member(all_86_1, all_20_7) = 0
% 13.94/2.76 | | | | | | | | | (170) apply(all_20_6, all_20_5, all_86_1) = 0
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | GROUND_INST: instantiating (6) with all_20_6, all_20_7,
% 13.94/2.76 | | | | | | | | | all_20_4, all_86_1, all_20_2, all_86_0,
% 13.94/2.76 | | | | | | | | | simplifying with (12), (13), (15), (24), (165),
% 13.94/2.76 | | | | | | | | | (167) gives:
% 13.94/2.76 | | | | | | | | | (171) all_86_0 = 0 | ? [v0: any] : ? [v1: any] :
% 13.94/2.76 | | | | | | | | | (apply(all_20_6, all_20_4, all_86_1) = v1 &
% 13.94/2.76 | | | | | | | | | member(all_86_1, all_20_7) = v0 & ( ~ (v1 = 0) | ~
% 13.94/2.76 | | | | | | | | | (v0 = 0)))
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | BETA: splitting (171) gives:
% 13.94/2.76 | | | | | | | | |
% 13.94/2.76 | | | | | | | | | Case 1:
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | (172) all_86_0 = 0
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | REDUCE: (164), (172) imply:
% 13.94/2.76 | | | | | | | | | | (173) $false
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | CLOSE: (173) is inconsistent.
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | Case 2:
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | (174) ? [v0: any] : ? [v1: any] : (apply(all_20_6,
% 13.94/2.76 | | | | | | | | | | all_20_4, all_86_1) = v1 & member(all_86_1,
% 13.94/2.76 | | | | | | | | | | all_20_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | DELTA: instantiating (174) with fresh symbols all_99_0,
% 13.94/2.76 | | | | | | | | | | all_99_1 gives:
% 13.94/2.76 | | | | | | | | | | (175) apply(all_20_6, all_20_4, all_86_1) = all_99_0 &
% 13.94/2.76 | | | | | | | | | | member(all_86_1, all_20_7) = all_99_1 & ( ~
% 13.94/2.76 | | | | | | | | | | (all_99_0 = 0) | ~ (all_99_1 = 0))
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | ALPHA: (175) implies:
% 13.94/2.76 | | | | | | | | | | (176) member(all_86_1, all_20_7) = all_99_1
% 13.94/2.76 | | | | | | | | | | (177) apply(all_20_6, all_20_4, all_86_1) = all_99_0
% 13.94/2.76 | | | | | | | | | | (178) ~ (all_99_0 = 0) | ~ (all_99_1 = 0)
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_99_1, all_20_7,
% 13.94/2.76 | | | | | | | | | | all_86_1, simplifying with (169), (176) gives:
% 13.94/2.76 | | | | | | | | | | (179) all_99_1 = 0
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | BETA: splitting (178) gives:
% 13.94/2.76 | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | Case 1:
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | (180) ~ (all_99_0 = 0)
% 13.94/2.76 | | | | | | | | | | |
% 13.94/2.76 | | | | | | | | | | | GROUND_INST: instantiating (28) with all_20_5, all_86_1,
% 13.94/2.76 | | | | | | | | | | | simplifying with (14), (165), (170) gives:
% 13.94/2.76 | | | | | | | | | | | (181) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 13.94/2.76 | | | | | | | | | | | (apply(all_20_6, all_86_1, all_20_5) = v2 &
% 13.94/2.76 | | | | | | | | | | | member(all_86_1, all_20_7) = v1 &
% 13.94/2.76 | | | | | | | | | | | member(all_20_5, all_20_7) = v0 & ( ~ (v1 = 0) |
% 13.94/2.76 | | | | | | | | | | | ~ (v0 = 0) | v2 = 0))
% 13.94/2.76 | | | | | | | | | | |
% 14.29/2.76 | | | | | | | | | | | GROUND_INST: instantiating (29) with all_20_4, all_32_0,
% 14.29/2.76 | | | | | | | | | | | all_86_1, all_99_0, simplifying with (15), (34),
% 14.29/2.76 | | | | | | | | | | | (48), (165), (177) gives:
% 14.29/2.77 | | | | | | | | | | | (182) all_99_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 14.29/2.77 | | | | | | | | | | | [v2: any] : ? [v3: any] : (apply(all_20_6,
% 14.29/2.77 | | | | | | | | | | | all_32_0, all_86_1) = v3 & member(all_86_1,
% 14.29/2.77 | | | | | | | | | | | all_20_7) = v2 & member(all_32_0, all_20_7) =
% 14.29/2.77 | | | | | | | | | | | v1 & member(all_20_4, all_20_7) = v0 & ( ~ (v3 =
% 14.29/2.77 | | | | | | | | | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 14.29/2.77 | | | | | | | | | | | 0)))
% 14.29/2.77 | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | DELTA: instantiating (181) with fresh symbols all_114_0,
% 14.29/2.77 | | | | | | | | | | | all_114_1, all_114_2 gives:
% 14.29/2.77 | | | | | | | | | | | (183) apply(all_20_6, all_86_1, all_20_5) = all_114_0 &
% 14.29/2.77 | | | | | | | | | | | member(all_86_1, all_20_7) = all_114_1 &
% 14.29/2.77 | | | | | | | | | | | member(all_20_5, all_20_7) = all_114_2 & ( ~
% 14.29/2.77 | | | | | | | | | | | (all_114_1 = 0) | ~ (all_114_2 = 0) | all_114_0
