TSTP Solution File: SET759+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET759+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.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 15:26:19 EDT 2023
% Result : Theorem 11.79s 2.26s
% Output : Proof 14.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET759+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 10:09:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.35/1.16 Prover 4: Preprocessing ...
% 3.78/1.18 Prover 1: Preprocessing ...
% 3.78/1.20 Prover 5: Preprocessing ...
% 3.78/1.20 Prover 0: Preprocessing ...
% 3.78/1.20 Prover 2: Preprocessing ...
% 3.78/1.20 Prover 6: Preprocessing ...
% 3.78/1.20 Prover 3: Preprocessing ...
% 8.67/1.85 Prover 2: Proving ...
% 8.67/1.86 Prover 5: Proving ...
% 9.09/1.91 Prover 6: Proving ...
% 9.62/1.99 Prover 3: Constructing countermodel ...
% 9.62/1.99 Prover 1: Constructing countermodel ...
% 11.79/2.26 Prover 3: proved (1626ms)
% 11.79/2.26
% 11.79/2.26 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.79/2.26
% 11.79/2.27 Prover 2: stopped
% 11.79/2.28 Prover 5: stopped
% 11.79/2.28 Prover 6: stopped
% 12.05/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.05/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.05/2.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.05/2.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.05/2.33 Prover 7: Preprocessing ...
% 12.35/2.34 Prover 8: Preprocessing ...
% 12.35/2.36 Prover 10: Preprocessing ...
% 12.35/2.37 Prover 11: Preprocessing ...
% 12.87/2.44 Prover 7: Warning: ignoring some quantifiers
% 13.34/2.48 Prover 10: Warning: ignoring some quantifiers
% 13.34/2.50 Prover 1: Found proof (size 96)
% 13.34/2.50 Prover 1: proved (1870ms)
% 13.34/2.51 Prover 7: Constructing countermodel ...
% 13.34/2.51 Prover 10: Constructing countermodel ...
% 13.34/2.52 Prover 11: stopped
% 13.34/2.52 Prover 10: stopped
% 13.34/2.53 Prover 4: Constructing countermodel ...
% 13.34/2.54 Prover 7: stopped
% 13.34/2.55 Prover 0: Proving ...
% 13.34/2.55 Prover 0: stopped
% 13.34/2.56 Prover 4: stopped
% 14.23/2.60 Prover 8: Warning: ignoring some quantifiers
% 14.23/2.61 Prover 8: Constructing countermodel ...
% 14.23/2.62 Prover 8: stopped
% 14.23/2.62
% 14.23/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.23/2.62
% 14.23/2.63 % SZS output start Proof for theBenchmark
% 14.23/2.63 Assumptions after simplification:
% 14.23/2.63 ---------------------------------
% 14.23/2.63
% 14.23/2.63 (equal_set)
% 14.42/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 14.42/2.66 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 14.42/2.66 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 14.42/2.66 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 14.42/2.66 (subset(v1, v0) = 0 & subset(v0, v1) = 0))
% 14.42/2.66
% 14.42/2.66 (image3)
% 14.42/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.42/2.66 int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = v5) |
% 14.42/2.66 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~ (v6 = 0) &
% 14.42/2.66 member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v6, v3) = 0) | ~
% 14.42/2.66 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) & ! [v0:
% 14.42/2.66 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 14.42/2.66 (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~ $i(v2)
% 14.42/2.66 | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] : (apply(v0, v5,
% 14.42/2.66 v3) = 0 & member(v5, v1) = 0 & $i(v5))))
% 14.42/2.66
% 14.42/2.66 (injective)
% 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.42/2.67 (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 14.42/2.67 $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 &
% 14.42/2.67 apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 &
% 14.42/2.67 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 14.42/2.67 $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1)
% 14.42/2.67 | ~ $i(v0) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~
% 14.42/2.67 (apply(v0, v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~
% 14.42/2.67 $i(v4) | ~ $i(v3) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 14.42/2.67 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8
% 14.42/2.67 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))))
% 14.42/2.67
% 14.42/2.67 (inverse_image3)
% 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.42/2.67 int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) =
% 14.42/2.67 v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: int] : ( ~
% 14.42/2.67 (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~ (apply(v0, v3, v6) =
% 14.42/2.67 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & member(v6, v1) = v7))) &
% 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 14.42/2.67 (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) | ~
% 14.42/2.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i] :
% 14.42/2.67 (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5))))
% 14.42/2.67
% 14.42/2.67 (maps)
% 14.42/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.42/2.67 (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 14.42/2.67 ? [v5: $i] : ? [v6: $i] : ( ~ (v6 = v5) & apply(v0, v4, v6) = 0 & apply(v0,
% 14.42/2.67 v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0 & member(v4, v1) =
% 14.42/2.67 0 & $i(v6) & $i(v5) & $i(v4)) | ? [v4: $i] : (member(v4, v1) = 0 & $i(v4)
% 14.42/2.67 & ! [v5: $i] : ( ~ (apply(v0, v4, v5) = 0) | ~ $i(v5) | ? [v6: int] : (
% 14.42/2.67 ~ (v6 = 0) & member(v5, v2) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 14.42/2.67 [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (
% 14.42/2.67 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5)
% 14.42/2.67 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3)
% 14.42/2.67 | ? [v6: any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 14.42/2.67 member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0)
% 14.42/2.67 | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1) = 0) | ~
% 14.42/2.67 $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & member(v4, v2) = 0 &
% 14.42/2.67 $i(v4)))))
% 14.42/2.67
% 14.42/2.67 (subset)
