TSTP Solution File: SEU234+3 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU234+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 : n022.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 17:43:32 EDT 2023
% Result : Theorem 142.12s 19.58s
% Output : Proof 144.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU234+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.31 % Computer : n022.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Wed Aug 23 16:34:41 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.61 ________ _____
% 0.16/0.61 ___ __ \_________(_)________________________________
% 0.16/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.61
% 0.16/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.61 (2023-06-19)
% 0.16/0.61
% 0.16/0.61 (c) Philipp Rümmer, 2009-2023
% 0.16/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.61 Amanda Stjerna.
% 0.16/0.61 Free software under BSD-3-Clause.
% 0.16/0.61
% 0.16/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.61
% 0.16/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.63 Running up to 7 provers in parallel.
% 0.16/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.16/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.11/1.23 Prover 4: Preprocessing ...
% 3.11/1.23 Prover 1: Preprocessing ...
% 3.29/1.30 Prover 5: Preprocessing ...
% 3.29/1.30 Prover 2: Preprocessing ...
% 3.29/1.30 Prover 6: Preprocessing ...
% 3.29/1.30 Prover 3: Preprocessing ...
% 3.29/1.30 Prover 0: Preprocessing ...
% 6.20/1.72 Prover 2: Proving ...
% 6.58/1.72 Prover 5: Proving ...
% 7.37/1.86 Prover 1: Warning: ignoring some quantifiers
% 7.72/1.91 Prover 1: Constructing countermodel ...
% 7.72/1.93 Prover 3: Warning: ignoring some quantifiers
% 8.16/1.95 Prover 3: Constructing countermodel ...
% 8.16/1.95 Prover 6: Proving ...
% 8.33/2.02 Prover 4: Warning: ignoring some quantifiers
% 8.68/2.05 Prover 4: Constructing countermodel ...
% 8.68/2.20 Prover 0: Proving ...
% 12.45/2.60 Prover 3: gave up
% 12.45/2.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.26/2.69 Prover 7: Preprocessing ...
% 13.95/2.77 Prover 7: Warning: ignoring some quantifiers
% 13.95/2.78 Prover 7: Constructing countermodel ...
% 16.33/3.09 Prover 1: gave up
% 16.33/3.11 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 17.05/3.20 Prover 8: Preprocessing ...
% 19.06/3.45 Prover 7: gave up
% 19.06/3.45 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 19.06/3.45 Prover 8: Warning: ignoring some quantifiers
% 19.30/3.51 Prover 8: Constructing countermodel ...
% 19.78/3.54 Prover 9: Preprocessing ...
% 22.10/3.88 Prover 9: Warning: ignoring some quantifiers
% 22.10/3.90 Prover 9: Constructing countermodel ...
% 23.85/4.11 Prover 8: gave up
% 24.23/4.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.38/4.17 Prover 10: Preprocessing ...
% 25.32/4.29 Prover 10: Warning: ignoring some quantifiers
% 25.32/4.29 Prover 10: Constructing countermodel ...
% 25.32/4.50 Prover 10: gave up
% 25.32/4.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 28.00/4.64 Prover 11: Preprocessing ...
% 30.33/4.96 Prover 11: Warning: ignoring some quantifiers
% 30.33/4.97 Prover 11: Constructing countermodel ...
% 56.81/8.48 Prover 2: stopped
% 56.81/8.49 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 57.67/8.55 Prover 12: Preprocessing ...
% 58.79/8.69 Prover 12: Proving ...
% 71.46/10.34 Prover 12: stopped
% 71.46/10.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 72.00/10.41 Prover 13: Preprocessing ...
% 72.00/10.46 Prover 13: Warning: ignoring some quantifiers
% 72.00/10.46 Prover 13: Constructing countermodel ...
% 73.89/10.63 Prover 13: gave up
% 73.89/10.63 Prover 14: Options: -triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=414236379
% 73.89/10.69 Prover 14: Preprocessing ...
% 75.15/10.82 Prover 14: Proving ...
% 99.35/13.98 Prover 5: stopped
% 99.35/13.99 Prover 15: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=723048181
% 99.73/14.05 Prover 15: Preprocessing ...
% 99.73/14.22 Prover 15: Proving ...
% 129.07/17.89 Prover 6: stopped
% 129.07/17.91 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 129.07/17.96 Prover 16: Preprocessing ...
% 129.85/17.99 Prover 16: Warning: ignoring some quantifiers
% 129.85/17.99 Prover 16: Constructing countermodel ...
% 132.43/18.42 Prover 16: gave up
% 132.43/18.42 Prover 17: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=642448422
% 133.51/18.45 Prover 17: Preprocessing ...
% 133.51/18.51 Prover 17: Proving ...
% 141.58/19.56 Prover 11: Found proof (size 8251)
% 141.58/19.56 Prover 11: proved (15011ms)
% 141.58/19.56 Prover 17: stopped
% 141.58/19.56 Prover 9: stopped
% 142.10/19.56 Prover 15: stopped
% 142.10/19.56 Prover 14: stopped
% 142.10/19.56 Prover 0: stopped
% 142.12/19.56 Prover 4: stopped
% 142.12/19.56
% 142.12/19.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 142.12/19.58
% 142.42/19.64 % SZS output start Proof for theBenchmark
% 142.42/19.65 Assumptions after simplification:
% 142.42/19.65 ---------------------------------
% 142.42/19.65
% 142.42/19.65 (antisymmetry_r2_hidden)
% 142.42/19.69 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 142.42/19.69 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : (
% 142.42/19.69 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 142.42/19.69 in(v1, v0) = v2))
% 142.42/19.69
% 142.42/19.69 (cc3_ordinal1)
% 142.42/19.70 ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) |
% 142.42/19.70 ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & v1 = 0 &
% 142.42/19.70 ordinal(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & empty(v0)
% 142.42/19.70 = v2))) & ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~
% 142.42/19.70 $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & v1
% 142.42/19.70 = 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~ (v2
% 142.42/19.70 = 0) & empty(v0) = v2))) & ! [v0: $i] : ! [v1: any] : ( ~
% 142.42/19.70 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ?
% 142.42/19.70 [v4: int] : ((v4 = 0 & v3 = 0 & v1 = 0 & epsilon_transitive(v0) = 0 &
% 142.42/19.70 ordinal(v0) = 0) | ( ~ (v2 = 0) & empty(v0) = v2))) & ! [v0: $i] : ( ~
% 142.42/19.70 (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0) = 0 & ordinal(v0) = 0
% 142.42/19.70 & epsilon_connected(v0) = 0))
% 142.42/19.70
% 142.42/19.70 (d2_ordinal1)
% 142.42/19.71 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v1, v0) = v2)
% 142.42/19.71 | ~ (epsilon_transitive(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : (
% 142.42/19.71 ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 142.42/19.71 (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~
% 142.42/19.71 (v3 = 0) & subset(v2, v0) = v3 & in(v2, v0) = 0 & $i(v2))) & ! [v0: $i] :
% 142.42/19.71 ! [v1: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ (in(v1, v0) = 0) | ~
% 142.42/19.71 $i(v1) | ~ $i(v0) | subset(v1, v0) = 0)
% 142.42/19.71
% 142.42/19.71 (d3_ordinal1)
% 142.42/19.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 = v1 |
% 142.42/19.72 ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 142.42/19.72 | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] : ((v6 = 0 & in(v1,
% 142.42/19.72 v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4 = 0) & in(v1, v0)
% 142.42/19.72 = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 142.42/19.72 0 | v2 = v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 142.42/19.72 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int]
% 142.42/19.72 : ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4 =
% 142.42/19.72 0) & in(v1, v0) = v4))) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~
% 142.42/19.72 (epsilon_connected(v0) = v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ?
% 142.42/19.72 [v4: int] : ? [v5: int] : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) &
% 142.42/19.72 in(v3, v2) = v5 & in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 &
% 142.42/19.72 $i(v3) & $i(v2)))
% 142.42/19.72
% 142.42/19.72 (d4_ordinal1)
% 142.42/19.72 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 142.42/19.72 [v2: int] : ? [v3: int] : (( ~ (v3 = 0) & epsilon_connected(v0) = v3) | ( ~
% 142.42/19.72 (v2 = 0) & epsilon_transitive(v0) = v2))) & ! [v0: $i] : ! [v1: any] :
% 142.42/19.72 ( ~ (epsilon_transitive(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] :
% 142.42/19.72 ((v3 = 0 & v1 = 0 & epsilon_connected(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0)
% 142.42/19.72 = v2))) & ! [v0: $i] : ! [v1: any] : ( ~ (epsilon_connected(v0) = v1)
% 142.42/19.72 | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 &
% 142.42/19.72 epsilon_transitive(v0) = 0) | ( ~ (v2 = 0) & ordinal(v0) = v2))) & !
% 142.42/19.72 [v0: $i] : ( ~ (epsilon_transitive(v0) = 0) | ~ $i(v0) | ? [v1: int] : ?
% 142.42/19.72 [v2: int] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) &
% 142.42/19.72 epsilon_connected(v0) = v1))) & ! [v0: $i] : ( ~ (ordinal(v0) = 0) | ~
% 142.42/19.72 $i(v0) | (epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0)) & ! [v0:
% 142.42/19.72 $i] : ( ~ (epsilon_connected(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2:
% 142.42/19.72 int] : ((v2 = 0 & ordinal(v0) = 0) | ( ~ (v1 = 0) & epsilon_transitive(v0)
% 142.42/19.72 = v1)))
% 142.42/19.72
% 142.42/19.72 (fc2_ordinal1)
% 142.42/19.73 relation_empty_yielding(empty_set) = 0 & one_to_one(empty_set) = 0 &
% 142.42/19.73 relation(empty_set) = 0 & epsilon_transitive(empty_set) = 0 &
% 142.42/19.73 ordinal(empty_set) = 0 & epsilon_connected(empty_set) = 0 &
% 142.42/19.73 function(empty_set) = 0 & empty(empty_set) = 0 & $i(empty_set)
% 142.42/19.73
% 142.42/19.73 (rc1_ordinal1)
% 142.42/19.73 ? [v0: $i] : (epsilon_transitive(v0) = 0 & ordinal(v0) = 0 &
% 142.42/19.73 epsilon_connected(v0) = 0 & $i(v0))
% 142.42/19.73
% 142.42/19.73 (rc1_relat_1)
% 142.42/19.73 ? [v0: $i] : (relation(v0) = 0 & empty(v0) = 0 & $i(v0))
% 142.42/19.73
% 142.42/19.73 (rc1_xboole_0)
% 142.42/19.73 ? [v0: $i] : (empty(v0) = 0 & $i(v0))
% 142.42/19.73
% 142.42/19.73 (rc2_funct_1)
% 142.42/19.73 ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & empty(v0) = 0 & $i(v0))
% 142.42/19.73
% 142.42/19.73 (rc2_ordinal1)
% 142.42/19.73 ? [v0: $i] : (one_to_one(v0) = 0 & relation(v0) = 0 & epsilon_transitive(v0)
% 142.42/19.73 = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0 & function(v0) = 0 &
% 142.42/19.73 empty(v0) = 0 & $i(v0))
% 142.42/19.73
% 142.42/19.73 (rc3_ordinal1)
% 142.85/19.73 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & epsilon_transitive(v0) = 0 &
% 142.85/19.73 ordinal(v0) = 0 & epsilon_connected(v0) = 0 & empty(v0) = v1 & $i(v0))
% 142.85/19.73
% 142.85/19.73 (t24_ordinal1)
% 142.85/19.73 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~ (ordinal(v0)
% 142.85/19.73 = 0) | ~ (in(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 142.85/19.73 [v4: int] : ((v4 = 0 & in(v0, v1) = 0) | ( ~ (v3 = 0) & ordinal(v1) = v3)))
% 142.85/19.73 & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 142.85/19.73 (ordinal(v0) = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 142.85/19.73 int] : ? [v4: int] : ((v4 = 0 & in(v1, v0) = 0) | ( ~ (v3 = 0) &
% 142.85/19.73 ordinal(v1) = v3))) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~
% 142.85/19.73 (ordinal(v1) = 0) | ~ (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 142.85/19.73 int] : ? [v3: int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) =
% 142.85/19.73 0)))
% 142.85/19.73
% 142.85/19.73 (t2_subset)
% 142.85/19.74 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 142.85/19.74 $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0 & empty(v1) = 0)
% 142.85/19.74 | ( ~ (v3 = 0) & element(v0, v1) = v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 142.85/19.74 (element(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int]
% 142.85/19.74 : ((v3 = 0 & in(v0, v1) = 0) | (v2 = 0 & empty(v1) = 0)))
% 142.85/19.74
% 142.85/19.74 (t31_ordinal1)
% 142.85/19.74 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & ordinal(v0) = v1 & $i(v0) & !
% 142.85/19.74 [v2: $i] : ! [v3: any] : ( ~ (subset(v2, v0) = v3) | ~ $i(v2) | ? [v4:
% 142.85/19.74 int] : ? [v5: int] : ((v5 = 0 & v3 = 0 & ordinal(v2) = 0) | ( ~ (v4 =
% 142.85/19.74 0) & in(v2, v0) = v4))) & ! [v2: $i] : ! [v3: any] : ( ~
% 142.85/19.74 (ordinal(v2) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5: int] : ((v5 = 0 &
% 142.85/19.74 v3 = 0 & subset(v2, v0) = 0) | ( ~ (v4 = 0) & in(v2, v0) = v4))) & !
% 142.85/19.74 [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | (subset(v2, v0) = 0 &
% 142.85/19.74 ordinal(v2) = 0)))
% 142.85/19.74
% 142.85/19.74 (t3_subset)
% 142.85/19.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 142.85/19.74 (powerset(v1) = v2) | ~ (element(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ?
% 142.85/19.74 [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i]
% 142.85/19.74 : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 142.85/19.74 ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & powerset(v1) = v3 & element(v0,
% 142.85/19.74 v3) = v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 142.85/19.74 (powerset(v1) = v2) | ~ (element(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 142.85/19.74 subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) |
% 142.85/19.74 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) =
% 142.85/19.74 0 & $i(v2)))
% 142.85/19.74
% 142.85/19.74 (t4_subset)
% 142.85/19.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 142.85/19.75 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) =
% 142.85/19.75 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 142.85/19.75 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 142.85/19.75 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 142.85/19.75 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 142.85/19.75 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : !
% 142.85/19.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~
% 142.85/19.75 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 142.85/19.75 $i(v0) | element(v0, v2) = 0)
% 142.85/19.75
% 142.85/19.75 (t6_boole)
% 142.85/19.75 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 142.85/19.75 $i(v0))
% 142.85/19.75
% 142.85/19.75 (t7_boole)
% 142.85/19.75 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 142.85/19.75 [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 142.85/19.75
% 142.85/19.75 (t8_boole)
% 142.85/19.75 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 142.85/19.75 | ~ $i(v1) | ~ $i(v0))
% 142.85/19.75
% 142.85/19.75 (function-axioms)
% 142.85/19.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 142.85/19.75 [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) &
% 142.85/19.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 142.85/19.75 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 142.85/19.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 142.85/19.75 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: $i]
% 142.85/19.75 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~
% 142.85/19.75 (powerset(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 142.85/19.75 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (relation_non_empty(v2) =
% 142.85/19.75 v1) | ~ (relation_non_empty(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 142.85/19.75 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 142.85/19.75 (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0))
% 142.85/19.75 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 142.85/19.75 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0:
% 142.85/19.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 142.85/19.76 ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0: MultipleValueBool]
% 142.85/19.76 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 142.85/19.76 (epsilon_transitive(v2) = v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0:
% 142.85/19.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 142.85/19.76 ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] :
% 142.85/19.76 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~
% 142.85/19.76 (epsilon_connected(v2) = v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0:
% 142.85/19.76 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 142.85/19.76 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 142.85/19.76 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) |
% 142.85/19.76 ~ (empty(v2) = v0))
% 142.85/19.76
% 142.85/19.76 Further assumptions not needed in the proof:
% 142.85/19.76 --------------------------------------------
% 142.85/19.76 cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, cc2_ordinal1,
% 142.85/19.76 existence_m1_subset_1, fc12_relat_1, fc1_xboole_0, fc4_relat_1, rc1_funct_1,
% 142.85/19.76 rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1, rc5_funct_1,
% 142.85/19.76 reflexivity_r1_tarski, t1_subset, t5_subset
% 142.85/19.76
% 142.85/19.76 Those formulas are unsatisfiable:
% 142.85/19.76 ---------------------------------
% 142.85/19.76
% 142.85/19.76 Begin of proof
% 142.85/19.76 |
% 142.85/19.76 | ALPHA: (antisymmetry_r2_hidden) implies:
% 142.85/19.76 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~
% 142.85/19.76 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 142.85/19.76 |
% 142.85/19.76 | ALPHA: (cc3_ordinal1) implies:
% 142.85/19.76 | (2) ! [v0: $i] : ( ~ (empty(v0) = 0) | ~ $i(v0) | (epsilon_transitive(v0)
% 142.85/19.76 | = 0 & ordinal(v0) = 0 & epsilon_connected(v0) = 0))
% 142.85/19.76 | (3) ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 142.85/19.76 | [v2: int] : ? [v3: int] : ? [v4: int] : ((v4 = 0 & v3 = 0 & v1 = 0
% 142.85/19.76 | & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0) | ( ~
% 142.85/19.76 | (v2 = 0) & empty(v0) = v2)))
% 142.85/19.76 |
% 142.85/19.76 | ALPHA: (d2_ordinal1) implies:
% 142.85/19.76 | (4) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 142.85/19.76 | | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 142.85/19.76 | v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 142.85/19.76 |
% 142.85/19.76 | ALPHA: (d3_ordinal1) implies:
% 142.85/19.77 | (5) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1)
% 142.85/19.77 | | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int]
% 142.85/19.77 | : ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 &
% 142.85/19.77 | in(v3, v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) &
% 142.85/19.77 | $i(v2)))
% 142.85/19.77 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 142.85/19.77 | v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~
% 142.85/19.77 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 142.85/19.77 | [v6: int] : ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 142.85/19.77 | v5) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 142.85/19.77 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 142.85/19.77 | v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~
% 142.85/19.77 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ?
