TSTP Solution File: SEU290+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% 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 17:43:52 EDT 2023
% Result : Theorem 14.68s 2.76s
% Output : Proof 31.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU290+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 13:07:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.72/1.10 Prover 1: Preprocessing ...
% 2.72/1.10 Prover 4: Preprocessing ...
% 2.72/1.14 Prover 6: Preprocessing ...
% 2.72/1.14 Prover 0: Preprocessing ...
% 2.72/1.14 Prover 2: Preprocessing ...
% 2.72/1.14 Prover 5: Preprocessing ...
% 2.72/1.14 Prover 3: Preprocessing ...
% 6.09/1.62 Prover 1: Warning: ignoring some quantifiers
% 7.09/1.69 Prover 5: Proving ...
% 7.09/1.69 Prover 1: Constructing countermodel ...
% 7.09/1.73 Prover 6: Proving ...
% 7.09/1.73 Prover 3: Warning: ignoring some quantifiers
% 7.63/1.75 Prover 2: Proving ...
% 7.63/1.76 Prover 3: Constructing countermodel ...
% 8.38/1.86 Prover 4: Warning: ignoring some quantifiers
% 8.38/1.92 Prover 4: Constructing countermodel ...
% 8.96/1.96 Prover 0: Proving ...
% 9.99/2.24 Prover 3: gave up
% 9.99/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.90/2.31 Prover 7: Preprocessing ...
% 12.40/2.45 Prover 7: Warning: ignoring some quantifiers
% 13.06/2.48 Prover 7: Constructing countermodel ...
% 13.39/2.53 Prover 1: gave up
% 13.39/2.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.13/2.62 Prover 8: Preprocessing ...
% 14.68/2.72 Prover 7: gave up
% 14.68/2.74 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 14.68/2.76 Prover 0: proved (2121ms)
% 14.68/2.76
% 14.68/2.76 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.68/2.76
% 14.68/2.76 Prover 8: Warning: ignoring some quantifiers
% 14.68/2.77 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.68/2.77 Prover 5: stopped
% 14.68/2.77 Prover 6: stopped
% 15.32/2.78 Prover 2: stopped
% 15.32/2.78 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.32/2.78 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.37/2.78 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.37/2.78 Prover 9: Preprocessing ...
% 15.37/2.79 Prover 8: Constructing countermodel ...
% 15.37/2.82 Prover 10: Preprocessing ...
% 15.37/2.83 Prover 13: Preprocessing ...
% 15.37/2.84 Prover 16: Preprocessing ...
% 15.37/2.85 Prover 11: Preprocessing ...
% 15.92/2.91 Prover 10: Warning: ignoring some quantifiers
% 15.92/2.92 Prover 10: Constructing countermodel ...
% 16.41/2.96 Prover 16: Warning: ignoring some quantifiers
% 16.41/2.98 Prover 16: Constructing countermodel ...
% 16.41/2.99 Prover 13: Warning: ignoring some quantifiers
% 16.41/3.01 Prover 13: Constructing countermodel ...
% 17.15/3.06 Prover 10: gave up
% 17.15/3.06 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 17.15/3.08 Prover 11: Warning: ignoring some quantifiers
% 17.67/3.10 Prover 9: Warning: ignoring some quantifiers
% 17.67/3.10 Prover 11: Constructing countermodel ...
% 17.67/3.11 Prover 9: Constructing countermodel ...
% 17.67/3.14 Prover 9: stopped
% 17.67/3.16 Prover 19: Preprocessing ...
% 18.75/3.32 Prover 19: Warning: ignoring some quantifiers
% 19.48/3.33 Prover 19: Constructing countermodel ...
% 19.97/3.39 Prover 8: gave up
% 22.40/3.74 Prover 19: gave up
% 29.94/4.92 Prover 4: Found proof (size 155)
% 29.94/4.92 Prover 4: proved (4272ms)
% 29.94/4.92 Prover 11: stopped
% 29.94/4.92 Prover 13: stopped
% 29.94/4.92 Prover 16: stopped
% 29.94/4.93
% 29.94/4.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.94/4.93
% 29.94/4.93 % SZS output start Proof for theBenchmark
% 29.94/4.94 Assumptions after simplification:
% 29.94/4.94 ---------------------------------
% 29.94/4.94
% 29.94/4.94 (antisymmetry_r2_hidden)
% 30.68/4.96 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 30.68/4.96 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : (
% 30.68/4.96 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 30.68/4.96 in(v1, v0) = v2))
% 30.68/4.96
% 30.68/4.96 (cc1_relset_1)
% 30.68/4.96 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 30.68/4.96 (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) = v4) | ~ (element(v2,
% 30.68/4.96 v4) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation(v2) = 0)
% 30.68/4.96
% 30.68/4.96 (cc2_funct_1)
% 30.68/4.97 ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ? [v2:
% 30.68/4.97 any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 & function(v0) =
% 30.68/4.97 v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0)))
% 30.68/4.97 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 30.68/4.97 any] : ? [v3: any] : (one_to_one(v0) = v3 & function(v0) = v2 & empty(v0)
% 30.68/4.97 = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~
% 30.68/4.97 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ? [v3: any]
% 30.68/4.97 : (one_to_one(v0) = v3 & relation(v0) = v1 & empty(v0) = v2 & ( ~ (v2 = 0) |
% 30.68/4.97 ~ (v1 = 0) | v3 = 0))) & ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0)
% 30.68/4.97 | ? [v1: any] : ? [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 &
% 30.68/4.97 relation(v0) = v1 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 =
% 30.68/4.97 0)))
% 30.68/4.97
% 30.68/4.97 (d1_funct_2)
% 30.68/4.98 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 30.68/4.98 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 30.68/4.98 $i(v0) | ? [v4: any] : ? [v5: any] : (relation_of2_as_subset(v2, v0, v1) =
% 30.68/4.98 v4 & quasi_total(v2, v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v1 = empty_set) |
% 30.68/4.98 v0 = empty_set | (( ~ (v5 = 0) | v2 = empty_set) & ( ~ (v2 =
% 30.68/4.98 empty_set) | v5 = 0))) & ((v1 = empty_set & ~ (v0 =
% 30.68/4.98 empty_set)) | (( ~ (v5 = 0) | v3 = v0) & ( ~ (v3 = v0) | v5 =
% 30.68/4.98 0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 30.68/4.98 any] : ( ~ (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 30.68/4.98 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) =
% 30.68/4.98 v5 & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) | ((
% 30.68/4.98 ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 =
% 30.68/4.98 empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set
% 30.68/4.98 & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0) & ( ~ (v3 = 0) |
% 30.68/4.98 v5 = v0))))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 30.68/4.98 (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)
% 30.68/4.98 | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v4 &
% 30.68/4.98 quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 = empty_set) | v0 =
% 30.68/4.98 empty_set | (( ~ (v3 = 0) | v2 = empty_set) & ( ~ (v2 = empty_set) | v3
% 30.68/4.98 = 0))) & ((v1 = empty_set & ~ (v0 = empty_set)) | (( ~ (v4 = v0) |
% 30.68/4.98 v3 = 0) & ( ~ (v3 = 0) | v4 = v0)))))
% 30.68/4.98
% 30.68/4.98 (d5_funct_1)
% 31.20/4.99 ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) | ? [v2:
% 31.20/4.99 any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 & relation(v0)
% 31.20/4.99 = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~ (v2 = 0) | ( ! [v5:
% 31.20/4.99 $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (apply(v0, v7) = v5)
% 31.20/4.99 | ~ (in(v5, v1) = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v1) | ? [v8:
% 31.20/4.99 int] : ( ~ (v8 = 0) & in(v7, v4) = v8)) & ! [v5: $i] : ! [v6:
% 31.20/4.99 int] : ! [v7: $i] : (v6 = 0 | ~ (in(v7, v4) = 0) | ~ (in(v5, v1)
% 31.20/4.99 = v6) | ~ $i(v7) | ~ $i(v5) | ~ $i(v1) | ? [v8: $i] : ( ~ (v8
% 31.20/4.99 = v5) & apply(v0, v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~
% 31.20/4.99 (in(v5, v1) = 0) | ~ $i(v5) | ~ $i(v1) | ? [v6: $i] : (apply(v0,
% 31.20/4.99 v6) = v5 & in(v6, v4) = 0 & $i(v6))) & ? [v5: $i] : (v5 = v1 |
% 31.20/4.99 ~ $i(v5) | ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] :
% 31.20/4.99 ? [v10: $i] : (in(v6, v5) = v7 & $i(v8) & $i(v6) & ( ~ (v7 = 0) | (
% 31.20/4.99 ! [v11: $i] : ( ~ (apply(v0, v11) = v6) | ~ $i(v11) | ?
% 31.20/4.99 [v12: int] : ( ~ (v12 = 0) & in(v11, v4) = v12)) & ! [v11:
% 31.20/4.99 $i] : ( ~ (in(v11, v4) = 0) | ~ $i(v11) | ? [v12: $i] : (
% 31.20/4.99 ~ (v12 = v6) & apply(v0, v11) = v12 & $i(v12))))) & (v7 =
% 31.20/4.99 0 | (v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v4) =
% 31.20/4.99 0)))))))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0)
% 31.20/4.99 = v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: $i] :
% 31.20/4.99 (relation_rng(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & $i(v4) & (
% 31.20/4.99 ~ (v3 = 0) | ~ (v2 = 0) | ( ! [v5: $i] : ! [v6: int] : ! [v7: $i] :
% 31.20/4.99 (v6 = 0 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = v6) | ~ $i(v7) |
% 31.20/4.99 ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & in(v7, v1) = v8)) & !
% 31.20/4.99 [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (in(v7, v1) = 0)
% 31.20/4.99 | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) | ? [v8: $i] : ( ~
% 31.20/4.99 (v8 = v5) & apply(v0, v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~
% 31.20/4.99 (in(v5, v4) = 0) | ~ $i(v5) | ? [v6: $i] : (apply(v0, v6) = v5 &
% 31.20/4.99 in(v6, v1) = 0 & $i(v6))) & ? [v5: $i] : (v5 = v4 | ~ $i(v5) |
% 31.20/4.99 ? [v6: $i] : ? [v7: any] : ? [v8: $i] : ? [v9: int] : ? [v10:
% 31.20/4.99 $i] : (in(v6, v5) = v7 & $i(v8) & $i(v6) & ( ~ (v7 = 0) | ( !
% 31.20/4.99 [v11: $i] : ( ~ (apply(v0, v11) = v6) | ~ $i(v11) | ? [v12:
% 31.20/4.99 int] : ( ~ (v12 = 0) & in(v11, v1) = v12)) & ! [v11: $i]
% 31.20/4.99 : ( ~ (in(v11, v1) = 0) | ~ $i(v11) | ? [v12: $i] : ( ~ (v12
% 31.20/4.99 = v6) & apply(v0, v11) = v12 & $i(v12))))) & (v7 = 0 |
% 31.20/4.99 (v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8, v1) = 0))))))))
% 31.20/4.99 & ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 31.20/4.99 $i] : ? [v3: $i] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 &
% 31.20/4.99 function(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ( ! [v4: $i] : !
% 31.20/4.99 [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (apply(v0, v6) = v4) | ~
% 31.20/4.99 (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: int] : ( ~ (v7 =
% 31.20/4.99 0) & in(v6, v3) = v7)) & ! [v4: $i] : ! [v5: int] : ! [v6:
% 31.20/4.99 $i] : (v5 = 0 | ~ (in(v6, v3) = 0) | ~ (in(v4, v2) = v5) | ~
% 31.20/4.99 $i(v6) | ~ $i(v4) | ? [v7: $i] : ( ~ (v7 = v4) & apply(v0, v6) =
% 31.20/4.99 v7 & $i(v7))) & ! [v4: $i] : ( ~ (in(v4, v2) = 0) | ~ $i(v4) |
% 31.20/4.99 ? [v5: $i] : (apply(v0, v5) = v4 & in(v5, v3) = 0 & $i(v5))) & ?