% 14.42/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 14.42/2.68 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 14.42/2.68 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 14.42/2.68 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 14.42/2.68 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 14.42/2.68
% 14.42/2.68 (thIIa09)
% 14.42/2.68 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 14.42/2.68 $i] : ? [v6: int] : ( ~ (v6 = 0) & inverse_image3(v0, v4, v1) = v5 &
% 14.42/2.68 image3(v0, v3, v2) = v4 & injective(v0, v1, v2) = 0 & maps(v0, v1, v2) = 0 &
% 14.42/2.68 equal_set(v5, v3) = v6 & subset(v3, v1) = 0 & $i(v5) & $i(v4) & $i(v3) &
% 14.42/2.68 $i(v2) & $i(v1) & $i(v0))
% 14.42/2.68
% 14.42/2.68 (function-axioms)
% 14.42/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.42/2.69 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 14.42/2.69 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 14.42/2.69 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.42/2.69 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 14.42/2.69 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.42/2.69 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 14.42/2.69 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.42/2.69 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 14.42/2.69 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 14.42/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 14.42/2.69 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 14.42/2.69 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 14.42/2.69 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.42/2.69 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 14.42/2.69 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.42/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 14.42/2.69 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 14.42/2.69 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.42/2.69 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 14.42/2.69 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 14.42/2.69 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 14.42/2.69 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.42/2.69 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 14.42/2.69 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.42/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 14.42/2.69 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 14.42/2.69 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 14.42/2.69 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 14.42/2.69 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.42/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 14.42/2.69 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 14.42/2.69 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.42/2.69 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 14.42/2.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.42/2.69 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 14.42/2.69 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 14.42/2.69 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 14.42/2.69 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 14.42/2.69 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 14.42/2.69 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.42/2.69 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 14.42/2.69 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.42/2.69 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 14.42/2.69 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.42/2.69 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 14.42/2.69 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 14.42/2.69 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 14.42/2.69 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 14.42/2.69 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.42/2.69 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 14.42/2.69 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.42/2.69 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 14.42/2.69 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 14.42/2.69 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.42/2.69 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 14.42/2.69 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 14.42/2.69 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 14.42/2.69 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 14.42/2.69 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 14.42/2.69 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 14.42/2.69 (power_set(v2) = v0))
% 14.42/2.69
% 14.42/2.69 Further assumptions not needed in the proof:
% 14.42/2.69 --------------------------------------------
% 14.42/2.69 compose_function, compose_predicate, decreasing_function, difference, empty_set,
% 14.42/2.69 equal_maps, identity, image2, increasing_function, intersection,
% 14.42/2.69 inverse_function, inverse_image2, inverse_predicate, isomorphism, one_to_one,
% 14.42/2.69 power_set, product, singleton, sum, surjective, union, unordered_pair
% 14.42/2.69
% 14.42/2.69 Those formulas are unsatisfiable:
% 14.42/2.69 ---------------------------------
% 14.42/2.69
% 14.42/2.69 Begin of proof
% 14.42/2.69 |
% 14.42/2.69 | ALPHA: (subset) implies:
% 14.42/2.69 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 14.42/2.69 | $i(v0) | ! [v2: $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) |
% 14.42/2.69 | member(v2, v1) = 0))
% 14.42/2.69 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 14.42/2.69 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 14.42/2.69 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 14.42/2.69 |
% 14.42/2.69 | ALPHA: (equal_set) implies:
% 14.42/2.69 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0,
% 14.42/2.69 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 14.42/2.69 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 14.42/2.69 | 0))))
% 14.42/2.69 |
% 14.42/2.69 | ALPHA: (maps) implies:
% 14.42/2.70 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (maps(v0, v1, v2) = 0) |
% 14.42/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ( ! [v3: $i] : ! [v4: $i] : !