% 142.85/19.77 | [v6: int] : ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 142.85/19.77 | v5) | ( ~ (v4 = 0) & in(v1, v0) = v4)))
% 142.85/19.77 |
% 142.85/19.77 | ALPHA: (d4_ordinal1) implies:
% 142.85/19.77 | (8) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (ordinal(v0) = v1) | ~
% 142.85/19.77 | $i(v0) | ? [v2: int] : ? [v3: int] : (( ~ (v3 = 0) &
% 142.85/19.77 | epsilon_connected(v0) = v3) | ( ~ (v2 = 0) &
% 142.85/19.77 | epsilon_transitive(v0) = v2)))
% 142.85/19.77 |
% 142.85/19.77 | ALPHA: (fc2_ordinal1) implies:
% 142.85/19.77 | (9) ordinal(empty_set) = 0
% 142.85/19.77 |
% 142.85/19.77 | ALPHA: (t24_ordinal1) implies:
% 142.85/19.77 | (10) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 142.85/19.77 | (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 142.85/19.77 | int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 142.85/19.77 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 142.85/19.77 | (ordinal(v0) = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) |
% 142.85/19.77 | ? [v3: int] : ? [v4: int] : ((v4 = 0 & in(v1, v0) = 0) | ( ~ (v3 =
% 142.85/19.77 | 0) & ordinal(v1) = v3)))
% 142.85/19.77 |
% 142.85/19.77 | ALPHA: (t2_subset) implies:
% 142.85/19.77 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~
% 142.85/19.77 | $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & in(v0, v1) = 0) |
% 142.85/19.77 | (v2 = 0 & empty(v1) = 0)))
% 142.85/19.77 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 142.85/19.77 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 =
% 142.85/19.78 | 0 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 142.85/19.78 |
% 142.85/19.78 | ALPHA: (t3_subset) implies:
% 142.85/19.78 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 142.85/19.78 | $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 142.85/19.78 | $i(v2)))
% 142.85/19.78 |
% 142.85/19.78 | ALPHA: (t4_subset) implies:
% 142.85/19.78 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 142.85/19.78 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 142.85/19.78 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0)
% 142.85/19.78 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 142.85/19.78 | (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1)
% 142.85/19.78 | | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 142.85/19.78 | powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4)))
% 142.85/19.78 | (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 142.85/19.78 | (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~
% 142.85/19.78 | (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 142.85/19.78 | int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 142.85/19.78 |
% 142.85/19.78 | ALPHA: (t6_boole) implies:
% 142.85/19.78 | (18) $i(empty_set)
% 142.85/19.78 | (19) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 142.85/19.78 |
% 142.85/19.78 | ALPHA: (function-axioms) implies:
% 142.85/19.78 | (20) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 142.85/19.78 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 142.85/19.78 | (21) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 142.85/19.78 | : (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 142.85/19.78 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2)
% 142.85/19.78 | = v1) | ~ (powerset(v2) = v0))
% 142.85/19.78 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 142.85/19.78 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 142.85/19.79 | v0))
% 142.85/19.79 | (24) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 142.85/19.79 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 142.85/19.79 | v2) = v0))
% 142.85/19.79 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 142.85/19.79 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 142.85/19.79 | v2) = v0))
% 142.85/19.79 |
% 142.85/19.79 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_24_0 gives:
% 142.85/19.79 | (26) empty(all_24_0) = 0 & $i(all_24_0)
% 142.85/19.79 |
% 142.85/19.79 | ALPHA: (26) implies:
% 142.85/19.79 | (27) $i(all_24_0)
% 142.85/19.79 | (28) empty(all_24_0) = 0
% 142.85/19.79 |
% 142.85/19.79 | DELTA: instantiating (rc1_relat_1) with fresh symbol all_27_0 gives:
% 142.85/19.79 | (29) relation(all_27_0) = 0 & empty(all_27_0) = 0 & $i(all_27_0)
% 142.85/19.79 |
% 142.85/19.79 | ALPHA: (29) implies:
% 142.85/19.79 | (30) $i(all_27_0)
% 142.85/19.79 | (31) empty(all_27_0) = 0
% 142.85/19.79 |
% 142.85/19.79 | DELTA: instantiating (rc2_funct_1) with fresh symbol all_35_0 gives:
% 142.85/19.79 | (32) relation(all_35_0) = 0 & function(all_35_0) = 0 & empty(all_35_0) = 0
% 142.85/19.79 | & $i(all_35_0)
% 142.85/19.79 |
% 142.85/19.79 | ALPHA: (32) implies:
% 142.85/19.79 | (33) $i(all_35_0)
% 142.85/19.79 | (34) empty(all_35_0) = 0
% 142.85/19.79 |
% 142.85/19.79 | DELTA: instantiating (rc1_ordinal1) with fresh symbol all_39_0 gives:
% 142.85/19.79 | (35) epsilon_transitive(all_39_0) = 0 & ordinal(all_39_0) = 0 &
% 142.85/19.79 | epsilon_connected(all_39_0) = 0 & $i(all_39_0)
% 142.85/19.79 |
% 142.85/19.79 | ALPHA: (35) implies:
% 142.85/19.79 | (36) $i(all_39_0)
% 142.85/19.79 | (37) epsilon_connected(all_39_0) = 0
% 142.85/19.79 | (38) ordinal(all_39_0) = 0
% 142.85/19.79 |
% 142.85/19.79 | DELTA: instantiating (rc3_ordinal1) with fresh symbols all_47_0, all_47_1
% 142.85/19.79 | gives:
% 142.85/19.79 | (39) ~ (all_47_0 = 0) & epsilon_transitive(all_47_1) = 0 &
% 142.85/19.79 | ordinal(all_47_1) = 0 & epsilon_connected(all_47_1) = 0 &
% 142.85/19.79 | empty(all_47_1) = all_47_0 & $i(all_47_1)
% 142.85/19.79 |
% 142.85/19.79 | ALPHA: (39) implies:
% 143.15/19.79 | (40) ~ (all_47_0 = 0)
% 143.15/19.79 | (41) $i(all_47_1)
% 143.15/19.79 | (42) empty(all_47_1) = all_47_0
% 143.15/19.79 | (43) epsilon_connected(all_47_1) = 0
% 143.15/19.79 | (44) ordinal(all_47_1) = 0
% 143.15/19.79 |
% 143.15/19.79 | DELTA: instantiating (rc2_ordinal1) with fresh symbol all_49_0 gives:
% 143.15/19.79 | (45) one_to_one(all_49_0) = 0 & relation(all_49_0) = 0 &
% 143.15/19.79 | epsilon_transitive(all_49_0) = 0 & ordinal(all_49_0) = 0 &
% 143.15/19.79 | epsilon_connected(all_49_0) = 0 & function(all_49_0) = 0 &
% 143.15/19.79 | empty(all_49_0) = 0 & $i(all_49_0)
% 143.15/19.79 |
% 143.15/19.79 | ALPHA: (45) implies:
% 143.15/19.79 | (46) $i(all_49_0)
% 143.15/19.79 | (47) empty(all_49_0) = 0
% 143.15/19.79 | (48) ordinal(all_49_0) = 0
% 143.15/19.79 |
% 143.15/19.79 | DELTA: instantiating (t31_ordinal1) with fresh symbols all_51_0, all_51_1
% 143.15/19.79 | gives:
% 143.15/19.80 | (49) ~ (all_51_0 = 0) & ordinal(all_51_1) = all_51_0 & $i(all_51_1) & !
% 143.15/19.80 | [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_51_1) = v1) | ~ $i(v0)
% 143.15/19.80 | | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 & ordinal(v0) = 0)
% 143.15/19.80 | | ( ~ (v2 = 0) & in(v0, all_51_1) = v2))) & ! [v0: $i] : ! [v1:
% 143.15/19.80 | any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 143.15/19.80 | int] : ((v3 = 0 & v1 = 0 & subset(v0, all_51_1) = 0) | ( ~ (v2 =
% 143.15/19.80 | 0) & in(v0, all_51_1) = v2))) & ! [v0: $i] : ( ~ (in(v0,
% 143.15/19.80 | all_51_1) = 0) | ~ $i(v0) | (subset(v0, all_51_1) = 0 &
% 143.15/19.80 | ordinal(v0) = 0))
% 143.15/19.80 |
% 143.15/19.80 | ALPHA: (49) implies:
% 143.15/19.80 | (50) ~ (all_51_0 = 0)
% 143.15/19.80 | (51) $i(all_51_1)
% 143.15/19.80 | (52) ordinal(all_51_1) = all_51_0
% 143.15/19.80 | (53) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 143.15/19.80 | all_51_1) = 0 & ordinal(v0) = 0))
% 143.15/19.80 | (54) ! [v0: $i] : ! [v1: any] : ( ~ (ordinal(v0) = v1) | ~ $i(v0) | ?
% 143.15/19.80 | [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 & subset(v0, all_51_1)
% 143.15/19.80 | = 0) | ( ~ (v2 = 0) & in(v0, all_51_1) = v2)))
% 143.15/19.80 | (55) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_51_1) = v1) | ~
% 143.15/19.80 | $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 &
% 143.15/19.80 | ordinal(v0) = 0) | ( ~ (v2 = 0) & in(v0, all_51_1) = v2)))
% 143.15/19.80 |
% 143.15/19.80 | GROUND_INST: instantiating (2) with all_24_0, simplifying with (27), (28)
% 143.15/19.80 | gives:
% 143.15/19.80 | (56) epsilon_transitive(all_24_0) = 0 & ordinal(all_24_0) = 0 &
% 143.15/19.80 | epsilon_connected(all_24_0) = 0
% 143.15/19.80 |
% 143.15/19.80 | ALPHA: (56) implies:
% 143.15/19.80 | (57) epsilon_connected(all_24_0) = 0
% 143.15/19.80 | (58) ordinal(all_24_0) = 0
% 143.15/19.80 |
% 143.15/19.80 | GROUND_INST: instantiating (t8_boole) with all_24_0, all_27_0, simplifying
% 143.15/19.80 | with (27), (28), (30), (31) gives:
% 143.15/19.81 | (59) all_27_0 = all_24_0
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (t8_boole) with all_27_0, all_35_0, simplifying
% 143.15/19.81 | with (30), (31), (33), (34) gives:
% 143.15/19.81 | (60) all_35_0 = all_27_0
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (t8_boole) with all_35_0, all_49_0, simplifying
% 143.15/19.81 | with (33), (34), (46), (47) gives:
% 143.15/19.81 | (61) all_49_0 = all_35_0
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (19) with all_49_0, simplifying with (46), (47)
% 143.15/19.81 | gives:
% 143.15/19.81 | (62) all_49_0 = empty_set
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (54) with empty_set, 0, simplifying with (9), (18)
% 143.15/19.81 | gives:
% 143.15/19.81 | (63) ? [v0: int] : ? [v1: int] : ((v1 = 0 & subset(empty_set, all_51_1) =
% 143.15/19.81 | 0) | ( ~ (v0 = 0) & in(empty_set, all_51_1) = v0))
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (10) with all_39_0, empty_set, simplifying with
% 143.15/19.81 | (9), (18), (36), (38) gives:
% 143.15/19.81 | (64) all_39_0 = empty_set | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.81 | in(empty_set, all_39_0) = 0) | (v0 = 0 & in(all_39_0, empty_set) =
% 143.15/19.81 | 0))
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (54) with all_39_0, 0, simplifying with (36), (38)
% 143.15/19.81 | gives:
% 143.15/19.81 | (65) ? [v0: int] : ? [v1: int] : ((v1 = 0 & subset(all_39_0, all_51_1) =
% 143.15/19.81 | 0) | ( ~ (v0 = 0) & in(all_39_0, all_51_1) = v0))
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (10) with all_39_0, all_47_1, simplifying with
% 143.15/19.81 | (36), (38), (41), (44) gives:
% 143.15/19.81 | (66) all_47_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.81 | in(all_47_1, all_39_0) = 0) | (v0 = 0 & in(all_39_0, all_47_1) =
% 143.15/19.81 | 0))
% 143.15/19.81 |
% 143.15/19.81 | GROUND_INST: instantiating (10) with all_47_1, all_39_0, simplifying with
% 143.15/19.81 | (36), (38), (41), (44) gives:
% 143.15/19.81 | (67) all_47_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.81 | in(all_39_0, all_47_1) = 0) | (v0 = 0 & in(all_47_1, all_39_0) =
% 143.15/19.81 | 0))
% 143.15/19.81 |
% 143.15/19.82 | GROUND_INST: instantiating (10) with all_47_1, empty_set, simplifying with
% 143.15/19.82 | (9), (18), (41), (44) gives:
% 143.15/19.82 | (68) all_47_1 = empty_set | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.82 | in(empty_set, all_47_1) = 0) | (v0 = 0 & in(all_47_1, empty_set) =
% 143.15/19.82 | 0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (54) with all_47_1, 0, simplifying with (41), (44)
% 143.15/19.82 | gives:
% 143.15/19.82 | (69) ? [v0: int] : ? [v1: int] : ((v1 = 0 & subset(all_47_1, all_51_1) =
% 143.15/19.82 | 0) | ( ~ (v0 = 0) & in(all_47_1, all_51_1) = v0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (10) with all_47_1, all_49_0, simplifying with
% 143.15/19.82 | (41), (44), (46), (48) gives:
% 143.15/19.82 | (70) all_49_0 = all_47_1 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.82 | in(all_49_0, all_47_1) = 0) | (v0 = 0 & in(all_47_1, all_49_0) =
% 143.15/19.82 | 0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (10) with all_39_0, all_49_0, simplifying with
% 143.15/19.82 | (36), (38), (46), (48) gives:
% 143.15/19.82 | (71) all_49_0 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.82 | in(all_49_0, all_39_0) = 0) | (v0 = 0 & in(all_39_0, all_49_0) =
% 143.15/19.82 | 0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (10) with all_49_0, all_39_0, simplifying with
% 143.15/19.82 | (36), (38), (46), (48) gives:
% 143.15/19.82 | (72) all_49_0 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.82 | in(all_39_0, all_49_0) = 0) | (v0 = 0 & in(all_49_0, all_39_0) =
% 143.15/19.82 | 0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (54) with all_49_0, 0, simplifying with (46), (48)
% 143.15/19.82 | gives:
% 143.15/19.82 | (73) ? [v0: int] : ? [v1: int] : ((v1 = 0 & subset(all_49_0, all_51_1) =
% 143.15/19.82 | 0) | ( ~ (v0 = 0) & in(all_49_0, all_51_1) = v0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (8) with all_51_1, all_51_0, simplifying with (51),
% 143.15/19.82 | (52) gives:
% 143.15/19.82 | (74) all_51_0 = 0 | ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 143.15/19.82 | epsilon_connected(all_51_1) = v1) | ( ~ (v0 = 0) &
% 143.15/19.82 | epsilon_transitive(all_51_1) = v0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (3) with all_51_1, all_51_0, simplifying with (51),
% 143.15/19.82 | (52) gives:
% 143.15/19.82 | (75) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & v1 = 0 &
% 143.15/19.82 | all_51_0 = 0 & epsilon_transitive(all_51_1) = 0 &
% 143.15/19.82 | epsilon_connected(all_51_1) = 0) | ( ~ (v0 = 0) & empty(all_51_1)
% 143.15/19.82 | = v0))
% 143.15/19.82 |
% 143.15/19.82 | GROUND_INST: instantiating (54) with all_51_1, all_51_0, simplifying with
% 143.15/19.82 | (51), (52) gives:
% 143.15/19.82 | (76) ? [v0: int] : ? [v1: int] : ((v1 = 0 & all_51_0 = 0 &
% 143.15/19.82 | subset(all_51_1, all_51_1) = 0) | ( ~ (v0 = 0) & in(all_51_1,
% 143.15/19.82 | all_51_1) = v0))
% 143.15/19.82 |
% 143.15/19.82 | COMBINE_EQS: (61), (62) imply:
% 143.15/19.82 | (77) all_35_0 = empty_set
% 143.15/19.82 |
% 143.15/19.82 | SIMP: (77) implies:
% 143.15/19.82 | (78) all_35_0 = empty_set
% 143.15/19.82 |
% 143.15/19.82 | COMBINE_EQS: (60), (78) imply:
% 143.15/19.82 | (79) all_27_0 = empty_set
% 143.15/19.82 |
% 143.15/19.82 | SIMP: (79) implies:
% 143.15/19.82 | (80) all_27_0 = empty_set
% 143.15/19.82 |
% 143.15/19.82 | COMBINE_EQS: (59), (80) imply:
% 143.15/19.82 | (81) all_24_0 = empty_set
% 143.15/19.82 |
% 143.15/19.82 | DELTA: instantiating (65) with fresh symbols all_60_0, all_60_1 gives:
% 143.15/19.82 | (82) (all_60_0 = 0 & subset(all_39_0, all_51_1) = 0) | ( ~ (all_60_1 = 0) &
% 143.15/19.82 | in(all_39_0, all_51_1) = all_60_1)
% 143.15/19.82 |
% 143.15/19.83 | DELTA: instantiating (63) with fresh symbols all_61_0, all_61_1 gives:
% 143.15/19.83 | (83) (all_61_0 = 0 & subset(empty_set, all_51_1) = 0) | ( ~ (all_61_1 = 0)
% 143.15/19.83 | & in(empty_set, all_51_1) = all_61_1)
% 143.15/19.83 |
% 143.15/19.83 | DELTA: instantiating (73) with fresh symbols all_62_0, all_62_1 gives:
% 143.15/19.83 | (84) (all_62_0 = 0 & subset(all_49_0, all_51_1) = 0) | ( ~ (all_62_1 = 0) &
% 143.15/19.83 | in(all_49_0, all_51_1) = all_62_1)
% 143.15/19.83 |
% 143.15/19.83 | DELTA: instantiating (69) with fresh symbols all_63_0, all_63_1 gives:
% 143.15/19.83 | (85) (all_63_0 = 0 & subset(all_47_1, all_51_1) = 0) | ( ~ (all_63_1 = 0) &
% 143.15/19.83 | in(all_47_1, all_51_1) = all_63_1)
% 143.15/19.83 |
% 143.15/19.83 | DELTA: instantiating (76) with fresh symbols all_64_0, all_64_1 gives:
% 143.15/19.83 | (86) (all_64_0 = 0 & all_51_0 = 0 & subset(all_51_1, all_51_1) = 0) | ( ~
% 143.15/19.83 | (all_64_1 = 0) & in(all_51_1, all_51_1) = all_64_1)
% 143.15/19.83 |
% 143.15/19.83 | DELTA: instantiating (75) with fresh symbols all_71_0, all_71_1, all_71_2
% 143.15/19.83 | gives:
% 143.15/19.83 | (87) (all_71_0 = 0 & all_71_1 = 0 & all_51_0 = 0 &
% 143.15/19.83 | epsilon_transitive(all_51_1) = 0 & epsilon_connected(all_51_1) = 0)
% 143.15/19.83 | | ( ~ (all_71_2 = 0) & empty(all_51_1) = all_71_2)
% 143.15/19.83 |
% 143.15/19.83 | REDUCE: (57), (81) imply:
% 143.15/19.83 | (88) epsilon_connected(empty_set) = 0
% 143.15/19.83 |
% 143.15/19.83 | REDUCE: (28), (81) imply:
% 143.15/19.83 | (89) empty(empty_set) = 0
% 143.15/19.83 |
% 143.15/19.83 | BETA: splitting (87) gives:
% 143.15/19.83 |
% 143.15/19.83 | Case 1:
% 143.15/19.83 | |
% 143.15/19.83 | | (90) all_71_0 = 0 & all_71_1 = 0 & all_51_0 = 0 &
% 143.15/19.83 | | epsilon_transitive(all_51_1) = 0 & epsilon_connected(all_51_1) = 0
% 143.15/19.83 | |
% 143.15/19.83 | | ALPHA: (90) implies:
% 143.15/19.83 | | (91) all_51_0 = 0
% 143.15/19.83 | |
% 143.15/19.83 | | REDUCE: (50), (91) imply:
% 143.15/19.83 | | (92) $false
% 143.15/19.83 | |
% 143.15/19.83 | | CLOSE: (92) is inconsistent.