% 31.20/4.99 [v4: $i] : (v4 = v2 | ~ $i(v4) | ? [v5: $i] : ? [v6: any] : ? [v7:
% 31.20/4.99 $i] : ? [v8: int] : ? [v9: $i] : (in(v5, v4) = v6 & $i(v7) &
% 31.20/4.99 $i(v5) & ( ~ (v6 = 0) | ( ! [v10: $i] : ( ~ (apply(v0, v10) = v5)
% 31.20/4.99 | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0) & in(v10, v3) =
% 31.20/4.99 v11)) & ! [v10: $i] : ( ~ (in(v10, v3) = 0) | ~ $i(v10)
% 31.20/4.99 | ? [v11: $i] : ( ~ (v11 = v5) & apply(v0, v10) = v11 &
% 31.20/4.99 $i(v11))))) & (v6 = 0 | (v9 = v5 & v8 = 0 & apply(v0, v7)
% 31.20/4.99 = v5 & in(v7, v3) = 0)))))))) & ! [v0: $i] : ( ~
% 31.20/4.99 (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : ? [v3: $i] :
% 31.20/4.99 (relation_rng(v0) = v2 & relation_dom(v0) = v3 & relation(v0) = v1 & $i(v3)
% 31.20/4.99 & $i(v2) & ( ~ (v1 = 0) | ( ! [v4: $i] : ! [v5: int] : ! [v6: $i] : (v5
% 31.20/4.99 = 0 | ~ (apply(v0, v6) = v4) | ~ (in(v4, v2) = v5) | ~ $i(v6) |
% 31.20/4.99 ~ $i(v4) | ? [v7: int] : ( ~ (v7 = 0) & in(v6, v3) = v7)) & ! [v4:
% 31.20/4.99 $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (in(v6, v3) = 0) |
% 31.20/4.99 ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7: $i] : ( ~ (v7
% 31.20/4.99 = v4) & apply(v0, v6) = v7 & $i(v7))) & ! [v4: $i] : ( ~
% 31.20/4.99 (in(v4, v2) = 0) | ~ $i(v4) | ? [v5: $i] : (apply(v0, v5) = v4 &
% 31.20/4.99 in(v5, v3) = 0 & $i(v5))) & ? [v4: $i] : (v4 = v2 | ~ $i(v4) |
% 31.20/4.99 ? [v5: $i] : ? [v6: any] : ? [v7: $i] : ? [v8: int] : ? [v9: $i]
% 31.20/4.99 : (in(v5, v4) = v6 & $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! [v10: $i]
% 31.20/4.99 : ( ~ (apply(v0, v10) = v5) | ~ $i(v10) | ? [v11: int] : ( ~
% 31.20/4.99 (v11 = 0) & in(v10, v3) = v11)) & ! [v10: $i] : ( ~
% 31.20/4.99 (in(v10, v3) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~ (v11 =
% 31.20/4.99 v5) & apply(v0, v10) = v11 & $i(v11))))) & (v6 = 0 | (v9
% 31.20/4.99 = v5 & v8 = 0 & apply(v0, v7) = v5 & in(v7, v3) = 0))))))))
% 31.20/4.99
% 31.20/4.99 (dt_k4_relset_1)
% 31.20/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 31.20/5.00 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 31.20/5.00 $i(v0) | ? [v4: any] : ? [v5: $i] : ? [v6: any] : (relation_of2(v2, v0,
% 31.20/5.00 v1) = v4 & powerset(v0) = v5 & element(v3, v5) = v6 & $i(v5) & ( ~ (v4 =
% 31.20/5.00 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 31.20/5.00 (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 31.20/5.00 $i] : ? [v4: $i] : (relation_dom_as_subset(v0, v1, v2) = v3 &
% 31.20/5.00 powerset(v0) = v4 & element(v3, v4) = 0 & $i(v4) & $i(v3)))
% 31.20/5.00
% 31.20/5.00 (dt_m2_relset_1)
% 31.20/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 31.20/5.00 int] : (v5 = 0 | ~ (cartesian_product2(v0, v1) = v3) | ~ (powerset(v3) =
% 31.20/5.00 v4) | ~ (element(v2, v4) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 31.20/5.00 [v6: int] : ( ~ (v6 = 0) & relation_of2_as_subset(v2, v0, v1) = v6)) & !
% 31.20/5.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0, v1)
% 31.20/5.00 = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 31.20/5.00 (cartesian_product2(v0, v1) = v3 & powerset(v3) = v4 & element(v2, v4) = 0 &
% 31.20/5.00 $i(v4) & $i(v3)))
% 31.20/5.00
% 31.20/5.00 (fc5_relat_1)
% 31.20/5.00 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 31.20/5.00 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_dom(v0) = v3 &
% 31.20/5.00 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 31.20/5.00 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~
% 31.20/5.00 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 31.20/5.00 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 31.20/5.00 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 31.20/5.00 : ? [v3: any] : (relation_dom(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 31.20/5.00 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 31.20/5.00
% 31.20/5.00 (fc6_relat_1)
% 31.20/5.00 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 31.20/5.00 [v2: any] : ? [v3: $i] : ? [v4: any] : (relation_rng(v0) = v3 &
% 31.20/5.00 relation(v0) = v2 & empty(v3) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v2 =
% 31.20/5.00 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~
% 31.20/5.00 $i(v0) | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 31.20/5.00 empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) &
% 31.20/5.00 ! [v0: $i] : ( ~ (relation(v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: $i]
% 31.20/5.00 : ? [v3: any] : (relation_rng(v0) = v2 & empty(v2) = v3 & empty(v0) = v1 &
% 31.20/5.00 $i(v2) & ( ~ (v3 = 0) | v1 = 0)))
% 31.20/5.00
% 31.20/5.00 (redefinition_k4_relset_1)
% 31.20/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 31.20/5.00 (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 31.20/5.00 $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_of2(v2, v0, v1) = v4 &
% 31.20/5.00 relation_dom(v2) = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))) & ! [v0: $i] :
% 31.20/5.00 ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~ $i(v2) |
% 31.20/5.00 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (relation_dom(v2) = v3 &
% 31.20/5.00 relation_dom_as_subset(v0, v1, v2) = v3 & $i(v3)))
% 31.20/5.00
% 31.20/5.00 (redefinition_m2_relset_1)
% 31.20/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 31.20/5.00 (relation_of2(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 31.20/5.00 [v4: int] : ( ~ (v4 = 0) & relation_of2_as_subset(v2, v0, v1) = v4)) & !
% 31.20/5.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 31.20/5.00 (relation_of2_as_subset(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 31.20/5.00 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & relation_of2(v2, v0, v1) = v4)) & !
% 31.20/5.00 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1) = 0) | ~
% 31.20/5.00 $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2_as_subset(v2, v0, v1) = 0) &
% 31.20/5.00 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2_as_subset(v2, v0,
% 31.20/5.00 v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | relation_of2(v2, v0, v1)
% 31.20/5.00 = 0)
% 31.20/5.00
% 31.20/5.00 (t2_subset)
% 31.20/5.01 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 31.20/5.01 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 31.20/5.01 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : ! [v1: $i] : (
% 31.20/5.01 ~ (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3:
% 31.20/5.01 any] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 31.20/5.01
% 31.20/5.01 (t6_funct_2)
% 31.20/5.01 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 31.20/5.01 [v4: $i] : ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v1 = empty_set) &
% 31.20/5.01 relation_rng(v3) = v5 & apply(v3, v2) = v4 & relation_of2_as_subset(v3, v0,
% 31.20/5.01 v1) = 0 & quasi_total(v3, v0, v1) = 0 & function(v3) = 0 & in(v4, v5) = v6
% 31.20/5.01 & in(v2, v0) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 31.20/5.01
% 31.20/5.01 (function-axioms)
% 31.20/5.01 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 31.20/5.01 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_of2(v4, v3, v2) = v1) | ~
% 31.20/5.01 (relation_of2(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 31.20/5.01 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2)
% 31.20/5.01 = v1) | ~ (relation_dom_as_subset(v4, v3, v2) = v0)) & ! [v0:
% 31.20/5.01 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 31.20/5.01 : ! [v4: $i] : (v1 = v0 | ~ (relation_of2_as_subset(v4, v3, v2) = v1) | ~
% 31.20/5.01 (relation_of2_as_subset(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 31.20/5.01 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 31.20/5.01 ~ (quasi_total(v4, v3, v2) = v1) | ~ (quasi_total(v4, v3, v2) = v0)) & !
% 31.20/5.01 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 31.20/5.01 $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & !
% 31.20/5.01 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3,
% 31.20/5.01 v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 31.20/5.01 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~
% 31.20/5.01 (cartesian_product2(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.20/5.01 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 31.20/5.01 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 31.20/5.01 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 31.20/5.01 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 31.20/5.01 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 31.20/5.01 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 31.20/5.01 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (relation_rng(v2) =
% 31.20/5.01 v1) | ~ (relation_rng(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 31.20/5.01 $i] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) &
% 31.20/5.01 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 =
% 31.20/5.01 v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0: $i] : !
% 31.20/5.01 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 31.20/5.01 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 31.20/5.01 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 31.20/5.01 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 31.20/5.01 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 31.20/5.01 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 31.20/5.01 ~ (empty(v2) = v0))
% 31.20/5.01
% 31.20/5.01 Further assumptions not needed in the proof:
% 31.20/5.01 --------------------------------------------
% 31.20/5.01 cc1_funct_1, cc1_relat_1, dt_k1_funct_1, dt_k1_relat_1, dt_k1_xboole_0,
% 31.20/5.01 dt_k1_zfmisc_1, dt_k2_relat_1, dt_k2_zfmisc_1, dt_m1_relset_1, dt_m1_subset_1,
% 31.20/5.01 existence_m1_relset_1, existence_m1_subset_1, existence_m2_relset_1,
% 31.20/5.01 fc12_relat_1, fc1_subset_1, fc1_xboole_0, fc4_relat_1, fc4_subset_1,
% 31.20/5.01 fc7_relat_1, fc8_relat_1, rc1_funct_1, rc1_funct_2, rc1_partfun1, rc1_relat_1,
% 31.20/5.01 rc1_subset_1, rc1_xboole_0, rc2_funct_1, rc2_partfun1, rc2_relat_1,
% 31.20/5.01 rc2_subset_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1,
% 31.20/5.01 reflexivity_r1_tarski, t1_subset, t3_subset, t4_subset, t5_subset, t6_boole,
% 31.20/5.01 t7_boole, t8_boole
% 31.20/5.01
% 31.20/5.01 Those formulas are unsatisfiable:
% 31.20/5.01 ---------------------------------
% 31.20/5.01
% 31.20/5.01 Begin of proof
% 31.20/5.01 |
% 31.20/5.01 | ALPHA: (antisymmetry_r2_hidden) implies:
% 31.20/5.01 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~
% 31.20/5.01 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 31.20/5.01 |
% 31.20/5.01 | ALPHA: (cc2_funct_1) implies:
% 31.20/5.02 | (2) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 31.20/5.02 | [v2: any] : ? [v3: any] : (one_to_one(v0) = v3 & relation(v0) = v1 &
% 31.20/5.02 | empty(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | v3 = 0)))
% 31.20/5.02 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (one_to_one(v0) = v1) | ~ $i(v0) | ?
