TSTP Solution File: SET765+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET765+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 : n012.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 15:26:21 EDT 2023
% Result : Theorem 8.90s 1.91s
% Output : Proof 11.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET765+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n012.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 14:35:40 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.09/1.10 Prover 1: Preprocessing ...
% 3.09/1.11 Prover 4: Preprocessing ...
% 3.09/1.14 Prover 3: Preprocessing ...
% 3.09/1.14 Prover 5: Preprocessing ...
% 3.09/1.14 Prover 2: Preprocessing ...
% 3.09/1.14 Prover 6: Preprocessing ...
% 3.09/1.14 Prover 0: Preprocessing ...
% 6.66/1.66 Prover 5: Proving ...
% 7.24/1.69 Prover 6: Proving ...
% 7.24/1.69 Prover 2: Proving ...
% 7.42/1.72 Prover 1: Constructing countermodel ...
% 7.58/1.73 Prover 3: Constructing countermodel ...
% 8.31/1.85 Prover 4: Constructing countermodel ...
% 8.31/1.88 Prover 0: Proving ...
% 8.90/1.91 Prover 3: proved (1282ms)
% 8.90/1.91
% 8.90/1.91 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.90/1.91
% 8.90/1.91 Prover 0: stopped
% 8.90/1.91 Prover 6: stopped
% 8.90/1.94 Prover 5: stopped
% 8.90/1.94 Prover 2: stopped
% 8.90/1.95 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 8.90/1.95 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 8.90/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.90/1.95 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.90/1.95 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.90/1.96 Prover 7: Preprocessing ...
% 9.48/1.98 Prover 8: Preprocessing ...
% 9.48/2.00 Prover 11: Preprocessing ...
% 9.48/2.02 Prover 13: Preprocessing ...
% 9.48/2.02 Prover 10: Preprocessing ...
% 9.48/2.06 Prover 7: Warning: ignoring some quantifiers
% 9.48/2.10 Prover 1: Found proof (size 87)
% 9.48/2.10 Prover 1: proved (1479ms)
% 9.48/2.10 Prover 4: stopped
% 9.48/2.10 Prover 11: stopped
% 9.48/2.10 Prover 13: stopped
% 9.48/2.11 Prover 7: Constructing countermodel ...
% 9.48/2.12 Prover 7: stopped
% 9.48/2.12 Prover 10: Warning: ignoring some quantifiers
% 9.48/2.13 Prover 10: Constructing countermodel ...
% 10.07/2.14 Prover 10: stopped
% 10.71/2.17 Prover 8: Warning: ignoring some quantifiers
% 10.71/2.18 Prover 8: Constructing countermodel ...
% 10.71/2.18 Prover 8: stopped
% 10.71/2.18
% 10.71/2.18 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.71/2.18
% 10.71/2.20 % SZS output start Proof for theBenchmark
% 10.71/2.20 Assumptions after simplification:
% 10.71/2.20 ---------------------------------
% 10.71/2.20
% 10.71/2.20 (equivalence)
% 10.71/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equivalence(v1, v0) =
% 10.71/2.23 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ?
% 10.71/2.23 [v6: int] : ( ~ (v6 = 0) & apply(v1, v4, v5) = 0 & apply(v1, v3, v5) = v6 &
% 10.71/2.23 apply(v1, v3, v4) = 0 & member(v5, v0) = 0 & member(v4, v0) = 0 &
% 10.71/2.23 member(v3, v0) = 0 & $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i]
% 10.71/2.23 : ? [v5: int] : ( ~ (v5 = 0) & apply(v1, v4, v3) = v5 & apply(v1, v3, v4) =
% 10.71/2.23 0 & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3)) | ? [v3:
% 10.71/2.23 $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v1, v3, v3) = v4 & member(v3,
% 10.71/2.23 v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1,
% 10.71/2.23 v0) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4:
% 10.71/2.23 $i] : ! [v5: int] : (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~
% 10.71/2.23 (apply(v1, v2, v3) = 0) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6:
% 10.71/2.23 any] : ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4)
% 10.71/2.23 = v9 & member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6
% 10.71/2.23 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v2:
% 10.71/2.23 $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) | ~ $i(v2) |
% 10.71/2.23 ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v2: $i] : !