% 143.15/19.83 | |
% 143.15/19.83 | Case 2:
% 143.15/19.83 | |
% 143.15/19.83 | | (93) ~ (all_71_2 = 0) & empty(all_51_1) = all_71_2
% 143.15/19.83 | |
% 143.15/19.83 | | ALPHA: (93) implies:
% 143.15/19.83 | | (94) ~ (all_71_2 = 0)
% 143.15/19.83 | | (95) empty(all_51_1) = all_71_2
% 143.15/19.83 | |
% 143.15/19.83 | | BETA: splitting (86) gives:
% 143.15/19.83 | |
% 143.15/19.83 | | Case 1:
% 143.15/19.83 | | |
% 143.15/19.83 | | | (96) all_64_0 = 0 & all_51_0 = 0 & subset(all_51_1, all_51_1) = 0
% 143.15/19.83 | | |
% 143.15/19.83 | | | ALPHA: (96) implies:
% 143.15/19.83 | | | (97) all_51_0 = 0
% 143.15/19.83 | | |
% 143.15/19.83 | | | REDUCE: (50), (97) imply:
% 143.15/19.83 | | | (98) $false
% 143.15/19.83 | | |
% 143.15/19.83 | | | CLOSE: (98) is inconsistent.
% 143.15/19.83 | | |
% 143.15/19.83 | | Case 2:
% 143.15/19.83 | | |
% 143.15/19.83 | | | (99) ~ (all_64_1 = 0) & in(all_51_1, all_51_1) = all_64_1
% 143.15/19.83 | | |
% 143.15/19.83 | | | ALPHA: (99) implies:
% 143.15/19.83 | | | (100) ~ (all_64_1 = 0)
% 143.15/19.83 | | | (101) in(all_51_1, all_51_1) = all_64_1
% 143.15/19.83 | | |
% 143.15/19.83 | | | BETA: splitting (74) gives:
% 143.15/19.83 | | |
% 143.15/19.83 | | | Case 1:
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | (102) all_51_0 = 0
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | REDUCE: (50), (102) imply:
% 143.15/19.83 | | | | (103) $false
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | CLOSE: (103) is inconsistent.
% 143.15/19.83 | | | |
% 143.15/19.83 | | | Case 2:
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | (104) ? [v0: int] : ? [v1: int] : (( ~ (v1 = 0) &
% 143.15/19.83 | | | | epsilon_connected(all_51_1) = v1) | ( ~ (v0 = 0) &
% 143.15/19.83 | | | | epsilon_transitive(all_51_1) = v0))
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | DELTA: instantiating (104) with fresh symbols all_125_0, all_125_1
% 143.15/19.83 | | | | gives:
% 143.15/19.83 | | | | (105) ( ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0)
% 143.15/19.83 | | | | | ( ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) =
% 143.15/19.83 | | | | all_125_1)
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | GROUND_INST: instantiating (13) with all_51_1, all_51_1, all_64_1,
% 143.15/19.83 | | | | simplifying with (51), (101) gives:
% 143.15/19.83 | | | | (106) all_64_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.83 | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_51_1,
% 143.15/19.83 | | | | all_51_1) = v0))
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | BETA: splitting (106) gives:
% 143.15/19.83 | | | |
% 143.15/19.83 | | | | Case 1:
% 143.15/19.83 | | | | |
% 143.15/19.83 | | | | | (107) all_64_1 = 0
% 143.15/19.83 | | | | |
% 143.15/19.83 | | | | | REDUCE: (100), (107) imply:
% 143.15/19.84 | | | | | (108) $false
% 143.15/19.84 | | | | |
% 143.15/19.84 | | | | | CLOSE: (108) is inconsistent.
% 143.15/19.84 | | | | |
% 143.15/19.84 | | | | Case 2:
% 143.15/19.84 | | | | |
% 143.15/19.84 | | | | | (109) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0)
% 143.15/19.84 | | | | | | ( ~ (v0 = 0) & element(all_51_1, all_51_1) = v0))
% 143.15/19.84 | | | | |
% 143.15/19.84 | | | | | DELTA: instantiating (109) with fresh symbols all_137_0, all_137_1
% 143.15/19.84 | | | | | gives:
% 143.15/19.84 | | | | | (110) (all_137_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_137_1 = 0) &
% 143.15/19.84 | | | | | element(all_51_1, all_51_1) = all_137_1)
% 143.15/19.84 | | | | |
% 143.15/19.84 | | | | | BETA: splitting (110) gives:
% 143.15/19.84 | | | | |
% 143.15/19.84 | | | | | Case 1:
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | (111) all_137_0 = 0 & empty(all_51_1) = 0
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | ALPHA: (111) implies:
% 143.15/19.84 | | | | | | (112) empty(all_51_1) = 0
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | REF_CLOSE: (20), (94), (95), (112) are inconsistent by sub-proof
% 143.15/19.84 | | | | | | #23.
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | Case 2:
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | (113) ~ (all_137_1 = 0) & element(all_51_1, all_51_1) =
% 143.15/19.84 | | | | | | all_137_1
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | ALPHA: (113) implies:
% 143.15/19.84 | | | | | | (114) ~ (all_137_1 = 0)
% 143.15/19.84 | | | | | | (115) element(all_51_1, all_51_1) = all_137_1
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | BETA: splitting (68) gives:
% 143.15/19.84 | | | | | |
% 143.15/19.84 | | | | | | Case 1:
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | (116) all_47_1 = empty_set
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | REDUCE: (42), (116) imply:
% 143.15/19.84 | | | | | | | (117) empty(empty_set) = all_47_0
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | GROUND_INST: instantiating (20) with 0, all_47_0, empty_set,
% 143.15/19.84 | | | | | | | simplifying with (89), (117) gives:
% 143.15/19.84 | | | | | | | (118) all_47_0 = 0
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | REDUCE: (40), (118) imply:
% 143.15/19.84 | | | | | | | (119) $false
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | CLOSE: (119) is inconsistent.
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | Case 2:
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | (120) ~ (all_47_1 = empty_set)
% 143.15/19.84 | | | | | | | (121) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(empty_set,
% 143.15/19.84 | | | | | | | all_47_1) = 0) | (v0 = 0 & in(all_47_1, empty_set)
% 143.15/19.84 | | | | | | | = 0))
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | DELTA: instantiating (121) with fresh symbols all_149_0, all_149_1
% 143.15/19.84 | | | | | | | gives:
% 143.15/19.84 | | | | | | | (122) (all_149_0 = 0 & in(empty_set, all_47_1) = 0) |
% 143.15/19.84 | | | | | | | (all_149_1 = 0 & in(all_47_1, empty_set) = 0)
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | BETA: splitting (70) gives:
% 143.15/19.84 | | | | | | |
% 143.15/19.84 | | | | | | | Case 1:
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | (123) all_49_0 = all_47_1
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | COMBINE_EQS: (62), (123) imply:
% 143.15/19.84 | | | | | | | | (124) all_47_1 = empty_set
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | SIMP: (124) implies:
% 143.15/19.84 | | | | | | | | (125) all_47_1 = empty_set
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | REDUCE: (120), (125) imply:
% 143.15/19.84 | | | | | | | | (126) $false
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | CLOSE: (126) is inconsistent.
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | Case 2:
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | (127) ~ (all_49_0 = all_47_1)
% 143.15/19.84 | | | | | | | | (128) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_49_0,
% 143.15/19.84 | | | | | | | | all_47_1) = 0) | (v0 = 0 & in(all_47_1, all_49_0)
% 143.15/19.84 | | | | | | | | = 0))
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | DELTA: instantiating (128) with fresh symbols all_162_0,
% 143.15/19.84 | | | | | | | | all_162_1 gives:
% 143.15/19.84 | | | | | | | | (129) (all_162_0 = 0 & in(all_49_0, all_47_1) = 0) |
% 143.15/19.84 | | | | | | | | (all_162_1 = 0 & in(all_47_1, all_49_0) = 0)
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | REDUCE: (62), (127) imply:
% 143.15/19.84 | | | | | | | | (130) ~ (all_47_1 = empty_set)
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | BETA: splitting (64) gives:
% 143.15/19.84 | | | | | | | |
% 143.15/19.84 | | | | | | | | Case 1:
% 143.15/19.84 | | | | | | | | |
% 143.15/19.84 | | | | | | | | | (131) all_39_0 = empty_set
% 143.15/19.84 | | | | | | | | |
% 143.15/19.84 | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (13),
% 143.15/19.84 | | | | | | | | | (14), (16), (17), (18), (20), (21), (22), (23),
% 143.15/19.84 | | | | | | | | | (24), (41), (43), (44), (50), (51), (52), (53),
% 143.15/19.84 | | | | | | | | | (62), (67), (82), (83), (84), (85), (88), (89),
% 143.15/19.84 | | | | | | | | | (94), (95), (105), (114), (115), (120), (122),
% 143.15/19.84 | | | | | | | | | (129), (131), (t7_boole) are inconsistent by
% 143.15/19.84 | | | | | | | | | sub-proof #15.
% 143.15/19.84 | | | | | | | | |
% 143.15/19.84 | | | | | | | | Case 2:
% 143.15/19.84 | | | | | | | | |
% 143.15/19.84 | | | | | | | | | (132) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.84 | | | | | | | | | in(empty_set, all_39_0) = 0) | (v0 = 0 &
% 143.15/19.84 | | | | | | | | | in(all_39_0, empty_set) = 0))
% 143.15/19.84 | | | | | | | | |
% 143.15/19.84 | | | | | | | | | DELTA: instantiating (132) with fresh symbols all_175_0,
% 143.15/19.84 | | | | | | | | | all_175_1 gives:
% 143.15/19.85 | | | | | | | | | (133) (all_175_0 = 0 & in(empty_set, all_39_0) = 0) |
% 143.15/19.85 | | | | | | | | | (all_175_1 = 0 & in(all_39_0, empty_set) = 0)
% 143.15/19.85 | | | | | | | | |
% 143.15/19.85 | | | | | | | | | BETA: splitting (72) gives:
% 143.15/19.85 | | | | | | | | |
% 143.15/19.85 | | | | | | | | | Case 1:
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | (134) all_49_0 = all_39_0
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | COMBINE_EQS: (62), (134) imply:
% 143.15/19.85 | | | | | | | | | | (135) all_39_0 = empty_set
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | SIMP: (135) implies:
% 143.15/19.85 | | | | | | | | | | (136) all_39_0 = empty_set
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (13),
% 143.15/19.85 | | | | | | | | | | (14), (16), (17), (18), (20), (21), (22), (23),
% 143.15/19.85 | | | | | | | | | | (24), (41), (43), (44), (50), (51), (52), (53),
% 143.15/19.85 | | | | | | | | | | (62), (67), (82), (83), (84), (85), (88), (89),
% 143.15/19.85 | | | | | | | | | | (94), (95), (105), (114), (115), (120), (122),
% 143.15/19.85 | | | | | | | | | | (129), (136), (t7_boole) are inconsistent by
% 143.15/19.85 | | | | | | | | | | sub-proof #15.
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | Case 2:
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | (137) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.85 | | | | | | | | | | in(all_39_0, all_49_0) = 0) | (v0 = 0 &
% 143.15/19.85 | | | | | | | | | | in(all_49_0, all_39_0) = 0))
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | DELTA: instantiating (137) with fresh symbols all_179_0,
% 143.15/19.85 | | | | | | | | | | all_179_1 gives:
% 143.15/19.85 | | | | | | | | | | (138) (all_179_0 = 0 & in(all_39_0, all_49_0) = 0) |
% 143.15/19.85 | | | | | | | | | | (all_179_1 = 0 & in(all_49_0, all_39_0) = 0)
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | BETA: splitting (71) gives:
% 143.15/19.85 | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | Case 1:
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | (139) all_49_0 = all_39_0
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | COMBINE_EQS: (62), (139) imply:
% 143.15/19.85 | | | | | | | | | | | (140) all_39_0 = empty_set
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | SIMP: (140) implies:
% 143.15/19.85 | | | | | | | | | | | (141) all_39_0 = empty_set
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (13),
% 143.15/19.85 | | | | | | | | | | | (14), (16), (17), (18), (20), (21), (22), (23),
% 143.15/19.85 | | | | | | | | | | | (24), (41), (43), (44), (50), (51), (52), (53),
% 143.15/19.85 | | | | | | | | | | | (62), (67), (82), (83), (84), (85), (88), (89),
% 143.15/19.85 | | | | | | | | | | | (94), (95), (105), (114), (115), (120), (122),
% 143.15/19.85 | | | | | | | | | | | (129), (141), (t7_boole) are inconsistent by
% 143.15/19.85 | | | | | | | | | | | sub-proof #15.
