TSTP Solution File: SEU227+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU227+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 17:43:28 EDT 2023
% Result : Theorem 12.58s 2.42s
% Output : Proof 14.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU227+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.18/0.35 % Computer : n020.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Wed Aug 23 19:49:00 EDT 2023
% 0.18/0.35 % CPUTime :
% 0.22/0.61 ________ _____
% 0.22/0.61 ___ __ \_________(_)________________________________
% 0.22/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.61
% 0.22/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.61 (2023-06-19)
% 0.22/0.61
% 0.22/0.61 (c) Philipp Rümmer, 2009-2023
% 0.22/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.61 Amanda Stjerna.
% 0.22/0.61 Free software under BSD-3-Clause.
% 0.22/0.61
% 0.22/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.61
% 0.22/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.22/0.62 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.50/1.08 Prover 1: Preprocessing ...
% 2.50/1.08 Prover 4: Preprocessing ...
% 3.00/1.12 Prover 2: Preprocessing ...
% 3.00/1.12 Prover 5: Preprocessing ...
% 3.00/1.12 Prover 0: Preprocessing ...
% 3.00/1.12 Prover 3: Preprocessing ...
% 3.00/1.12 Prover 6: Preprocessing ...
% 6.44/1.67 Prover 1: Warning: ignoring some quantifiers
% 7.31/1.71 Prover 5: Proving ...
% 7.31/1.71 Prover 1: Constructing countermodel ...
% 7.48/1.75 Prover 6: Proving ...
% 7.48/1.76 Prover 3: Warning: ignoring some quantifiers
% 7.48/1.77 Prover 2: Proving ...
% 7.48/1.78 Prover 3: Constructing countermodel ...
% 7.48/1.79 Prover 4: Warning: ignoring some quantifiers
% 8.09/1.87 Prover 0: Proving ...
% 8.09/1.87 Prover 4: Constructing countermodel ...
% 12.58/2.42 Prover 3: proved (1773ms)
% 12.58/2.42
% 12.58/2.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.58/2.42
% 12.58/2.44 Prover 2: stopped
% 12.58/2.44 Prover 6: stopped
% 12.58/2.46 Prover 5: stopped
% 12.58/2.46 Prover 0: stopped
% 12.58/2.46 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.58/2.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.58/2.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.58/2.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.58/2.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.58/2.49 Prover 7: Preprocessing ...
% 12.58/2.50 Prover 8: Preprocessing ...
% 12.58/2.50 Prover 11: Preprocessing ...
% 13.26/2.52 Prover 13: Preprocessing ...
% 13.26/2.53 Prover 10: Preprocessing ...
% 13.26/2.58 Prover 1: Found proof (size 75)
% 13.26/2.58 Prover 1: proved (1944ms)
% 13.26/2.58 Prover 13: stopped
% 13.26/2.58 Prover 4: stopped
% 13.26/2.58 Prover 10: stopped
% 13.26/2.58 Prover 11: stopped
% 13.86/2.60 Prover 7: Warning: ignoring some quantifiers
% 13.86/2.61 Prover 7: Constructing countermodel ...
% 13.86/2.62 Prover 7: stopped
% 13.86/2.63 Prover 8: Warning: ignoring some quantifiers
% 13.86/2.64 Prover 8: Constructing countermodel ...
% 13.86/2.64 Prover 8: stopped
% 13.86/2.64
% 13.86/2.64 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.86/2.64
% 13.86/2.65 % SZS output start Proof for theBenchmark
% 13.86/2.65 Assumptions after simplification:
% 13.86/2.65 ---------------------------------
% 13.86/2.65
% 13.86/2.66 (d13_relat_1)
% 14.35/2.69 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i]
% 14.35/2.69 : ! [v3: $i] : (v3 = v1 | ~ (relation_image(v0, v2) = v3) | ~ $i(v2) |
% 14.35/2.69 ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 & $i(v4) & ( ~
% 14.35/2.69 (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~ (ordered_pair(v6, v4) =
% 14.35/2.69 v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 =
% 14.35/2.69 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6: $i] : ? [v7: $i]
% 14.35/2.69 : (ordered_pair(v6, v4) = v7 & in(v7, v0) = 0 & in(v6, v2) = 0 &
% 14.35/2.69 $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] : ( ~
% 14.35/2.69 (relation_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( ! [v3: $i] :
% 14.35/2.69 ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) | ! [v5: $i]
% 14.35/2.69 : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = v6) | ~ (in(v6, v0) =
% 14.35/2.69 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) & in(v5, v1) =
% 14.35/2.69 v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4:
% 14.35/2.69 $i] : ? [v5: $i] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 &
% 14.35/2.69 in(v4, v1) = 0 & $i(v5) & $i(v4)))))))
% 14.35/2.69
% 14.35/2.69 (d14_relat_1)
% 14.35/2.69 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ( ? [v1: $i] : ! [v2: $i]
% 14.35/2.69 : ! [v3: $i] : (v3 = v1 | ~ (relation_inverse_image(v0, v2) = v3) | ~
% 14.35/2.69 $i(v2) | ~ $i(v1) | ? [v4: $i] : ? [v5: any] : (in(v4, v1) = v5 &
% 14.35/2.69 $i(v4) & ( ~ (v5 = 0) | ! [v6: $i] : ! [v7: $i] : ( ~
% 14.35/2.69 (ordered_pair(v4, v6) = v7) | ~ (in(v7, v0) = 0) | ~ $i(v6) | ?