% 10.71/2.23 [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3) | ~ $i(v2) | ? [v4:
% 10.71/2.23 any] : ? [v5: any] : ? [v6: any] : (apply(v1, v3, v2) = v6 &
% 10.71/2.23 member(v3, v0) = v5 & member(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)
% 10.71/2.23 | v6 = 0)))))
% 10.71/2.23
% 10.71/2.23 (subset)
% 10.71/2.23 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 10.71/2.23 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 10.71/2.23 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 10.71/2.23 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 10.71/2.23 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 10.71/2.23
% 10.71/2.23 (thIII01)
% 10.71/2.23 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 10.71/2.23 equivalence(v1, v2) = v3 & equivalence(v1, v0) = 0 & subset(v2, v0) = 0 &
% 10.71/2.23 $i(v2) & $i(v1) & $i(v0))
% 10.71/2.23
% 10.71/2.23 (function-axioms)
% 10.71/2.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 10.71/2.24 | ~ (equivalence_class(v4, v3, v2) = v1) | ~ (equivalence_class(v4, v3,
% 10.71/2.24 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 10.71/2.24 ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) =
% 10.71/2.24 v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.71/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.71/2.24 (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & ! [v0:
% 10.71/2.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 10.71/2.24 : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) = v0)) &
% 10.71/2.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 10.71/2.24 $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~ (partition(v3, v2) = v0))
% 10.71/2.24 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 10.71/2.24 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 10.71/2.24 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.71/2.24 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 10.71/2.24 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.71/2.24 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 10.71/2.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 10.71/2.24 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 10.71/2.24 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 10.71/2.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 10.71/2.24 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 10.71/2.24 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 10.71/2.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 10.71/2.24 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 10.71/2.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 10.71/2.24 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 10.71/2.24 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 10.71/2.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 10.71/2.24 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 10.71/2.24 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 10.71/2.24 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 10.71/2.24 (power_set(v2) = v0))
% 10.71/2.24
% 10.71/2.24 Further assumptions not needed in the proof:
% 10.71/2.24 --------------------------------------------
% 10.71/2.24 difference, disjoint, empty_set, equal_set, equivalence_class, intersection,
% 10.71/2.24 partition, power_set, pre_order, product, singleton, sum, union, unordered_pair
% 10.71/2.24
% 10.71/2.24 Those formulas are unsatisfiable:
% 10.71/2.24 ---------------------------------
% 10.71/2.24
% 10.71/2.24 Begin of proof
% 10.71/2.24 |
% 10.71/2.24 | ALPHA: (subset) implies:
% 10.71/2.24 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 10.71/2.24 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 10.71/2.24 | member(v2, v1) = 0))
% 10.71/2.24 |
% 10.71/2.24 | ALPHA: (equivalence) implies:
% 10.71/2.25 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (equivalence(v1, v0) = 0) | ~ $i(v1) |
% 10.71/2.25 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: int] :
% 10.71/2.25 | (v5 = 0 | ~ (apply(v1, v2, v4) = v5) | ~ (apply(v1, v2, v3) = 0)
% 10.71/2.25 | | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ? [v6: any] : ? [v7: any]
% 10.71/2.25 | : ? [v8: any] : ? [v9: any] : (apply(v1, v3, v4) = v9 &
% 10.71/2.25 | member(v4, v0) = v8 & member(v3, v0) = v7 & member(v2, v0) = v6
% 10.71/2.25 | & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) &
% 10.71/2.25 | ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (apply(v1, v2, v2) = v3) |
% 10.71/2.25 | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &
% 10.71/2.25 | ! [v2: $i] : ! [v3: $i] : ( ~ (apply(v1, v2, v3) = 0) | ~ $i(v3)
% 10.71/2.25 | | ~ $i(v2) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 10.71/2.25 | (apply(v1, v3, v2) = v6 & member(v3, v0) = v5 & member(v2, v0) =
% 10.71/2.25 | v4 & ( ~ (v5 = 0) | ~ (v4 = 0) | v6 = 0)))))
% 10.71/2.25 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~
% 10.71/2.25 | (equivalence(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 10.71/2.25 | [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & apply(v1, v4,
% 10.71/2.25 | v5) = 0 & apply(v1, v3, v5) = v6 & apply(v1, v3, v4) = 0 &
% 10.71/2.25 | member(v5, v0) = 0 & member(v4, v0) = 0 & member(v3, v0) = 0 &
% 10.71/2.25 | $i(v5) & $i(v4) & $i(v3)) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 10.71/2.25 | int] : ( ~ (v5 = 0) & apply(v1, v4, v3) = v5 & apply(v1, v3, v4) =
% 10.71/2.25 | 0 & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3)) | ?