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | Case 2:
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | (142) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.85 | | | | | | | | | | | in(all_49_0, all_39_0) = 0) | (v0 = 0 &
% 143.15/19.85 | | | | | | | | | | | in(all_39_0, all_49_0) = 0))
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | DELTA: instantiating (142) with fresh symbols all_183_0,
% 143.15/19.85 | | | | | | | | | | | all_183_1 gives:
% 143.15/19.85 | | | | | | | | | | | (143) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) |
% 143.15/19.85 | | | | | | | | | | | (all_183_1 = 0 & in(all_39_0, all_49_0) = 0)
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | BETA: splitting (83) gives:
% 143.15/19.85 | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | Case 1:
% 143.15/19.85 | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | (144) all_61_0 = 0 & subset(empty_set, all_51_1) = 0
% 143.15/19.85 | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | ALPHA: (144) implies:
% 143.15/19.85 | | | | | | | | | | | | (145) subset(empty_set, all_51_1) = 0
% 143.15/19.85 | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | BETA: splitting (67) gives:
% 143.15/19.85 | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | Case 1:
% 143.15/19.85 | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | (146) all_47_1 = all_39_0
% 143.15/19.85 | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | REDUCE: (42), (146) imply:
% 143.15/19.85 | | | | | | | | | | | | | (147) empty(all_39_0) = all_47_0
% 143.15/19.85 | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | BETA: splitting (82) gives:
% 143.15/19.85 | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | Case 1:
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | | (148) all_60_0 = 0 & subset(all_39_0, all_51_1) = 0
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | | ALPHA: (148) implies:
% 143.15/19.85 | | | | | | | | | | | | | | (149) subset(all_39_0, all_51_1) = 0
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (10), (12), (13), (14),
% 143.15/19.85 | | | | | | | | | | | | | | (17), (18), (19), (20), (22), (23), (24), (36),
% 143.15/19.85 | | | | | | | | | | | | | | (37), (40), (41), (43), (51), (53), (62), (85),
% 143.15/19.85 | | | | | | | | | | | | | | (89), (94), (95), (105), (114), (115), (133),
% 143.15/19.85 | | | | | | | | | | | | | | (143), (145), (146), (147), (149), (t7_boole) are
% 143.15/19.85 | | | | | | | | | | | | | | inconsistent by sub-proof #9.
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | Case 2:
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | | (150) ~ (all_60_1 = 0) & in(all_39_0, all_51_1) =
% 143.15/19.85 | | | | | | | | | | | | | | all_60_1
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | | ALPHA: (150) implies:
% 143.15/19.85 | | | | | | | | | | | | | | (151) in(all_39_0, all_51_1) = all_60_1
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12),
% 143.15/19.85 | | | | | | | | | | | | | | (13), (14), (16), (17), (18), (19), (20), (21),
% 143.15/19.85 | | | | | | | | | | | | | | (22), (23), (24), (36), (37), (40), (41), (43),
% 143.15/19.85 | | | | | | | | | | | | | | (44), (50), (51), (52), (53), (62), (67), (82),
% 143.15/19.85 | | | | | | | | | | | | | | (83), (84), (85), (88), (89), (94), (95), (105),
% 143.15/19.85 | | | | | | | | | | | | | | (114), (115), (120), (122), (129), (133), (143),
% 143.15/19.85 | | | | | | | | | | | | | | (145), (146), (147), (151), (t7_boole) are
% 143.15/19.85 | | | | | | | | | | | | | | inconsistent by sub-proof #8.
% 143.15/19.85 | | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | | End of split
% 143.15/19.85 | | | | | | | | | | | | |
% 143.15/19.85 | | | | | | | | | | | | Case 2:
% 143.15/19.85 | | | | | | | | | | | | |
% 143.15/19.86 | | | | | | | | | | | | | (152) ~ (all_47_1 = all_39_0)
% 143.15/19.86 | | | | | | | | | | | | | (153) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.15/19.86 | | | | | | | | | | | | | in(all_39_0, all_47_1) = 0) | (v0 = 0 &
% 143.15/19.86 | | | | | | | | | | | | | in(all_47_1, all_39_0) = 0))
% 143.15/19.86 | | | | | | | | | | | | |
% 143.15/19.86 | | | | | | | | | | | | | DELTA: instantiating (153) with fresh symbols all_196_0,
% 143.15/19.86 | | | | | | | | | | | | | all_196_1 gives:
% 143.15/19.86 | | | | | | | | | | | | | (154) (all_196_0 = 0 & in(all_39_0, all_47_1) = 0) |
% 143.15/19.86 | | | | | | | | | | | | | (all_196_1 = 0 & in(all_47_1, all_39_0) = 0)
% 143.15/19.86 | | | | | | | | | | | | |
% 143.15/19.86 | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (10), (12), (13), (14),
% 143.15/19.86 | | | | | | | | | | | | | (15), (17), (18), (19), (20), (22), (23), (24),
% 143.15/19.86 | | | | | | | | | | | | | (25), (36), (37), (41), (43), (51), (53), (55),
% 143.15/19.86 | | | | | | | | | | | | | (62), (66), (82), (85), (88), (89), (94), (95),
% 143.15/19.86 | | | | | | | | | | | | | (105), (120), (122), (133), (138), (143), (145),
% 143.15/19.86 | | | | | | | | | | | | | (152), (154), (t7_boole) are inconsistent by
% 143.15/19.86 | | | | | | | | | | | | | sub-proof #1.
% 143.15/19.86 | | | | | | | | | | | | |
% 143.15/19.86 | | | | | | | | | | | | End of split
% 143.15/19.86 | | | | | | | | | | | |
% 143.15/19.86 | | | | | | | | | | | Case 2:
% 143.15/19.86 | | | | | | | | | | | |
% 143.15/19.86 | | | | | | | | | | | | (155) ~ (all_61_1 = 0) & in(empty_set, all_51_1) =
% 143.15/19.86 | | | | | | | | | | | | all_61_1
% 143.47/19.86 | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | ALPHA: (155) implies:
% 143.47/19.86 | | | | | | | | | | | | (156) ~ (all_61_1 = 0)
% 143.47/19.86 | | | | | | | | | | | | (157) in(empty_set, all_51_1) = all_61_1
% 143.47/19.86 | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | BETA: splitting (67) gives:
% 143.47/19.86 | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | Case 1:
% 143.47/19.86 | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | (158) all_47_1 = all_39_0
% 143.47/19.86 | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | REDUCE: (42), (158) imply:
% 143.47/19.86 | | | | | | | | | | | | | (159) empty(all_39_0) = all_47_0
% 143.47/19.86 | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | BETA: splitting (82) gives:
% 143.47/19.86 | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | Case 1:
% 143.47/19.86 | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | (160) all_60_0 = 0 & subset(all_39_0, all_51_1) = 0
% 143.47/19.86 | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | ALPHA: (160) implies:
% 143.47/19.86 | | | | | | | | | | | | | | (161) subset(all_39_0, all_51_1) = 0
% 143.47/19.86 | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 143.47/19.86 | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | Case 1:
% 143.47/19.86 | | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | | (162) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 143.47/19.86 | | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 143.47/19.86 | | | | | | | | | | | | | | | (163) subset(all_47_1, all_51_1) = 0
% 143.47/19.86 | | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_39_0, all_51_1,
% 143.47/19.86 | | | | | | | | | | | | | | | simplifying with (36), (51), (161) gives:
% 143.47/19.86 | | | | | | | | | | | | | | | (164) ? [v0: $i] : (powerset(all_51_1) = v0 &
% 143.47/19.86 | | | | | | | | | | | | | | | element(all_39_0, v0) = 0 & $i(v0))
% 143.47/19.86 | | | | | | | | | | | | | | |
% 143.47/19.86 | | | | | | | | | | | | | | | DELTA: instantiating (164) with fresh symbol all_223_0
% 143.47/19.86 | | | | | | | | | | | | | | | gives:
% 143.47/19.86 | | | | | | | | | | | | | | | (165) powerset(all_51_1) = all_223_0 & element(all_39_0,
% 143.47/19.86 | | | | | | | | | | | | | | | all_223_0) = 0 & $i(all_223_0)
% 143.49/19.86 | | | | | | | | | | | | | | |
% 143.49/19.86 | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 143.49/19.86 | | | | | | | | | | | | | | | (166) element(all_39_0, all_223_0) = 0
% 143.49/19.86 | | | | | | | | | | | | | | | (167) powerset(all_51_1) = all_223_0
% 143.49/19.86 | | | | | | | | | | | | | | |
% 143.49/19.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_51_1, all_39_0,
% 143.49/19.86 | | | | | | | | | | | | | | | all_51_1, all_223_0, all_137_1, simplifying with
% 143.49/19.86 | | | | | | | | | | | | | | | (36), (51), (115), (166), (167) gives:
% 143.49/19.86 | | | | | | | | | | | | | | | (168) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 143.49/19.86 | | | | | | | | | | | | | | | in(all_51_1, all_39_0) = v0)
% 143.49/19.86 | | | | | | | | | | | | | | |
% 143.49/19.86 | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 143.49/19.86 | | | | | | | | | | | | | | |
% 143.49/19.86 | | | | | | | | | | | | | | | Case 1:
% 143.49/19.86 | | | | | | | | | | | | | | | |
% 143.49/19.86 | | | | | | | | | | | | | | | | (169) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 143.49/19.86 | | | | | | | | | | | | | | | | all_125_0
% 143.49/19.86 | | | | | | | | | | | | | | | |
% 143.49/19.86 | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 143.49/19.86 | | | | | | | | | | | | | | | | (170) ~ (all_125_0 = 0)
% 143.49/19.86 | | | | | | | | | | | | | | | | (171) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.86 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (10), (18), (20), (23), (36), (41),
% 143.49/19.87 | | | | | | | | | | | | | | | | (43), (51), (53), (62), (89), (133), (143), (170),
% 143.49/19.87 | | | | | | | | | | | | | | | | (171), (t7_boole) are inconsistent by sub-proof
% 143.49/19.87 | | | | | | | | | | | | | | | | #13.
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | Case 2:
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | (172) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1)
% 143.49/19.87 | | | | | | | | | | | | | | | | = all_125_1
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 143.49/19.87 | | | | | | | | | | | | | | | | (173) ~ (all_125_1 = 0)
% 143.49/19.87 | | | | | | | | | | | | | | | | (174) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (13), (18), (20), (23), (24), (36),
% 143.49/19.87 | | | | | | | | | | | | | | | | (40), (51), (53), (62), (89), (114), (133), (143),
% 143.49/19.87 | | | | | | | | | | | | | | | | (159), (168), (173), (174), (t7_boole) are
% 143.49/19.87 | | | | | | | | | | | | | | | | inconsistent by sub-proof #12.
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | End of split
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | Case 2:
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | (175) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) =
% 143.49/19.87 | | | | | | | | | | | | | | | all_63_1
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 143.49/19.87 | | | | | | | | | | | | | | | (176) ~ (all_63_1 = 0)
% 143.49/19.87 | | | | | | | | | | | | | | | (177) in(all_47_1, all_51_1) = all_63_1
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | REDUCE: (158), (177) imply:
% 143.49/19.87 | | | | | | | | | | | | | | | (178) in(all_39_0, all_51_1) = all_63_1
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_39_0, all_39_0,
% 143.49/19.87 | | | | | | | | | | | | | | | all_51_1, all_63_1, simplifying with (36), (37),
% 143.49/19.87 | | | | | | | | | | | | | | | (51), (178) gives:
% 143.49/19.87 | | | | | | | | | | | | | | | (179) all_63_1 = 0 | all_51_1 = all_39_0 | ? [v0: int]
% 143.49/19.87 | | | | | | | | | | | | | | | : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 143.49/19.87 | | | | | | | | | | | | | | | in(all_51_1, all_39_0) = 0) | ( ~ (v1 = 0) &
% 143.49/19.87 | | | | | | | | | | | | | | | in(all_51_1, all_39_0) = v1) | ( ~ (v0 = 0) &
% 143.49/19.87 | | | | | | | | | | | | | | | in(all_39_0, all_39_0) = v0))
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_39_0, all_51_1,
% 143.49/19.87 | | | | | | | | | | | | | | | simplifying with (36), (51), (161) gives:
% 143.49/19.87 | | | | | | | | | | | | | | | (180) ? [v0: $i] : (powerset(all_51_1) = v0 &
% 143.49/19.87 | | | | | | | | | | | | | | | element(all_39_0, v0) = 0 & $i(v0))
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | DELTA: instantiating (180) with fresh symbol all_223_0
% 143.49/19.87 | | | | | | | | | | | | | | | gives:
% 143.49/19.87 | | | | | | | | | | | | | | | (181) powerset(all_51_1) = all_223_0 & element(all_39_0,
% 143.49/19.87 | | | | | | | | | | | | | | | all_223_0) = 0 & $i(all_223_0)
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 143.49/19.87 | | | | | | | | | | | | | | | (182) element(all_39_0, all_223_0) = 0
% 143.49/19.87 | | | | | | | | | | | | | | | (183) powerset(all_51_1) = all_223_0
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_51_1, all_39_0,
% 143.49/19.87 | | | | | | | | | | | | | | | all_51_1, all_223_0, all_137_1, simplifying with
% 143.49/19.87 | | | | | | | | | | | | | | | (36), (51), (115), (182), (183) gives:
% 143.49/19.87 | | | | | | | | | | | | | | | (184) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 143.49/19.87 | | | | | | | | | | | | | | | in(all_51_1, all_39_0) = v0)
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 143.49/19.87 | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | Case 1:
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | (185) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 143.49/19.87 | | | | | | | | | | | | | | | | all_125_0
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 143.49/19.87 | | | | | | | | | | | | | | | | (186) ~ (all_125_0 = 0)
% 143.49/19.87 | | | | | | | | | | | | | | | | (187) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10), (23), (41), (43), (51), (53),
% 143.49/19.87 | | | | | | | | | | | | | | | | (176), (179), (186), (187) are inconsistent by
% 143.49/19.87 | | | | | | | | | | | | | | | | sub-proof #11.
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | Case 2:
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | (188) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1)
% 143.49/19.87 | | | | | | | | | | | | | | | | = all_125_1
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 143.49/19.87 | | | | | | | | | | | | | | | | (189) ~ (all_125_1 = 0)
% 143.49/19.87 | | | | | | | | | | | | | | | | (190) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.87 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (13), (18), (20), (23), (24), (36),
% 143.49/19.87 | | | | | | | | | | | | | | | | (40), (51), (53), (62), (89), (114), (133), (143),
% 143.49/19.87 | | | | | | | | | | | | | | | | (159), (184), (189), (190), (t7_boole) are
% 143.49/19.87 | | | | | | | | | | | | | | | | inconsistent by sub-proof #12.
% 143.49/19.87 | | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | End of split
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | End of split
% 143.49/19.88 | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | Case 2:
% 143.49/19.88 | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | (191) ~ (all_60_1 = 0) & in(all_39_0, all_51_1) =
% 143.49/19.88 | | | | | | | | | | | | | | all_60_1
% 143.49/19.88 | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | ALPHA: (191) implies:
% 143.49/19.88 | | | | | | | | | | | | | | (192) in(all_39_0, all_51_1) = all_60_1
% 143.49/19.88 | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 143.49/19.88 | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | Case 1:
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | (193) all_62_0 = 0 & subset(all_49_0, all_51_1) = 0
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 143.49/19.88 | | | | | | | | | | | | | | | (194) subset(all_49_0, all_51_1) = 0
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | REDUCE: (62), (194) imply:
% 143.49/19.88 | | | | | | | | | | | | | | | (195) subset(empty_set, all_51_1) = 0
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (10), (11), (12),
% 143.49/19.88 | | | | | | | | | | | | | | | (13), (14), (16), (17), (18), (19), (20), (21),
% 143.49/19.88 | | | | | | | | | | | | | | | (22), (23), (24), (36), (37), (40), (41), (43),
% 143.49/19.88 | | | | | | | | | | | | | | | (44), (50), (51), (52), (53), (62), (67), (82),
% 143.49/19.88 | | | | | | | | | | | | | | | (83), (84), (85), (88), (89), (94), (95), (105),
% 143.49/19.88 | | | | | | | | | | | | | | | (114), (115), (120), (122), (129), (133), (143),
% 143.49/19.88 | | | | | | | | | | | | | | | (158), (159), (192), (195), (t7_boole) are
% 143.49/19.88 | | | | | | | | | | | | | | | inconsistent by sub-proof #8.
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | Case 2:
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | (196) ~ (all_62_1 = 0) & in(all_49_0, all_51_1) =
% 143.49/19.88 | | | | | | | | | | | | | | | all_62_1
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 143.49/19.88 | | | | | | | | | | | | | | | (197) ~ (all_62_1 = 0)
% 143.49/19.88 | | | | | | | | | | | | | | | (198) in(all_49_0, all_51_1) = all_62_1
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | REDUCE: (62), (198) imply:
% 143.49/19.88 | | | | | | | | | | | | | | | (199) in(empty_set, all_51_1) = all_62_1
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_61_1, all_62_1,
% 143.49/19.88 | | | | | | | | | | | | | | | all_51_1, empty_set, simplifying with (157), (199)
% 143.49/19.88 | | | | | | | | | | | | | | | gives:
% 143.49/19.88 | | | | | | | | | | | | | | | (200) all_62_1 = all_61_1
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with empty_set, all_51_1,
% 143.49/19.88 | | | | | | | | | | | | | | | all_61_1, simplifying with (18), (51), (157)
% 143.49/19.88 | | | | | | | | | | | | | | | gives:
% 143.49/19.88 | | | | | | | | | | | | | | | (201) all_61_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 143.49/19.88 | | | | | | | | | | | | | | | = 0 & empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 143.49/19.88 | | | | | | | | | | | | | | | element(empty_set, all_51_1) = v0))
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 143.49/19.88 | | | | | | | | | | | | | | |
% 143.49/19.88 | | | | | | | | | | | | | | | Case 1:
% 143.49/19.88 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | (202) all_61_1 = 0
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | REDUCE: (156), (202) imply:
% 143.49/19.89 | | | | | | | | | | | | | | | | (203) $false
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | CLOSE: (203) is inconsistent.