% 14.35/2.70 [v8: int] : ( ~ (v8 = 0) & in(v6, v2) = v8))) & (v5 = 0 | ? [v6:
% 14.35/2.70 $i] : ? [v7: $i] : (ordered_pair(v4, v6) = v7 & in(v7, v0) = 0 &
% 14.35/2.70 in(v6, v2) = 0 & $i(v7) & $i(v6))))) & ! [v1: $i] : ! [v2: $i] :
% 14.35/2.70 ( ~ (relation_inverse_image(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ( !
% 14.35/2.70 [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (in(v3, v2) = v4) | ~ $i(v3) |
% 14.35/2.70 ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) = v6) | ~
% 14.35/2.70 (in(v6, v0) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) &
% 14.35/2.70 in(v5, v1) = v7))) & ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~
% 14.35/2.70 $i(v3) | ? [v4: $i] : ? [v5: $i] : (ordered_pair(v3, v4) = v5 &
% 14.35/2.70 in(v5, v0) = 0 & in(v4, v1) = 0 & $i(v5) & $i(v4)))))))
% 14.35/2.70
% 14.35/2.70 (d3_tarski)
% 14.35/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 14.35/2.70 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 14.35/2.70 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 14.35/2.70 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 14.35/2.70 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 14.35/2.70
% 14.35/2.70 (d4_relat_1)
% 14.35/2.70 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.35/2.70 int] : ( ~ (v2 = 0) & relation(v0) = v2) | ( ? [v2: $i] : (v2 = v1 | ~
% 14.35/2.70 $i(v2) | ? [v3: $i] : ? [v4: any] : (in(v3, v2) = v4 & $i(v3) & ( ~
% 14.35/2.70 (v4 = 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 14.35/2.70 v6) | ~ (in(v6, v0) = 0) | ~ $i(v5))) & (v4 = 0 | ? [v5: $i]
% 14.35/2.70 : ? [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, v0) = 0 & $i(v6)
% 14.35/2.70 & $i(v5))))) & ( ~ $i(v1) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0
% 14.35/2.70 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 14.35/2.70 (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ $i(v4))) &
% 14.35/2.70 ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4:
% 14.35/2.70 $i] : (ordered_pair(v2, v3) = v4 & in(v4, v0) = 0 & $i(v4) &
% 14.35/2.70 $i(v3)))))))
% 14.35/2.70
% 14.35/2.70 (fc5_relat_1)
% 14.35/2.70 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.35/2.70 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 & empty(v1) = v4 &
% 14.35/2.70 empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 14.35/2.70
% 14.35/2.70 (fc7_relat_1)
% 14.35/2.70 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) | ? [v2:
% 14.35/2.70 any] : ? [v3: any] : ? [v4: any] : (relation(v1) = v4 & empty(v1) = v3 &
% 14.35/2.70 empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 14.35/2.70
% 14.35/2.70 (t146_funct_1)
% 14.35/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 14.35/2.70 int] : ( ~ (v5 = 0) & relation_dom(v1) = v2 & subset(v0, v4) = v5 &
% 14.35/2.70 subset(v0, v2) = 0 & relation_inverse_image(v1, v3) = v4 &
% 14.35/2.70 relation_image(v1, v0) = v3 & relation(v1) = 0 & $i(v4) & $i(v3) & $i(v2) &
% 14.35/2.70 $i(v1) & $i(v0))
% 14.35/2.70
% 14.35/2.70 (t7_boole)
% 14.35/2.70 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 14.35/2.70 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 14.35/2.70
% 14.35/2.70 (function-axioms)
% 14.35/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.35/2.71 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 14.35/2.71 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 14.35/2.71 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 14.35/2.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.35/2.71 (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) =
% 14.35/2.71 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 |
% 14.35/2.71 ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & !
% 14.35/2.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 14.35/2.71 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: $i]
% 14.35/2.71 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3,
% 14.35/2.71 v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 14.35/2.71 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 14.35/2.71 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i] : !
% 14.35/2.71 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 14.35/2.71 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 14.35/2.71 $i] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~
% 14.35/2.71 (relation_empty_yielding(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 14.35/2.71 $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & !
% 14.35/2.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) |
% 14.35/2.71 ~ (relation_dom(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.35/2.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~
% 14.35/2.71 (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.35/2.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~
% 14.35/2.71 (relation(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.35/2.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (function(v2) = v1) | ~
% 14.35/2.71 (function(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 14.35/2.71 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 14.35/2.71 (empty(v2) = v0))
% 14.35/2.71
% 14.35/2.71 Further assumptions not needed in the proof:
% 14.35/2.71 --------------------------------------------
% 14.35/2.71 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1,
% 14.35/2.71 commutativity_k2_tarski, d5_tarski, existence_m1_subset_1, fc12_relat_1,
% 14.35/2.71 fc1_subset_1, fc1_xboole_0, fc1_zfmisc_1, fc2_subset_1, fc3_subset_1,
% 14.35/2.71 fc4_relat_1, rc1_funct_1, rc1_relat_1, rc1_subset_1, rc1_xboole_0, rc2_funct_1,
% 14.35/2.71 rc2_relat_1, rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1,
% 14.35/2.71 reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, t5_subset,
% 14.35/2.71 t6_boole, t8_boole
% 14.35/2.71
% 14.35/2.71 Those formulas are unsatisfiable:
% 14.35/2.71 ---------------------------------
% 14.35/2.71
% 14.35/2.71 Begin of proof
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (d3_tarski) implies:
% 14.35/2.71 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 14.35/2.71 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1)
% 14.35/2.71 | = 0))
% 14.35/2.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 14.35/2.71 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 14.35/2.71 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 14.35/2.71 |
% 14.35/2.71 | ALPHA: (function-axioms) implies:
% 14.35/2.71 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.35/2.71 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 14.35/2.71 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.35/2.71 | (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 14.35/2.71 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 14.35/2.71 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 14.35/2.71 |
% 14.35/2.71 | DELTA: instantiating (t146_funct_1) with fresh symbols all_49_0, all_49_1,
% 14.35/2.71 | all_49_2, all_49_3, all_49_4, all_49_5 gives:
% 14.35/2.72 | (6) ~ (all_49_0 = 0) & relation_dom(all_49_4) = all_49_3 &
% 14.35/2.72 | subset(all_49_5, all_49_1) = all_49_0 & subset(all_49_5, all_49_3) = 0
% 14.35/2.72 | & relation_inverse_image(all_49_4, all_49_2) = all_49_1 &
% 14.35/2.72 | relation_image(all_49_4, all_49_5) = all_49_2 & relation(all_49_4) = 0
% 14.35/2.72 | & $i(all_49_1) & $i(all_49_2) & $i(all_49_3) & $i(all_49_4) &
% 14.35/2.72 | $i(all_49_5)
% 14.35/2.72 |
% 14.35/2.72 | ALPHA: (6) implies:
% 14.35/2.72 | (7) ~ (all_49_0 = 0)
% 14.35/2.72 | (8) $i(all_49_5)
% 14.35/2.72 | (9) $i(all_49_4)
% 14.35/2.72 | (10) $i(all_49_3)
% 14.35/2.72 | (11) $i(all_49_2)
% 14.35/2.72 | (12) $i(all_49_1)
% 14.35/2.72 | (13) relation(all_49_4) = 0
% 14.35/2.72 | (14) relation_image(all_49_4, all_49_5) = all_49_2
% 14.35/2.72 | (15) relation_inverse_image(all_49_4, all_49_2) = all_49_1
% 14.35/2.72 | (16) subset(all_49_5, all_49_3) = 0
% 14.35/2.72 | (17) subset(all_49_5, all_49_1) = all_49_0
% 14.35/2.72 | (18) relation_dom(all_49_4) = all_49_3
% 14.35/2.72 |
% 14.35/2.72 | GROUND_INST: instantiating (d14_relat_1) with all_49_4, simplifying with (9),
% 14.35/2.72 | (13) gives:
% 14.35/2.72 | (19) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 14.35/2.72 | (relation_inverse_image(all_49_4, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 14.35/2.72 | | ? [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 =
% 14.35/2.72 | 0) | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v3, v5) =
% 14.35/2.72 | v6) | ~ (in(v6, all_49_4) = 0) | ~ $i(v5) | ? [v7: int] :
% 14.35/2.72 | ( ~ (v7 = 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ?
% 14.35/2.72 | [v6: $i] : (ordered_pair(v3, v5) = v6 & in(v6, all_49_4) = 0 &
% 14.35/2.72 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1:
% 14.35/2.72 | $i] : ( ~ (relation_inverse_image(all_49_4, v0) = v1) | ~ $i(v1) |
% 14.35/2.72 | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) =
% 14.35/2.72 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 14.35/2.72 | (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_49_4) = 0) | ~
% 14.35/2.72 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & !
% 14.35/2.72 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 14.35/2.72 | [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4, all_49_4) = 0 &
% 14.35/2.72 | in(v3, v0) = 0 & $i(v4) & $i(v3)))))
% 14.35/2.72 |
% 14.35/2.72 | ALPHA: (19) implies:
% 14.35/2.72 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_inverse_image(all_49_4, v0)
% 14.35/2.72 | = v1) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3
% 14.35/2.72 | = 0 | ~ (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5:
% 14.35/2.72 | $i] : ( ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, all_49_4) =
% 14.35/2.72 | 0) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) =
% 14.35/2.72 | v6))) & ! [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ?