% 31.20/5.02 | [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v2 &
% 31.20/5.02 | function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) |
% 31.20/5.02 | ~ (v2 = 0) | v1 = 0)))
% 31.20/5.02 |
% 31.20/5.02 | ALPHA: (d1_funct_2) implies:
% 31.20/5.02 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 31.20/5.02 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 31.20/5.02 | $i(v0) | ? [v3: any] : ? [v4: $i] : (relation_dom_as_subset(v0, v1,
% 31.20/5.02 | v2) = v4 & quasi_total(v2, v0, v1) = v3 & $i(v4) & ( ~ (v1 =
% 31.20/5.02 | empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 = empty_set) &
% 31.20/5.02 | ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 = empty_set & ~ (v0 =
% 31.20/5.02 | empty_set)) | (( ~ (v4 = v0) | v3 = 0) & ( ~ (v3 = 0) | v4 =
% 31.20/5.02 | v0)))))
% 31.20/5.02 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 31.20/5.02 | (quasi_total(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 31.20/5.02 | ? [v4: any] : ? [v5: $i] : (relation_dom_as_subset(v0, v1, v2) = v5
% 31.20/5.02 | & relation_of2_as_subset(v2, v0, v1) = v4 & $i(v5) & ( ~ (v4 = 0) |
% 31.20/5.02 | (( ~ (v1 = empty_set) | v0 = empty_set | (( ~ (v3 = 0) | v2 =
% 31.20/5.02 | empty_set) & ( ~ (v2 = empty_set) | v3 = 0))) & ((v1 =
% 31.20/5.02 | empty_set & ~ (v0 = empty_set)) | (( ~ (v5 = v0) | v3 = 0)
% 31.20/5.02 | & ( ~ (v3 = 0) | v5 = v0)))))))
% 31.20/5.02 |
% 31.20/5.02 | ALPHA: (d5_funct_1) implies:
% 31.20/5.02 | (6) ! [v0: $i] : ( ~ (function(v0) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 31.20/5.02 | [v2: $i] : ? [v3: $i] : (relation_rng(v0) = v2 & relation_dom(v0) =
% 31.20/5.02 | v3 & relation(v0) = v1 & $i(v3) & $i(v2) & ( ~ (v1 = 0) | ( ! [v4:
% 31.20/5.02 | $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (apply(v0,
% 31.20/5.02 | v6) = v4) | ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4)
% 31.20/5.02 | | ? [v7: int] : ( ~ (v7 = 0) & in(v6, v3) = v7)) & ! [v4:
% 31.20/5.02 | $i] : ! [v5: int] : ! [v6: $i] : (v5 = 0 | ~ (in(v6, v3) =
% 31.20/5.02 | 0) | ~ (in(v4, v2) = v5) | ~ $i(v6) | ~ $i(v4) | ? [v7:
% 31.20/5.02 | $i] : ( ~ (v7 = v4) & apply(v0, v6) = v7 & $i(v7))) & !
% 31.20/5.02 | [v4: $i] : ( ~ (in(v4, v2) = 0) | ~ $i(v4) | ? [v5: $i] :
% 31.20/5.02 | (apply(v0, v5) = v4 & in(v5, v3) = 0 & $i(v5))) & ? [v4: $i]
% 31.20/5.02 | : (v4 = v2 | ~ $i(v4) | ? [v5: $i] : ? [v6: any] : ? [v7:
% 31.20/5.02 | $i] : ? [v8: int] : ? [v9: $i] : (in(v5, v4) = v6 &
% 31.20/5.02 | $i(v7) & $i(v5) & ( ~ (v6 = 0) | ( ! [v10: $i] : ( ~
% 31.20/5.02 | (apply(v0, v10) = v5) | ~ $i(v10) | ? [v11: int] :
% 31.20/5.02 | ( ~ (v11 = 0) & in(v10, v3) = v11)) & ! [v10: $i] :
% 31.20/5.02 | ( ~ (in(v10, v3) = 0) | ~ $i(v10) | ? [v11: $i] : ( ~
% 31.20/5.02 | (v11 = v5) & apply(v0, v10) = v11 & $i(v11))))) &
% 31.20/5.02 | (v6 = 0 | (v9 = v5 & v8 = 0 & apply(v0, v7) = v5 & in(v7,
% 31.20/5.02 | v3) = 0))))))))
% 31.20/5.03 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 31.20/5.03 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (relation_rng(v0) = v4 &
% 31.20/5.03 | relation(v0) = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~
% 31.20/5.03 | (v2 = 0) | ( ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 |
% 31.20/5.03 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v4) = v6) | ~ $i(v7) |
% 31.20/5.03 | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) & in(v7, v1) = v8)) &
% 31.20/5.03 | ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 | ~ (in(v7,
% 31.20/5.03 | v1) = 0) | ~ (in(v5, v4) = v6) | ~ $i(v7) | ~ $i(v5) |
% 31.20/5.03 | ? [v8: $i] : ( ~ (v8 = v5) & apply(v0, v7) = v8 & $i(v8))) &
% 31.20/5.03 | ! [v5: $i] : ( ~ (in(v5, v4) = 0) | ~ $i(v5) | ? [v6: $i] :
% 31.20/5.03 | (apply(v0, v6) = v5 & in(v6, v1) = 0 & $i(v6))) & ? [v5: $i]
% 31.20/5.03 | : (v5 = v4 | ~ $i(v5) | ? [v6: $i] : ? [v7: any] : ? [v8:
% 31.20/5.03 | $i] : ? [v9: int] : ? [v10: $i] : (in(v6, v5) = v7 &
% 31.20/5.03 | $i(v8) & $i(v6) & ( ~ (v7 = 0) | ( ! [v11: $i] : ( ~
% 31.20/5.03 | (apply(v0, v11) = v6) | ~ $i(v11) | ? [v12: int] :
% 31.20/5.03 | ( ~ (v12 = 0) & in(v11, v1) = v12)) & ! [v11: $i] :
% 31.20/5.03 | ( ~ (in(v11, v1) = 0) | ~ $i(v11) | ? [v12: $i] : ( ~
% 31.20/5.03 | (v12 = v6) & apply(v0, v11) = v12 & $i(v12))))) &
% 31.20/5.03 | (v7 = 0 | (v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8,
% 31.20/5.03 | v1) = 0))))))))
% 31.20/5.03 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 31.20/5.03 | ? [v2: any] : ? [v3: any] : ? [v4: $i] : (relation_dom(v0) = v4 &
% 31.20/5.03 | relation(v0) = v2 & function(v0) = v3 & $i(v4) & ( ~ (v3 = 0) | ~
% 31.20/5.03 | (v2 = 0) | ( ! [v5: $i] : ! [v6: int] : ! [v7: $i] : (v6 = 0 |
% 31.20/5.03 | ~ (apply(v0, v7) = v5) | ~ (in(v5, v1) = v6) | ~ $i(v7) |
% 31.20/5.03 | ~ $i(v5) | ~ $i(v1) | ? [v8: int] : ( ~ (v8 = 0) & in(v7,
% 31.20/5.03 | v4) = v8)) & ! [v5: $i] : ! [v6: int] : ! [v7: $i] :
% 31.20/5.03 | (v6 = 0 | ~ (in(v7, v4) = 0) | ~ (in(v5, v1) = v6) | ~
% 31.20/5.03 | $i(v7) | ~ $i(v5) | ~ $i(v1) | ? [v8: $i] : ( ~ (v8 = v5)
% 31.20/5.03 | & apply(v0, v7) = v8 & $i(v8))) & ! [v5: $i] : ( ~ (in(v5,
% 31.20/5.03 | v1) = 0) | ~ $i(v5) | ~ $i(v1) | ? [v6: $i] :
% 31.20/5.03 | (apply(v0, v6) = v5 & in(v6, v4) = 0 & $i(v6))) & ? [v5: $i]
% 31.20/5.03 | : (v5 = v1 | ~ $i(v5) | ? [v6: $i] : ? [v7: any] : ? [v8:
% 31.20/5.03 | $i] : ? [v9: int] : ? [v10: $i] : (in(v6, v5) = v7 &
% 31.20/5.03 | $i(v8) & $i(v6) & ( ~ (v7 = 0) | ( ! [v11: $i] : ( ~
% 31.20/5.03 | (apply(v0, v11) = v6) | ~ $i(v11) | ? [v12: int] :
% 31.20/5.03 | ( ~ (v12 = 0) & in(v11, v4) = v12)) & ! [v11: $i] :
% 31.20/5.03 | ( ~ (in(v11, v4) = 0) | ~ $i(v11) | ? [v12: $i] : ( ~
% 31.20/5.03 | (v12 = v6) & apply(v0, v11) = v12 & $i(v12))))) &
% 31.20/5.03 | (v7 = 0 | (v10 = v6 & v9 = 0 & apply(v0, v8) = v6 & in(v8,
% 31.20/5.03 | v4) = 0))))))))
% 31.20/5.03 |
% 31.20/5.03 | ALPHA: (dt_k4_relset_1) implies:
% 31.20/5.03 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0, v1)
% 31.20/5.03 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 31.20/5.03 | $i] : (relation_dom_as_subset(v0, v1, v2) = v3 & powerset(v0) = v4
% 31.20/5.03 | & element(v3, v4) = 0 & $i(v4) & $i(v3)))
% 31.20/5.03 |
% 31.20/5.03 | ALPHA: (dt_m2_relset_1) implies:
% 31.20/5.03 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 31.20/5.03 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) |
% 31.20/5.03 | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (cartesian_product2(v0, v1) =
% 31.20/5.03 | v3 & powerset(v3) = v4 & element(v2, v4) = 0 & $i(v4) & $i(v3)))
% 31.20/5.03 |
% 31.20/5.03 | ALPHA: (fc5_relat_1) implies:
% 31.20/5.03 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_dom(v0) = v1) | ~ $i(v0) |
% 31.20/5.03 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 31.20/5.03 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2
% 31.20/5.03 | = 0)))
% 31.20/5.03 |
% 31.20/5.03 | ALPHA: (fc6_relat_1) implies:
% 31.20/5.03 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (relation_rng(v0) = v1) | ~ $i(v0) |
% 31.20/5.03 | ? [v2: any] : ? [v3: any] : ? [v4: any] : (relation(v0) = v3 &
% 31.20/5.03 | empty(v1) = v4 & empty(v0) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2
% 31.20/5.03 | = 0)))
% 31.20/5.03 |
% 31.20/5.03 | ALPHA: (redefinition_k4_relset_1) implies:
% 31.20/5.04 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_of2(v2, v0,
% 31.20/5.04 | v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 31.20/5.04 | (relation_dom(v2) = v3 & relation_dom_as_subset(v0, v1, v2) = v3 &
% 31.20/5.04 | $i(v3)))
% 31.20/5.04 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 31.20/5.04 | (relation_dom_as_subset(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) |
% 31.20/5.04 | ~ $i(v0) | ? [v4: any] : ? [v5: $i] : (relation_of2(v2, v0, v1) =
% 31.20/5.04 | v4 & relation_dom(v2) = v5 & $i(v5) & ( ~ (v4 = 0) | v5 = v3)))
% 31.20/5.04 |
% 31.20/5.04 | ALPHA: (redefinition_m2_relset_1) implies:
% 31.20/5.04 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 31.20/5.04 | (relation_of2_as_subset(v2, v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) |
% 31.20/5.04 | ~ $i(v0) | relation_of2(v2, v0, v1) = 0)
% 31.20/5.04 |
% 31.20/5.04 | ALPHA: (t2_subset) implies:
% 31.20/5.04 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 31.20/5.04 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 31.20/5.04 | (element(v0, v1) = v3 & empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 31.20/5.04 |