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | Case 2:
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | (204) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.89 | | | | | | | | | | | | | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 143.49/19.89 | | | | | | | | | | | | | | | | element(empty_set, all_51_1) = v0))
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | DELTA: instantiating (204) with fresh symbols all_233_0,
% 143.49/19.89 | | | | | | | | | | | | | | | | all_233_1 gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | (205) (all_233_0 = 0 & empty(all_51_1) = 0) | ( ~
% 143.49/19.89 | | | | | | | | | | | | | | | | (all_233_1 = 0) & element(empty_set, all_51_1) =
% 143.49/19.89 | | | | | | | | | | | | | | | | all_233_1)
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | (206) all_233_0 = 0 & empty(all_51_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | (207) empty(all_51_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (94), (95), (207) are inconsistent by
% 143.49/19.89 | | | | | | | | | | | | | | | | | sub-proof #23.
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | (208) ~ (all_233_1 = 0) & element(empty_set, all_51_1)
% 143.49/19.89 | | | | | | | | | | | | | | | | | = all_233_1
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | (209) ~ (all_233_1 = 0)
% 143.49/19.89 | | | | | | | | | | | | | | | | | (210) element(empty_set, all_51_1) = all_233_1
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (211) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 143.49/19.89 | | | | | | | | | | | | | | | | | | all_125_0
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (212) ~ (all_125_0 = 0)
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (213) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (10), (18), (20), (23), (36), (41),
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (43), (51), (53), (62), (89), (133), (143), (212),
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (213), (t7_boole) are inconsistent by sub-proof
% 143.49/19.89 | | | | | | | | | | | | | | | | | | #13.
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (214) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1)
% 143.49/19.89 | | | | | | | | | | | | | | | | | | = all_125_1
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (215) ~ (all_125_1 = 0)
% 143.49/19.89 | | | | | | | | | | | | | | | | | | (216) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (217) all_149_0 = 0 & in(empty_set, all_47_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (218) in(empty_set, all_47_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | REDUCE: (158), (218) imply:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (219) in(empty_set, all_39_0) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with empty_set, all_39_0,
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | all_51_1, all_233_1, simplifying with (18), (36),
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (51), (210), (219) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (220) all_233_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (v1 = 0) & powerset(all_51_1) = v0 &
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | element(all_39_0, v0) = v1 & $i(v0))
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_51_1, all_125_1,
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | simplifying with (51), (216) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (221) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (v1 = 0) & subset(v0, all_51_1) = v1 & in(v0,
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | all_51_1) = 0 & $i(v0))
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (222) all_125_1 = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | REDUCE: (215), (222) imply:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (223) $false
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | CLOSE: (223) is inconsistent.
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (224) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | & $i(v0))
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (224) with fresh symbols all_514_0,
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | all_514_1 gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (225) ~ (all_514_0 = 0) & subset(all_514_1, all_51_1) =
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | all_514_0 & in(all_514_1, all_51_1) = 0 &
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | $i(all_514_1)
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (226) ~ (all_514_0 = 0)
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (227) $i(all_514_1)
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (228) in(all_514_1, all_51_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | (229) subset(all_514_1, all_51_1) = all_514_0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | (230) all_233_1 = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (209), (230) imply:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | (231) $false
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with all_514_1, simplifying
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | with (227), (228) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | (232) subset(all_514_1, all_51_1) = 0 &
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | ordinal(all_514_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | (233) subset(all_514_1, all_51_1) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_514_0, 0, all_51_1,
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | all_514_1, simplifying with (229), (233) gives:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | (234) all_514_0 = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | REDUCE: (226), (234) imply:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | (235) $false
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | | CLOSE: (235) is inconsistent.
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (236) all_149_1 = 0 & in(all_47_1, empty_set) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (237) in(all_47_1, empty_set) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | REDUCE: (158), (237) imply:
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (238) in(all_39_0, empty_set) = 0
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (20), (23), (36), (62), (89), (143),
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | (238), (t7_boole) are inconsistent by sub-proof
% 143.49/19.89 | | | | | | | | | | | | | | | | | | | #14.
% 143.49/19.89 | | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | | End of split
% 143.49/19.89 | | | | | | | | | | | | | |
% 143.49/19.89 | | | | | | | | | | | | | End of split
% 143.49/19.90 | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | Case 2:
% 143.49/19.90 | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | (239) ~ (all_47_1 = all_39_0)
% 143.49/19.90 | | | | | | | | | | | | | (240) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.90 | | | | | | | | | | | | | in(all_39_0, all_47_1) = 0) | (v0 = 0 &
% 143.49/19.90 | | | | | | | | | | | | | in(all_47_1, all_39_0) = 0))
% 143.49/19.90 | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | BETA: splitting (82) gives:
% 143.49/19.90 | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | Case 1:
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | (241) all_60_0 = 0 & subset(all_39_0, all_51_1) = 0
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | ALPHA: (241) implies:
% 143.49/19.90 | | | | | | | | | | | | | | (242) subset(all_39_0, all_51_1) = 0
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with empty_set, all_51_1,
% 143.49/19.90 | | | | | | | | | | | | | | all_61_1, simplifying with (18), (51), (157)
% 143.49/19.90 | | | | | | | | | | | | | | gives:
% 143.49/19.90 | | | | | | | | | | | | | | (243) all_61_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 143.49/19.90 | | | | | | | | | | | | | | = 0 & empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 143.49/19.90 | | | | | | | | | | | | | | element(empty_set, all_51_1) = v0))
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_39_0, all_51_1,
% 143.49/19.90 | | | | | | | | | | | | | | simplifying with (36), (51), (242) gives:
% 143.49/19.90 | | | | | | | | | | | | | | (244) ? [v0: $i] : (powerset(all_51_1) = v0 &
% 143.49/19.90 | | | | | | | | | | | | | | element(all_39_0, v0) = 0 & $i(v0))
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | DELTA: instantiating (244) with fresh symbol all_229_0
% 143.49/19.90 | | | | | | | | | | | | | | gives:
% 143.49/19.90 | | | | | | | | | | | | | | (245) powerset(all_51_1) = all_229_0 & element(all_39_0,
% 143.49/19.90 | | | | | | | | | | | | | | all_229_0) = 0 & $i(all_229_0)
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | ALPHA: (245) implies:
% 143.49/19.90 | | | | | | | | | | | | | | (246) element(all_39_0, all_229_0) = 0
% 143.49/19.90 | | | | | | | | | | | | | | (247) powerset(all_51_1) = all_229_0
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 143.49/19.90 | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | Case 1:
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | (248) all_61_1 = 0
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | REDUCE: (156), (248) imply:
% 143.49/19.90 | | | | | | | | | | | | | | | (249) $false
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent.
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | Case 2:
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | (250) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.90 | | | | | | | | | | | | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 143.49/19.90 | | | | | | | | | | | | | | | element(empty_set, all_51_1) = v0))
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | DELTA: instantiating (250) with fresh symbols all_236_0,
% 143.49/19.90 | | | | | | | | | | | | | | | all_236_1 gives:
% 143.49/19.90 | | | | | | | | | | | | | | | (251) (all_236_0 = 0 & empty(all_51_1) = 0) | ( ~
% 143.49/19.90 | | | | | | | | | | | | | | | (all_236_1 = 0) & element(empty_set, all_51_1) =
% 143.49/19.90 | | | | | | | | | | | | | | | all_236_1)
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 143.49/19.90 | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | Case 1:
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | (252) all_236_0 = 0 & empty(all_51_1) = 0
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 143.49/19.90 | | | | | | | | | | | | | | | | (253) empty(all_51_1) = 0
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | REF_CLOSE: (20), (94), (95), (253) are inconsistent by
% 143.49/19.90 | | | | | | | | | | | | | | | | sub-proof #23.
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | Case 2:
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | (254) ~ (all_236_1 = 0) & element(empty_set, all_51_1)
% 143.49/19.90 | | | | | | | | | | | | | | | | = all_236_1
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | ALPHA: (254) implies:
% 143.49/19.90 | | | | | | | | | | | | | | | | (255) ~ (all_236_1 = 0)
% 143.49/19.90 | | | | | | | | | | | | | | | | (256) element(empty_set, all_51_1) = all_236_1
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with empty_set, all_39_0,
% 143.49/19.90 | | | | | | | | | | | | | | | | all_51_1, all_229_0, all_236_1, simplifying with
% 143.49/19.90 | | | | | | | | | | | | | | | | (18), (36), (51), (246), (247), (256) gives:
% 143.49/19.90 | | | | | | | | | | | | | | | | (257) all_236_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 143.49/19.90 | | | | | | | | | | | | | | | | in(empty_set, all_39_0) = v0)
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | BETA: splitting (257) gives:
% 143.49/19.90 | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | (258) all_236_1 = 0
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | REDUCE: (255), (258) imply:
% 143.49/19.90 | | | | | | | | | | | | | | | | | (259) $false
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | CLOSE: (259) is inconsistent.
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | (260) ? [v0: int] : ( ~ (v0 = 0) & in(empty_set,
% 143.49/19.90 | | | | | | | | | | | | | | | | | all_39_0) = v0)
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | DELTA: instantiating (260) with fresh symbol all_393_0
% 143.49/19.90 | | | | | | | | | | | | | | | | | gives:
% 143.49/19.90 | | | | | | | | | | | | | | | | | (261) ~ (all_393_0 = 0) & in(empty_set, all_39_0) =
% 143.49/19.90 | | | | | | | | | | | | | | | | | all_393_0
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 143.49/19.90 | | | | | | | | | | | | | | | | | (262) ~ (all_393_0 = 0)
% 143.49/19.90 | | | | | | | | | | | | | | | | | (263) in(empty_set, all_39_0) = all_393_0
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 143.49/19.90 | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | | (264) all_175_0 = 0 & in(empty_set, all_39_0) = 0
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 143.49/19.90 | | | | | | | | | | | | | | | | | | (265) in(empty_set, all_39_0) = 0
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_393_0, all_39_0,
% 143.49/19.90 | | | | | | | | | | | | | | | | | | empty_set, simplifying with (263), (265) gives:
% 143.49/19.90 | | | | | | | | | | | | | | | | | | (266) all_393_0 = 0
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | | REDUCE: (262), (266) imply:
% 143.49/19.90 | | | | | | | | | | | | | | | | | | (267) $false
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.90 | | | | | | | | | | | | | | | | | |
% 143.49/19.90 | | | | | | | | | | | | | | | | | | (268) all_175_1 = 0 & in(all_39_0, empty_set) = 0
% 143.49/19.91 | | | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 143.49/19.91 | | | | | | | | | | | | | | | | | | (269) in(all_39_0, empty_set) = 0
% 143.49/19.91 | | | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (20), (23), (36), (62), (89), (143),
% 143.49/19.91 | | | | | | | | | | | | | | | | | | (269), (t7_boole) are inconsistent by sub-proof
% 143.49/19.91 | | | | | | | | | | | | | | | | | | #14.
% 143.49/19.91 | | | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | | End of split
% 143.49/19.91 | | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | End of split
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | End of split
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | End of split
% 143.49/19.91 | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | Case 2:
% 143.49/19.91 | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | (270) ~ (all_60_1 = 0) & in(all_39_0, all_51_1) =
% 143.49/19.91 | | | | | | | | | | | | | | all_60_1
% 143.49/19.91 | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | ALPHA: (270) implies:
% 143.49/19.91 | | | | | | | | | | | | | | (271) ~ (all_60_1 = 0)
% 143.49/19.91 | | | | | | | | | | | | | | (272) in(all_39_0, all_51_1) = all_60_1
% 143.49/19.91 | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 143.49/19.91 | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | Case 1:
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | (273) all_62_0 = 0 & subset(all_49_0, all_51_1) = 0
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 143.49/19.91 | | | | | | | | | | | | | | | (274) subset(all_49_0, all_51_1) = 0
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | REDUCE: (62), (274) imply:
% 143.49/19.91 | | | | | | | | | | | | | | | (275) subset(empty_set, all_51_1) = 0
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | DELTA: instantiating (240) with fresh symbols all_196_0,
% 143.49/19.91 | | | | | | | | | | | | | | | all_196_1 gives:
% 143.49/19.91 | | | | | | | | | | | | | | | (276) (all_196_0 = 0 & in(all_39_0, all_47_1) = 0) |
% 143.49/19.91 | | | | | | | | | | | | | | | (all_196_1 = 0 & in(all_47_1, all_39_0) = 0)
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (6), (7), (10), (12), (13), (14),
% 143.49/19.91 | | | | | | | | | | | | | | | (15), (17), (18), (19), (20), (22), (23), (24),
% 143.49/19.91 | | | | | | | | | | | | | | | (25), (36), (37), (41), (43), (51), (53), (55),
% 143.49/19.91 | | | | | | | | | | | | | | | (62), (66), (82), (85), (88), (89), (94), (95),
% 143.49/19.91 | | | | | | | | | | | | | | | (105), (120), (122), (133), (138), (143), (239),
% 143.49/19.91 | | | | | | | | | | | | | | | (275), (276), (t7_boole) are inconsistent by
% 143.49/19.91 | | | | | | | | | | | | | | | sub-proof #1.
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | Case 2:
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | (277) ~ (all_62_1 = 0) & in(all_49_0, all_51_1) =
% 143.49/19.91 | | | | | | | | | | | | | | | all_62_1
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 143.49/19.91 | | | | | | | | | | | | | | | (278) ~ (all_62_1 = 0)
% 143.49/19.91 | | | | | | | | | | | | | | | (279) in(all_49_0, all_51_1) = all_62_1
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | REDUCE: (62), (279) imply:
% 143.49/19.91 | | | | | | | | | | | | | | | (280) in(empty_set, all_51_1) = all_62_1
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with all_61_1, all_62_1,
% 143.49/19.91 | | | | | | | | | | | | | | | all_51_1, empty_set, simplifying with (157), (280)
% 143.49/19.91 | | | | | | | | | | | | | | | gives:
% 143.49/19.91 | | | | | | | | | | | | | | | (281) all_62_1 = all_61_1
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 143.49/19.91 | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | Case 1:
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | (282) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 143.49/19.91 | | | | | | | | | | | | | | | | (283) subset(all_47_1, all_51_1) = 0
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with empty_set, all_51_1,
% 143.49/19.91 | | | | | | | | | | | | | | | | all_61_1, simplifying with (18), (51), (157)
% 143.49/19.91 | | | | | | | | | | | | | | | | gives:
% 143.49/19.91 | | | | | | | | | | | | | | | | (284) all_61_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1
% 143.49/19.91 | | | | | | | | | | | | | | | | = 0 & empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 143.49/19.91 | | | | | | | | | | | | | | | | element(empty_set, all_51_1) = v0))
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_47_1, all_51_1,
% 143.49/19.91 | | | | | | | | | | | | | | | | all_39_0, all_60_1, simplifying with (36), (41),
% 143.49/19.91 | | | | | | | | | | | | | | | | (43), (51), (272) gives:
% 143.49/19.91 | | | | | | | | | | | | | | | | (285) all_60_1 = 0 | all_51_1 = all_39_0 | ? [v0: int]
% 143.49/19.91 | | | | | | | | | | | | | | | | : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 143.49/19.91 | | | | | | | | | | | | | | | | in(all_51_1, all_39_0) = 0) | ( ~ (v1 = 0) &
% 143.49/19.91 | | | | | | | | | | | | | | | | in(all_39_0, all_47_1) = v1) | ( ~ (v0 = 0) &
% 143.49/19.91 | | | | | | | | | | | | | | | | in(all_51_1, all_47_1) = v0))
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_47_1, all_51_1,
% 143.49/19.91 | | | | | | | | | | | | | | | | simplifying with (41), (51), (283) gives:
% 143.49/19.91 | | | | | | | | | | | | | | | | (286) ? [v0: $i] : (powerset(all_51_1) = v0 &
% 143.49/19.91 | | | | | | | | | | | | | | | | element(all_47_1, v0) = 0 & $i(v0))
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | DELTA: instantiating (286) with fresh symbol all_229_0
% 143.49/19.91 | | | | | | | | | | | | | | | | gives:
% 143.49/19.91 | | | | | | | | | | | | | | | | (287) powerset(all_51_1) = all_229_0 & element(all_47_1,
% 143.49/19.91 | | | | | | | | | | | | | | | | all_229_0) = 0 & $i(all_229_0)
% 143.49/19.91 | | | | | | | | | | | | | | | |
% 143.49/19.91 | | | | | | | | | | | | | | | | ALPHA: (287) implies:
% 143.49/19.92 | | | | | | | | | | | | | | | | (288) element(all_47_1, all_229_0) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | (289) powerset(all_51_1) = all_229_0
% 143.49/19.92 | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 143.49/19.92 | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | (290) all_61_1 = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | REDUCE: (156), (290) imply:
% 143.49/19.92 | | | | | | | | | | | | | | | | | (291) $false
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | CLOSE: (291) is inconsistent.