% 10.71/2.25 | [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v1, v3, v3) = v4 &
% 10.71/2.25 | member(v3, v0) = 0 & $i(v3)))
% 10.71/2.25 |
% 10.71/2.25 | ALPHA: (function-axioms) implies:
% 10.71/2.25 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.71/2.25 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 10.71/2.25 | = v0))
% 10.71/2.25 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 10.71/2.25 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 10.71/2.25 | (apply(v4, v3, v2) = v0))
% 10.71/2.25 |
% 10.71/2.25 | DELTA: instantiating (thIII01) with fresh symbols all_20_0, all_20_1,
% 10.71/2.25 | all_20_2, all_20_3 gives:
% 10.71/2.25 | (6) ~ (all_20_0 = 0) & equivalence(all_20_2, all_20_1) = all_20_0 &
% 10.71/2.25 | equivalence(all_20_2, all_20_3) = 0 & subset(all_20_1, all_20_3) = 0 &
% 10.71/2.25 | $i(all_20_1) & $i(all_20_2) & $i(all_20_3)
% 10.71/2.25 |
% 10.71/2.25 | ALPHA: (6) implies:
% 10.71/2.25 | (7) ~ (all_20_0 = 0)
% 10.71/2.25 | (8) $i(all_20_3)
% 10.71/2.25 | (9) $i(all_20_2)
% 10.71/2.25 | (10) $i(all_20_1)
% 10.71/2.25 | (11) subset(all_20_1, all_20_3) = 0
% 10.71/2.25 | (12) equivalence(all_20_2, all_20_3) = 0
% 10.71/2.25 | (13) equivalence(all_20_2, all_20_1) = all_20_0
% 10.71/2.25 |
% 10.71/2.25 | GROUND_INST: instantiating (1) with all_20_1, all_20_3, simplifying with (8),
% 10.71/2.25 | (10), (11) gives:
% 10.71/2.25 | (14) ! [v0: $i] : ( ~ (member(v0, all_20_1) = 0) | ~ $i(v0) | member(v0,
% 10.71/2.25 | all_20_3) = 0)
% 10.71/2.25 |
% 10.71/2.25 | GROUND_INST: instantiating (2) with all_20_3, all_20_2, simplifying with (8),
% 10.71/2.25 | (9), (12) gives:
% 10.71/2.26 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 10.71/2.26 | (apply(all_20_2, v0, v2) = v3) | ~ (apply(all_20_2, v0, v1) = 0) |
% 10.71/2.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 10.71/2.26 | [v6: any] : ? [v7: any] : (apply(all_20_2, v1, v2) = v7 &
% 11.19/2.26 | member(v2, all_20_3) = v6 & member(v1, all_20_3) = v5 & member(v0,
% 11.19/2.26 | all_20_3) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 11.19/2.26 | (v4 = 0)))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 11.19/2.26 | (apply(all_20_2, v0, v0) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2
% 11.19/2.26 | = 0) & member(v0, all_20_3) = v2)) & ! [v0: $i] : ! [v1: $i] :
% 11.19/2.26 | ( ~ (apply(all_20_2, v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 11.19/2.26 | any] : ? [v3: any] : ? [v4: any] : (apply(all_20_2, v1, v0) = v4
% 11.19/2.26 | & member(v1, all_20_3) = v3 & member(v0, all_20_3) = v2 & ( ~ (v3
% 11.19/2.26 | = 0) | ~ (v2 = 0) | v4 = 0)))
% 11.19/2.26 |
% 11.19/2.26 | ALPHA: (15) implies:
% 11.19/2.26 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (apply(all_20_2, v0, v1) = 0) | ~
% 11.19/2.26 | $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 11.19/2.26 | (apply(all_20_2, v1, v0) = v4 & member(v1, all_20_3) = v3 &
% 11.19/2.26 | member(v0, all_20_3) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0) | v4 = 0)))
% 11.19/2.26 | (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (apply(all_20_2, v0, v0) =
% 11.19/2.26 | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & member(v0,
% 11.19/2.26 | all_20_3) = v2))
% 11.19/2.26 | (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.19/2.26 | (apply(all_20_2, v0, v2) = v3) | ~ (apply(all_20_2, v0, v1) = 0) |
% 11.19/2.26 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ?
% 11.19/2.26 | [v6: any] : ? [v7: any] : (apply(all_20_2, v1, v2) = v7 &
% 11.19/2.26 | member(v2, all_20_3) = v6 & member(v1, all_20_3) = v5 & member(v0,
% 11.19/2.26 | all_20_3) = v4 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | ~
% 11.19/2.26 | (v4 = 0))))
% 11.19/2.26 |
% 11.19/2.26 | GROUND_INST: instantiating (3) with all_20_1, all_20_2, all_20_0, simplifying
% 11.19/2.26 | with (9), (10), (13) gives:
% 11.19/2.26 | (19) all_20_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int]
% 11.19/2.26 | : ( ~ (v3 = 0) & apply(all_20_2, v1, v2) = 0 & apply(all_20_2, v0, v2)
% 11.19/2.26 | = v3 & apply(all_20_2, v0, v1) = 0 & member(v2, all_20_1) = 0 &
% 11.19/2.26 | member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v2) &
% 11.19/2.26 | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~
% 11.19/2.26 | (v2 = 0) & apply(all_20_2, v1, v0) = v2 & apply(all_20_2, v0, v1) =
% 11.19/2.26 | 0 & member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v1) &
% 11.19/2.26 | $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.19/2.26 | apply(all_20_2, v0, v0) = v1 & member(v0, all_20_1) = 0 & $i(v0))
% 11.19/2.26 |
% 11.19/2.26 | BETA: splitting (19) gives:
% 11.19/2.26 |
% 11.19/2.26 | Case 1:
% 11.19/2.26 | |
% 11.19/2.26 | | (20) all_20_0 = 0
% 11.19/2.26 | |
% 11.19/2.26 | | REDUCE: (7), (20) imply:
% 11.19/2.26 | | (21) $false
% 11.19/2.26 | |
% 11.19/2.26 | | CLOSE: (21) is inconsistent.