% 14.42/2.70 | [v5: $i] : (v5 = v4 | ~ (apply(v0, v3, v5) = 0) | ~ (apply(v0,
% 14.42/2.70 | v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6:
% 14.42/2.70 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 14.42/2.70 | member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~
% 14.42/2.70 | (v7 = 0) | ~ (v6 = 0)))) & ! [v3: $i] : ( ~ (member(v3, v1)
% 14.42/2.70 | = 0) | ~ $i(v3) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 14.42/2.70 | member(v4, v2) = 0 & $i(v4)))))
% 14.42/2.70 |
% 14.42/2.70 | ALPHA: (injective) implies:
% 14.42/2.70 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) =
% 14.42/2.70 | 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ! [v4: $i]
% 14.42/2.70 | : ! [v5: $i] : (v4 = v3 | ~ (apply(v0, v4, v5) = 0) | ~ (apply(v0,
% 14.42/2.70 | v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ? [v6: any]
% 14.42/2.70 | : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4,
% 14.42/2.70 | v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) |
% 14.42/2.70 | ~ (v6 = 0)))))
% 14.42/2.70 |
% 14.42/2.70 | ALPHA: (image3) implies:
% 14.42/2.70 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 14.42/2.70 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~ $i(v3) |
% 14.42/2.70 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ? [v5: $i]
% 14.42/2.70 | : (apply(v0, v5, v3) = 0 & member(v5, v1) = 0 & $i(v5))))
% 14.42/2.70 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 14.42/2.70 | ! [v5: int] : (v5 = 0 | ~ (image3(v0, v1, v2) = v4) | ~ (member(v3,
% 14.42/2.70 | v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 14.42/2.70 | [v6: int] : ( ~ (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] : ( ~
% 14.42/2.70 | (apply(v0, v6, v3) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) &
% 14.42/2.70 | member(v6, v1) = v7)))
% 14.42/2.70 |
% 14.42/2.70 | ALPHA: (inverse_image3) implies:
% 14.42/2.70 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 14.42/2.70 | ~ (inverse_image3(v0, v1, v2) = v4) | ~ (member(v3, v4) = 0) | ~
% 14.42/2.70 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v3, v2) = 0 & ?
% 14.42/2.70 | [v5: $i] : (apply(v0, v3, v5) = 0 & member(v5, v1) = 0 & $i(v5))))
% 14.42/2.70 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 14.42/2.70 | ! [v5: int] : (v5 = 0 | ~ (inverse_image3(v0, v1, v2) = v4) | ~
% 14.42/2.70 | (member(v3, v4) = v5) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 14.42/2.70 | | ? [v6: int] : ( ~ (v6 = 0) & member(v3, v2) = v6) | ! [v6: $i] :
% 14.42/2.70 | ( ~ (apply(v0, v3, v6) = 0) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0)
% 14.42/2.70 | & member(v6, v1) = v7)))
% 14.42/2.70 |
% 14.42/2.70 | ALPHA: (function-axioms) implies:
% 14.42/2.71 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 14.42/2.71 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 14.42/2.71 | v2) = v0))
% 14.42/2.71 |
% 14.42/2.71 | DELTA: instantiating (thIIa09) with fresh symbols all_32_0, all_32_1,
% 14.42/2.71 | all_32_2, all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 14.42/2.71 | (11) ~ (all_32_0 = 0) & inverse_image3(all_32_6, all_32_2, all_32_5) =
% 14.42/2.71 | all_32_1 & image3(all_32_6, all_32_3, all_32_4) = all_32_2 &
% 14.42/2.71 | injective(all_32_6, all_32_5, all_32_4) = 0 & maps(all_32_6, all_32_5,
% 14.42/2.71 | all_32_4) = 0 & equal_set(all_32_1, all_32_3) = all_32_0 &
% 14.42/2.71 | subset(all_32_3, all_32_5) = 0 & $i(all_32_1) & $i(all_32_2) &
% 14.42/2.71 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6)
% 14.42/2.71 |
% 14.42/2.71 | ALPHA: (11) implies:
% 14.42/2.71 | (12) ~ (all_32_0 = 0)
% 14.42/2.71 | (13) $i(all_32_6)
% 14.42/2.71 | (14) $i(all_32_5)
% 14.42/2.71 | (15) $i(all_32_4)
% 14.42/2.71 | (16) $i(all_32_3)
% 14.42/2.71 | (17) $i(all_32_2)
% 14.42/2.71 | (18) $i(all_32_1)
% 14.42/2.71 | (19) subset(all_32_3, all_32_5) = 0
% 14.42/2.71 | (20) equal_set(all_32_1, all_32_3) = all_32_0
% 14.42/2.71 | (21) maps(all_32_6, all_32_5, all_32_4) = 0
% 14.42/2.71 | (22) injective(all_32_6, all_32_5, all_32_4) = 0
% 14.42/2.71 | (23) image3(all_32_6, all_32_3, all_32_4) = all_32_2
% 14.42/2.71 | (24) inverse_image3(all_32_6, all_32_2, all_32_5) = all_32_1
% 14.42/2.71 |
% 14.42/2.71 | GROUND_INST: instantiating (1) with all_32_3, all_32_5, simplifying with (14),
% 14.42/2.71 | (16), (19) gives:
% 14.42/2.71 | (25) ! [v0: $i] : ( ~ (member(v0, all_32_3) = 0) | ~ $i(v0) | member(v0,
% 14.42/2.71 | all_32_5) = 0)
% 14.42/2.71 |
% 14.42/2.71 | GROUND_INST: instantiating (3) with all_32_1, all_32_3, all_32_0, simplifying
% 14.42/2.71 | with (16), (18), (20) gives:
% 14.42/2.71 | (26) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_32_1,
% 14.42/2.71 | all_32_3) = v0 & subset(all_32_3, all_32_1) = v1 & ( ~ (v1 = 0) |
% 14.42/2.71 | ~ (v0 = 0)))
% 14.42/2.71 |
% 14.42/2.71 | GROUND_INST: instantiating (4) with all_32_6, all_32_5, all_32_4, simplifying
% 14.42/2.71 | with (13), (14), (15), (21) gives:
% 14.42/2.72 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~
% 14.42/2.72 | (apply(all_32_6, v0, v2) = 0) | ~ (apply(all_32_6, v0, v1) = 0) |
% 14.42/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 14.42/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_4) = v4 &
% 14.42/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 14.42/2.72 | 0)))) & ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~
% 14.42/2.72 | $i(v0) | ? [v1: $i] : (apply(all_32_6, v0, v1) = 0 & member(v1,
% 14.42/2.72 | all_32_4) = 0 & $i(v1)))
% 14.42/2.72 |
% 14.42/2.72 | ALPHA: (27) implies:
% 14.42/2.72 | (28) ! [v0: $i] : ( ~ (member(v0, all_32_5) = 0) | ~ $i(v0) | ? [v1: $i]
% 14.42/2.72 | : (apply(all_32_6, v0, v1) = 0 & member(v1, all_32_4) = 0 & $i(v1)))
% 14.42/2.72 |
% 14.42/2.72 | GROUND_INST: instantiating (5) with all_32_6, all_32_5, all_32_4, simplifying
% 14.42/2.72 | with (13), (14), (15), (22) gives:
% 14.42/2.72 | (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 14.42/2.72 | (apply(all_32_6, v1, v2) = 0) | ~ (apply(all_32_6, v0, v2) = 0) |
% 14.42/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ?