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | (292) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.92 | | | | | | | | | | | | | | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 143.49/19.92 | | | | | | | | | | | | | | | | | element(empty_set, all_51_1) = v0))
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | DELTA: instantiating (292) with fresh symbols all_236_0,
% 143.49/19.92 | | | | | | | | | | | | | | | | | all_236_1 gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | | (293) (all_236_0 = 0 & empty(all_51_1) = 0) | ( ~
% 143.49/19.92 | | | | | | | | | | | | | | | | | (all_236_1 = 0) & element(empty_set, all_51_1) =
% 143.49/19.92 | | | | | | | | | | | | | | | | | all_236_1)
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (294) all_236_0 = 0 & empty(all_51_1) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (295) empty(all_51_1) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (94), (95), (295) are inconsistent by
% 143.49/19.92 | | | | | | | | | | | | | | | | | | sub-proof #23.
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (296) ~ (all_236_1 = 0) & element(empty_set, all_51_1)
% 143.49/19.92 | | | | | | | | | | | | | | | | | | = all_236_1
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (297) ~ (all_236_1 = 0)
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (298) element(empty_set, all_51_1) = all_236_1
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with empty_set, all_47_1,
% 143.49/19.92 | | | | | | | | | | | | | | | | | | all_51_1, all_229_0, all_236_1, simplifying with
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (18), (41), (51), (288), (289), (298) gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | (299) all_236_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 143.49/19.92 | | | | | | | | | | | | | | | | | | in(empty_set, all_47_1) = v0)
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | (300) all_149_0 = 0 & in(empty_set, all_47_1) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | (301) in(empty_set, all_47_1) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (302) all_236_1 = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | REDUCE: (297), (302) imply:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (303) $false
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | CLOSE: (303) is inconsistent.
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (304) ? [v0: int] : ( ~ (v0 = 0) & in(empty_set,
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | all_47_1) = v0)
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (304) with fresh symbol all_378_0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (305) ~ (all_378_0 = 0) & in(empty_set, all_47_1) =
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | all_378_0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (305) implies:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (306) ~ (all_378_0 = 0)
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (307) in(empty_set, all_47_1) = all_378_0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (23) with 0, all_378_0, all_47_1,
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | empty_set, simplifying with (301), (307) gives:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (308) all_378_0 = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | REDUCE: (306), (308) imply:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | (309) $false
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | | CLOSE: (309) is inconsistent.
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | End of split
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | (310) all_149_1 = 0 & in(all_47_1, empty_set) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | (311) in(all_47_1, empty_set) = 0
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (20), (41), (89), (271), (285), (311),
% 143.49/19.92 | | | | | | | | | | | | | | | | | | | (t7_boole) are inconsistent by sub-proof #2.
% 143.49/19.92 | | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | | End of split
% 143.49/19.92 | | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | | End of split
% 143.49/19.92 | | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | End of split
% 143.49/19.92 | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | Case 2:
% 143.49/19.92 | | | | | | | | | | | | | | | |
% 143.49/19.92 | | | | | | | | | | | | | | | | (312) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) =
% 143.49/19.93 | | | | | | | | | | | | | | | | all_63_1
% 143.49/19.93 | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 143.49/19.93 | | | | | | | | | | | | | | | | (313) ~ (all_63_1 = 0)
% 143.49/19.93 | | | | | | | | | | | | | | | | (314) in(all_47_1, all_51_1) = all_63_1
% 143.49/19.93 | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_39_0, all_47_1,
% 143.49/19.93 | | | | | | | | | | | | | | | | all_51_1, all_63_1, simplifying with (36), (37),
% 143.49/19.93 | | | | | | | | | | | | | | | | (41), (51), (314) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | (315) all_63_1 = 0 | all_51_1 = all_47_1 | ? [v0: int]
% 143.49/19.93 | | | | | | | | | | | | | | | | : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 143.49/19.93 | | | | | | | | | | | | | | | | in(all_51_1, all_47_1) = 0) | ( ~ (v1 = 0) &
% 143.49/19.93 | | | | | | | | | | | | | | | | in(all_51_1, all_39_0) = v1) | ( ~ (v0 = 0) &
% 143.49/19.93 | | | | | | | | | | | | | | | | in(all_47_1, all_39_0) = v0))
% 143.49/19.93 | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | (316) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 143.49/19.93 | | | | | | | | | | | | | | | | | all_125_0
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | ALPHA: (316) implies:
% 143.49/19.93 | | | | | | | | | | | | | | | | | (317) ~ (all_125_0 = 0)
% 143.49/19.93 | | | | | | | | | | | | | | | | | (318) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (10), (18), (20), (23), (36), (41),
% 143.49/19.93 | | | | | | | | | | | | | | | | | (43), (51), (53), (62), (89), (133), (143), (317),
% 143.49/19.93 | | | | | | | | | | | | | | | | | (318), (t7_boole) are inconsistent by sub-proof
% 143.49/19.93 | | | | | | | | | | | | | | | | | #13.
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | (319) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1)
% 143.49/19.93 | | | | | | | | | | | | | | | | | = all_125_1
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 143.49/19.93 | | | | | | | | | | | | | | | | | (320) ~ (all_125_1 = 0)
% 143.49/19.93 | | | | | | | | | | | | | | | | | (321) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_51_1, all_125_1,
% 143.49/19.93 | | | | | | | | | | | | | | | | | simplifying with (51), (321) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | | (322) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 143.49/19.93 | | | | | | | | | | | | | | | | | (v1 = 0) & subset(v0, all_51_1) = v1 & in(v0,
% 143.49/19.93 | | | | | | | | | | | | | | | | | all_51_1) = 0 & $i(v0))
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | BETA: splitting (322) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (323) all_125_1 = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | REDUCE: (320), (323) imply:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (324) $false
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (325) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 143.49/19.93 | | | | | | | | | | | | | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | | & $i(v0))
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | DELTA: instantiating (325) with fresh symbols all_396_0,
% 143.49/19.93 | | | | | | | | | | | | | | | | | | all_396_1 gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (326) ~ (all_396_0 = 0) & subset(all_396_1, all_51_1) =
% 143.49/19.93 | | | | | | | | | | | | | | | | | | all_396_0 & in(all_396_1, all_51_1) = 0 &
% 143.49/19.93 | | | | | | | | | | | | | | | | | | $i(all_396_1)
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (327) ~ (all_396_0 = 0)
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (328) $i(all_396_1)
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (329) in(all_396_1, all_51_1) = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | | (330) subset(all_396_1, all_51_1) = all_396_0
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | BETA: splitting (315) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | Case 1:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | (331) all_63_1 = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | REDUCE: (313), (331) imply:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | (332) $false
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | CLOSE: (332) is inconsistent.
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | Case 2:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (53) with all_396_1, simplifying
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | with (328), (329) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | (333) subset(all_396_1, all_51_1) = 0 &
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | ordinal(all_396_1) = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | (334) subset(all_396_1, all_51_1) = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_396_0, 0, all_51_1,
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | all_396_1, simplifying with (330), (334) gives:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | (335) all_396_0 = 0
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | REDUCE: (327), (335) imply:
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | (336) $false
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 143.49/19.93 | | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | | End of split
% 143.49/19.93 | | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | | End of split
% 143.49/19.93 | | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | | End of split
% 143.49/19.93 | | | | | | | | | | | | | | | |
% 143.49/19.93 | | | | | | | | | | | | | | | End of split
% 143.49/19.93 | | | | | | | | | | | | | | |
% 143.49/19.94 | | | | | | | | | | | | | | End of split
% 143.49/19.94 | | | | | | | | | | | | | |
% 143.49/19.94 | | | | | | | | | | | | | End of split
% 143.49/19.94 | | | | | | | | | | | | |
% 143.49/19.94 | | | | | | | | | | | | End of split
% 143.49/19.94 | | | | | | | | | | | |
% 143.49/19.94 | | | | | | | | | | | End of split
% 143.49/19.94 | | | | | | | | | | |
% 143.49/19.94 | | | | | | | | | | End of split
% 143.49/19.94 | | | | | | | | | |
% 143.49/19.94 | | | | | | | | | End of split
% 143.49/19.94 | | | | | | | | |
% 143.49/19.94 | | | | | | | | End of split
% 143.49/19.94 | | | | | | | |
% 143.49/19.94 | | | | | | | End of split
% 143.49/19.94 | | | | | | |
% 143.49/19.94 | | | | | | End of split
% 143.49/19.94 | | | | | |
% 143.49/19.94 | | | | | End of split
% 143.49/19.94 | | | | |
% 143.49/19.94 | | | | End of split
% 143.49/19.94 | | | |
% 143.49/19.94 | | | End of split
% 143.49/19.94 | | |
% 143.49/19.94 | | End of split
% 143.49/19.94 | |
% 143.49/19.94 | End of split
% 143.49/19.94 |
% 143.49/19.94 End of proof
% 143.49/19.94
% 143.49/19.94 Sub-proof #1 shows that the following formulas are inconsistent:
% 143.49/19.94 ----------------------------------------------------------------
% 143.49/19.94 (1) $i(all_51_1)
% 143.49/19.94 (2) (all_179_0 = 0 & in(all_39_0, all_49_0) = 0) | (all_179_1 = 0 &
% 143.49/19.94 in(all_49_0, all_39_0) = 0)
% 143.49/19.94 (3) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 143.49/19.94 all_51_1) = 0 & ordinal(v0) = 0))
% 143.49/19.94 (4) empty(all_51_1) = all_71_2
% 143.49/19.94 (5) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 143.49/19.94 $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 143.49/19.94 $i(v2)))
% 143.49/19.94 (6) all_47_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.94 in(all_47_1, all_39_0) = 0) | (v0 = 0 & in(all_39_0, all_47_1) = 0))
% 143.49/19.94 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2)
% 143.49/19.94 = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) |
% 143.49/19.94 ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0)
% 143.49/19.94 (8) ~ (all_47_1 = empty_set)
% 143.49/19.94 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 143.49/19.94 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 143.49/19.94 (10) $i(all_39_0)
% 143.49/19.94 (11) (all_175_0 = 0 & in(empty_set, all_39_0) = 0) | (all_175_1 = 0 &
% 143.49/19.94 in(all_39_0, empty_set) = 0)
% 143.49/19.94 (12) $i(empty_set)
% 143.49/19.94 (13) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 143.49/19.94 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 143.49/19.94 (14) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 143.49/19.94 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 143.49/19.94 (15) empty(empty_set) = 0
% 143.49/19.94 (16) (all_63_0 = 0 & subset(all_47_1, all_51_1) = 0) | ( ~ (all_63_1 = 0) &
% 143.49/19.94 in(all_47_1, all_51_1) = all_63_1)
% 143.49/19.94 (17) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 143.49/19.94 in(all_39_0, all_49_0) = 0)
% 143.49/19.94 (18) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 143.49/19.94 (19) subset(empty_set, all_51_1) = 0
% 143.49/19.94 (20) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 143.49/19.94 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 143.49/19.94 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 143.49/19.94 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 143.49/19.94 (21) epsilon_connected(all_47_1) = 0
% 143.49/19.94 (22) ~ (all_47_1 = all_39_0)
% 143.49/19.94 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 143.49/19.94 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 143.49/19.94 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 143.49/19.94 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 143.49/19.94 = 0) & in(v1, v0) = v4)))
% 143.49/19.94 (24) ~ (all_71_2 = 0)
% 143.49/19.94 (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 143.49/19.94 ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2)
% 143.49/19.94 = v0))
% 143.49/19.94 (26) all_49_0 = empty_set
% 143.49/19.94 (27) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 143.49/19.94 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 143.49/19.94 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 143.49/19.94 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 143.49/19.94 v1) | ~ (powerset(v2) = v0))
% 143.49/19.94 (29) (all_196_0 = 0 & in(all_39_0, all_47_1) = 0) | (all_196_1 = 0 &
% 143.49/19.94 in(all_47_1, all_39_0) = 0)
% 143.49/19.94 (30) ( ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0) | ( ~
% 143.49/19.94 (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1)
% 143.49/19.94 (31) epsilon_connected(empty_set) = 0
% 143.49/19.94 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 143.49/19.94 (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~
% 143.49/19.94 (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 143.49/19.94 int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 143.49/19.94 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 143.49/19.94 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 143.49/19.94 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 143.49/19.95 (34) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 143.49/19.95 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 143.49/19.95 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 143.49/19.95 (35) ! [v0: $i] : ! [v1: any] : ( ~ (subset(v0, all_51_1) = v1) | ~ $i(v0)
% 143.49/19.95 | ? [v2: int] : ? [v3: int] : ((v3 = 0 & v1 = 0 & ordinal(v0) = 0) |
% 143.49/19.95 ( ~ (v2 = 0) & in(v0, all_51_1) = v2)))
% 143.49/19.95 (36) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~
% 143.49/19.95 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & in(v0, v1) = 0) |
% 143.49/19.95 (v2 = 0 & empty(v1) = 0)))
% 143.49/19.95 (37) $i(all_47_1)
% 143.49/19.95 (38) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 143.49/19.95 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 143.49/19.95 v0))
% 143.49/19.95 (39) (all_149_0 = 0 & in(empty_set, all_47_1) = 0) | (all_149_1 = 0 &
% 143.49/19.95 in(all_47_1, empty_set) = 0)
% 143.49/19.95 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 143.49/19.95 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~ $i(v2)
% 143.49/19.95 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 143.49/19.95 ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 143.49/19.95 = 0) & in(v1, v0) = v4)))
% 143.49/19.95 (41) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 143.49/19.95 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 143.49/19.95 (42) epsilon_connected(all_39_0) = 0
% 143.49/19.95 (43) (all_60_0 = 0 & subset(all_39_0, all_51_1) = 0) | ( ~ (all_60_1 = 0) &
% 143.49/19.95 in(all_39_0, all_51_1) = all_60_1)
% 143.49/19.95
% 143.49/19.95 Begin of proof
% 143.49/19.95 |
% 143.49/19.95 | BETA: splitting (6) gives:
% 143.49/19.95 |
% 143.49/19.95 | Case 1:
% 143.49/19.95 | |
% 143.49/19.95 | | (44) all_47_1 = all_39_0
% 143.49/19.95 | |
% 143.49/19.95 | | REDUCE: (22), (44) imply:
% 143.49/19.95 | | (45) $false
% 143.49/19.95 | |
% 143.49/19.95 | | CLOSE: (45) is inconsistent.