% 11.19/2.26 | |
% 11.19/2.26 | Case 2:
% 11.19/2.26 | |
% 11.19/2.27 | | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 11.19/2.27 | | 0) & apply(all_20_2, v1, v2) = 0 & apply(all_20_2, v0, v2) = v3
% 11.19/2.27 | | & apply(all_20_2, v0, v1) = 0 & member(v2, all_20_1) = 0 &
% 11.19/2.27 | | member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v2) &
% 11.19/2.27 | | $i(v1) & $i(v0)) | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~
% 11.19/2.27 | | (v2 = 0) & apply(all_20_2, v1, v0) = v2 & apply(all_20_2, v0, v1)
% 11.19/2.27 | | = 0 & member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v1)
% 11.19/2.27 | | & $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.19/2.27 | | apply(all_20_2, v0, v0) = v1 & member(v0, all_20_1) = 0 & $i(v0))
% 11.19/2.27 | |
% 11.19/2.27 | | BETA: splitting (22) gives:
% 11.19/2.27 | |
% 11.19/2.27 | | Case 1:
% 11.19/2.27 | | |
% 11.19/2.27 | | | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 =
% 11.19/2.27 | | | 0) & apply(all_20_2, v1, v2) = 0 & apply(all_20_2, v0, v2) =
% 11.19/2.27 | | | v3 & apply(all_20_2, v0, v1) = 0 & member(v2, all_20_1) = 0 &
% 11.19/2.27 | | | member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v2) &
% 11.19/2.27 | | | $i(v1) & $i(v0))
% 11.19/2.27 | | |
% 11.19/2.27 | | | DELTA: instantiating (23) with fresh symbols all_40_0, all_40_1, all_40_2,
% 11.19/2.27 | | | all_40_3 gives:
% 11.19/2.27 | | | (24) ~ (all_40_0 = 0) & apply(all_20_2, all_40_2, all_40_1) = 0 &
% 11.19/2.27 | | | apply(all_20_2, all_40_3, all_40_1) = all_40_0 & apply(all_20_2,
% 11.19/2.27 | | | all_40_3, all_40_2) = 0 & member(all_40_1, all_20_1) = 0 &
% 11.19/2.27 | | | member(all_40_2, all_20_1) = 0 & member(all_40_3, all_20_1) = 0 &
% 11.19/2.27 | | | $i(all_40_1) & $i(all_40_2) & $i(all_40_3)
% 11.19/2.27 | | |
% 11.19/2.27 | | | ALPHA: (24) implies:
% 11.19/2.27 | | | (25) ~ (all_40_0 = 0)
% 11.19/2.27 | | | (26) $i(all_40_3)
% 11.19/2.27 | | | (27) $i(all_40_2)
% 11.19/2.27 | | | (28) $i(all_40_1)
% 11.19/2.27 | | | (29) member(all_40_3, all_20_1) = 0
% 11.19/2.27 | | | (30) member(all_40_2, all_20_1) = 0
% 11.19/2.27 | | | (31) member(all_40_1, all_20_1) = 0
% 11.19/2.27 | | | (32) apply(all_20_2, all_40_3, all_40_2) = 0
% 11.19/2.27 | | | (33) apply(all_20_2, all_40_3, all_40_1) = all_40_0
% 11.19/2.27 | | | (34) apply(all_20_2, all_40_2, all_40_1) = 0
% 11.19/2.27 | | |
% 11.19/2.27 | | | GROUND_INST: instantiating (14) with all_40_3, simplifying with (26), (29)
% 11.19/2.27 | | | gives:
% 11.19/2.27 | | | (35) member(all_40_3, all_20_3) = 0
% 11.19/2.27 | | |
% 11.19/2.27 | | | GROUND_INST: instantiating (14) with all_40_2, simplifying with (27), (30)
% 11.19/2.27 | | | gives:
% 11.19/2.27 | | | (36) member(all_40_2, all_20_3) = 0
% 11.19/2.27 | | |
% 11.19/2.27 | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (28), (31)
% 11.19/2.27 | | | gives:
% 11.19/2.27 | | | (37) member(all_40_1, all_20_3) = 0
% 11.19/2.27 | | |
% 11.19/2.27 | | | GROUND_INST: instantiating (16) with all_40_3, all_40_2, simplifying with
% 11.19/2.27 | | | (26), (27), (32) gives:
% 11.19/2.27 | | | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_20_2,
% 11.19/2.27 | | | all_40_2, all_40_3) = v2 & member(all_40_2, all_20_3) = v1 &
% 11.19/2.27 | | | member(all_40_3, all_20_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 11.19/2.27 | | | v2 = 0))
% 11.19/2.27 | | |
% 11.19/2.27 | | | GROUND_INST: instantiating (18) with all_40_3, all_40_2, all_40_1,
% 11.19/2.27 | | | all_40_0, simplifying with (26), (27), (28), (32), (33)
% 11.19/2.27 | | | gives:
% 11.19/2.27 | | | (39) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: any] : ?