% 31.20/5.04 | ALPHA: (t6_funct_2) implies:
% 31.20/5.04 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 31.20/5.04 | ? [v5: $i] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v1 = empty_set) &
% 31.20/5.04 | relation_rng(v3) = v5 & apply(v3, v2) = v4 &
% 31.20/5.04 | relation_of2_as_subset(v3, v0, v1) = 0 & quasi_total(v3, v0, v1) = 0
% 31.20/5.04 | & function(v3) = 0 & in(v4, v5) = v6 & in(v2, v0) = 0 & $i(v5) &
% 31.20/5.04 | $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 31.20/5.04 |
% 31.20/5.04 | ALPHA: (function-axioms) implies:
% 31.20/5.04 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.20/5.04 | : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 31.20/5.04 | (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.20/5.04 | : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 31.20/5.04 | (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.20/5.04 | (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 31.20/5.04 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 31.20/5.04 | (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 31.20/5.04 | (22) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.20/5.04 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 31.20/5.04 | v0))
% 31.20/5.04 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 31.20/5.04 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (quasi_total(v4, v3, v2) =
% 31.20/5.04 | v1) | ~ (quasi_total(v4, v3, v2) = v0))
% 31.20/5.04 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 31.20/5.04 | (v1 = v0 | ~ (relation_dom_as_subset(v4, v3, v2) = v1) | ~
% 31.20/5.04 | (relation_dom_as_subset(v4, v3, v2) = v0))
% 31.20/5.04 |
% 31.20/5.04 | DELTA: instantiating (17) with fresh symbols all_57_0, all_57_1, all_57_2,
% 31.20/5.04 | all_57_3, all_57_4, all_57_5, all_57_6 gives:
% 31.20/5.04 | (25) ~ (all_57_0 = 0) & ~ (all_57_5 = empty_set) & relation_rng(all_57_3)
% 31.20/5.04 | = all_57_1 & apply(all_57_3, all_57_4) = all_57_2 &
% 31.20/5.04 | relation_of2_as_subset(all_57_3, all_57_6, all_57_5) = 0 &
% 31.20/5.04 | quasi_total(all_57_3, all_57_6, all_57_5) = 0 & function(all_57_3) = 0
% 31.20/5.04 | & in(all_57_2, all_57_1) = all_57_0 & in(all_57_4, all_57_6) = 0 &
% 31.20/5.04 | $i(all_57_1) & $i(all_57_2) & $i(all_57_3) & $i(all_57_4) &
% 31.20/5.04 | $i(all_57_5) & $i(all_57_6)
% 31.20/5.04 |
% 31.20/5.04 | ALPHA: (25) implies:
% 31.20/5.04 | (26) ~ (all_57_5 = empty_set)
% 31.20/5.04 | (27) ~ (all_57_0 = 0)
% 31.20/5.04 | (28) $i(all_57_6)
% 31.20/5.04 | (29) $i(all_57_5)
% 31.20/5.04 | (30) $i(all_57_4)
% 31.20/5.04 | (31) $i(all_57_3)
% 31.20/5.04 | (32) $i(all_57_2)
% 31.20/5.04 | (33) $i(all_57_1)
% 31.20/5.04 | (34) in(all_57_4, all_57_6) = 0
% 31.20/5.04 | (35) in(all_57_2, all_57_1) = all_57_0
% 31.20/5.04 | (36) function(all_57_3) = 0
% 31.20/5.04 | (37) quasi_total(all_57_3, all_57_6, all_57_5) = 0
% 31.20/5.04 | (38) relation_of2_as_subset(all_57_3, all_57_6, all_57_5) = 0
% 31.20/5.04 | (39) apply(all_57_3, all_57_4) = all_57_2
% 31.20/5.04 | (40) relation_rng(all_57_3) = all_57_1
% 31.20/5.04 |
% 31.20/5.04 | GROUND_INST: instantiating (1) with all_57_6, all_57_4, simplifying with (28),
% 31.20/5.04 | (30), (34) gives:
% 31.20/5.04 | (41) ? [v0: int] : ( ~ (v0 = 0) & in(all_57_6, all_57_4) = v0)
% 31.20/5.04 |
% 31.20/5.04 | GROUND_INST: instantiating (16) with all_57_2, all_57_1, all_57_0, simplifying
% 31.20/5.04 | with (32), (33), (35) gives:
% 31.20/5.05 | (42) all_57_0 = 0 | ? [v0: any] : ? [v1: any] : (element(all_57_2,
% 31.20/5.05 | all_57_1) = v0 & empty(all_57_1) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (6) with all_57_3, simplifying with (31), (36)
% 31.20/5.05 | gives:
% 31.20/5.05 | (43) ? [v0: any] : ? [v1: $i] : ? [v2: $i] : (relation_rng(all_57_3) =
% 31.20/5.05 | v1 & relation_dom(all_57_3) = v2 & relation(all_57_3) = v0 & $i(v2)
% 31.20/5.05 | & $i(v1) & ( ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : ! [v5: $i]
% 31.20/5.05 | : (v4 = 0 | ~ (apply(all_57_3, v5) = v3) | ~ (in(v3, v1) = v4)
% 31.20/5.05 | | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) & in(v5,
% 31.20/5.05 | v2) = v6)) & ! [v3: $i] : ! [v4: int] : ! [v5: $i] :
% 31.20/5.05 | (v4 = 0 | ~ (in(v5, v2) = 0) | ~ (in(v3, v1) = v4) | ~ $i(v5)
% 31.20/5.05 | | ~ $i(v3) | ? [v6: $i] : ( ~ (v6 = v3) & apply(all_57_3,
% 31.20/5.05 | v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ (in(v3, v1) = 0) |
% 31.20/5.05 | ~ $i(v3) | ? [v4: $i] : (apply(all_57_3, v4) = v3 & in(v4,
% 31.20/5.05 | v2) = 0 & $i(v4))) & ? [v3: $i] : (v3 = v1 | ~ $i(v3) |
% 31.20/5.05 | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: int] : ?
% 31.20/5.05 | [v8: $i] : (in(v4, v3) = v5 & $i(v6) & $i(v4) & ( ~ (v5 = 0) |
% 31.20/5.05 | ( ! [v9: $i] : ( ~ (apply(all_57_3, v9) = v4) | ~ $i(v9)
% 31.20/5.05 | | ? [v10: int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) &
% 31.20/5.05 | ! [v9: $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ?
% 31.20/5.05 | [v10: $i] : ( ~ (v10 = v4) & apply(all_57_3, v9) = v10
% 31.20/5.05 | & $i(v10))))) & (v5 = 0 | (v8 = v4 & v7 = 0 &
% 31.20/5.05 | apply(all_57_3, v6) = v4 & in(v6, v2) = 0)))))))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (2) with all_57_3, simplifying with (31), (36)
% 31.20/5.05 | gives:
% 31.20/5.05 | (44) ? [v0: any] : ? [v1: any] : ? [v2: any] : (one_to_one(all_57_3) =
% 31.20/5.05 | v2 & relation(all_57_3) = v0 & empty(all_57_3) = v1 & ( ~ (v1 = 0) |
% 31.20/5.05 | ~ (v0 = 0) | v2 = 0))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (5) with all_57_6, all_57_5, all_57_3, 0,
% 31.20/5.05 | simplifying with (28), (29), (31), (37) gives:
% 31.20/5.05 | (45) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_57_6,
% 31.20/5.05 | all_57_5, all_57_3) = v1 & relation_of2_as_subset(all_57_3,
% 31.20/5.05 | all_57_6, all_57_5) = v0 & $i(v1) & ( ~ (v0 = 0) | (( ~ (all_57_5
% 31.20/5.05 | = empty_set) | all_57_3 = empty_set | all_57_6 = empty_set)
% 31.20/5.05 | & (v1 = all_57_6 | (all_57_5 = empty_set & ~ (all_57_6 =
% 31.20/5.05 | empty_set))))))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (15) with all_57_6, all_57_5, all_57_3, simplifying
% 31.20/5.05 | with (28), (29), (31), (38) gives:
% 31.20/5.05 | (46) relation_of2(all_57_3, all_57_6, all_57_5) = 0
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (4) with all_57_6, all_57_5, all_57_3, simplifying
% 31.20/5.05 | with (28), (29), (31), (38) gives:
% 31.20/5.05 | (47) ? [v0: any] : ? [v1: $i] : (relation_dom_as_subset(all_57_6,
% 31.20/5.05 | all_57_5, all_57_3) = v1 & quasi_total(all_57_3, all_57_6,
% 31.20/5.05 | all_57_5) = v0 & $i(v1) & ( ~ (all_57_5 = empty_set) | all_57_6 =
% 31.20/5.05 | empty_set | (( ~ (v0 = 0) | all_57_3 = empty_set) & ( ~ (all_57_3
% 31.20/5.05 | = empty_set) | v0 = 0))) & ((all_57_5 = empty_set & ~
% 31.20/5.05 | (all_57_6 = empty_set)) | (( ~ (v1 = all_57_6) | v0 = 0) & ( ~
% 31.20/5.05 | (v0 = 0) | v1 = all_57_6))))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (10) with all_57_6, all_57_5, all_57_3, simplifying
% 31.20/5.05 | with (28), (29), (31), (38) gives:
% 31.20/5.05 | (48) ? [v0: $i] : ? [v1: $i] : (cartesian_product2(all_57_6, all_57_5) =
% 31.20/5.05 | v0 & powerset(v0) = v1 & element(all_57_3, v1) = 0 & $i(v1) &
% 31.20/5.05 | $i(v0))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (8) with all_57_3, all_57_1, simplifying with (31),
% 31.20/5.05 | (40) gives:
% 31.20/5.05 | (49) ? [v0: any] : ? [v1: any] : ? [v2: $i] : (relation_dom(all_57_3) =
% 31.20/5.05 | v2 & relation(all_57_3) = v0 & function(all_57_3) = v1 & $i(v2) & (
% 31.20/5.05 | ~ (v1 = 0) | ~ (v0 = 0) | ( ! [v3: $i] : ! [v4: int] : ! [v5:
% 31.20/5.05 | $i] : (v4 = 0 | ~ (apply(all_57_3, v5) = v3) | ~ (in(v3,
% 31.20/5.05 | all_57_1) = v4) | ~ $i(v5) | ~ $i(v3) | ~ $i(all_57_1)
% 31.20/5.05 | | ? [v6: int] : ( ~ (v6 = 0) & in(v5, v2) = v6)) & ! [v3:
% 31.20/5.05 | $i] : ! [v4: int] : ! [v5: $i] : (v4 = 0 | ~ (in(v5, v2) =
% 31.20/5.05 | 0) | ~ (in(v3, all_57_1) = v4) | ~ $i(v5) | ~ $i(v3) | ~
% 31.20/5.05 | $i(all_57_1) | ? [v6: $i] : ( ~ (v6 = v3) & apply(all_57_3,
% 31.20/5.05 | v5) = v6 & $i(v6))) & ! [v3: $i] : ( ~ (in(v3, all_57_1)
% 31.20/5.05 | = 0) | ~ $i(v3) | ~ $i(all_57_1) | ? [v4: $i] :
% 31.20/5.05 | (apply(all_57_3, v4) = v3 & in(v4, v2) = 0 & $i(v4))) & ?