% 143.49/19.95 | |
% 143.49/19.95 | Case 2:
% 143.49/19.95 | |
% 143.49/19.95 | | (46) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_47_1, all_39_0) = 0)
% 143.49/19.95 | | | (v0 = 0 & in(all_39_0, all_47_1) = 0))
% 143.49/19.95 | |
% 143.49/19.95 | | DELTA: instantiating (46) with fresh symbols all_201_0, all_201_1 gives:
% 143.49/19.95 | | (47) (all_201_0 = 0 & in(all_47_1, all_39_0) = 0) | (all_201_1 = 0 &
% 143.49/19.95 | | in(all_39_0, all_47_1) = 0)
% 143.49/19.95 | |
% 143.49/19.95 | | BETA: splitting (43) gives:
% 143.49/19.95 | |
% 143.49/19.95 | | Case 1:
% 143.49/19.95 | | |
% 143.49/19.95 | | | (48) all_60_0 = 0 & subset(all_39_0, all_51_1) = 0
% 143.49/19.95 | | |
% 143.49/19.95 | | | ALPHA: (48) implies:
% 143.49/19.95 | | | (49) subset(all_39_0, all_51_1) = 0
% 143.49/19.95 | | |
% 143.49/19.95 | | | BETA: splitting (16) gives:
% 143.49/19.95 | | |
% 143.49/19.95 | | | Case 1:
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | (50) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | ALPHA: (50) implies:
% 143.49/19.95 | | | | (51) subset(all_47_1, all_51_1) = 0
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | GROUND_INST: instantiating (5) with empty_set, all_51_1, simplifying
% 143.49/19.95 | | | | with (1), (12), (19) gives:
% 143.49/19.95 | | | | (52) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0)
% 143.49/19.95 | | | | = 0 & $i(v0))
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | GROUND_INST: instantiating (5) with all_39_0, all_51_1, simplifying with
% 143.49/19.95 | | | | (1), (10), (49) gives:
% 143.49/19.95 | | | | (53) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_39_0, v0) =
% 143.49/19.95 | | | | 0 & $i(v0))
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | GROUND_INST: instantiating (35) with all_39_0, 0, simplifying with (10),
% 143.49/19.95 | | | | (49) gives:
% 143.49/19.95 | | | | (54) ? [v0: int] : ? [v1: int] : ((v1 = 0 & ordinal(all_39_0) = 0)
% 143.49/19.95 | | | | | ( ~ (v0 = 0) & in(all_39_0, all_51_1) = v0))
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | GROUND_INST: instantiating (5) with all_47_1, all_51_1, simplifying with
% 143.49/19.95 | | | | (1), (37), (51) gives:
% 143.49/19.95 | | | | (55) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_47_1, v0) =
% 143.49/19.95 | | | | 0 & $i(v0))
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | DELTA: instantiating (55) with fresh symbol all_225_0 gives:
% 143.49/19.95 | | | | (56) powerset(all_51_1) = all_225_0 & element(all_47_1, all_225_0) =
% 143.49/19.95 | | | | 0 & $i(all_225_0)
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | ALPHA: (56) implies:
% 143.49/19.95 | | | | (57) element(all_47_1, all_225_0) = 0
% 143.49/19.95 | | | | (58) powerset(all_51_1) = all_225_0
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | DELTA: instantiating (53) with fresh symbol all_227_0 gives:
% 143.49/19.95 | | | | (59) powerset(all_51_1) = all_227_0 & element(all_39_0, all_227_0) =
% 143.49/19.95 | | | | 0 & $i(all_227_0)
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | ALPHA: (59) implies:
% 143.49/19.95 | | | | (60) $i(all_227_0)
% 143.49/19.95 | | | | (61) element(all_39_0, all_227_0) = 0
% 143.49/19.95 | | | | (62) powerset(all_51_1) = all_227_0
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | DELTA: instantiating (52) with fresh symbol all_229_0 gives:
% 143.49/19.95 | | | | (63) powerset(all_51_1) = all_229_0 & element(empty_set, all_229_0) =
% 143.49/19.95 | | | | 0 & $i(all_229_0)
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | ALPHA: (63) implies:
% 143.49/19.95 | | | | (64) powerset(all_51_1) = all_229_0
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | DELTA: instantiating (54) with fresh symbols all_232_0, all_232_1 gives:
% 143.49/19.95 | | | | (65) (all_232_0 = 0 & ordinal(all_39_0) = 0) | ( ~ (all_232_1 = 0) &
% 143.49/19.95 | | | | in(all_39_0, all_51_1) = all_232_1)
% 143.49/19.95 | | | |
% 143.49/19.95 | | | | GROUND_INST: instantiating (28) with all_227_0, all_229_0, all_51_1,
% 143.49/19.96 | | | | simplifying with (62), (64) gives:
% 143.49/19.96 | | | | (66) all_229_0 = all_227_0
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | GROUND_INST: instantiating (28) with all_225_0, all_229_0, all_51_1,
% 143.49/19.96 | | | | simplifying with (58), (64) gives:
% 143.49/19.96 | | | | (67) all_229_0 = all_225_0
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | COMBINE_EQS: (66), (67) imply:
% 143.49/19.96 | | | | (68) all_227_0 = all_225_0
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | SIMP: (68) implies:
% 143.49/19.96 | | | | (69) all_227_0 = all_225_0
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | REDUCE: (61), (69) imply:
% 143.49/19.96 | | | | (70) element(all_39_0, all_225_0) = 0
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | REDUCE: (60), (69) imply:
% 143.49/19.96 | | | | (71) $i(all_225_0)
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | GROUND_INST: instantiating (36) with all_39_0, all_225_0, simplifying
% 143.49/19.96 | | | | with (10), (70), (71) gives:
% 143.49/19.96 | | | | (72) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_39_0, all_225_0)
% 143.49/19.96 | | | | = 0) | (v0 = 0 & empty(all_225_0) = 0))
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | GROUND_INST: instantiating (36) with all_47_1, all_225_0, simplifying
% 143.49/19.96 | | | | with (37), (57), (71) gives:
% 143.49/19.96 | | | | (73) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_47_1, all_225_0)
% 143.49/19.96 | | | | = 0) | (v0 = 0 & empty(all_225_0) = 0))
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | DELTA: instantiating (73) with fresh symbols all_361_0, all_361_1 gives:
% 143.49/19.96 | | | | (74) (all_361_0 = 0 & in(all_47_1, all_225_0) = 0) | (all_361_1 = 0 &
% 143.49/19.96 | | | | empty(all_225_0) = 0)
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | DELTA: instantiating (72) with fresh symbols all_362_0, all_362_1 gives:
% 143.49/19.96 | | | | (75) (all_362_0 = 0 & in(all_39_0, all_225_0) = 0) | (all_362_1 = 0 &
% 143.49/19.96 | | | | empty(all_225_0) = 0)
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | BETA: splitting (30) gives:
% 143.49/19.96 | | | |
% 143.49/19.96 | | | | Case 1:
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | (76) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | ALPHA: (76) implies:
% 143.49/19.96 | | | | | (77) ~ (all_125_0 = 0)
% 143.49/19.96 | | | | | (78) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | REF_CLOSE: (1), (3), (9), (10), (11), (12), (13), (14), (15), (17),
% 143.49/19.96 | | | | | (20), (21), (23), (26), (34), (37), (41), (77), (78) are
% 143.49/19.96 | | | | | inconsistent by sub-proof #13.
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | Case 2:
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | (79) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | ALPHA: (79) implies:
% 143.49/19.96 | | | | | (80) ~ (all_125_1 = 0)
% 143.49/19.96 | | | | | (81) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | BETA: splitting (39) gives:
% 143.49/19.96 | | | | |
% 143.49/19.96 | | | | | Case 1:
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | (82) all_149_0 = 0 & in(empty_set, all_47_1) = 0
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | ALPHA: (82) implies:
% 143.49/19.96 | | | | | | (83) in(empty_set, all_47_1) = 0
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | BETA: splitting (47) gives:
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | Case 1:
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | GROUND_INST: instantiating (27) with all_51_1, all_125_1,
% 143.49/19.96 | | | | | | | simplifying with (1), (81) gives:
% 143.49/19.96 | | | | | | | (84) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0)
% 143.49/19.96 | | | | | | | & subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 &
% 143.49/19.96 | | | | | | | $i(v0))
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | REF_CLOSE: (2), (3), (9), (10), (13), (14), (17), (18), (26),
% 143.49/19.96 | | | | | | | (37), (38), (41), (71), (74), (75), (80), (83), (84)
% 143.49/19.96 | | | | | | | are inconsistent by sub-proof #5.
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | Case 2:
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | (85) all_201_1 = 0 & in(all_39_0, all_47_1) = 0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | ALPHA: (85) implies:
% 143.49/19.96 | | | | | | | (86) in(all_39_0, all_47_1) = 0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | BETA: splitting (65) gives:
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | Case 1:
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | GROUND_INST: instantiating (27) with all_51_1, all_125_1,
% 143.49/19.96 | | | | | | | | simplifying with (1), (81) gives:
% 143.49/19.96 | | | | | | | | (87) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 =
% 143.49/19.96 | | | | | | | | 0) & subset(v0, all_51_1) = v1 & in(v0, all_51_1) =
% 143.49/19.96 | | | | | | | | 0 & $i(v0))
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | REF_CLOSE: (2), (3), (9), (10), (13), (14), (17), (18), (26),
% 143.49/19.96 | | | | | | | | (37), (38), (41), (71), (74), (75), (80), (83), (87)
% 143.49/19.96 | | | | | | | | are inconsistent by sub-proof #5.
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | Case 2:
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | (88) ~ (all_232_1 = 0) & in(all_39_0, all_51_1) = all_232_1
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | REF_CLOSE: (1), (4), (7), (10), (24), (25), (33), (37), (41),
% 143.49/19.96 | | | | | | | | (57), (58), (86), (88) are inconsistent by sub-proof
% 143.49/19.96 | | | | | | | | #4.
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | End of split
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | End of split
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | Case 2:
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | (89) all_149_1 = 0 & in(all_47_1, empty_set) = 0
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | ALPHA: (89) implies:
% 143.49/19.96 | | | | | | (90) in(all_47_1, empty_set) = 0
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | BETA: splitting (29) gives:
% 143.49/19.96 | | | | | |
% 143.49/19.96 | | | | | | Case 1:
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | (91) all_196_0 = 0 & in(all_39_0, all_47_1) = 0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | ALPHA: (91) implies:
% 143.49/19.96 | | | | | | | (92) in(all_39_0, all_47_1) = 0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | BETA: splitting (65) gives:
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | Case 1:
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | GROUND_INST: instantiating (13) with all_47_1, empty_set,
% 143.49/19.96 | | | | | | | | simplifying with (12), (37), (90) gives:
% 143.49/19.96 | | | | | | | | (93) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | DELTA: instantiating (93) with fresh symbol all_473_0 gives:
% 143.49/19.96 | | | | | | | | (94) ~ (all_473_0 = 0) & empty(empty_set) = all_473_0
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | ALPHA: (94) implies:
% 143.49/19.96 | | | | | | | | (95) ~ (all_473_0 = 0)
% 143.49/19.96 | | | | | | | | (96) empty(empty_set) = all_473_0
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | GROUND_INST: instantiating (41) with 0, all_473_0, empty_set,
% 143.49/19.96 | | | | | | | | simplifying with (15), (96) gives:
% 143.49/19.96 | | | | | | | | (97) all_473_0 = 0
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | REDUCE: (95), (97) imply:
% 143.49/19.96 | | | | | | | | (98) $false
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | CLOSE: (98) is inconsistent.
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | Case 2:
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | (99) ~ (all_232_1 = 0) & in(all_39_0, all_51_1) = all_232_1
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | | REF_CLOSE: (1), (4), (7), (10), (24), (25), (33), (37), (41),
% 143.49/19.96 | | | | | | | | (57), (58), (92), (99) are inconsistent by sub-proof
% 143.49/19.96 | | | | | | | | #4.
% 143.49/19.96 | | | | | | | |
% 143.49/19.96 | | | | | | | End of split
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | Case 2:
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | GROUND_INST: instantiating (13) with all_47_1, empty_set,
% 143.49/19.96 | | | | | | | simplifying with (12), (37), (90) gives:
% 143.49/19.96 | | | | | | | (100) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | DELTA: instantiating (100) with fresh symbol all_473_0 gives:
% 143.49/19.96 | | | | | | | (101) ~ (all_473_0 = 0) & empty(empty_set) = all_473_0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | ALPHA: (101) implies:
% 143.49/19.96 | | | | | | | (102) ~ (all_473_0 = 0)
% 143.49/19.96 | | | | | | | (103) empty(empty_set) = all_473_0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | GROUND_INST: instantiating (41) with 0, all_473_0, empty_set,
% 143.49/19.96 | | | | | | | simplifying with (15), (103) gives:
% 143.49/19.96 | | | | | | | (104) all_473_0 = 0
% 143.49/19.96 | | | | | | |
% 143.49/19.96 | | | | | | | REDUCE: (102), (104) imply:
% 143.49/19.97 | | | | | | | (105) $false
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | CLOSE: (105) is inconsistent.
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | End of split
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | End of split
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | End of split
% 143.49/19.97 | | | |
% 143.49/19.97 | | | Case 2:
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | (106) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) = all_63_1
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | ALPHA: (106) implies:
% 143.49/19.97 | | | | (107) ~ (all_63_1 = 0)
% 143.49/19.97 | | | | (108) in(all_47_1, all_51_1) = all_63_1
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | GROUND_INST: instantiating (40) with all_39_0, all_47_1, all_51_1,
% 143.49/19.97 | | | | all_63_1, simplifying with (1), (10), (37), (42), (108)
% 143.49/19.97 | | | | gives:
% 143.49/19.97 | | | | (109) all_63_1 = 0 | all_51_1 = all_47_1 | ? [v0: int] : ? [v1:
% 143.49/19.97 | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, all_47_1) = 0)
% 143.49/19.97 | | | | | ( ~ (v1 = 0) & in(all_51_1, all_39_0) = v1) | ( ~ (v0 = 0)
% 143.49/19.97 | | | | & in(all_47_1, all_39_0) = v0))
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | GROUND_INST: instantiating (33) with all_47_1, all_51_1, all_63_1,
% 143.49/19.97 | | | | simplifying with (1), (37), (108) gives:
% 143.49/19.97 | | | | (110) all_63_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.97 | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_47_1,
% 143.49/19.97 | | | | all_51_1) = v0))
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | GROUND_INST: instantiating (5) with empty_set, all_51_1, simplifying
% 143.49/19.97 | | | | with (1), (12), (19) gives:
% 143.49/19.97 | | | | (111) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0)
% 143.49/19.97 | | | | = 0 & $i(v0))
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | GROUND_INST: instantiating (5) with all_39_0, all_51_1, simplifying with
% 143.49/19.97 | | | | (1), (10), (49) gives:
% 143.49/19.97 | | | | (112) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_39_0, v0)
% 143.49/19.97 | | | | = 0 & $i(v0))
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | DELTA: instantiating (112) with fresh symbol all_225_0 gives:
% 143.49/19.97 | | | | (113) powerset(all_51_1) = all_225_0 & element(all_39_0, all_225_0) =
% 143.49/19.97 | | | | 0 & $i(all_225_0)
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | ALPHA: (113) implies:
% 143.49/19.97 | | | | (114) element(all_39_0, all_225_0) = 0
% 143.49/19.97 | | | | (115) powerset(all_51_1) = all_225_0
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | DELTA: instantiating (111) with fresh symbol all_227_0 gives:
% 143.49/19.97 | | | | (116) powerset(all_51_1) = all_227_0 & element(empty_set, all_227_0)
% 143.49/19.97 | | | | = 0 & $i(all_227_0)
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | ALPHA: (116) implies:
% 143.49/19.97 | | | | (117) powerset(all_51_1) = all_227_0
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | BETA: splitting (110) gives:
% 143.49/19.97 | | | |
% 143.49/19.97 | | | | Case 1:
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | (118) all_63_1 = 0
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | REDUCE: (107), (118) imply:
% 143.49/19.97 | | | | | (119) $false
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | CLOSE: (119) is inconsistent.
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | Case 2:
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | (120) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0)
% 143.49/19.97 | | | | | | ( ~ (v0 = 0) & element(all_47_1, all_51_1) = v0))
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | DELTA: instantiating (120) with fresh symbols all_235_0, all_235_1
% 143.49/19.97 | | | | | gives:
% 143.49/19.97 | | | | | (121) (all_235_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_235_1 = 0) &
% 143.49/19.97 | | | | | element(all_47_1, all_51_1) = all_235_1)
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | BETA: splitting (121) gives:
% 143.49/19.97 | | | | |
% 143.49/19.97 | | | | | Case 1:
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | (122) all_235_0 = 0 & empty(all_51_1) = 0
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | ALPHA: (122) implies:
% 143.49/19.97 | | | | | | (123) empty(all_51_1) = 0
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | REF_CLOSE: (4), (24), (41), (123) are inconsistent by sub-proof #23.
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | Case 2:
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | (124) ~ (all_235_1 = 0) & element(all_47_1, all_51_1) =
% 143.49/19.97 | | | | | | all_235_1
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | ALPHA: (124) implies:
% 143.49/19.97 | | | | | | (125) ~ (all_235_1 = 0)
% 143.49/19.97 | | | | | | (126) element(all_47_1, all_51_1) = all_235_1
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | GROUND_INST: instantiating (28) with all_225_0, all_227_0, all_51_1,
% 143.49/19.97 | | | | | | simplifying with (115), (117) gives:
% 143.49/19.97 | | | | | | (127) all_227_0 = all_225_0
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | GROUND_INST: instantiating (32) with all_47_1, all_39_0, all_51_1,
% 143.49/19.97 | | | | | | all_225_0, all_235_1, simplifying with (1), (10), (37),
% 143.49/19.97 | | | | | | (114), (115), (126) gives:
% 143.49/19.97 | | | | | | (128) all_235_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1,
% 143.49/19.97 | | | | | | all_39_0) = v0)
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | BETA: splitting (30) gives:
% 143.49/19.97 | | | | | |
% 143.49/19.97 | | | | | | Case 1:
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | (129) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 143.49/19.97 | | | | | | | all_125_0
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | ALPHA: (129) implies:
% 143.49/19.97 | | | | | | | (130) ~ (all_125_0 = 0)
% 143.49/19.97 | | | | | | | (131) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | REF_CLOSE: (1), (3), (9), (10), (11), (12), (13), (14), (15),
% 143.49/19.97 | | | | | | | (17), (20), (21), (23), (26), (34), (37), (41), (130),
% 143.49/19.97 | | | | | | | (131) are inconsistent by sub-proof #13.
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | Case 2:
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | (132) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) =
% 143.49/19.97 | | | | | | | all_125_1
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | ALPHA: (132) implies:
% 143.49/19.97 | | | | | | | (133) ~ (all_125_1 = 0)
% 143.49/19.97 | | | | | | | (134) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | BETA: splitting (128) gives:
% 143.49/19.97 | | | | | | |
% 143.49/19.97 | | | | | | | Case 1:
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | (135) all_235_1 = 0
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | REDUCE: (125), (135) imply:
% 143.49/19.97 | | | | | | | | (136) $false
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | CLOSE: (136) is inconsistent.