% 14.42/2.72 | [v5: any] : (member(v2, all_32_4) = v5 & member(v1, all_32_5) = v4 &
% 14.42/2.72 | member(v0, all_32_5) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 14.42/2.72 | 0))))
% 14.42/2.72 |
% 14.42/2.72 | BETA: splitting (26) gives:
% 14.42/2.72 |
% 14.42/2.72 | Case 1:
% 14.42/2.72 | |
% 14.42/2.72 | | (30) all_32_0 = 0
% 14.42/2.72 | |
% 14.42/2.72 | | REDUCE: (12), (30) imply:
% 14.42/2.72 | | (31) $false
% 14.42/2.72 | |
% 14.42/2.72 | | CLOSE: (31) is inconsistent.
% 14.42/2.72 | |
% 14.42/2.72 | Case 2:
% 14.42/2.72 | |
% 14.42/2.72 | | (32) ? [v0: any] : ? [v1: any] : (subset(all_32_1, all_32_3) = v0 &
% 14.42/2.72 | | subset(all_32_3, all_32_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 14.42/2.72 | |
% 14.42/2.72 | | DELTA: instantiating (32) with fresh symbols all_45_0, all_45_1 gives:
% 14.42/2.72 | | (33) subset(all_32_1, all_32_3) = all_45_1 & subset(all_32_3, all_32_1) =
% 14.42/2.72 | | all_45_0 & ( ~ (all_45_0 = 0) | ~ (all_45_1 = 0))
% 14.42/2.72 | |
% 14.42/2.72 | | ALPHA: (33) implies:
% 14.42/2.72 | | (34) subset(all_32_3, all_32_1) = all_45_0
% 14.42/2.72 | | (35) subset(all_32_1, all_32_3) = all_45_1
% 14.42/2.72 | | (36) ~ (all_45_0 = 0) | ~ (all_45_1 = 0)
% 14.42/2.72 | |
% 14.42/2.72 | | GROUND_INST: instantiating (2) with all_32_3, all_32_1, all_45_0,
% 14.42/2.72 | | simplifying with (16), (18), (34) gives:
% 14.42/2.72 | | (37) all_45_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 14.42/2.72 | | member(v0, all_32_1) = v1 & member(v0, all_32_3) = 0 & $i(v0))
% 14.42/2.72 | |
% 14.42/2.72 | | GROUND_INST: instantiating (2) with all_32_1, all_32_3, all_45_1,
% 14.42/2.72 | | simplifying with (16), (18), (35) gives:
% 14.42/2.72 | | (38) all_45_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 14.42/2.72 | | member(v0, all_32_1) = 0 & member(v0, all_32_3) = v1 & $i(v0))
% 14.42/2.72 | |
% 14.42/2.72 | | BETA: splitting (36) gives:
% 14.42/2.72 | |
% 14.42/2.72 | | Case 1:
% 14.42/2.72 | | |
% 14.42/2.72 | | | (39) ~ (all_45_0 = 0)
% 14.42/2.72 | | |
% 14.42/2.72 | | | BETA: splitting (37) gives:
% 14.42/2.72 | | |
% 14.42/2.72 | | | Case 1:
% 14.42/2.72 | | | |
% 14.42/2.72 | | | | (40) all_45_0 = 0
% 14.42/2.72 | | | |
% 14.42/2.72 | | | | REDUCE: (39), (40) imply:
% 14.42/2.72 | | | | (41) $false
% 14.42/2.72 | | | |
% 14.42/2.72 | | | | CLOSE: (41) is inconsistent.