% 14.29/2.77 | | | | | | | | | | | = 0)
% 14.29/2.77 | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | ALPHA: (183) implies:
% 14.29/2.77 | | | | | | | | | | | (184) member(all_20_5, all_20_7) = all_114_2
% 14.29/2.77 | | | | | | | | | | | (185) member(all_86_1, all_20_7) = all_114_1
% 14.29/2.77 | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | BETA: splitting (182) gives:
% 14.29/2.77 | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | Case 1:
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | | (186) all_99_0 = 0
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | | REDUCE: (180), (186) imply:
% 14.29/2.77 | | | | | | | | | | | | (187) $false
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | | CLOSE: (187) is inconsistent.
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | Case 2:
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | | (188) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 14.29/2.77 | | | | | | | | | | | | [v3: any] : (apply(all_20_6, all_32_0, all_86_1) =
% 14.29/2.77 | | | | | | | | | | | | v3 & member(all_86_1, all_20_7) = v2 &
% 14.29/2.77 | | | | | | | | | | | | member(all_32_0, all_20_7) = v1 &
% 14.29/2.77 | | | | | | | | | | | | member(all_20_4, all_20_7) = v0 & ( ~ (v3 = 0) |
% 14.29/2.77 | | | | | | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | | DELTA: instantiating (188) with fresh symbols all_120_0,
% 14.29/2.77 | | | | | | | | | | | | all_120_1, all_120_2, all_120_3 gives:
% 14.29/2.77 | | | | | | | | | | | | (189) apply(all_20_6, all_32_0, all_86_1) = all_120_0 &
% 14.29/2.77 | | | | | | | | | | | | member(all_86_1, all_20_7) = all_120_1 &
% 14.29/2.77 | | | | | | | | | | | | member(all_32_0, all_20_7) = all_120_2 &
% 14.29/2.77 | | | | | | | | | | | | member(all_20_4, all_20_7) = all_120_3 & ( ~
% 14.29/2.77 | | | | | | | | | | | | (all_120_0 = 0) | ~ (all_120_1 = 0) | ~
% 14.29/2.77 | | | | | | | | | | | | (all_120_2 = 0) | ~ (all_120_3 = 0))
% 14.29/2.77 | | | | | | | | | | | |
% 14.29/2.77 | | | | | | | | | | | | ALPHA: (189) implies:
% 14.30/2.77 | | | | | | | | | | | | (190) member(all_20_4, all_20_7) = all_120_3
% 14.30/2.77 | | | | | | | | | | | | (191) member(all_32_0, all_20_7) = all_120_2
% 14.30/2.77 | | | | | | | | | | | | (192) member(all_86_1, all_20_7) = all_120_1
% 14.30/2.77 | | | | | | | | | | | | (193) apply(all_20_6, all_32_0, all_86_1) = all_120_0
% 14.30/2.77 | | | | | | | | | | | | (194) ~ (all_120_0 = 0) | ~ (all_120_1 = 0) | ~
% 14.30/2.77 | | | | | | | | | | | | (all_120_2 = 0) | ~ (all_120_3 = 0)
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_114_2, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | all_20_5, simplifying with (18), (184) gives:
% 14.30/2.77 | | | | | | | | | | | | (195) all_114_2 = 0
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_120_3, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | all_20_4, simplifying with (19), (190) gives:
% 14.30/2.77 | | | | | | | | | | | | (196) all_120_3 = 0
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_120_2, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | all_32_0, simplifying with (47), (191) gives:
% 14.30/2.77 | | | | | | | | | | | | (197) all_120_2 = 0
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_120_1, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | all_86_1, simplifying with (169), (192) gives:
% 14.30/2.77 | | | | | | | | | | | | (198) all_120_1 = 0
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_114_1, all_120_1,
% 14.30/2.77 | | | | | | | | | | | | all_20_7, all_86_1, simplifying with (185), (192)
% 14.30/2.77 | | | | | | | | | | | | gives:
% 14.30/2.77 | | | | | | | | | | | | (199) all_120_1 = all_114_1
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | COMBINE_EQS: (198), (199) imply:
% 14.30/2.77 | | | | | | | | | | | | (200) all_114_1 = 0
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | BETA: splitting (194) gives:
% 14.30/2.77 | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | Case 1:
% 14.30/2.77 | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | (201) ~ (all_120_0 = 0)
% 14.30/2.77 | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | GROUND_INST: instantiating (29) with all_32_0, all_20_5,
% 14.30/2.77 | | | | | | | | | | | | | all_86_1, all_120_0, simplifying with (14), (34),
% 14.30/2.77 | | | | | | | | | | | | | (77), (165), (193) gives:
% 14.30/2.77 | | | | | | | | | | | | | (202) all_120_0 = 0 | ? [v0: any] : ? [v1: any] : ?