% 11.19/2.27 | | | [v3: any] : (apply(all_20_2, all_40_2, all_40_1) = v3 &
% 11.19/2.27 | | | member(all_40_1, all_20_3) = v2 & member(all_40_2, all_20_3) =
% 11.19/2.27 | | | v1 & member(all_40_3, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 =
% 11.19/2.27 | | | 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 11.19/2.27 | | |
% 11.19/2.27 | | | GROUND_INST: instantiating (16) with all_40_2, all_40_1, simplifying with
% 11.19/2.27 | | | (27), (28), (34) gives:
% 11.19/2.27 | | | (40) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_20_2,
% 11.19/2.27 | | | all_40_1, all_40_2) = v2 & member(all_40_1, all_20_3) = v1 &
% 11.19/2.27 | | | member(all_40_2, all_20_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 11.19/2.27 | | | v2 = 0))
% 11.19/2.27 | | |
% 11.19/2.27 | | | DELTA: instantiating (40) with fresh symbols all_48_0, all_48_1, all_48_2
% 11.19/2.27 | | | gives:
% 11.19/2.28 | | | (41) apply(all_20_2, all_40_1, all_40_2) = all_48_0 & member(all_40_1,
% 11.19/2.28 | | | all_20_3) = all_48_1 & member(all_40_2, all_20_3) = all_48_2 & (
% 11.19/2.28 | | | ~ (all_48_1 = 0) | ~ (all_48_2 = 0) | all_48_0 = 0)
% 11.19/2.28 | | |
% 11.19/2.28 | | | ALPHA: (41) implies:
% 11.19/2.28 | | | (42) member(all_40_2, all_20_3) = all_48_2
% 11.19/2.28 | | | (43) member(all_40_1, all_20_3) = all_48_1
% 11.19/2.28 | | |
% 11.19/2.28 | | | DELTA: instantiating (38) with fresh symbols all_50_0, all_50_1, all_50_2
% 11.19/2.28 | | | gives:
% 11.19/2.28 | | | (44) apply(all_20_2, all_40_2, all_40_3) = all_50_0 & member(all_40_2,
% 11.19/2.28 | | | all_20_3) = all_50_1 & member(all_40_3, all_20_3) = all_50_2 & (
% 11.19/2.28 | | | ~ (all_50_1 = 0) | ~ (all_50_2 = 0) | all_50_0 = 0)
% 11.19/2.28 | | |
% 11.19/2.28 | | | ALPHA: (44) implies:
% 11.19/2.28 | | | (45) member(all_40_3, all_20_3) = all_50_2
% 11.19/2.28 | | | (46) member(all_40_2, all_20_3) = all_50_1
% 11.19/2.28 | | |
% 11.19/2.28 | | | GROUND_INST: instantiating (4) with 0, all_50_2, all_20_3, all_40_3,
% 11.19/2.28 | | | simplifying with (35), (45) gives:
% 11.19/2.28 | | | (47) all_50_2 = 0
% 11.19/2.28 | | |
% 11.19/2.28 | | | GROUND_INST: instantiating (4) with all_48_2, all_50_1, all_20_3,
% 11.19/2.28 | | | all_40_2, simplifying with (42), (46) gives:
% 11.19/2.28 | | | (48) all_50_1 = all_48_2
% 11.19/2.28 | | |
% 11.19/2.28 | | | GROUND_INST: instantiating (4) with 0, all_50_1, all_20_3, all_40_2,
% 11.19/2.28 | | | simplifying with (36), (46) gives:
% 11.19/2.28 | | | (49) all_50_1 = 0
% 11.19/2.28 | | |
% 11.19/2.28 | | | GROUND_INST: instantiating (4) with 0, all_48_1, all_20_3, all_40_1,
% 11.19/2.28 | | | simplifying with (37), (43) gives:
% 11.19/2.28 | | | (50) all_48_1 = 0
% 11.19/2.28 | | |
% 11.19/2.28 | | | COMBINE_EQS: (48), (49) imply:
% 11.19/2.28 | | | (51) all_48_2 = 0
% 11.19/2.28 | | |
% 11.19/2.28 | | | SIMP: (51) implies:
% 11.19/2.28 | | | (52) all_48_2 = 0
% 11.19/2.28 | | |
% 11.19/2.28 | | | BETA: splitting (39) gives:
% 11.19/2.28 | | |
% 11.19/2.28 | | | Case 1:
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | (53) all_40_0 = 0
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | REDUCE: (25), (53) imply:
% 11.19/2.28 | | | | (54) $false
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | CLOSE: (54) is inconsistent.