% 14.42/2.72 | | | |
% 14.42/2.72 | | | Case 2:
% 14.42/2.72 | | | |
% 14.42/2.73 | | | | (42) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 14.42/2.73 | | | | = v1 & member(v0, all_32_3) = 0 & $i(v0))
% 14.42/2.73 | | | |
% 14.42/2.73 | | | | DELTA: instantiating (42) with fresh symbols all_58_0, all_58_1 gives:
% 14.42/2.73 | | | | (43) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = all_58_0 &
% 14.42/2.73 | | | | member(all_58_1, all_32_3) = 0 & $i(all_58_1)
% 14.42/2.73 | | | |
% 14.42/2.73 | | | | ALPHA: (43) implies:
% 14.42/2.73 | | | | (44) ~ (all_58_0 = 0)
% 14.42/2.73 | | | | (45) $i(all_58_1)
% 14.42/2.73 | | | | (46) member(all_58_1, all_32_3) = 0
% 14.42/2.73 | | | | (47) member(all_58_1, all_32_1) = all_58_0
% 14.42/2.73 | | | |
% 14.42/2.73 | | | | GROUND_INST: instantiating (25) with all_58_1, simplifying with (45),
% 14.42/2.73 | | | | (46) gives:
% 14.42/2.73 | | | | (48) member(all_58_1, all_32_5) = 0
% 14.42/2.73 | | | |
% 14.42/2.73 | | | | GROUND_INST: instantiating (9) with all_32_6, all_32_2, all_32_5,
% 14.42/2.73 | | | | all_58_1, all_32_1, all_58_0, simplifying with (13), (14),
% 14.42/2.73 | | | | (17), (24), (45), (47) gives:
% 14.42/2.73 | | | | (49) all_58_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1,
% 14.42/2.73 | | | | all_32_5) = v0) | ! [v0: $i] : ( ~ (apply(all_32_6,
% 14.42/2.73 | | | | all_58_1, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 14.42/2.73 | | | | 0) & member(v0, all_32_2) = v1))
% 14.42/2.73 | | | |
% 14.42/2.73 | | | | BETA: splitting (49) gives:
% 14.42/2.73 | | | |
% 14.42/2.73 | | | | Case 1:
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | | (50) all_58_0 = 0
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | | REDUCE: (44), (50) imply:
% 14.42/2.73 | | | | | (51) $false
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | | CLOSE: (51) is inconsistent.
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | Case 2:
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | | (52) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_5) = v0)
% 14.42/2.73 | | | | | | ! [v0: $i] : ( ~ (apply(all_32_6, all_58_1, v0) = 0) | ~
% 14.42/2.73 | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_2)
% 14.42/2.73 | | | | | = v1))
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | | BETA: splitting (52) gives:
% 14.42/2.73 | | | | |
% 14.42/2.73 | | | | | Case 1:
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_5) =
% 14.42/2.73 | | | | | | v0)
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | DELTA: instantiating (53) with fresh symbol all_73_0 gives:
% 14.42/2.73 | | | | | | (54) ~ (all_73_0 = 0) & member(all_58_1, all_32_5) = all_73_0
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | ALPHA: (54) implies:
% 14.42/2.73 | | | | | | (55) ~ (all_73_0 = 0)
% 14.42/2.73 | | | | | | (56) member(all_58_1, all_32_5) = all_73_0
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | GROUND_INST: instantiating (10) with 0, all_73_0, all_32_5,
% 14.42/2.73 | | | | | | all_58_1, simplifying with (48), (56) gives:
% 14.42/2.73 | | | | | | (57) all_73_0 = 0
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | REDUCE: (55), (57) imply:
% 14.42/2.73 | | | | | | (58) $false
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | CLOSE: (58) is inconsistent.