% 31.20/5.05 | [v3: any] : (v3 = all_57_1 | ~ $i(v3) | ? [v4: $i] : ? [v5:
% 31.20/5.05 | any] : ? [v6: $i] : ? [v7: int] : ? [v8: $i] : (in(v4,
% 31.20/5.05 | v3) = v5 & $i(v6) & $i(v4) & ( ~ (v5 = 0) | ( ! [v9: $i] :
% 31.20/5.05 | ( ~ (apply(all_57_3, v9) = v4) | ~ $i(v9) | ? [v10:
% 31.20/5.05 | int] : ( ~ (v10 = 0) & in(v9, v2) = v10)) & ! [v9:
% 31.20/5.05 | $i] : ( ~ (in(v9, v2) = 0) | ~ $i(v9) | ? [v10: $i]
% 31.20/5.05 | : ( ~ (v10 = v4) & apply(all_57_3, v9) = v10 &
% 31.20/5.05 | $i(v10))))) & (v5 = 0 | (v8 = v4 & v7 = 0 &
% 31.20/5.05 | apply(all_57_3, v6) = v4 & in(v6, v2) = 0)))))))
% 31.20/5.05 |
% 31.20/5.05 | GROUND_INST: instantiating (12) with all_57_3, all_57_1, simplifying with
% 31.20/5.05 | (31), (40) gives:
% 31.20/5.05 | (50) ? [v0: any] : ? [v1: any] : ? [v2: any] : (relation(all_57_3) = v1
% 31.20/5.05 | & empty(all_57_1) = v2 & empty(all_57_3) = v0 & ( ~ (v2 = 0) | ~
% 31.20/5.05 | (v1 = 0) | v0 = 0))
% 31.20/5.05 |
% 31.20/5.05 | DELTA: instantiating (41) with fresh symbol all_65_0 gives:
% 31.20/5.05 | (51) ~ (all_65_0 = 0) & in(all_57_6, all_57_4) = all_65_0
% 31.20/5.05 |
% 31.20/5.05 | ALPHA: (51) implies:
% 31.20/5.05 | (52) ~ (all_65_0 = 0)
% 31.20/5.05 | (53) in(all_57_6, all_57_4) = all_65_0
% 31.20/5.05 |
% 31.20/5.05 | DELTA: instantiating (48) with fresh symbols all_101_0, all_101_1 gives:
% 31.20/5.05 | (54) cartesian_product2(all_57_6, all_57_5) = all_101_1 &
% 31.20/5.05 | powerset(all_101_1) = all_101_0 & element(all_57_3, all_101_0) = 0 &
% 31.20/5.05 | $i(all_101_0) & $i(all_101_1)
% 31.20/5.05 |
% 31.20/5.05 | ALPHA: (54) implies:
% 31.20/5.05 | (55) element(all_57_3, all_101_0) = 0
% 31.20/5.05 | (56) powerset(all_101_1) = all_101_0
% 31.20/5.05 | (57) cartesian_product2(all_57_6, all_57_5) = all_101_1
% 31.20/5.05 |
% 31.20/5.05 | DELTA: instantiating (44) with fresh symbols all_153_0, all_153_1, all_153_2
% 31.20/5.05 | gives:
% 31.20/5.06 | (58) one_to_one(all_57_3) = all_153_0 & relation(all_57_3) = all_153_2 &
% 31.20/5.06 | empty(all_57_3) = all_153_1 & ( ~ (all_153_1 = 0) | ~ (all_153_2 = 0)
% 31.20/5.06 | | all_153_0 = 0)
% 31.20/5.06 |
% 31.20/5.06 | ALPHA: (58) implies:
% 31.20/5.06 | (59) relation(all_57_3) = all_153_2
% 31.20/5.06 | (60) one_to_one(all_57_3) = all_153_0
% 31.20/5.06 |
% 31.20/5.06 | DELTA: instantiating (50) with fresh symbols all_171_0, all_171_1, all_171_2
% 31.20/5.06 | gives:
% 31.20/5.06 | (61) relation(all_57_3) = all_171_1 & empty(all_57_1) = all_171_0 &
% 31.20/5.06 | empty(all_57_3) = all_171_2 & ( ~ (all_171_0 = 0) | ~ (all_171_1 = 0)
% 31.20/5.06 | | all_171_2 = 0)
% 31.20/5.06 |
% 31.20/5.06 | ALPHA: (61) implies:
% 31.20/5.06 | (62) relation(all_57_3) = all_171_1
% 31.20/5.06 |
% 31.20/5.06 | DELTA: instantiating (45) with fresh symbols all_177_0, all_177_1 gives:
% 31.20/5.06 | (63) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) = all_177_0 &
% 31.20/5.06 | relation_of2_as_subset(all_57_3, all_57_6, all_57_5) = all_177_1 &
% 31.20/5.06 | $i(all_177_0) & ( ~ (all_177_1 = 0) | (( ~ (all_57_5 = empty_set) |
% 31.20/5.06 | all_57_3 = empty_set | all_57_6 = empty_set) & (all_177_0 =
% 31.20/5.06 | all_57_6 | (all_57_5 = empty_set & ~ (all_57_6 = empty_set)))))
% 31.20/5.06 |
% 31.20/5.06 | ALPHA: (63) implies:
% 31.20/5.06 | (64) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) = all_177_0
% 31.20/5.06 |
% 31.20/5.06 | DELTA: instantiating (47) with fresh symbols all_179_0, all_179_1 gives:
% 31.20/5.06 | (65) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) = all_179_0 &
% 31.20/5.06 | quasi_total(all_57_3, all_57_6, all_57_5) = all_179_1 & $i(all_179_0)
% 31.20/5.06 | & ( ~ (all_57_5 = empty_set) | all_57_6 = empty_set | (( ~ (all_179_1
% 31.20/5.06 | = 0) | all_57_3 = empty_set) & ( ~ (all_57_3 = empty_set) |
% 31.20/5.06 | all_179_1 = 0))) & ((all_57_5 = empty_set & ~ (all_57_6 =
% 31.20/5.06 | empty_set)) | (( ~ (all_179_0 = all_57_6) | all_179_1 = 0) & ( ~
% 31.20/5.06 | (all_179_1 = 0) | all_179_0 = all_57_6)))
% 31.20/5.06 |
% 31.20/5.06 | ALPHA: (65) implies:
% 31.20/5.06 | (66) $i(all_179_0)
% 31.20/5.06 | (67) quasi_total(all_57_3, all_57_6, all_57_5) = all_179_1
% 31.20/5.06 | (68) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) = all_179_0
% 31.20/5.06 | (69) (all_57_5 = empty_set & ~ (all_57_6 = empty_set)) | (( ~ (all_179_0 =
% 31.20/5.06 | all_57_6) | all_179_1 = 0) & ( ~ (all_179_1 = 0) | all_179_0 =
% 31.20/5.06 | all_57_6))
% 31.20/5.06 |
% 31.20/5.06 | DELTA: instantiating (43) with fresh symbols all_199_0, all_199_1, all_199_2
% 31.20/5.06 | gives:
% 31.61/5.06 | (70) relation_rng(all_57_3) = all_199_1 & relation_dom(all_57_3) =
% 31.61/5.06 | all_199_0 & relation(all_57_3) = all_199_2 & $i(all_199_0) &
% 31.61/5.06 | $i(all_199_1) & ( ~ (all_199_2 = 0) | ( ! [v0: $i] : ! [v1: int] : !
% 31.61/5.06 | [v2: $i] : (v1 = 0 | ~ (apply(all_57_3, v2) = v0) | ~ (in(v0,
% 31.61/5.06 | all_199_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : (
% 31.61/5.06 | ~ (v3 = 0) & in(v2, all_199_0) = v3)) & ! [v0: $i] : ! [v1:
% 31.61/5.06 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_199_0) = 0) | ~
% 31.61/5.06 | (in(v0, all_199_1) = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] :
% 31.61/5.06 | ( ~ (v3 = v0) & apply(all_57_3, v2) = v3 & $i(v3))) & ! [v0:
% 31.61/5.06 | $i] : ( ~ (in(v0, all_199_1) = 0) | ~ $i(v0) | ? [v1: $i] :
% 31.61/5.06 | (apply(all_57_3, v1) = v0 & in(v1, all_199_0) = 0 & $i(v1))) &
% 31.61/5.06 | ? [v0: any] : (v0 = all_199_1 | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 31.61/5.06 | any] : ? [v3: $i] : ? [v4: int] : ? [v5: $i] : (in(v1, v0)
% 31.61/5.06 | = v2 & $i(v3) & $i(v1) & ( ~ (v2 = 0) | ( ! [v6: $i] : ( ~
% 31.61/5.06 | (apply(all_57_3, v6) = v1) | ~ $i(v6) | ? [v7: int] :
% 31.61/5.06 | ( ~ (v7 = 0) & in(v6, all_199_0) = v7)) & ! [v6: $i] :
% 31.61/5.06 | ( ~ (in(v6, all_199_0) = 0) | ~ $i(v6) | ? [v7: $i] : (
% 31.61/5.06 | ~ (v7 = v1) & apply(all_57_3, v6) = v7 & $i(v7))))) &
% 31.61/5.06 | (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_57_3, v3) = v1 &
% 31.61/5.06 | in(v3, all_199_0) = 0))))))
% 31.61/5.06 |
% 31.61/5.06 | ALPHA: (70) implies:
% 31.61/5.06 | (71) relation(all_57_3) = all_199_2
% 31.61/5.06 | (72) relation_dom(all_57_3) = all_199_0
% 31.61/5.06 | (73) relation_rng(all_57_3) = all_199_1
% 31.61/5.06 |
% 31.61/5.06 | DELTA: instantiating (49) with fresh symbols all_211_0, all_211_1, all_211_2
% 31.61/5.06 | gives:
% 31.61/5.06 | (74) relation_dom(all_57_3) = all_211_0 & relation(all_57_3) = all_211_2 &
% 31.61/5.06 | function(all_57_3) = all_211_1 & $i(all_211_0) & ( ~ (all_211_1 = 0) |
% 31.61/5.06 | ~ (all_211_2 = 0) | ( ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1
% 31.61/5.06 | = 0 | ~ (apply(all_57_3, v2) = v0) | ~ (in(v0, all_57_1) = v1)
% 31.61/5.06 | | ~ $i(v2) | ~ $i(v0) | ~ $i(all_57_1) | ? [v3: int] : ( ~
% 31.61/5.06 | (v3 = 0) & in(v2, all_211_0) = v3)) & ! [v0: $i] : ! [v1:
% 31.61/5.06 | int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_211_0) = 0) | ~
% 31.61/5.06 | (in(v0, all_57_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 31.61/5.06 | $i(all_57_1) | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_57_3, v2)
% 31.61/5.06 | = v3 & $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_57_1) = 0) |
% 31.61/5.06 | ~ $i(v0) | ~ $i(all_57_1) | ? [v1: $i] : (apply(all_57_3, v1)
% 31.61/5.06 | = v0 & in(v1, all_211_0) = 0 & $i(v1))) & ? [v0: any] : (v0 =
% 31.61/5.06 | all_57_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i]
% 31.61/5.06 | : ? [v4: int] : ? [v5: $i] : (in(v1, v0) = v2 & $i(v3) &
% 31.61/5.06 | $i(v1) & ( ~ (v2 = 0) | ( ! [v6: $i] : ( ~ (apply(all_57_3,
% 31.61/5.06 | v6) = v1) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0)
% 31.61/5.06 | & in(v6, all_211_0) = v7)) & ! [v6: $i] : ( ~ (in(v6,
% 31.61/5.06 | all_211_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7
% 31.61/5.06 | = v1) & apply(all_57_3, v6) = v7 & $i(v7))))) & (v2
% 31.61/5.06 | = 0 | (v5 = v1 & v4 = 0 & apply(all_57_3, v3) = v1 & in(v3,
% 31.61/5.06 | all_211_0) = 0))))))
% 31.61/5.06 |
% 31.61/5.06 | ALPHA: (74) implies:
% 31.61/5.06 | (75) function(all_57_3) = all_211_1
% 31.61/5.06 | (76) relation(all_57_3) = all_211_2
% 31.61/5.06 | (77) relation_dom(all_57_3) = all_211_0
% 31.61/5.06 | (78) ~ (all_211_1 = 0) | ~ (all_211_2 = 0) | ( ! [v0: $i] : ! [v1: int]
% 31.61/5.06 | : ! [v2: $i] : (v1 = 0 | ~ (apply(all_57_3, v2) = v0) | ~ (in(v0,
% 31.61/5.06 | all_57_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~ $i(all_57_1) | ?
% 31.61/5.06 | [v3: int] : ( ~ (v3 = 0) & in(v2, all_211_0) = v3)) & ! [v0: $i]
% 31.61/5.06 | : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_211_0) = 0)
% 31.61/5.06 | | ~ (in(v0, all_57_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 31.61/5.06 | $i(all_57_1) | ? [v3: $i] : ( ~ (v3 = v0) & apply(all_57_3, v2) =
% 31.61/5.06 | v3 & $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_57_1) = 0) | ~
% 31.61/5.06 | $i(v0) | ~ $i(all_57_1) | ? [v1: $i] : (apply(all_57_3, v1) = v0
% 31.61/5.06 | & in(v1, all_211_0) = 0 & $i(v1))) & ? [v0: any] : (v0 =
% 31.61/5.06 | all_57_1 | ~ $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i] :
% 31.61/5.06 | ? [v4: int] : ? [v5: $i] : (in(v1, v0) = v2 & $i(v3) & $i(v1) & (
% 31.61/5.06 | ~ (v2 = 0) | ( ! [v6: $i] : ( ~ (apply(all_57_3, v6) = v1) |
% 31.61/5.06 | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & in(v6, all_211_0)
% 31.61/5.06 | = v7)) & ! [v6: $i] : ( ~ (in(v6, all_211_0) = 0) | ~
% 31.61/5.06 | $i(v6) | ? [v7: $i] : ( ~ (v7 = v1) & apply(all_57_3, v6)
% 31.61/5.06 | = v7 & $i(v7))))) & (v2 = 0 | (v5 = v1 & v4 = 0 &
% 31.61/5.06 | apply(all_57_3, v3) = v1 & in(v3, all_211_0) = 0)))))
% 31.61/5.06 |
% 31.61/5.06 | BETA: splitting (42) gives:
% 31.61/5.06 |
% 31.61/5.06 | Case 1:
% 31.61/5.06 | |
% 31.61/5.06 | | (79) all_57_0 = 0
% 31.61/5.06 | |
% 31.61/5.06 | | REDUCE: (27), (79) imply:
% 31.61/5.06 | | (80) $false
% 31.61/5.07 | |
% 31.61/5.07 | | CLOSE: (80) is inconsistent.