% 14.35/2.72 | [v3: $i] : ? [v4: $i] : (ordered_pair(v2, v3) = v4 & in(v4,
% 14.35/2.72 | all_49_4) = 0 & in(v3, v0) = 0 & $i(v4) & $i(v3)))))
% 14.35/2.72 |
% 14.35/2.72 | GROUND_INST: instantiating (d13_relat_1) with all_49_4, simplifying with (9),
% 14.35/2.72 | (13) gives:
% 14.35/2.73 | (21) ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~
% 14.35/2.73 | (relation_image(all_49_4, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 14.35/2.73 | [v3: $i] : ? [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) |
% 14.35/2.73 | ! [v5: $i] : ! [v6: $i] : ( ~ (ordered_pair(v5, v3) = v6) | ~
% 14.35/2.73 | (in(v6, all_49_4) = 0) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 =
% 14.35/2.73 | 0) & in(v5, v1) = v7))) & (v4 = 0 | ? [v5: $i] : ? [v6:
% 14.35/2.73 | $i] : (ordered_pair(v5, v3) = v6 & in(v6, all_49_4) = 0 &
% 14.35/2.73 | in(v5, v1) = 0 & $i(v6) & $i(v5))))) & ! [v0: $i] : ! [v1:
% 14.35/2.73 | $i] : ( ~ (relation_image(all_49_4, v0) = v1) | ~ $i(v1) | ~
% 14.35/2.73 | $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (in(v2, v1) =
% 14.35/2.73 | v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 14.35/2.73 | (ordered_pair(v4, v2) = v5) | ~ (in(v5, all_49_4) = 0) | ~
% 14.35/2.73 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & !
% 14.35/2.73 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 14.35/2.73 | [v4: $i] : (ordered_pair(v3, v2) = v4 & in(v4, all_49_4) = 0 &
% 14.35/2.73 | in(v3, v0) = 0 & $i(v4) & $i(v3)))))
% 14.35/2.73 |
% 14.35/2.73 | ALPHA: (21) implies:
% 14.35/2.73 | (22) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_image(all_49_4, v0) = v1) |
% 14.35/2.73 | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 14.35/2.73 | (in(v2, v1) = v3) | ~ $i(v2) | ! [v4: $i] : ! [v5: $i] : ( ~
% 14.35/2.73 | (ordered_pair(v4, v2) = v5) | ~ (in(v5, all_49_4) = 0) | ~
% 14.35/2.73 | $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6))) & !
% 14.35/2.73 | [v2: $i] : ( ~ (in(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ?
% 14.35/2.73 | [v4: $i] : (ordered_pair(v3, v2) = v4 & in(v4, all_49_4) = 0 &
% 14.35/2.73 | in(v3, v0) = 0 & $i(v4) & $i(v3)))))
% 14.35/2.73 |
% 14.35/2.73 | GROUND_INST: instantiating (1) with all_49_5, all_49_3, simplifying with (8),
% 14.35/2.73 | (10), (16) gives:
% 14.35/2.73 | (23) ! [v0: $i] : ( ~ (in(v0, all_49_5) = 0) | ~ $i(v0) | in(v0,
% 14.35/2.73 | all_49_3) = 0)
% 14.35/2.73 |
% 14.35/2.73 | GROUND_INST: instantiating (2) with all_49_5, all_49_1, all_49_0, simplifying
% 14.35/2.73 | with (8), (12), (17) gives:
% 14.35/2.73 | (24) all_49_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 14.35/2.73 | all_49_1) = v1 & in(v0, all_49_5) = 0 & $i(v0))
% 14.35/2.73 |
% 14.35/2.73 | GROUND_INST: instantiating (fc7_relat_1) with all_49_4, all_49_3, simplifying
% 14.35/2.73 | with (9), (18) gives:
% 14.35/2.73 | (25) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_49_3) = v2
% 14.35/2.73 | & empty(all_49_3) = v1 & empty(all_49_4) = v0 & ( ~ (v0 = 0) | (v2 =
% 14.35/2.73 | 0 & v1 = 0)))
% 14.35/2.73 |
% 14.35/2.73 | GROUND_INST: instantiating (fc5_relat_1) with all_49_4, all_49_3, simplifying
% 14.35/2.73 | with (9), (18) gives:
% 14.35/2.73 | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_49_4) = v1
% 14.35/2.73 | & empty(all_49_3) = v2 & empty(all_49_4) = v0 & ( ~ (v2 = 0) | ~
% 14.35/2.73 | (v1 = 0) | v0 = 0))
% 14.35/2.73 |
% 14.35/2.73 | GROUND_INST: instantiating (d4_relat_1) with all_49_4, all_49_3, simplifying
% 14.35/2.73 | with (9), (18) gives:
% 14.35/2.73 | (27) ? [v0: int] : ( ~ (v0 = 0) & relation(all_49_4) = v0) | ( ? [v0: any]
% 14.35/2.73 | : (v0 = all_49_3 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : (in(v1,
% 14.35/2.73 | v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i] : ! [v4: $i] :
% 14.35/2.73 | ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4, all_49_4) = 0) |