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | Case 2:
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | (59) ! [v0: $i] : ( ~ (apply(all_32_6, all_58_1, v0) = 0) | ~
% 14.42/2.73 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 14.42/2.73 | | | | | | all_32_2) = v1))
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | GROUND_INST: instantiating (28) with all_58_1, simplifying with
% 14.42/2.73 | | | | | | (45), (48) gives:
% 14.42/2.73 | | | | | | (60) ? [v0: $i] : (apply(all_32_6, all_58_1, v0) = 0 &
% 14.42/2.73 | | | | | | member(v0, all_32_4) = 0 & $i(v0))
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | DELTA: instantiating (60) with fresh symbol all_78_0 gives:
% 14.42/2.73 | | | | | | (61) apply(all_32_6, all_58_1, all_78_0) = 0 & member(all_78_0,
% 14.42/2.73 | | | | | | all_32_4) = 0 & $i(all_78_0)
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | ALPHA: (61) implies:
% 14.42/2.73 | | | | | | (62) $i(all_78_0)
% 14.42/2.73 | | | | | | (63) member(all_78_0, all_32_4) = 0
% 14.42/2.73 | | | | | | (64) apply(all_32_6, all_58_1, all_78_0) = 0
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | GROUND_INST: instantiating (59) with all_78_0, simplifying with
% 14.42/2.73 | | | | | | (62), (64) gives:
% 14.42/2.73 | | | | | | (65) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_0, all_32_2) =
% 14.42/2.73 | | | | | | v0)
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | DELTA: instantiating (65) with fresh symbol all_85_0 gives:
% 14.42/2.73 | | | | | | (66) ~ (all_85_0 = 0) & member(all_78_0, all_32_2) = all_85_0
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | ALPHA: (66) implies:
% 14.42/2.73 | | | | | | (67) ~ (all_85_0 = 0)
% 14.42/2.73 | | | | | | (68) member(all_78_0, all_32_2) = all_85_0
% 14.42/2.73 | | | | | |
% 14.42/2.73 | | | | | | GROUND_INST: instantiating (7) with all_32_6, all_32_3, all_32_4,
% 14.42/2.73 | | | | | | all_78_0, all_32_2, all_85_0, simplifying with (13),
% 14.42/2.73 | | | | | | (15), (16), (23), (62), (68) gives:
% 14.42/2.74 | | | | | | (69) all_85_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 14.42/2.74 | | | | | | member(all_78_0, all_32_4) = v0) | ! [v0: $i] : ( ~
% 14.42/2.74 | | | | | | (apply(all_32_6, v0, all_78_0) = 0) | ~ $i(v0) | ? [v1:
% 14.42/2.74 | | | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_3) = v1))
% 14.42/2.74 | | | | | |
% 14.42/2.74 | | | | | | BETA: splitting (69) gives:
% 14.42/2.74 | | | | | |
% 14.42/2.74 | | | | | | Case 1:
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | | (70) all_85_0 = 0
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | | REDUCE: (67), (70) imply:
% 14.42/2.74 | | | | | | | (71) $false
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | | CLOSE: (71) is inconsistent.
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | Case 2:
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_0, all_32_4) =
% 14.42/2.74 | | | | | | | v0) | ! [v0: $i] : ( ~ (apply(all_32_6, v0, all_78_0) =
% 14.42/2.74 | | | | | | | 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 14.42/2.74 | | | | | | | member(v0, all_32_3) = v1))
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | | BETA: splitting (72) gives:
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | | Case 1:
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | (73) ? [v0: int] : ( ~ (v0 = 0) & member(all_78_0, all_32_4)
% 14.42/2.74 | | | | | | | | = v0)
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | DELTA: instantiating (73) with fresh symbol all_103_0 gives:
% 14.42/2.74 | | | | | | | | (74) ~ (all_103_0 = 0) & member(all_78_0, all_32_4) =
% 14.42/2.74 | | | | | | | | all_103_0
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | ALPHA: (74) implies:
% 14.42/2.74 | | | | | | | | (75) ~ (all_103_0 = 0)
% 14.42/2.74 | | | | | | | | (76) member(all_78_0, all_32_4) = all_103_0
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_103_0, all_32_4,
% 14.42/2.74 | | | | | | | | all_78_0, simplifying with (63), (76) gives:
% 14.42/2.74 | | | | | | | | (77) all_103_0 = 0
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | REDUCE: (75), (77) imply:
% 14.42/2.74 | | | | | | | | (78) $false
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | CLOSE: (78) is inconsistent.
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | Case 2:
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | (79) ! [v0: $i] : ( ~ (apply(all_32_6, v0, all_78_0) = 0) |
% 14.42/2.74 | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 14.42/2.74 | | | | | | | | all_32_3) = v1))
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | GROUND_INST: instantiating (79) with all_58_1, simplifying with
% 14.42/2.74 | | | | | | | | (45), (64) gives:
% 14.42/2.74 | | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & member(all_58_1, all_32_3)
% 14.42/2.74 | | | | | | | | = v0)
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | DELTA: instantiating (80) with fresh symbol all_104_0 gives:
% 14.42/2.74 | | | | | | | | (81) ~ (all_104_0 = 0) & member(all_58_1, all_32_3) =
% 14.42/2.74 | | | | | | | | all_104_0
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | ALPHA: (81) implies:
% 14.42/2.74 | | | | | | | | (82) ~ (all_104_0 = 0)
% 14.42/2.74 | | | | | | | | (83) member(all_58_1, all_32_3) = all_104_0
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | GROUND_INST: instantiating (10) with 0, all_104_0, all_32_3,
% 14.42/2.74 | | | | | | | | all_58_1, simplifying with (46), (83) gives:
% 14.42/2.74 | | | | | | | | (84) all_104_0 = 0
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | REDUCE: (82), (84) imply:
% 14.42/2.74 | | | | | | | | (85) $false
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | | CLOSE: (85) is inconsistent.
% 14.42/2.74 | | | | | | | |
% 14.42/2.74 | | | | | | | End of split
% 14.42/2.74 | | | | | | |
% 14.42/2.74 | | | | | | End of split
% 14.42/2.74 | | | | | |
% 14.42/2.74 | | | | | End of split
% 14.42/2.74 | | | | |
% 14.42/2.74 | | | | End of split
% 14.42/2.74 | | | |
% 14.42/2.74 | | | End of split
% 14.42/2.74 | | |
% 14.42/2.74 | | Case 2:
% 14.42/2.74 | | |
% 14.42/2.74 | | | (86) ~ (all_45_1 = 0)
% 14.42/2.74 | | |
% 14.42/2.74 | | | BETA: splitting (38) gives:
% 14.42/2.74 | | |
% 14.42/2.74 | | | Case 1:
% 14.42/2.74 | | | |
% 14.42/2.74 | | | | (87) all_45_1 = 0
% 14.42/2.74 | | | |
% 14.42/2.74 | | | | REDUCE: (86), (87) imply:
% 14.42/2.74 | | | | (88) $false
% 14.42/2.74 | | | |
% 14.42/2.74 | | | | CLOSE: (88) is inconsistent.