% 31.61/5.07 | |
% 31.61/5.07 | Case 2:
% 31.61/5.07 | |
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (18) with 0, all_211_1, all_57_3, simplifying
% 31.61/5.07 | | with (36), (75) gives:
% 31.61/5.07 | | (81) all_211_1 = 0
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (19) with all_171_1, all_199_2, all_57_3,
% 31.61/5.07 | | simplifying with (62), (71) gives:
% 31.61/5.07 | | (82) all_199_2 = all_171_1
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (19) with all_199_2, all_211_2, all_57_3,
% 31.61/5.07 | | simplifying with (71), (76) gives:
% 31.61/5.07 | | (83) all_211_2 = all_199_2
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (19) with all_153_2, all_211_2, all_57_3,
% 31.61/5.07 | | simplifying with (59), (76) gives:
% 31.61/5.07 | | (84) all_211_2 = all_153_2
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (23) with 0, all_179_1, all_57_5, all_57_6,
% 31.61/5.07 | | all_57_3, simplifying with (37), (67) gives:
% 31.61/5.07 | | (85) all_179_1 = 0
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (24) with all_177_0, all_179_0, all_57_3,
% 31.61/5.07 | | all_57_5, all_57_6, simplifying with (64), (68) gives:
% 31.61/5.07 | | (86) all_179_0 = all_177_0
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (20) with all_199_0, all_211_0, all_57_3,
% 31.61/5.07 | | simplifying with (72), (77) gives:
% 31.61/5.07 | | (87) all_211_0 = all_199_0
% 31.61/5.07 | |
% 31.61/5.07 | | GROUND_INST: instantiating (21) with all_57_1, all_199_1, all_57_3,
% 31.61/5.07 | | simplifying with (40), (73) gives:
% 31.61/5.07 | | (88) all_199_1 = all_57_1
% 31.61/5.07 | |
% 31.61/5.07 | | COMBINE_EQS: (83), (84) imply:
% 31.61/5.07 | | (89) all_199_2 = all_153_2
% 31.61/5.07 | |
% 31.61/5.07 | | SIMP: (89) implies:
% 31.61/5.07 | | (90) all_199_2 = all_153_2
% 31.61/5.07 | |
% 31.61/5.07 | | COMBINE_EQS: (82), (90) imply:
% 31.61/5.07 | | (91) all_171_1 = all_153_2
% 31.61/5.07 | |
% 31.61/5.07 | | SIMP: (91) implies:
% 31.61/5.07 | | (92) all_171_1 = all_153_2
% 31.61/5.07 | |
% 31.61/5.07 | | REDUCE: (66), (86) imply:
% 31.61/5.07 | | (93) $i(all_177_0)
% 31.61/5.07 | |
% 31.61/5.07 | | BETA: splitting (69) gives:
% 31.61/5.07 | |
% 31.61/5.07 | | Case 1:
% 31.61/5.07 | | |
% 31.61/5.07 | | | (94) all_57_5 = empty_set & ~ (all_57_6 = empty_set)
% 31.61/5.07 | | |
% 31.61/5.07 | | | ALPHA: (94) implies:
% 31.61/5.07 | | | (95) all_57_5 = empty_set
% 31.61/5.07 | | |
% 31.61/5.07 | | | REDUCE: (26), (95) imply:
% 31.61/5.07 | | | (96) $false
% 31.61/5.07 | | |
% 31.61/5.07 | | | CLOSE: (96) is inconsistent.
% 31.61/5.07 | | |
% 31.61/5.07 | | Case 2:
% 31.61/5.07 | | |
% 31.61/5.07 | | | (97) ( ~ (all_179_0 = all_57_6) | all_179_1 = 0) & ( ~ (all_179_1 = 0)
% 31.61/5.07 | | | | all_179_0 = all_57_6)
% 31.61/5.07 | | |
% 31.61/5.07 | | | ALPHA: (97) implies:
% 31.61/5.07 | | | (98) ~ (all_179_1 = 0) | all_179_0 = all_57_6
% 31.61/5.07 | | |
% 31.61/5.07 | | | BETA: splitting (98) gives:
% 31.61/5.07 | | |
% 31.61/5.07 | | | Case 1:
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | (99) ~ (all_179_1 = 0)
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | REDUCE: (85), (99) imply:
% 31.61/5.07 | | | | (100) $false
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | CLOSE: (100) is inconsistent.
% 31.61/5.07 | | | |
% 31.61/5.07 | | | Case 2:
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | (101) all_179_0 = all_57_6
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | COMBINE_EQS: (86), (101) imply:
% 31.61/5.07 | | | | (102) all_177_0 = all_57_6
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | SIMP: (102) implies:
% 31.61/5.07 | | | | (103) all_177_0 = all_57_6
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | REDUCE: (64), (103) imply:
% 31.61/5.07 | | | | (104) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) = all_57_6
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (16) with all_57_6, all_57_4, all_65_0,
% 31.61/5.07 | | | | simplifying with (28), (30), (53) gives:
% 31.61/5.07 | | | | (105) all_65_0 = 0 | ? [v0: any] : ? [v1: any] : (element(all_57_6,
% 31.61/5.07 | | | | all_57_4) = v0 & empty(all_57_4) = v1 & ( ~ (v0 = 0) | v1 =
% 31.61/5.07 | | | | 0))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (cc1_relset_1) with all_57_6, all_57_5,
% 31.61/5.07 | | | | all_57_3, all_101_1, all_101_0, simplifying with (28),
% 31.61/5.07 | | | | (29), (31), (55), (56), (57) gives:
% 31.61/5.07 | | | | (106) relation(all_57_3) = 0
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (3) with all_57_3, all_153_0, simplifying
% 31.61/5.07 | | | | with (31), (60) gives:
% 31.61/5.07 | | | | (107) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 31.61/5.07 | | | | (relation(all_57_3) = v0 & function(all_57_3) = v2 &
% 31.61/5.07 | | | | empty(all_57_3) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 31.61/5.07 | | | | 0) | all_153_0 = 0))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (14) with all_57_6, all_57_5, all_57_3,
% 31.61/5.07 | | | | all_57_6, simplifying with (28), (29), (31), (104) gives:
% 31.61/5.07 | | | | (108) ? [v0: any] : ? [v1: $i] : (relation_of2(all_57_3, all_57_6,
% 31.61/5.07 | | | | all_57_5) = v0 & relation_dom(all_57_3) = v1 & $i(v1) & ( ~
% 31.61/5.07 | | | | (v0 = 0) | v1 = all_57_6))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (7) with all_57_3, all_199_0, simplifying
% 31.61/5.07 | | | | with (31), (72) gives:
% 31.61/5.07 | | | | (109) ? [v0: any] : ? [v1: any] : ? [v2: $i] :
% 31.61/5.07 | | | | (relation_rng(all_57_3) = v2 & relation(all_57_3) = v0 &
% 31.61/5.07 | | | | function(all_57_3) = v1 & $i(v2) & ( ~ (v1 = 0) | ~ (v0 = 0)
% 31.61/5.07 | | | | | ( ! [v3: $i] : ! [v4: int] : ! [v5: $i] : (v4 = 0 | ~
% 31.61/5.07 | | | | (apply(all_57_3, v5) = v3) | ~ (in(v3, v2) = v4) | ~
% 31.61/5.07 | | | | $i(v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 = 0) &
% 31.61/5.07 | | | | in(v5, all_199_0) = v6)) & ! [v3: $i] : ! [v4: int]
% 31.61/5.07 | | | | : ! [v5: $i] : (v4 = 0 | ~ (in(v5, all_199_0) = 0) | ~
% 31.61/5.07 | | | | (in(v3, v2) = v4) | ~ $i(v5) | ~ $i(v3) | ? [v6: $i]
% 31.61/5.07 | | | | : ( ~ (v6 = v3) & apply(all_57_3, v5) = v6 & $i(v6))) &
% 31.61/5.07 | | | | ! [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3) | ? [v4:
% 31.61/5.07 | | | | $i] : (apply(all_57_3, v4) = v3 & in(v4, all_199_0) =
% 31.61/5.07 | | | | 0 & $i(v4))) & ? [v3: $i] : (v3 = v2 | ~ $i(v3) |
% 31.61/5.07 | | | | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: int]
% 31.61/5.07 | | | | : ? [v8: $i] : (in(v4, v3) = v5 & $i(v6) & $i(v4) & (
% 31.61/5.07 | | | | ~ (v5 = 0) | ( ! [v9: $i] : ( ~ (apply(all_57_3,
% 31.61/5.07 | | | | v9) = v4) | ~ $i(v9) | ? [v10: int] : ( ~
% 31.61/5.07 | | | | (v10 = 0) & in(v9, all_199_0) = v10)) & !
% 31.61/5.07 | | | | [v9: $i] : ( ~ (in(v9, all_199_0) = 0) | ~
% 31.61/5.07 | | | | $i(v9) | ? [v10: $i] : ( ~ (v10 = v4) &
% 31.61/5.07 | | | | apply(all_57_3, v9) = v10 & $i(v10))))) & (v5
% 31.61/5.07 | | | | = 0 | (v8 = v4 & v7 = 0 & apply(all_57_3, v6) = v4
% 31.61/5.07 | | | | & in(v6, all_199_0) = 0)))))))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (11) with all_57_3, all_199_0, simplifying
% 31.61/5.07 | | | | with (31), (72) gives:
% 31.61/5.07 | | | | (110) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 31.61/5.07 | | | | (relation(all_57_3) = v1 & empty(all_199_0) = v2 &
% 31.61/5.07 | | | | empty(all_57_3) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (9) with all_57_6, all_57_5, all_57_3,
% 31.61/5.07 | | | | simplifying with (28), (29), (31), (46) gives:
% 31.61/5.07 | | | | (111) ? [v0: $i] : ? [v1: $i] : (relation_dom_as_subset(all_57_6,
% 31.61/5.07 | | | | all_57_5, all_57_3) = v0 & powerset(all_57_6) = v1 &
% 31.61/5.07 | | | | element(v0, v1) = 0 & $i(v1) & $i(v0))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | GROUND_INST: instantiating (13) with all_57_6, all_57_5, all_57_3,
% 31.61/5.07 | | | | simplifying with (28), (29), (31), (46) gives:
% 31.61/5.07 | | | | (112) ? [v0: $i] : (relation_dom(all_57_3) = v0 &
% 31.61/5.07 | | | | relation_dom_as_subset(all_57_6, all_57_5, all_57_3) = v0 &
% 31.61/5.07 | | | | $i(v0))
% 31.61/5.07 | | | |
% 31.61/5.07 | | | | DELTA: instantiating (112) with fresh symbol all_359_0 gives:
% 31.61/5.08 | | | | (113) relation_dom(all_57_3) = all_359_0 &
% 31.61/5.08 | | | | relation_dom_as_subset(all_57_6, all_57_5, all_57_3) =
% 31.61/5.08 | | | | all_359_0 & $i(all_359_0)
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | ALPHA: (113) implies:
% 31.61/5.08 | | | | (114) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) =
% 31.61/5.08 | | | | all_359_0
% 31.61/5.08 | | | | (115) relation_dom(all_57_3) = all_359_0
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | DELTA: instantiating (108) with fresh symbols all_385_0, all_385_1
% 31.61/5.08 | | | | gives:
% 31.61/5.08 | | | | (116) relation_of2(all_57_3, all_57_6, all_57_5) = all_385_1 &
% 31.61/5.08 | | | | relation_dom(all_57_3) = all_385_0 & $i(all_385_0) & ( ~
% 31.61/5.08 | | | | (all_385_1 = 0) | all_385_0 = all_57_6)
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | ALPHA: (116) implies:
% 31.61/5.08 | | | | (117) relation_dom(all_57_3) = all_385_0
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | DELTA: instantiating (111) with fresh symbols all_387_0, all_387_1
% 31.61/5.08 | | | | gives:
% 31.61/5.08 | | | | (118) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) =
% 31.61/5.08 | | | | all_387_1 & powerset(all_57_6) = all_387_0 & element(all_387_1,
% 31.61/5.08 | | | | all_387_0) = 0 & $i(all_387_0) & $i(all_387_1)
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | ALPHA: (118) implies:
% 31.61/5.08 | | | | (119) relation_dom_as_subset(all_57_6, all_57_5, all_57_3) =
% 31.61/5.08 | | | | all_387_1
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | DELTA: instantiating (110) with fresh symbols all_453_0, all_453_1,
% 31.61/5.08 | | | | all_453_2 gives:
% 31.61/5.08 | | | | (120) relation(all_57_3) = all_453_1 & empty(all_199_0) = all_453_0 &
% 31.61/5.08 | | | | empty(all_57_3) = all_453_2 & ( ~ (all_453_0 = 0) | ~
% 31.61/5.08 | | | | (all_453_1 = 0) | all_453_2 = 0)
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | ALPHA: (120) implies:
% 31.61/5.08 | | | | (121) relation(all_57_3) = all_453_1
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | DELTA: instantiating (107) with fresh symbols all_457_0, all_457_1,
% 31.61/5.08 | | | | all_457_2 gives:
% 31.61/5.08 | | | | (122) relation(all_57_3) = all_457_2 & function(all_57_3) = all_457_0
% 31.61/5.08 | | | | & empty(all_57_3) = all_457_1 & ( ~ (all_457_0 = 0) | ~
% 31.61/5.08 | | | | (all_457_1 = 0) | ~ (all_457_2 = 0) | all_153_0 = 0)
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | ALPHA: (122) implies:
% 31.61/5.08 | | | | (123) function(all_57_3) = all_457_0
% 31.61/5.08 | | | | (124) relation(all_57_3) = all_457_2
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | DELTA: instantiating (109) with fresh symbols all_485_0, all_485_1,
% 31.61/5.08 | | | | all_485_2 gives:
% 31.61/5.08 | | | | (125) relation_rng(all_57_3) = all_485_0 & relation(all_57_3) =
% 31.61/5.08 | | | | all_485_2 & function(all_57_3) = all_485_1 & $i(all_485_0) & (
% 31.61/5.08 | | | | ~ (all_485_1 = 0) | ~ (all_485_2 = 0) | ( ! [v0: $i] : !