% 14.35/2.74 | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] : ? [v4: $i] :
% 14.35/2.74 | (ordered_pair(v1, v3) = v4 & in(v4, all_49_4) = 0 & $i(v4) &
% 14.35/2.74 | $i(v3))))) & ( ~ $i(all_49_3) | ( ! [v0: $i] : ! [v1: int]
% 14.35/2.74 | : (v1 = 0 | ~ (in(v0, all_49_3) = v1) | ~ $i(v0) | ! [v2: $i]
% 14.35/2.74 | : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3,
% 14.35/2.74 | all_49_4) = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0,
% 14.35/2.74 | all_49_3) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 14.35/2.74 | (ordered_pair(v0, v1) = v2 & in(v2, all_49_4) = 0 & $i(v2) &
% 14.35/2.74 | $i(v1))))))
% 14.35/2.74 |
% 14.35/2.74 | GROUND_INST: instantiating (22) with all_49_5, all_49_2, simplifying with (8),
% 14.35/2.74 | (11), (14) gives:
% 14.35/2.74 | (28) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_2) = v1) | ~
% 14.35/2.74 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3)
% 14.35/2.74 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 14.35/2.74 | 0) & in(v2, all_49_5) = v4))) & ! [v0: $i] : ( ~ (in(v0,
% 14.35/2.74 | all_49_2) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 14.35/2.74 | (ordered_pair(v1, v0) = v2 & in(v2, all_49_4) = 0 & in(v1, all_49_5)
% 14.35/2.74 | = 0 & $i(v2) & $i(v1)))
% 14.35/2.74 |
% 14.35/2.74 | ALPHA: (28) implies:
% 14.35/2.74 | (29) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_2) = v1) | ~
% 14.35/2.74 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v2, v0) = v3)
% 14.35/2.74 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 14.35/2.74 | 0) & in(v2, all_49_5) = v4)))
% 14.35/2.74 |
% 14.35/2.74 | GROUND_INST: instantiating (20) with all_49_2, all_49_1, simplifying with
% 14.35/2.74 | (11), (12), (15) gives:
% 14.35/2.74 | (30) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_1) = v1) | ~
% 14.35/2.74 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3)
% 14.35/2.74 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 14.35/2.74 | 0) & in(v2, all_49_2) = v4))) & ! [v0: $i] : ( ~ (in(v0,
% 14.35/2.74 | all_49_1) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 14.35/2.74 | (ordered_pair(v0, v1) = v2 & in(v2, all_49_4) = 0 & in(v1, all_49_2)
% 14.35/2.74 | = 0 & $i(v2) & $i(v1)))
% 14.35/2.74 |
% 14.35/2.74 | ALPHA: (30) implies:
% 14.35/2.74 | (31) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_1) = v1) | ~
% 14.35/2.74 | $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0, v2) = v3)
% 14.35/2.74 | | ~ (in(v3, all_49_4) = 0) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 =
% 14.35/2.74 | 0) & in(v2, all_49_2) = v4)))
% 14.35/2.74 |
% 14.35/2.74 | DELTA: instantiating (26) with fresh symbols all_78_0, all_78_1, all_78_2
% 14.35/2.74 | gives:
% 14.35/2.74 | (32) relation(all_49_4) = all_78_1 & empty(all_49_3) = all_78_0 &
% 14.35/2.74 | empty(all_49_4) = all_78_2 & ( ~ (all_78_0 = 0) | ~ (all_78_1 = 0) |
% 14.35/2.74 | all_78_2 = 0)
% 14.35/2.74 |
% 14.35/2.74 | ALPHA: (32) implies:
% 14.35/2.74 | (33) empty(all_49_3) = all_78_0
% 14.35/2.74 | (34) relation(all_49_4) = all_78_1
% 14.35/2.74 |
% 14.35/2.74 | DELTA: instantiating (25) with fresh symbols all_80_0, all_80_1, all_80_2
% 14.35/2.74 | gives:
% 14.35/2.74 | (35) relation(all_49_3) = all_80_0 & empty(all_49_3) = all_80_1 &
% 14.35/2.74 | empty(all_49_4) = all_80_2 & ( ~ (all_80_2 = 0) | (all_80_0 = 0 &
% 14.35/2.74 | all_80_1 = 0))
% 14.35/2.74 |
% 14.35/2.74 | ALPHA: (35) implies:
% 14.35/2.74 | (36) empty(all_49_3) = all_80_1
% 14.35/2.74 | (37) ~ (all_80_2 = 0) | (all_80_0 = 0 & all_80_1 = 0)
% 14.35/2.74 |
% 14.35/2.74 | BETA: splitting (24) gives:
% 14.35/2.74 |
% 14.35/2.74 | Case 1:
% 14.35/2.74 | |
% 14.35/2.74 | | (38) all_49_0 = 0
% 14.35/2.74 | |
% 14.35/2.74 | | REDUCE: (7), (38) imply:
% 14.35/2.74 | | (39) $false
% 14.35/2.75 | |
% 14.35/2.75 | | CLOSE: (39) is inconsistent.