% 14.42/2.74 | | | |
% 14.42/2.74 | | | Case 2:
% 14.42/2.74 | | | |
% 14.78/2.74 | | | | (89) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_1)
% 14.78/2.74 | | | | = 0 & member(v0, all_32_3) = v1 & $i(v0))
% 14.78/2.74 | | | |
% 14.78/2.74 | | | | DELTA: instantiating (89) with fresh symbols all_58_0, all_58_1 gives:
% 14.78/2.74 | | | | (90) ~ (all_58_0 = 0) & member(all_58_1, all_32_1) = 0 &
% 14.78/2.74 | | | | member(all_58_1, all_32_3) = all_58_0 & $i(all_58_1)
% 14.78/2.74 | | | |
% 14.78/2.74 | | | | ALPHA: (90) implies:
% 14.78/2.74 | | | | (91) ~ (all_58_0 = 0)
% 14.78/2.74 | | | | (92) $i(all_58_1)
% 14.78/2.74 | | | | (93) member(all_58_1, all_32_3) = all_58_0
% 14.78/2.74 | | | | (94) member(all_58_1, all_32_1) = 0
% 14.78/2.74 | | | |
% 14.78/2.74 | | | | GROUND_INST: instantiating (8) with all_32_6, all_32_2, all_32_5,
% 14.78/2.74 | | | | all_58_1, all_32_1, simplifying with (13), (14), (17),
% 14.78/2.74 | | | | (24), (92), (94) gives:
% 14.78/2.74 | | | | (95) member(all_58_1, all_32_5) = 0 & ? [v0: $i] : (apply(all_32_6,
% 14.78/2.74 | | | | all_58_1, v0) = 0 & member(v0, all_32_2) = 0 & $i(v0))
% 14.78/2.74 | | | |
% 14.78/2.74 | | | | ALPHA: (95) implies:
% 14.78/2.74 | | | | (96) member(all_58_1, all_32_5) = 0
% 14.78/2.74 | | | | (97) ? [v0: $i] : (apply(all_32_6, all_58_1, v0) = 0 & member(v0,
% 14.78/2.74 | | | | all_32_2) = 0 & $i(v0))
% 14.78/2.74 | | | |
% 14.78/2.74 | | | | DELTA: instantiating (97) with fresh symbol all_67_0 gives:
% 14.78/2.74 | | | | (98) apply(all_32_6, all_58_1, all_67_0) = 0 & member(all_67_0,
% 14.78/2.74 | | | | all_32_2) = 0 & $i(all_67_0)
% 14.78/2.74 | | | |
% 14.78/2.74 | | | | ALPHA: (98) implies:
% 14.78/2.74 | | | | (99) $i(all_67_0)
% 14.78/2.74 | | | | (100) member(all_67_0, all_32_2) = 0
% 14.78/2.74 | | | | (101) apply(all_32_6, all_58_1, all_67_0) = 0
% 14.78/2.74 | | | |
% 14.78/2.75 | | | | GROUND_INST: instantiating (6) with all_32_6, all_32_3, all_32_4,
% 14.78/2.75 | | | | all_67_0, all_32_2, simplifying with (13), (15), (16),
% 14.78/2.75 | | | | (23), (99), (100) gives:
% 14.78/2.75 | | | | (102) member(all_67_0, all_32_4) = 0 & ? [v0: $i] : (apply(all_32_6,
% 14.78/2.75 | | | | v0, all_67_0) = 0 & member(v0, all_32_3) = 0 & $i(v0))
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | ALPHA: (102) implies:
% 14.78/2.75 | | | | (103) member(all_67_0, all_32_4) = 0
% 14.78/2.75 | | | | (104) ? [v0: $i] : (apply(all_32_6, v0, all_67_0) = 0 & member(v0,
% 14.78/2.75 | | | | all_32_3) = 0 & $i(v0))
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | DELTA: instantiating (104) with fresh symbol all_75_0 gives:
% 14.78/2.75 | | | | (105) apply(all_32_6, all_75_0, all_67_0) = 0 & member(all_75_0,
% 14.78/2.75 | | | | all_32_3) = 0 & $i(all_75_0)
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | ALPHA: (105) implies:
% 14.78/2.75 | | | | (106) $i(all_75_0)
% 14.78/2.75 | | | | (107) member(all_75_0, all_32_3) = 0
% 14.78/2.75 | | | | (108) apply(all_32_6, all_75_0, all_67_0) = 0
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | GROUND_INST: instantiating (25) with all_75_0, simplifying with (106),
% 14.78/2.75 | | | | (107) gives:
% 14.78/2.75 | | | | (109) member(all_75_0, all_32_5) = 0
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | GROUND_INST: instantiating (29) with all_75_0, all_58_1, all_67_0,
% 14.78/2.75 | | | | simplifying with (92), (99), (101), (106), (108) gives:
% 14.78/2.75 | | | | (110) all_75_0 = all_58_1 | ? [v0: any] : ? [v1: any] : ? [v2:
% 14.78/2.75 | | | | any] : (member(all_75_0, all_32_5) = v0 & member(all_67_0,
% 14.78/2.75 | | | | all_32_4) = v2 & member(all_58_1, all_32_5) = v1 & ( ~ (v2
% 14.78/2.75 | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | BETA: splitting (110) gives:
% 14.78/2.75 | | | |
% 14.78/2.75 | | | | Case 1:
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | (111) all_75_0 = all_58_1
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | REDUCE: (107), (111) imply:
% 14.78/2.75 | | | | | (112) member(all_58_1, all_32_3) = 0
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with all_58_0, 0, all_32_3, all_58_1,
% 14.78/2.75 | | | | | simplifying with (93), (112) gives:
% 14.78/2.75 | | | | | (113) all_58_0 = 0
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | REDUCE: (91), (113) imply:
% 14.78/2.75 | | | | | (114) $false
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | CLOSE: (114) is inconsistent.