% 31.61/5.08 | | | | [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_57_3, v2)
% 31.61/5.08 | | | | = v0) | ~ (in(v0, all_485_0) = v1) | ~ $i(v2) | ~
% 31.61/5.08 | | | | $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & in(v2, all_199_0)
% 31.61/5.08 | | | | = v3)) & ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1
% 31.61/5.08 | | | | = 0 | ~ (in(v2, all_199_0) = 0) | ~ (in(v0, all_485_0)
% 31.61/5.08 | | | | = v1) | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 =
% 31.61/5.08 | | | | v0) & apply(all_57_3, v2) = v3 & $i(v3))) & ! [v0:
% 31.61/5.08 | | | | $i] : ( ~ (in(v0, all_485_0) = 0) | ~ $i(v0) | ? [v1:
% 31.61/5.08 | | | | $i] : (apply(all_57_3, v1) = v0 & in(v1, all_199_0) = 0
% 31.61/5.08 | | | | & $i(v1))) & ? [v0: any] : (v0 = all_485_0 | ~ $i(v0)
% 31.61/5.08 | | | | | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: int]
% 31.61/5.08 | | | | : ? [v5: $i] : (in(v1, v0) = v2 & $i(v3) & $i(v1) & ( ~
% 31.61/5.08 | | | | (v2 = 0) | ( ! [v6: $i] : ( ~ (apply(all_57_3, v6) =
% 31.61/5.08 | | | | v1) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) &
% 31.61/5.08 | | | | in(v6, all_199_0) = v7)) & ! [v6: $i] : ( ~
% 31.61/5.08 | | | | (in(v6, all_199_0) = 0) | ~ $i(v6) | ? [v7: $i]
% 31.61/5.08 | | | | : ( ~ (v7 = v1) & apply(all_57_3, v6) = v7 &
% 31.61/5.08 | | | | $i(v7))))) & (v2 = 0 | (v5 = v1 & v4 = 0 &
% 31.61/5.08 | | | | apply(all_57_3, v3) = v1 & in(v3, all_199_0) =
% 31.61/5.08 | | | | 0))))))
% 31.61/5.08 | | | |
% 31.61/5.08 | | | | ALPHA: (125) implies:
% 31.70/5.08 | | | | (126) $i(all_485_0)
% 31.70/5.08 | | | | (127) function(all_57_3) = all_485_1
% 31.70/5.08 | | | | (128) relation(all_57_3) = all_485_2
% 31.70/5.08 | | | | (129) relation_rng(all_57_3) = all_485_0
% 31.70/5.08 | | | | (130) ~ (all_485_1 = 0) | ~ (all_485_2 = 0) | ( ! [v0: $i] : !
% 31.70/5.08 | | | | [v1: int] : ! [v2: $i] : (v1 = 0 | ~ (apply(all_57_3, v2) =
% 31.70/5.08 | | | | v0) | ~ (in(v0, all_485_0) = v1) | ~ $i(v2) | ~ $i(v0)
% 31.70/5.08 | | | | | ? [v3: int] : ( ~ (v3 = 0) & in(v2, all_199_0) = v3)) &
% 31.70/5.08 | | | | ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~
% 31.70/5.08 | | | | (in(v2, all_199_0) = 0) | ~ (in(v0, all_485_0) = v1) | ~
% 31.70/5.08 | | | | $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v0) &
% 31.70/5.08 | | | | apply(all_57_3, v2) = v3 & $i(v3))) & ! [v0: $i] : ( ~
% 31.70/5.08 | | | | (in(v0, all_485_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 31.70/5.08 | | | | (apply(all_57_3, v1) = v0 & in(v1, all_199_0) = 0 &
% 31.70/5.08 | | | | $i(v1))) & ? [v0: any] : (v0 = all_485_0 | ~ $i(v0) |
% 31.70/5.08 | | | | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4: int] : ?
% 31.70/5.08 | | | | [v5: $i] : (in(v1, v0) = v2 & $i(v3) & $i(v1) & ( ~ (v2 =
% 31.70/5.08 | | | | 0) | ( ! [v6: $i] : ( ~ (apply(all_57_3, v6) = v1) |
% 31.70/5.08 | | | | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & in(v6,
% 31.70/5.08 | | | | all_199_0) = v7)) & ! [v6: $i] : ( ~ (in(v6,
% 31.70/5.08 | | | | all_199_0) = 0) | ~ $i(v6) | ? [v7: $i] : ( ~
% 31.70/5.08 | | | | (v7 = v1) & apply(all_57_3, v6) = v7 & $i(v7)))))
% 31.70/5.08 | | | | & (v2 = 0 | (v5 = v1 & v4 = 0 & apply(all_57_3, v3) = v1
% 31.70/5.08 | | | | & in(v3, all_199_0) = 0)))))
% 31.70/5.08 | | | |
% 31.70/5.08 | | | | BETA: splitting (105) gives:
% 31.70/5.08 | | | |
% 31.70/5.08 | | | | Case 1:
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | (131) all_65_0 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | REDUCE: (52), (131) imply:
% 31.70/5.08 | | | | | (132) $false
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | CLOSE: (132) is inconsistent.
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | Case 2:
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (18) with 0, all_485_1, all_57_3,
% 31.70/5.08 | | | | | simplifying with (36), (127) gives:
% 31.70/5.08 | | | | | (133) all_485_1 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (18) with all_457_0, all_485_1, all_57_3,
% 31.70/5.08 | | | | | simplifying with (123), (127) gives:
% 31.70/5.08 | | | | | (134) all_485_1 = all_457_0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (19) with all_453_1, all_457_2, all_57_3,
% 31.70/5.08 | | | | | simplifying with (121), (124) gives:
% 31.70/5.08 | | | | | (135) all_457_2 = all_453_1
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (19) with 0, all_457_2, all_57_3,
% 31.70/5.08 | | | | | simplifying with (106), (124) gives:
% 31.70/5.08 | | | | | (136) all_457_2 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (19) with all_153_2, all_485_2, all_57_3,
% 31.70/5.08 | | | | | simplifying with (59), (128) gives:
% 31.70/5.08 | | | | | (137) all_485_2 = all_153_2
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (19) with all_453_1, all_485_2, all_57_3,
% 31.70/5.08 | | | | | simplifying with (121), (128) gives:
% 31.70/5.08 | | | | | (138) all_485_2 = all_453_1
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (24) with all_57_6, all_387_1, all_57_3,
% 31.70/5.08 | | | | | all_57_5, all_57_6, simplifying with (104), (119) gives:
% 31.70/5.08 | | | | | (139) all_387_1 = all_57_6
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (24) with all_359_0, all_387_1, all_57_3,
% 31.70/5.08 | | | | | all_57_5, all_57_6, simplifying with (114), (119) gives:
% 31.70/5.08 | | | | | (140) all_387_1 = all_359_0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (20) with all_199_0, all_385_0, all_57_3,
% 31.70/5.08 | | | | | simplifying with (72), (117) gives:
% 31.70/5.08 | | | | | (141) all_385_0 = all_199_0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (20) with all_359_0, all_385_0, all_57_3,
% 31.70/5.08 | | | | | simplifying with (115), (117) gives:
% 31.70/5.08 | | | | | (142) all_385_0 = all_359_0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | GROUND_INST: instantiating (21) with all_57_1, all_485_0, all_57_3,
% 31.70/5.08 | | | | | simplifying with (40), (129) gives:
% 31.70/5.08 | | | | | (143) all_485_0 = all_57_1
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (133), (134) imply:
% 31.70/5.08 | | | | | (144) all_457_0 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (137), (138) imply:
% 31.70/5.08 | | | | | (145) all_453_1 = all_153_2
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | SIMP: (145) implies:
% 31.70/5.08 | | | | | (146) all_453_1 = all_153_2
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (135), (136) imply:
% 31.70/5.08 | | | | | (147) all_453_1 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | SIMP: (147) implies:
% 31.70/5.08 | | | | | (148) all_453_1 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (146), (148) imply:
% 31.70/5.08 | | | | | (149) all_153_2 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (139), (140) imply:
% 31.70/5.08 | | | | | (150) all_359_0 = all_57_6
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (141), (142) imply:
% 31.70/5.08 | | | | | (151) all_359_0 = all_199_0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | SIMP: (151) implies:
% 31.70/5.08 | | | | | (152) all_359_0 = all_199_0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (150), (152) imply:
% 31.70/5.08 | | | | | (153) all_199_0 = all_57_6
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (84), (149) imply:
% 31.70/5.08 | | | | | (154) all_211_2 = 0
% 31.70/5.08 | | | | |
% 31.70/5.08 | | | | | COMBINE_EQS: (87), (153) imply:
% 31.70/5.08 | | | | | (155) all_211_0 = all_57_6
% 31.70/5.08 | | | | |
% 31.70/5.09 | | | | | COMBINE_EQS: (137), (149) imply:
% 31.70/5.09 | | | | | (156) all_485_2 = 0
% 31.70/5.09 | | | | |
% 31.70/5.09 | | | | | BETA: splitting (130) gives:
% 31.70/5.09 | | | | |
% 31.70/5.09 | | | | | Case 1:
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | | (157) ~ (all_485_1 = 0)
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | | REDUCE: (133), (157) imply:
% 31.70/5.09 | | | | | | (158) $false
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | | CLOSE: (158) is inconsistent.
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | Case 2:
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | | (159) ~ (all_485_2 = 0) | ( ! [v0: $i] : ! [v1: int] : ! [v2:
% 31.70/5.09 | | | | | | $i] : (v1 = 0 | ~ (apply(all_57_3, v2) = v0) | ~
% 31.70/5.09 | | | | | | (in(v0, all_485_0) = v1) | ~ $i(v2) | ~ $i(v0) | ?