% 14.30/2.77 | | | | | | | | | | | | | [v2: any] : ? [v3: any] : (apply(all_20_6,
% 14.30/2.77 | | | | | | | | | | | | | all_20_5, all_86_1) = v3 & member(all_86_1,
% 14.30/2.77 | | | | | | | | | | | | | all_20_7) = v2 & member(all_32_0, all_20_7) =
% 14.30/2.77 | | | | | | | | | | | | | v0 & member(all_20_5, all_20_7) = v1 & ( ~ (v3 =
% 14.30/2.77 | | | | | | | | | | | | | 0) | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 14.30/2.77 | | | | | | | | | | | | | 0)))
% 14.30/2.77 | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | BETA: splitting (202) gives:
% 14.30/2.77 | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | Case 1:
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | (203) all_120_0 = 0
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | REDUCE: (201), (203) imply:
% 14.30/2.77 | | | | | | | | | | | | | | (204) $false
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | Case 2:
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | (205) ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 14.30/2.77 | | | | | | | | | | | | | | [v3: any] : (apply(all_20_6, all_20_5, all_86_1) =
% 14.30/2.77 | | | | | | | | | | | | | | v3 & member(all_86_1, all_20_7) = v2 &
% 14.30/2.77 | | | | | | | | | | | | | | member(all_32_0, all_20_7) = v0 &
% 14.30/2.77 | | | | | | | | | | | | | | member(all_20_5, all_20_7) = v1 & ( ~ (v3 = 0) |
% 14.30/2.77 | | | | | | | | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbols all_145_0,
% 14.30/2.77 | | | | | | | | | | | | | | all_145_1, all_145_2, all_145_3 gives:
% 14.30/2.77 | | | | | | | | | | | | | | (206) apply(all_20_6, all_20_5, all_86_1) = all_145_0 &
% 14.30/2.77 | | | | | | | | | | | | | | member(all_86_1, all_20_7) = all_145_1 &
% 14.30/2.77 | | | | | | | | | | | | | | member(all_32_0, all_20_7) = all_145_3 &
% 14.30/2.77 | | | | | | | | | | | | | | member(all_20_5, all_20_7) = all_145_2 & ( ~
% 14.30/2.77 | | | | | | | | | | | | | | (all_145_0 = 0) | ~ (all_145_1 = 0) | ~
% 14.30/2.77 | | | | | | | | | | | | | | (all_145_2 = 0) | ~ (all_145_3 = 0))
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | ALPHA: (206) implies:
% 14.30/2.77 | | | | | | | | | | | | | | (207) member(all_20_5, all_20_7) = all_145_2
% 14.30/2.77 | | | | | | | | | | | | | | (208) member(all_32_0, all_20_7) = all_145_3
% 14.30/2.77 | | | | | | | | | | | | | | (209) member(all_86_1, all_20_7) = all_145_1
% 14.30/2.77 | | | | | | | | | | | | | | (210) apply(all_20_6, all_20_5, all_86_1) = all_145_0
% 14.30/2.77 | | | | | | | | | | | | | | (211) ~ (all_145_0 = 0) | ~ (all_145_1 = 0) | ~
% 14.30/2.77 | | | | | | | | | | | | | | (all_145_2 = 0) | ~ (all_145_3 = 0)
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_145_2, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | | | all_20_5, simplifying with (18), (207) gives:
% 14.30/2.77 | | | | | | | | | | | | | | (212) all_145_2 = 0
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_145_3, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | | | all_32_0, simplifying with (47), (208) gives:
% 14.30/2.77 | | | | | | | | | | | | | | (213) all_145_3 = 0
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with 0, all_145_1, all_20_7,
% 14.30/2.77 | | | | | | | | | | | | | | all_86_1, simplifying with (169), (209) gives:
% 14.30/2.77 | | | | | | | | | | | | | | (214) all_145_1 = 0
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with 0, all_145_0, all_86_1,
% 14.30/2.77 | | | | | | | | | | | | | | all_20_5, all_20_6, simplifying with (170), (210)
% 14.30/2.77 | | | | | | | | | | | | | | gives:
% 14.30/2.77 | | | | | | | | | | | | | | (215) all_145_0 = 0
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 14.30/2.77 | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | Case 1:
% 14.30/2.77 | | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | | (216) ~ (all_145_0 = 0)
% 14.30/2.77 | | | | | | | | | | | | | | |
% 14.30/2.77 | | | | | | | | | | | | | | | REDUCE: (215), (216) imply:
% 14.30/2.78 | | | | | | | | | | | | | | | (217) $false
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | (218) ~ (all_145_1 = 0) | ~ (all_145_2 = 0) | ~
% 14.30/2.78 | | | | | | | | | | | | | | | (all_145_3 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | Case 1:
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | (219) ~ (all_145_1 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | REDUCE: (214), (219) imply:
% 14.30/2.78 | | | | | | | | | | | | | | | | (220) $false
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | CLOSE: (220) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | (221) ~ (all_145_2 = 0) | ~ (all_145_3 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | Case 1:
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | | (222) ~ (all_145_2 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | | REDUCE: (212), (222) imply:
% 14.30/2.78 | | | | | | | | | | | | | | | | | (223) $false
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | | (224) ~ (all_145_3 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | | REDUCE: (213), (224) imply:
% 14.30/2.78 | | | | | | | | | | | | | | | | | (225) $false
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | | CLOSE: (225) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | (226) ~ (all_120_1 = 0) | ~ (all_120_2 = 0) | ~
% 14.30/2.78 | | | | | | | | | | | | | (all_120_3 = 0)
% 14.30/2.78 | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | BETA: splitting (226) gives:
% 14.30/2.78 | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | Case 1:
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | (227) ~ (all_120_1 = 0)
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | REDUCE: (198), (227) imply:
% 14.30/2.78 | | | | | | | | | | | | | | (228) $false
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | (229) ~ (all_120_2 = 0) | ~ (all_120_3 = 0)
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | Case 1:
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | (230) ~ (all_120_2 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | REDUCE: (197), (230) imply:
% 14.30/2.78 | | | | | | | | | | | | | | | (231) $false
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | (232) ~ (all_120_3 = 0)
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | REDUCE: (196), (232) imply:
% 14.30/2.78 | | | | | | | | | | | | | | | (233) $false
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | | CLOSE: (233) is inconsistent.
% 14.30/2.78 | | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | Case 2:
% 14.30/2.78 | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | (234) ~ (all_99_1 = 0)
% 14.30/2.78 | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | REDUCE: (179), (234) imply:
% 14.30/2.78 | | | | | | | | | | | (235) $false
% 14.30/2.78 | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 14.30/2.78 | | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | | |
% 14.30/2.78 | | | | | | | | | End of split
% 14.30/2.78 | | | | | | | | |
% 14.30/2.78 | | | | | | | | End of split
% 14.30/2.78 | | | | | | | |
% 14.30/2.78 | | | | | | | End of split
% 14.30/2.78 | | | | | | |
% 14.30/2.78 | | | | | | End of split
% 14.30/2.78 | | | | | |
% 14.30/2.78 | | | | | End of split
% 14.30/2.78 | | | | |
% 14.30/2.78 | | | | End of split
% 14.30/2.78 | | | |
% 14.30/2.78 | | | End of split
% 14.30/2.78 | | |
% 14.30/2.78 | | End of split
% 14.30/2.78 | |
% 14.30/2.78 | End of split
% 14.30/2.78 |
% 14.30/2.78 End of proof
% 14.30/2.78 % SZS output end Proof for theBenchmark
% 14.30/2.78
% 14.30/2.78 2155ms
%------------------------------------------------------------------------------