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | Case 2:
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | (115) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 14.78/2.75 | | | | | (member(all_75_0, all_32_5) = v0 & member(all_67_0, all_32_4)
% 14.78/2.75 | | | | | = v2 & member(all_58_1, all_32_5) = v1 & ( ~ (v2 = 0) | ~
% 14.78/2.75 | | | | | (v1 = 0) | ~ (v0 = 0)))
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | DELTA: instantiating (115) with fresh symbols all_93_0, all_93_1,
% 14.78/2.75 | | | | | all_93_2 gives:
% 14.78/2.75 | | | | | (116) member(all_75_0, all_32_5) = all_93_2 & member(all_67_0,
% 14.78/2.75 | | | | | all_32_4) = all_93_0 & member(all_58_1, all_32_5) =
% 14.78/2.75 | | | | | all_93_1 & ( ~ (all_93_0 = 0) | ~ (all_93_1 = 0) | ~
% 14.78/2.75 | | | | | (all_93_2 = 0))
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | ALPHA: (116) implies:
% 14.78/2.75 | | | | | (117) member(all_58_1, all_32_5) = all_93_1
% 14.78/2.75 | | | | | (118) member(all_67_0, all_32_4) = all_93_0
% 14.78/2.75 | | | | | (119) member(all_75_0, all_32_5) = all_93_2
% 14.78/2.75 | | | | | (120) ~ (all_93_0 = 0) | ~ (all_93_1 = 0) | ~ (all_93_2 = 0)
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with 0, all_93_1, all_32_5, all_58_1,
% 14.78/2.75 | | | | | simplifying with (96), (117) gives:
% 14.78/2.75 | | | | | (121) all_93_1 = 0
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with 0, all_93_0, all_32_4, all_67_0,
% 14.78/2.75 | | | | | simplifying with (103), (118) gives:
% 14.78/2.75 | | | | | (122) all_93_0 = 0
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | GROUND_INST: instantiating (10) with 0, all_93_2, all_32_5, all_75_0,
% 14.78/2.75 | | | | | simplifying with (109), (119) gives:
% 14.78/2.75 | | | | | (123) all_93_2 = 0
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | BETA: splitting (120) gives:
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | | Case 1:
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | | (124) ~ (all_93_0 = 0)
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | | REDUCE: (122), (124) imply:
% 14.78/2.75 | | | | | | (125) $false
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | | CLOSE: (125) is inconsistent.
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | Case 2:
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | | (126) ~ (all_93_1 = 0) | ~ (all_93_2 = 0)
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | | BETA: splitting (126) gives:
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | | Case 1:
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | | (127) ~ (all_93_1 = 0)
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | | REDUCE: (121), (127) imply:
% 14.78/2.75 | | | | | | | (128) $false
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | | CLOSE: (128) is inconsistent.
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | Case 2:
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | | (129) ~ (all_93_2 = 0)
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | | REDUCE: (123), (129) imply:
% 14.78/2.75 | | | | | | | (130) $false
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | | CLOSE: (130) is inconsistent.
% 14.78/2.75 | | | | | | |
% 14.78/2.75 | | | | | | End of split
% 14.78/2.75 | | | | | |
% 14.78/2.75 | | | | | End of split
% 14.78/2.75 | | | | |
% 14.78/2.75 | | | | End of split
% 14.78/2.75 | | | |
% 14.78/2.75 | | | End of split
% 14.78/2.75 | | |
% 14.78/2.75 | | End of split
% 14.78/2.75 | |
% 14.78/2.75 | End of split
% 14.78/2.75 |
% 14.78/2.75 End of proof
% 14.78/2.75 % SZS output end Proof for theBenchmark
% 14.78/2.75
% 14.78/2.75 2137ms
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