% 31.70/5.09 | | | | | | [v3: int] : ( ~ (v3 = 0) & in(v2, all_199_0) = v3)) &
% 31.70/5.09 | | | | | | ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~
% 31.70/5.09 | | | | | | (in(v2, all_199_0) = 0) | ~ (in(v0, all_485_0) = v1) |
% 31.70/5.09 | | | | | | ~ $i(v2) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v0) &
% 31.70/5.09 | | | | | | apply(all_57_3, v2) = v3 & $i(v3))) & ! [v0: $i] : (
% 31.70/5.09 | | | | | | ~ (in(v0, all_485_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 31.70/5.09 | | | | | | (apply(all_57_3, v1) = v0 & in(v1, all_199_0) = 0 &
% 31.70/5.09 | | | | | | $i(v1))) & ? [v0: any] : (v0 = all_485_0 | ~ $i(v0)
% 31.70/5.09 | | | | | | | ? [v1: $i] : ? [v2: any] : ? [v3: $i] : ? [v4:
% 31.70/5.09 | | | | | | int] : ? [v5: $i] : (in(v1, v0) = v2 & $i(v3) &
% 31.70/5.09 | | | | | | $i(v1) & ( ~ (v2 = 0) | ( ! [v6: $i] : ( ~
% 31.70/5.09 | | | | | | (apply(all_57_3, v6) = v1) | ~ $i(v6) | ?
% 31.70/5.09 | | | | | | [v7: int] : ( ~ (v7 = 0) & in(v6, all_199_0) =
% 31.70/5.09 | | | | | | v7)) & ! [v6: $i] : ( ~ (in(v6, all_199_0) =
% 31.70/5.09 | | | | | | 0) | ~ $i(v6) | ? [v7: $i] : ( ~ (v7 = v1)
% 31.70/5.09 | | | | | | & apply(all_57_3, v6) = v7 & $i(v7))))) & (v2
% 31.70/5.09 | | | | | | = 0 | (v5 = v1 & v4 = 0 & apply(all_57_3, v3) = v1
% 31.70/5.09 | | | | | | & in(v3, all_199_0) = 0)))))
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | | BETA: splitting (78) gives:
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | | Case 1:
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | | (160) ~ (all_211_1 = 0)
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | | REDUCE: (81), (160) imply:
% 31.70/5.09 | | | | | | | (161) $false
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | | CLOSE: (161) is inconsistent.
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | Case 2:
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | | (162) ~ (all_211_2 = 0) | ( ! [v0: $i] : ! [v1: int] : !
% 31.70/5.09 | | | | | | | [v2: $i] : (v1 = 0 | ~ (apply(all_57_3, v2) = v0) | ~
% 31.70/5.09 | | | | | | | (in(v0, all_57_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 31.70/5.09 | | | | | | | $i(all_57_1) | ? [v3: int] : ( ~ (v3 = 0) & in(v2,
% 31.70/5.09 | | | | | | | all_211_0) = v3)) & ! [v0: $i] : ! [v1: int] :
% 31.70/5.09 | | | | | | | ! [v2: $i] : (v1 = 0 | ~ (in(v2, all_211_0) = 0) | ~
% 31.70/5.09 | | | | | | | (in(v0, all_57_1) = v1) | ~ $i(v2) | ~ $i(v0) | ~
% 31.70/5.09 | | | | | | | $i(all_57_1) | ? [v3: $i] : ( ~ (v3 = v0) &
% 31.70/5.09 | | | | | | | apply(all_57_3, v2) = v3 & $i(v3))) & ! [v0: $i] :
% 31.70/5.09 | | | | | | | ( ~ (in(v0, all_57_1) = 0) | ~ $i(v0) | ~
% 31.70/5.09 | | | | | | | $i(all_57_1) | ? [v1: $i] : (apply(all_57_3, v1) =
% 31.70/5.09 | | | | | | | v0 & in(v1, all_211_0) = 0 & $i(v1))) & ? [v0:
% 31.70/5.09 | | | | | | | any] : (v0 = all_57_1 | ~ $i(v0) | ? [v1: $i] : ?
% 31.70/5.09 | | | | | | | [v2: any] : ? [v3: $i] : ? [v4: int] : ? [v5: $i]
% 31.70/5.09 | | | | | | | : (in(v1, v0) = v2 & $i(v3) & $i(v1) & ( ~ (v2 = 0) |
% 31.70/5.09 | | | | | | | ( ! [v6: $i] : ( ~ (apply(all_57_3, v6) = v1) |
% 31.70/5.09 | | | | | | | ~ $i(v6) | ? [v7: int] : ( ~ (v7 = 0) &
% 31.70/5.09 | | | | | | | in(v6, all_211_0) = v7)) & ! [v6: $i] : (
% 31.70/5.09 | | | | | | | ~ (in(v6, all_211_0) = 0) | ~ $i(v6) | ?
% 31.70/5.09 | | | | | | | [v7: $i] : ( ~ (v7 = v1) & apply(all_57_3,
% 31.70/5.09 | | | | | | | v6) = v7 & $i(v7))))) & (v2 = 0 | (v5 =
% 31.70/5.09 | | | | | | | v1 & v4 = 0 & apply(all_57_3, v3) = v1 & in(v3,
% 31.70/5.09 | | | | | | | all_211_0) = 0)))))
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | | BETA: splitting (162) gives:
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | | Case 1:
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | (163) ~ (all_211_2 = 0)
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | REDUCE: (154), (163) imply:
% 31.70/5.09 | | | | | | | | (164) $false
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | CLOSE: (164) is inconsistent.
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | Case 2:
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | (165) ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~
% 31.70/5.09 | | | | | | | | (apply(all_57_3, v2) = v0) | ~ (in(v0, all_57_1) =
% 31.70/5.09 | | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ~ $i(all_57_1) | ?
% 31.70/5.09 | | | | | | | | [v3: int] : ( ~ (v3 = 0) & in(v2, all_211_0) = v3)) &
% 31.70/5.09 | | | | | | | | ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~
% 31.70/5.09 | | | | | | | | (in(v2, all_211_0) = 0) | ~ (in(v0, all_57_1) = v1)
% 31.70/5.09 | | | | | | | | | ~ $i(v2) | ~ $i(v0) | ~ $i(all_57_1) | ? [v3:
% 31.70/5.09 | | | | | | | | $i] : ( ~ (v3 = v0) & apply(all_57_3, v2) = v3 &
% 31.70/5.09 | | | | | | | | $i(v3))) & ! [v0: $i] : ( ~ (in(v0, all_57_1) = 0)
% 31.70/5.09 | | | | | | | | | ~ $i(v0) | ~ $i(all_57_1) | ? [v1: $i] :
% 31.70/5.09 | | | | | | | | (apply(all_57_3, v1) = v0 & in(v1, all_211_0) = 0 &
% 31.70/5.09 | | | | | | | | $i(v1))) & ? [v0: any] : (v0 = all_57_1 | ~
% 31.70/5.09 | | | | | | | | $i(v0) | ? [v1: $i] : ? [v2: any] : ? [v3: $i] :
% 31.70/5.09 | | | | | | | | ? [v4: int] : ? [v5: $i] : (in(v1, v0) = v2 & $i(v3)
% 31.70/5.09 | | | | | | | | & $i(v1) & ( ~ (v2 = 0) | ( ! [v6: $i] : ( ~
% 31.70/5.09 | | | | | | | | (apply(all_57_3, v6) = v1) | ~ $i(v6) | ?
% 31.70/5.09 | | | | | | | | [v7: int] : ( ~ (v7 = 0) & in(v6, all_211_0)
% 31.70/5.09 | | | | | | | | = v7)) & ! [v6: $i] : ( ~ (in(v6,
% 31.70/5.09 | | | | | | | | all_211_0) = 0) | ~ $i(v6) | ? [v7: $i]
% 31.70/5.09 | | | | | | | | : ( ~ (v7 = v1) & apply(all_57_3, v6) = v7 &
% 31.70/5.09 | | | | | | | | $i(v7))))) & (v2 = 0 | (v5 = v1 & v4 = 0 &
% 31.70/5.09 | | | | | | | | apply(all_57_3, v3) = v1 & in(v3, all_211_0) =
% 31.70/5.09 | | | | | | | | 0))))
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | ALPHA: (165) implies:
% 31.70/5.09 | | | | | | | | (166) ! [v0: $i] : ! [v1: int] : ! [v2: $i] : (v1 = 0 | ~
% 31.70/5.09 | | | | | | | | (apply(all_57_3, v2) = v0) | ~ (in(v0, all_57_1) =
% 31.70/5.09 | | | | | | | | v1) | ~ $i(v2) | ~ $i(v0) | ~ $i(all_57_1) | ?
% 31.70/5.09 | | | | | | | | [v3: int] : ( ~ (v3 = 0) & in(v2, all_211_0) = v3))
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | GROUND_INST: instantiating (166) with all_57_2, all_57_0,
% 31.70/5.09 | | | | | | | | all_57_4, simplifying with (30), (32), (33), (35),
% 31.70/5.09 | | | | | | | | (39) gives:
% 31.70/5.09 | | | | | | | | (167) all_57_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 31.70/5.09 | | | | | | | | in(all_57_4, all_211_0) = v0)
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | BETA: splitting (167) gives:
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | | Case 1:
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | | (168) all_57_0 = 0
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | | REDUCE: (27), (168) imply:
% 31.70/5.09 | | | | | | | | | (169) $false
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | | CLOSE: (169) is inconsistent.
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | Case 2:
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | | (170) ? [v0: int] : ( ~ (v0 = 0) & in(all_57_4, all_211_0)
% 31.70/5.09 | | | | | | | | | = v0)
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | | BETA: splitting (159) gives:
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | | Case 1:
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | (171) ~ (all_485_2 = 0)
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | REDUCE: (156), (171) imply:
% 31.70/5.09 | | | | | | | | | | (172) $false
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | CLOSE: (172) is inconsistent.
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | Case 2:
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | DELTA: instantiating (170) with fresh symbol all_719_0
% 31.70/5.09 | | | | | | | | | | gives:
% 31.70/5.09 | | | | | | | | | | (173) ~ (all_719_0 = 0) & in(all_57_4, all_211_0) =
% 31.70/5.09 | | | | | | | | | | all_719_0
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | ALPHA: (173) implies:
% 31.70/5.09 | | | | | | | | | | (174) ~ (all_719_0 = 0)
% 31.70/5.09 | | | | | | | | | | (175) in(all_57_4, all_211_0) = all_719_0
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | REDUCE: (155), (175) imply:
% 31.70/5.09 | | | | | | | | | | (176) in(all_57_4, all_57_6) = all_719_0
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | GROUND_INST: instantiating (22) with 0, all_719_0, all_57_6,
% 31.70/5.09 | | | | | | | | | | all_57_4, simplifying with (34), (176) gives:
% 31.70/5.09 | | | | | | | | | | (177) all_719_0 = 0
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | REDUCE: (174), (177) imply:
% 31.70/5.09 | | | | | | | | | | (178) $false
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | | CLOSE: (178) is inconsistent.
% 31.70/5.09 | | | | | | | | | |
% 31.70/5.09 | | | | | | | | | End of split
% 31.70/5.09 | | | | | | | | |
% 31.70/5.09 | | | | | | | | End of split
% 31.70/5.09 | | | | | | | |
% 31.70/5.09 | | | | | | | End of split
% 31.70/5.09 | | | | | | |
% 31.70/5.09 | | | | | | End of split
% 31.70/5.09 | | | | | |
% 31.70/5.09 | | | | | End of split
% 31.70/5.09 | | | | |
% 31.70/5.09 | | | | End of split
% 31.70/5.09 | | | |
% 31.70/5.09 | | | End of split
% 31.70/5.09 | | |
% 31.70/5.09 | | End of split
% 31.70/5.09 | |
% 31.70/5.09 | End of split
% 31.70/5.09 |
% 31.70/5.09 End of proof
% 31.70/5.09 % SZS output end Proof for theBenchmark
% 31.70/5.09
% 31.70/5.09 4472ms
%------------------------------------------------------------------------------