% 11.19/2.28 | | | |
% 11.19/2.28 | | | Case 2:
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | (55) ? [v0: any] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.19/2.28 | | | | (apply(all_20_2, all_40_2, all_40_1) = v3 & member(all_40_1,
% 11.19/2.28 | | | | all_20_3) = v2 & member(all_40_2, all_20_3) = v1 &
% 11.19/2.28 | | | | member(all_40_3, all_20_3) = v0 & ( ~ (v3 = 0) | ~ (v2 = 0) |
% 11.19/2.28 | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | DELTA: instantiating (55) with fresh symbols all_60_0, all_60_1,
% 11.19/2.28 | | | | all_60_2, all_60_3 gives:
% 11.19/2.28 | | | | (56) apply(all_20_2, all_40_2, all_40_1) = all_60_0 &
% 11.19/2.28 | | | | member(all_40_1, all_20_3) = all_60_1 & member(all_40_2,
% 11.19/2.28 | | | | all_20_3) = all_60_2 & member(all_40_3, all_20_3) = all_60_3 &
% 11.19/2.28 | | | | ( ~ (all_60_0 = 0) | ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | ~
% 11.19/2.28 | | | | (all_60_3 = 0))
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | ALPHA: (56) implies:
% 11.19/2.28 | | | | (57) member(all_40_3, all_20_3) = all_60_3
% 11.19/2.28 | | | | (58) member(all_40_2, all_20_3) = all_60_2
% 11.19/2.28 | | | | (59) member(all_40_1, all_20_3) = all_60_1
% 11.19/2.28 | | | | (60) apply(all_20_2, all_40_2, all_40_1) = all_60_0
% 11.19/2.28 | | | | (61) ~ (all_60_0 = 0) | ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | ~
% 11.19/2.28 | | | | (all_60_3 = 0)
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | GROUND_INST: instantiating (4) with 0, all_60_3, all_20_3, all_40_3,
% 11.19/2.28 | | | | simplifying with (35), (57) gives:
% 11.19/2.28 | | | | (62) all_60_3 = 0
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | GROUND_INST: instantiating (4) with 0, all_60_2, all_20_3, all_40_2,
% 11.19/2.28 | | | | simplifying with (36), (58) gives:
% 11.19/2.28 | | | | (63) all_60_2 = 0
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | GROUND_INST: instantiating (4) with 0, all_60_1, all_20_3, all_40_1,
% 11.19/2.28 | | | | simplifying with (37), (59) gives:
% 11.19/2.28 | | | | (64) all_60_1 = 0
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | GROUND_INST: instantiating (5) with 0, all_60_0, all_40_1, all_40_2,
% 11.19/2.28 | | | | all_20_2, simplifying with (34), (60) gives:
% 11.19/2.28 | | | | (65) all_60_0 = 0
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | BETA: splitting (61) gives:
% 11.19/2.28 | | | |
% 11.19/2.28 | | | | Case 1:
% 11.19/2.28 | | | | |
% 11.19/2.28 | | | | | (66) ~ (all_60_0 = 0)
% 11.19/2.28 | | | | |
% 11.19/2.28 | | | | | REDUCE: (65), (66) imply:
% 11.19/2.28 | | | | | (67) $false
% 11.19/2.28 | | | | |
% 11.19/2.28 | | | | | CLOSE: (67) is inconsistent.
% 11.19/2.28 | | | | |
% 11.19/2.28 | | | | Case 2:
% 11.19/2.28 | | | | |
% 11.19/2.29 | | | | | (68) ~ (all_60_1 = 0) | ~ (all_60_2 = 0) | ~ (all_60_3 = 0)
% 11.19/2.29 | | | | |
% 11.19/2.29 | | | | | BETA: splitting (68) gives:
% 11.19/2.29 | | | | |
% 11.19/2.29 | | | | | Case 1:
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | | (69) ~ (all_60_1 = 0)
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | | REDUCE: (64), (69) imply:
% 11.19/2.29 | | | | | | (70) $false
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | | CLOSE: (70) is inconsistent.
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | Case 2:
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | | (71) ~ (all_60_2 = 0) | ~ (all_60_3 = 0)
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | | BETA: splitting (71) gives:
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | | Case 1:
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | | (72) ~ (all_60_2 = 0)
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | | REDUCE: (63), (72) imply:
% 11.19/2.29 | | | | | | | (73) $false
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | | CLOSE: (73) is inconsistent.
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | Case 2:
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | | (74) ~ (all_60_3 = 0)
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | | REDUCE: (62), (74) imply:
% 11.19/2.29 | | | | | | | (75) $false
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | | CLOSE: (75) is inconsistent.