% 14.35/2.75 | |
% 14.35/2.75 | Case 2:
% 14.35/2.75 | |
% 14.35/2.75 | | (40) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_49_1) = v1 &
% 14.35/2.75 | | in(v0, all_49_5) = 0 & $i(v0))
% 14.35/2.75 | |
% 14.35/2.75 | | DELTA: instantiating (40) with fresh symbols all_118_0, all_118_1 gives:
% 14.35/2.75 | | (41) ~ (all_118_0 = 0) & in(all_118_1, all_49_1) = all_118_0 &
% 14.35/2.75 | | in(all_118_1, all_49_5) = 0 & $i(all_118_1)
% 14.35/2.75 | |
% 14.35/2.75 | | ALPHA: (41) implies:
% 14.35/2.75 | | (42) ~ (all_118_0 = 0)
% 14.35/2.75 | | (43) $i(all_118_1)
% 14.35/2.75 | | (44) in(all_118_1, all_49_5) = 0
% 14.35/2.75 | | (45) in(all_118_1, all_49_1) = all_118_0
% 14.35/2.75 | |
% 14.35/2.75 | | GROUND_INST: instantiating (3) with all_78_0, all_80_1, all_49_3,
% 14.35/2.75 | | simplifying with (33), (36) gives:
% 14.35/2.75 | | (46) all_80_1 = all_78_0
% 14.35/2.75 | |
% 14.35/2.75 | | GROUND_INST: instantiating (4) with 0, all_78_1, all_49_4, simplifying with
% 14.35/2.75 | | (13), (34) gives:
% 14.35/2.75 | | (47) all_78_1 = 0
% 14.35/2.75 | |
% 14.35/2.75 | | BETA: splitting (27) gives:
% 14.35/2.75 | |
% 14.35/2.75 | | Case 1:
% 14.35/2.75 | | |
% 14.35/2.75 | | | (48) ? [v0: int] : ( ~ (v0 = 0) & relation(all_49_4) = v0)
% 14.35/2.75 | | |
% 14.35/2.75 | | | DELTA: instantiating (48) with fresh symbol all_127_0 gives:
% 14.35/2.75 | | | (49) ~ (all_127_0 = 0) & relation(all_49_4) = all_127_0
% 14.35/2.75 | | |
% 14.35/2.75 | | | ALPHA: (49) implies:
% 14.35/2.75 | | | (50) ~ (all_127_0 = 0)
% 14.35/2.75 | | | (51) relation(all_49_4) = all_127_0
% 14.35/2.75 | | |
% 14.35/2.75 | | | GROUND_INST: instantiating (4) with 0, all_127_0, all_49_4, simplifying
% 14.35/2.75 | | | with (13), (51) gives:
% 14.35/2.75 | | | (52) all_127_0 = 0
% 14.35/2.75 | | |
% 14.35/2.75 | | | REDUCE: (50), (52) imply:
% 14.35/2.75 | | | (53) $false
% 14.35/2.75 | | |
% 14.35/2.75 | | | CLOSE: (53) is inconsistent.
% 14.35/2.75 | | |
% 14.35/2.75 | | Case 2:
% 14.35/2.75 | | |
% 14.35/2.75 | | | (54) ? [v0: any] : (v0 = all_49_3 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 14.35/2.75 | | | any] : (in(v1, v0) = v2 & $i(v1) & ( ~ (v2 = 0) | ! [v3: $i]
% 14.35/2.75 | | | : ! [v4: $i] : ( ~ (ordered_pair(v1, v3) = v4) | ~ (in(v4,
% 14.35/2.75 | | | all_49_4) = 0) | ~ $i(v3))) & (v2 = 0 | ? [v3: $i] :
% 14.35/2.75 | | | ? [v4: $i] : (ordered_pair(v1, v3) = v4 & in(v4, all_49_4)
% 14.35/2.75 | | | = 0 & $i(v4) & $i(v3))))) & ( ~ $i(all_49_3) | ( ! [v0:
% 14.35/2.75 | | | $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_3) = v1) |
% 14.35/2.75 | | | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~ (ordered_pair(v0,
% 14.35/2.75 | | | v2) = v3) | ~ (in(v3, all_49_4) = 0) | ~ $i(v2))) &
% 14.35/2.75 | | | ! [v0: $i] : ( ~ (in(v0, all_49_3) = 0) | ~ $i(v0) | ? [v1:
% 14.35/2.75 | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 14.35/2.75 | | | all_49_4) = 0 & $i(v2) & $i(v1)))))
% 14.35/2.75 | | |
% 14.35/2.75 | | | ALPHA: (54) implies:
% 14.35/2.75 | | | (55) ~ $i(all_49_3) | ( ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 14.35/2.75 | | | (in(v0, all_49_3) = v1) | ~ $i(v0) | ! [v2: $i] : ! [v3:
% 14.35/2.75 | | | $i] : ( ~ (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_49_4)
% 14.35/2.75 | | | = 0) | ~ $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_49_3) =
% 14.35/2.75 | | | 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 14.35/2.75 | | | (ordered_pair(v0, v1) = v2 & in(v2, all_49_4) = 0 & $i(v2) &
% 14.35/2.75 | | | $i(v1))))
% 14.35/2.75 | | |
% 14.35/2.75 | | | BETA: splitting (55) gives:
% 14.35/2.75 | | |
% 14.35/2.75 | | | Case 1:
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | (56) ~ $i(all_49_3)
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | PRED_UNIFY: (10), (56) imply:
% 14.35/2.75 | | | | (57) $false
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | CLOSE: (57) is inconsistent.