% 11.19/2.29 | | | | | | |
% 11.19/2.29 | | | | | | End of split
% 11.19/2.29 | | | | | |
% 11.19/2.29 | | | | | End of split
% 11.19/2.29 | | | | |
% 11.19/2.29 | | | | End of split
% 11.19/2.29 | | | |
% 11.19/2.29 | | | End of split
% 11.19/2.29 | | |
% 11.19/2.29 | | Case 2:
% 11.19/2.29 | | |
% 11.19/2.29 | | | (76) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 11.19/2.29 | | | apply(all_20_2, v1, v0) = v2 & apply(all_20_2, v0, v1) = 0 &
% 11.19/2.29 | | | member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v1) &
% 11.19/2.29 | | | $i(v0)) | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 11.19/2.29 | | | apply(all_20_2, v0, v0) = v1 & member(v0, all_20_1) = 0 &
% 11.19/2.29 | | | $i(v0))
% 11.19/2.29 | | |
% 11.19/2.29 | | | BETA: splitting (76) gives:
% 11.19/2.29 | | |
% 11.19/2.29 | | | Case 1:
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | (77) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 11.19/2.29 | | | | apply(all_20_2, v1, v0) = v2 & apply(all_20_2, v0, v1) = 0 &
% 11.19/2.29 | | | | member(v1, all_20_1) = 0 & member(v0, all_20_1) = 0 & $i(v1) &
% 11.19/2.29 | | | | $i(v0))
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | DELTA: instantiating (77) with fresh symbols all_40_0, all_40_1,
% 11.19/2.29 | | | | all_40_2 gives:
% 11.19/2.29 | | | | (78) ~ (all_40_0 = 0) & apply(all_20_2, all_40_1, all_40_2) =
% 11.19/2.29 | | | | all_40_0 & apply(all_20_2, all_40_2, all_40_1) = 0 &
% 11.19/2.29 | | | | member(all_40_1, all_20_1) = 0 & member(all_40_2, all_20_1) = 0
% 11.19/2.29 | | | | & $i(all_40_1) & $i(all_40_2)
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | ALPHA: (78) implies:
% 11.19/2.29 | | | | (79) ~ (all_40_0 = 0)
% 11.19/2.29 | | | | (80) $i(all_40_2)
% 11.19/2.29 | | | | (81) $i(all_40_1)
% 11.19/2.29 | | | | (82) member(all_40_2, all_20_1) = 0
% 11.19/2.29 | | | | (83) member(all_40_1, all_20_1) = 0
% 11.19/2.29 | | | | (84) apply(all_20_2, all_40_2, all_40_1) = 0
% 11.19/2.29 | | | | (85) apply(all_20_2, all_40_1, all_40_2) = all_40_0
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | GROUND_INST: instantiating (14) with all_40_2, simplifying with (80),
% 11.19/2.29 | | | | (82) gives:
% 11.19/2.29 | | | | (86) member(all_40_2, all_20_3) = 0
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (81),
% 11.19/2.29 | | | | (83) gives:
% 11.19/2.29 | | | | (87) member(all_40_1, all_20_3) = 0
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | GROUND_INST: instantiating (16) with all_40_2, all_40_1, simplifying
% 11.19/2.29 | | | | with (80), (81), (84) gives:
% 11.19/2.29 | | | | (88) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_20_2,
% 11.19/2.29 | | | | all_40_1, all_40_2) = v2 & member(all_40_1, all_20_3) = v1 &
% 11.19/2.29 | | | | member(all_40_2, all_20_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 11.19/2.29 | | | | v2 = 0))
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | DELTA: instantiating (88) with fresh symbols all_48_0, all_48_1,
% 11.19/2.29 | | | | all_48_2 gives:
% 11.19/2.29 | | | | (89) apply(all_20_2, all_40_1, all_40_2) = all_48_0 &
% 11.19/2.29 | | | | member(all_40_1, all_20_3) = all_48_1 & member(all_40_2,
% 11.19/2.29 | | | | all_20_3) = all_48_2 & ( ~ (all_48_1 = 0) | ~ (all_48_2 = 0)
% 11.19/2.29 | | | | | all_48_0 = 0)
% 11.19/2.29 | | | |
% 11.19/2.29 | | | | ALPHA: (89) implies:
% 11.19/2.29 | | | | (90) member(all_40_2, all_20_3) = all_48_2
% 11.19/2.29 | | | | (91) member(all_40_1, all_20_3) = all_48_1
% 11.19/2.29 | | | | (92) apply(all_20_2, all_40_1, all_40_2) = all_48_0
% 11.19/2.29 | | | | (93) ~ (all_48_1 = 0) | ~ (all_48_2 = 0) | all_48_0 = 0
% 11.19/2.29 | | | |
% 11.38/2.29 | | | | GROUND_INST: instantiating (4) with 0, all_48_2, all_20_3, all_40_2,
% 11.38/2.29 | | | | simplifying with (86), (90) gives:
% 11.38/2.30 | | | | (94) all_48_2 = 0
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | GROUND_INST: instantiating (4) with 0, all_48_1, all_20_3, all_40_1,
% 11.38/2.30 | | | | simplifying with (87), (91) gives:
% 11.38/2.30 | | | | (95) all_48_1 = 0
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | GROUND_INST: instantiating (5) with all_40_0, all_48_0, all_40_2,
% 11.38/2.30 | | | | all_40_1, all_20_2, simplifying with (85), (92) gives:
% 11.38/2.30 | | | | (96) all_48_0 = all_40_0
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | BETA: splitting (93) gives:
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | Case 1:
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | (97) ~ (all_48_1 = 0)
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | REDUCE: (95), (97) imply:
% 11.38/2.30 | | | | | (98) $false
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | CLOSE: (98) is inconsistent.