% 14.35/2.75 | | | |
% 14.35/2.75 | | | Case 2:
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | (58) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (in(v0, all_49_3) =
% 14.35/2.75 | | | | v1) | ~ $i(v0) | ! [v2: $i] : ! [v3: $i] : ( ~
% 14.35/2.75 | | | | (ordered_pair(v0, v2) = v3) | ~ (in(v3, all_49_4) = 0) | ~
% 14.35/2.75 | | | | $i(v2))) & ! [v0: $i] : ( ~ (in(v0, all_49_3) = 0) | ~
% 14.35/2.75 | | | | $i(v0) | ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) =
% 14.35/2.75 | | | | v2 & in(v2, all_49_4) = 0 & $i(v2) & $i(v1)))
% 14.35/2.75 | | | |
% 14.35/2.75 | | | | ALPHA: (58) implies:
% 14.35/2.76 | | | | (59) ! [v0: $i] : ( ~ (in(v0, all_49_3) = 0) | ~ $i(v0) | ? [v1:
% 14.35/2.76 | | | | $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 & in(v2,
% 14.35/2.76 | | | | all_49_4) = 0 & $i(v2) & $i(v1)))
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | GROUND_INST: instantiating (23) with all_118_1, simplifying with (43),
% 14.35/2.76 | | | | (44) gives:
% 14.35/2.76 | | | | (60) in(all_118_1, all_49_3) = 0
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | GROUND_INST: instantiating (31) with all_118_1, all_118_0, simplifying
% 14.35/2.76 | | | | with (43), (45) gives:
% 14.35/2.76 | | | | (61) all_118_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 14.35/2.76 | | | | (ordered_pair(all_118_1, v0) = v1) | ~ (in(v1, all_49_4) = 0)
% 14.35/2.76 | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_49_2) =
% 14.35/2.76 | | | | v2))
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | BETA: splitting (61) gives:
% 14.35/2.76 | | | |
% 14.35/2.76 | | | | Case 1:
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | (62) all_118_0 = 0
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | REDUCE: (42), (62) imply:
% 14.35/2.76 | | | | | (63) $false
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | CLOSE: (63) is inconsistent.
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | Case 2:
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | (64) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(all_118_1, v0) =
% 14.35/2.76 | | | | | v1) | ~ (in(v1, all_49_4) = 0) | ~ $i(v0) | ? [v2: int]
% 14.35/2.76 | | | | | : ( ~ (v2 = 0) & in(v0, all_49_2) = v2))
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | GROUND_INST: instantiating (59) with all_118_1, simplifying with (43),
% 14.35/2.76 | | | | | (60) gives:
% 14.35/2.76 | | | | | (65) ? [v0: $i] : ? [v1: $i] : (ordered_pair(all_118_1, v0) = v1
% 14.35/2.76 | | | | | & in(v1, all_49_4) = 0 & $i(v1) & $i(v0))
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | GROUND_INST: instantiating (t7_boole) with all_118_1, all_49_3,
% 14.35/2.76 | | | | | simplifying with (10), (43), (60) gives:
% 14.35/2.76 | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & empty(all_49_3) = v0)
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | DELTA: instantiating (66) with fresh symbol all_162_0 gives:
% 14.35/2.76 | | | | | (67) ~ (all_162_0 = 0) & empty(all_49_3) = all_162_0
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | ALPHA: (67) implies:
% 14.35/2.76 | | | | | (68) ~ (all_162_0 = 0)
% 14.35/2.76 | | | | | (69) empty(all_49_3) = all_162_0
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | DELTA: instantiating (65) with fresh symbols all_164_0, all_164_1
% 14.35/2.76 | | | | | gives:
% 14.35/2.76 | | | | | (70) ordered_pair(all_118_1, all_164_1) = all_164_0 & in(all_164_0,
% 14.35/2.76 | | | | | all_49_4) = 0 & $i(all_164_0) & $i(all_164_1)
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | ALPHA: (70) implies:
% 14.35/2.76 | | | | | (71) $i(all_164_1)
% 14.35/2.76 | | | | | (72) in(all_164_0, all_49_4) = 0
% 14.35/2.76 | | | | | (73) ordered_pair(all_118_1, all_164_1) = all_164_0
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | GROUND_INST: instantiating (3) with all_78_0, all_162_0, all_49_3,
% 14.35/2.76 | | | | | simplifying with (33), (69) gives:
% 14.35/2.76 | | | | | (74) all_162_0 = all_78_0
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | REDUCE: (68), (74) imply:
% 14.35/2.76 | | | | | (75) ~ (all_78_0 = 0)
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | BETA: splitting (37) gives:
% 14.35/2.76 | | | | |
% 14.35/2.76 | | | | | Case 1:
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | | GROUND_INST: instantiating (64) with all_164_1, all_164_0,
% 14.35/2.76 | | | | | | simplifying with (71), (72), (73) gives:
% 14.35/2.76 | | | | | | (76) ? [v0: int] : ( ~ (v0 = 0) & in(all_164_1, all_49_2) = v0)
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | | DELTA: instantiating (76) with fresh symbol all_183_0 gives:
% 14.35/2.76 | | | | | | (77) ~ (all_183_0 = 0) & in(all_164_1, all_49_2) = all_183_0
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | | ALPHA: (77) implies:
% 14.35/2.76 | | | | | | (78) ~ (all_183_0 = 0)
% 14.35/2.76 | | | | | | (79) in(all_164_1, all_49_2) = all_183_0
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | | GROUND_INST: instantiating (29) with all_164_1, all_183_0,
% 14.35/2.76 | | | | | | simplifying with (71), (79) gives:
% 14.35/2.76 | | | | | | (80) all_183_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~
% 14.35/2.76 | | | | | | (ordered_pair(v0, all_164_1) = v1) | ~ (in(v1, all_49_4)
% 14.35/2.76 | | | | | | = 0) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0,
% 14.35/2.76 | | | | | | all_49_5) = v2))
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | | BETA: splitting (80) gives:
% 14.35/2.76 | | | | | |
% 14.35/2.76 | | | | | | Case 1:
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | (81) all_183_0 = 0
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | REDUCE: (78), (81) imply:
% 14.35/2.76 | | | | | | | (82) $false
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | CLOSE: (82) is inconsistent.
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | Case 2:
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | (83) ! [v0: $i] : ! [v1: $i] : ( ~ (ordered_pair(v0,
% 14.35/2.76 | | | | | | | all_164_1) = v1) | ~ (in(v1, all_49_4) = 0) | ~
% 14.35/2.76 | | | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, all_49_5)
% 14.35/2.76 | | | | | | | = v2))
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | GROUND_INST: instantiating (83) with all_118_1, all_164_0,
% 14.35/2.76 | | | | | | | simplifying with (43), (72), (73) gives:
% 14.35/2.76 | | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & in(all_118_1, all_49_5) =
% 14.35/2.76 | | | | | | | v0)
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | DELTA: instantiating (84) with fresh symbol all_199_0 gives:
% 14.35/2.76 | | | | | | | (85) ~ (all_199_0 = 0) & in(all_118_1, all_49_5) = all_199_0
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | ALPHA: (85) implies:
% 14.35/2.76 | | | | | | | (86) ~ (all_199_0 = 0)
% 14.35/2.76 | | | | | | | (87) in(all_118_1, all_49_5) = all_199_0
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | GROUND_INST: instantiating (5) with 0, all_199_0, all_49_5,
% 14.35/2.76 | | | | | | | all_118_1, simplifying with (44), (87) gives:
% 14.35/2.76 | | | | | | | (88) all_199_0 = 0
% 14.35/2.76 | | | | | | |
% 14.35/2.76 | | | | | | | REDUCE: (86), (88) imply:
% 14.35/2.77 | | | | | | | (89) $false
% 14.35/2.77 | | | | | | |
% 14.35/2.77 | | | | | | | CLOSE: (89) is inconsistent.
% 14.35/2.77 | | | | | | |
% 14.35/2.77 | | | | | | End of split
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | Case 2:
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | | (90) all_80_0 = 0 & all_80_1 = 0
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | | ALPHA: (90) implies:
% 14.35/2.77 | | | | | | (91) all_80_1 = 0
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | | COMBINE_EQS: (46), (91) imply:
% 14.35/2.77 | | | | | | (92) all_78_0 = 0
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | | SIMP: (92) implies:
% 14.35/2.77 | | | | | | (93) all_78_0 = 0
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | | REDUCE: (75), (93) imply:
% 14.35/2.77 | | | | | | (94) $false
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | | CLOSE: (94) is inconsistent.
% 14.35/2.77 | | | | | |
% 14.35/2.77 | | | | | End of split
% 14.35/2.77 | | | | |
% 14.35/2.77 | | | | End of split
% 14.35/2.77 | | | |
% 14.35/2.77 | | | End of split
% 14.35/2.77 | | |
% 14.35/2.77 | | End of split
% 14.35/2.77 | |
% 14.35/2.77 | End of split
% 14.35/2.77 |
% 14.35/2.77 End of proof
% 14.35/2.77 % SZS output end Proof for theBenchmark
% 14.35/2.77
% 14.35/2.77 2154ms
%------------------------------------------------------------------------------