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | Case 2:
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | (99) ~ (all_48_2 = 0) | all_48_0 = 0
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | BETA: splitting (99) gives:
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | Case 1:
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | (100) ~ (all_48_2 = 0)
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | REDUCE: (94), (100) imply:
% 11.38/2.30 | | | | | | (101) $false
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | CLOSE: (101) is inconsistent.
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | Case 2:
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | (102) all_48_0 = 0
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | COMBINE_EQS: (96), (102) imply:
% 11.38/2.30 | | | | | | (103) all_40_0 = 0
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | REDUCE: (79), (103) imply:
% 11.38/2.30 | | | | | | (104) $false
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | | CLOSE: (104) is inconsistent.
% 11.38/2.30 | | | | | |
% 11.38/2.30 | | | | | End of split
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | End of split
% 11.38/2.30 | | | |
% 11.38/2.30 | | | Case 2:
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | (105) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_20_2, v0,
% 11.38/2.30 | | | | v0) = v1 & member(v0, all_20_1) = 0 & $i(v0))
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | DELTA: instantiating (105) with fresh symbols all_40_0, all_40_1 gives:
% 11.38/2.30 | | | | (106) ~ (all_40_0 = 0) & apply(all_20_2, all_40_1, all_40_1) =
% 11.38/2.30 | | | | all_40_0 & member(all_40_1, all_20_1) = 0 & $i(all_40_1)
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | ALPHA: (106) implies:
% 11.38/2.30 | | | | (107) ~ (all_40_0 = 0)
% 11.38/2.30 | | | | (108) $i(all_40_1)
% 11.38/2.30 | | | | (109) member(all_40_1, all_20_1) = 0
% 11.38/2.30 | | | | (110) apply(all_20_2, all_40_1, all_40_1) = all_40_0
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | GROUND_INST: instantiating (14) with all_40_1, simplifying with (108),
% 11.38/2.30 | | | | (109) gives:
% 11.38/2.30 | | | | (111) member(all_40_1, all_20_3) = 0
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | GROUND_INST: instantiating (17) with all_40_1, all_40_0, simplifying
% 11.38/2.30 | | | | with (108), (110) gives:
% 11.38/2.30 | | | | (112) all_40_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1,
% 11.38/2.30 | | | | all_20_3) = v0)
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | BETA: splitting (112) gives:
% 11.38/2.30 | | | |
% 11.38/2.30 | | | | Case 1:
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | (113) all_40_0 = 0
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | REDUCE: (107), (113) imply:
% 11.38/2.30 | | | | | (114) $false
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | CLOSE: (114) is inconsistent.
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | Case 2:
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | (115) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_20_3) =
% 11.38/2.30 | | | | | v0)
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | DELTA: instantiating (115) with fresh symbol all_52_0 gives:
% 11.38/2.30 | | | | | (116) ~ (all_52_0 = 0) & member(all_40_1, all_20_3) = all_52_0
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | ALPHA: (116) implies:
% 11.38/2.30 | | | | | (117) ~ (all_52_0 = 0)
% 11.38/2.30 | | | | | (118) member(all_40_1, all_20_3) = all_52_0
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | GROUND_INST: instantiating (4) with 0, all_52_0, all_20_3, all_40_1,
% 11.38/2.30 | | | | | simplifying with (111), (118) gives:
% 11.38/2.30 | | | | | (119) all_52_0 = 0
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | REDUCE: (117), (119) imply:
% 11.38/2.30 | | | | | (120) $false
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | | CLOSE: (120) is inconsistent.
% 11.38/2.30 | | | | |
% 11.38/2.30 | | | | End of split
% 11.38/2.30 | | | |
% 11.38/2.30 | | | End of split
% 11.38/2.30 | | |
% 11.38/2.30 | | End of split
% 11.38/2.30 | |
% 11.38/2.30 | End of split
% 11.38/2.30 |
% 11.38/2.30 End of proof
% 11.38/2.30 % SZS output end Proof for theBenchmark
% 11.38/2.30
% 11.38/2.30 1700ms
%------------------------------------------------------------------------------