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | Case 2:
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | (137) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1, all_39_0) =
% 143.49/19.97 | | | | | | | | v0)
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | DELTA: instantiating (137) with fresh symbol all_380_0 gives:
% 143.49/19.97 | | | | | | | | (138) ~ (all_380_0 = 0) & in(all_47_1, all_39_0) = all_380_0
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | ALPHA: (138) implies:
% 143.49/19.97 | | | | | | | | (139) ~ (all_380_0 = 0)
% 143.49/19.97 | | | | | | | | (140) in(all_47_1, all_39_0) = all_380_0
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | BETA: splitting (109) gives:
% 143.49/19.97 | | | | | | | |
% 143.49/19.97 | | | | | | | | Case 1:
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | (141) all_63_1 = 0
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | REDUCE: (107), (141) imply:
% 143.49/19.97 | | | | | | | | | (142) $false
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | CLOSE: (142) is inconsistent.
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | Case 2:
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | GROUND_INST: instantiating (40) with all_47_1, all_47_1,
% 143.49/19.97 | | | | | | | | | all_39_0, all_380_0, simplifying with (10), (21),
% 143.49/19.97 | | | | | | | | | (37), (140) gives:
% 143.49/19.97 | | | | | | | | | (143) all_380_0 = 0 | all_47_1 = all_39_0 | ? [v0: int] :
% 143.49/19.97 | | | | | | | | | ? [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_39_0,
% 143.49/19.97 | | | | | | | | | all_47_1) = 0) | ( ~ (v1 = 0) & in(all_39_0,
% 143.49/19.97 | | | | | | | | | all_47_1) = v1) | ( ~ (v0 = 0) & in(all_47_1,
% 143.49/19.97 | | | | | | | | | all_47_1) = v0))
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | GROUND_INST: instantiating (27) with all_51_1, all_125_1,
% 143.49/19.97 | | | | | | | | | simplifying with (1), (134) gives:
% 143.49/19.97 | | | | | | | | | (144) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1
% 143.49/19.97 | | | | | | | | | = 0) & subset(v0, all_51_1) = v1 & in(v0,
% 143.49/19.97 | | | | | | | | | all_51_1) = 0 & $i(v0))
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | BETA: splitting (144) gives:
% 143.49/19.97 | | | | | | | | |
% 143.49/19.97 | | | | | | | | | Case 1:
% 143.49/19.97 | | | | | | | | | |
% 143.49/19.97 | | | | | | | | | | (145) all_125_1 = 0
% 143.49/19.97 | | | | | | | | | |
% 143.49/19.97 | | | | | | | | | | REDUCE: (133), (145) imply:
% 143.49/19.97 | | | | | | | | | | (146) $false
% 143.49/19.97 | | | | | | | | | |
% 143.49/19.97 | | | | | | | | | | CLOSE: (146) is inconsistent.
% 143.49/19.97 | | | | | | | | | |
% 143.49/19.97 | | | | | | | | | Case 2:
% 143.49/19.97 | | | | | | | | | |
% 143.49/19.97 | | | | | | | | | | (147) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 143.49/19.97 | | | | | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0
% 143.49/19.97 | | | | | | | | | | & $i(v0))
% 143.49/19.97 | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | DELTA: instantiating (147) with fresh symbols all_513_0,
% 143.49/19.98 | | | | | | | | | | all_513_1 gives:
% 143.49/19.98 | | | | | | | | | | (148) ~ (all_513_0 = 0) & subset(all_513_1, all_51_1) =
% 143.49/19.98 | | | | | | | | | | all_513_0 & in(all_513_1, all_51_1) = 0 &
% 143.49/19.98 | | | | | | | | | | $i(all_513_1)
% 143.49/19.98 | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | ALPHA: (148) implies:
% 143.49/19.98 | | | | | | | | | | (149) ~ (all_513_0 = 0)
% 143.49/19.98 | | | | | | | | | | (150) $i(all_513_1)
% 143.49/19.98 | | | | | | | | | | (151) in(all_513_1, all_51_1) = 0
% 143.49/19.98 | | | | | | | | | | (152) subset(all_513_1, all_51_1) = all_513_0
% 143.49/19.98 | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | BETA: splitting (143) gives:
% 143.49/19.98 | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | Case 1:
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | (153) all_380_0 = 0
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | REDUCE: (139), (153) imply:
% 143.49/19.98 | | | | | | | | | | | (154) $false
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | CLOSE: (154) is inconsistent.
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | Case 2:
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | (155) all_47_1 = all_39_0 | ? [v0: int] : ? [v1: int]
% 143.49/19.98 | | | | | | | | | | | : ? [v2: int] : ((v2 = 0 & in(all_39_0, all_47_1)
% 143.49/19.98 | | | | | | | | | | | = 0) | ( ~ (v1 = 0) & in(all_39_0, all_47_1) =
% 143.49/19.98 | | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(all_47_1, all_47_1) =
% 143.49/19.98 | | | | | | | | | | | v0))
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | BETA: splitting (155) gives:
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | Case 1:
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | (156) all_47_1 = all_39_0
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | REDUCE: (22), (156) imply:
% 143.49/19.98 | | | | | | | | | | | | (157) $false
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | CLOSE: (157) is inconsistent.
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | Case 2:
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_513_1, simplifying with
% 143.49/19.98 | | | | | | | | | | | | (150), (151) gives:
% 143.49/19.98 | | | | | | | | | | | | (158) subset(all_513_1, all_51_1) = 0 &
% 143.49/19.98 | | | | | | | | | | | | ordinal(all_513_1) = 0
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | ALPHA: (158) implies:
% 143.49/19.98 | | | | | | | | | | | | (159) subset(all_513_1, all_51_1) = 0
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_513_0, 0, all_51_1,
% 143.49/19.98 | | | | | | | | | | | | all_513_1, simplifying with (152), (159) gives:
% 143.49/19.98 | | | | | | | | | | | | (160) all_513_0 = 0
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | REDUCE: (149), (160) imply:
% 143.49/19.98 | | | | | | | | | | | | (161) $false
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | | CLOSE: (161) is inconsistent.
% 143.49/19.98 | | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | | End of split
% 143.49/19.98 | | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | | End of split
% 143.49/19.98 | | | | | | | | | |
% 143.49/19.98 | | | | | | | | | End of split
% 143.49/19.98 | | | | | | | | |
% 143.49/19.98 | | | | | | | | End of split
% 143.49/19.98 | | | | | | | |
% 143.49/19.98 | | | | | | | End of split
% 143.49/19.98 | | | | | | |
% 143.49/19.98 | | | | | | End of split
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | End of split
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | End of split
% 143.49/19.98 | | | |
% 143.49/19.98 | | | End of split
% 143.49/19.98 | | |
% 143.49/19.98 | | Case 2:
% 143.49/19.98 | | |
% 143.49/19.98 | | | (162) ~ (all_60_1 = 0) & in(all_39_0, all_51_1) = all_60_1
% 143.49/19.98 | | |
% 143.49/19.98 | | | ALPHA: (162) implies:
% 143.49/19.98 | | | (163) ~ (all_60_1 = 0)
% 143.49/19.98 | | | (164) in(all_39_0, all_51_1) = all_60_1
% 143.49/19.98 | | |
% 143.49/19.98 | | | BETA: splitting (16) gives:
% 143.49/19.98 | | |
% 143.49/19.98 | | | Case 1:
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | (165) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | ALPHA: (165) implies:
% 143.49/19.98 | | | | (166) subset(all_47_1, all_51_1) = 0
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | GROUND_INST: instantiating (23) with all_47_1, all_51_1, all_39_0,
% 143.49/19.98 | | | | all_60_1, simplifying with (1), (10), (21), (37), (164)
% 143.49/19.98 | | | | gives:
% 143.49/19.98 | | | | (167) all_60_1 = 0 | all_51_1 = all_39_0 | ? [v0: int] : ? [v1:
% 143.49/19.98 | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, all_39_0) = 0)
% 143.49/19.98 | | | | | ( ~ (v1 = 0) & in(all_39_0, all_47_1) = v1) | ( ~ (v0 = 0)
% 143.49/19.98 | | | | & in(all_51_1, all_47_1) = v0))
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | GROUND_INST: instantiating (5) with empty_set, all_51_1, simplifying
% 143.49/19.98 | | | | with (1), (12), (19) gives:
% 143.49/19.98 | | | | (168) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0)
% 143.49/19.98 | | | | = 0 & $i(v0))
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | GROUND_INST: instantiating (5) with all_47_1, all_51_1, simplifying with
% 143.49/19.98 | | | | (1), (37), (166) gives:
% 143.49/19.98 | | | | (169) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_47_1, v0)
% 143.49/19.98 | | | | = 0 & $i(v0))
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | DELTA: instantiating (169) with fresh symbol all_225_0 gives:
% 143.49/19.98 | | | | (170) powerset(all_51_1) = all_225_0 & element(all_47_1, all_225_0) =
% 143.49/19.98 | | | | 0 & $i(all_225_0)
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | ALPHA: (170) implies:
% 143.49/19.98 | | | | (171) element(all_47_1, all_225_0) = 0
% 143.49/19.98 | | | | (172) powerset(all_51_1) = all_225_0
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | DELTA: instantiating (168) with fresh symbol all_227_0 gives:
% 143.49/19.98 | | | | (173) powerset(all_51_1) = all_227_0 & element(empty_set, all_227_0)
% 143.49/19.98 | | | | = 0 & $i(all_227_0)
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | ALPHA: (173) implies:
% 143.49/19.98 | | | | (174) $i(all_227_0)
% 143.49/19.98 | | | | (175) element(empty_set, all_227_0) = 0
% 143.49/19.98 | | | | (176) powerset(all_51_1) = all_227_0
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | GROUND_INST: instantiating (28) with all_225_0, all_227_0, all_51_1,
% 143.49/19.98 | | | | simplifying with (172), (176) gives:
% 143.49/19.98 | | | | (177) all_227_0 = all_225_0
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | REDUCE: (175), (177) imply:
% 143.49/19.98 | | | | (178) element(empty_set, all_225_0) = 0
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | REDUCE: (174), (177) imply:
% 143.49/19.98 | | | | (179) $i(all_225_0)
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | GROUND_INST: instantiating (36) with empty_set, all_225_0, simplifying
% 143.49/19.98 | | | | with (12), (178), (179) gives:
% 143.49/19.98 | | | | (180) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(empty_set,
% 143.49/19.98 | | | | all_225_0) = 0) | (v0 = 0 & empty(all_225_0) = 0))
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | GROUND_INST: instantiating (36) with all_47_1, all_225_0, simplifying
% 143.49/19.98 | | | | with (37), (171), (179) gives:
% 143.49/19.98 | | | | (181) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_47_1,
% 143.49/19.98 | | | | all_225_0) = 0) | (v0 = 0 & empty(all_225_0) = 0))
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | DELTA: instantiating (181) with fresh symbols all_351_0, all_351_1
% 143.49/19.98 | | | | gives:
% 143.49/19.98 | | | | (182) (all_351_0 = 0 & in(all_47_1, all_225_0) = 0) | (all_351_1 = 0
% 143.49/19.98 | | | | & empty(all_225_0) = 0)
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | DELTA: instantiating (180) with fresh symbols all_352_0, all_352_1
% 143.49/19.98 | | | | gives:
% 143.49/19.98 | | | | (183) (all_352_0 = 0 & in(empty_set, all_225_0) = 0) | (all_352_1 = 0
% 143.49/19.98 | | | | & empty(all_225_0) = 0)
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | BETA: splitting (30) gives:
% 143.49/19.98 | | | |
% 143.49/19.98 | | | | Case 1:
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | (184) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | ALPHA: (184) implies:
% 143.49/19.98 | | | | | (185) ~ (all_125_0 = 0)
% 143.49/19.98 | | | | | (186) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | REF_CLOSE: (1), (3), (9), (10), (11), (12), (13), (14), (15), (17),
% 143.49/19.98 | | | | | (20), (21), (23), (26), (34), (37), (41), (185), (186) are
% 143.49/19.98 | | | | | inconsistent by sub-proof #13.
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | Case 2:
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | (187) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | ALPHA: (187) implies:
% 143.49/19.98 | | | | | (188) ~ (all_125_1 = 0)
% 143.49/19.98 | | | | | (189) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | BETA: splitting (167) gives:
% 143.49/19.98 | | | | |
% 143.49/19.98 | | | | | Case 1:
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | | (190) all_60_1 = 0
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | | REDUCE: (163), (190) imply:
% 143.49/19.98 | | | | | | (191) $false
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | | CLOSE: (191) is inconsistent.
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | Case 2:
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | |
% 143.49/19.98 | | | | | | GROUND_INST: instantiating (27) with all_51_1, all_125_1,
% 143.49/19.98 | | | | | | simplifying with (1), (189) gives:
% 143.49/19.99 | | | | | | (192) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 143.49/19.99 | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 &
% 143.49/19.99 | | | | | | $i(v0))
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | BETA: splitting (192) gives:
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | Case 1:
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | (193) all_125_1 = 0
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | REDUCE: (188), (193) imply:
% 143.49/19.99 | | | | | | | (194) $false
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | CLOSE: (194) is inconsistent.
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | Case 2:
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | (195) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 143.49/19.99 | | | | | | | all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | DELTA: instantiating (195) with fresh symbols all_507_0, all_507_1
% 143.49/19.99 | | | | | | | gives:
% 143.49/19.99 | | | | | | | (196) ~ (all_507_0 = 0) & subset(all_507_1, all_51_1) =
% 143.49/19.99 | | | | | | | all_507_0 & in(all_507_1, all_51_1) = 0 & $i(all_507_1)
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | ALPHA: (196) implies:
% 143.49/19.99 | | | | | | | (197) ~ (all_507_0 = 0)
% 143.49/19.99 | | | | | | | (198) $i(all_507_1)
% 143.49/19.99 | | | | | | | (199) in(all_507_1, all_51_1) = 0
% 143.49/19.99 | | | | | | | (200) subset(all_507_1, all_51_1) = all_507_0
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | BETA: splitting (183) gives:
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | Case 1:
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | GROUND_INST: instantiating (3) with all_507_1, simplifying with
% 143.49/19.99 | | | | | | | | (198), (199) gives:
% 143.49/19.99 | | | | | | | | (201) subset(all_507_1, all_51_1) = 0 & ordinal(all_507_1) =
% 143.49/19.99 | | | | | | | | 0
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | REF_CLOSE: (38), (197), (200), (201) are inconsistent by
% 143.49/19.99 | | | | | | | | sub-proof #3.
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | Case 2:
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | (202) all_352_1 = 0 & empty(all_225_0) = 0
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | ALPHA: (202) implies:
% 143.49/19.99 | | | | | | | | (203) empty(all_225_0) = 0
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | BETA: splitting (182) gives:
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | Case 1:
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | (204) all_351_0 = 0 & in(all_47_1, all_225_0) = 0
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | ALPHA: (204) implies:
% 143.49/19.99 | | | | | | | | | (205) in(all_47_1, all_225_0) = 0
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | GROUND_INST: instantiating (18) with all_225_0, simplifying
% 143.49/19.99 | | | | | | | | | with (179), (203) gives:
% 143.49/19.99 | | | | | | | | | (206) all_225_0 = empty_set
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | REDUCE: (205), (206) imply:
% 143.49/19.99 | | | | | | | | | (207) in(all_47_1, empty_set) = 0
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | REF_CLOSE: (12), (13), (15), (37), (41), (163), (167), (207)
% 143.49/19.99 | | | | | | | | | are inconsistent by sub-proof #2.
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | Case 2:
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | GROUND_INST: instantiating (3) with all_507_1, simplifying with
% 143.49/19.99 | | | | | | | | | (198), (199) gives:
% 143.49/19.99 | | | | | | | | | (208) subset(all_507_1, all_51_1) = 0 & ordinal(all_507_1)
% 143.49/19.99 | | | | | | | | | = 0
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | | REF_CLOSE: (38), (197), (200), (208) are inconsistent by
% 143.49/19.99 | | | | | | | | | sub-proof #3.
% 143.49/19.99 | | | | | | | | |
% 143.49/19.99 | | | | | | | | End of split
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | End of split
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | End of split
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | End of split
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | End of split
% 143.49/19.99 | | | |
% 143.49/19.99 | | | Case 2:
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | (209) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) = all_63_1
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | ALPHA: (209) implies:
% 143.49/19.99 | | | | (210) ~ (all_63_1 = 0)
% 143.49/19.99 | | | | (211) in(all_47_1, all_51_1) = all_63_1
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | GROUND_INST: instantiating (23) with all_39_0, all_51_1, all_39_0,
% 143.49/19.99 | | | | all_60_1, simplifying with (1), (10), (42), (164) gives:
% 143.49/19.99 | | | | (212) all_60_1 = 0 | all_51_1 = all_39_0 | ? [v0: int] : ? [v1:
% 143.49/19.99 | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, all_39_0) = 0)
% 143.49/19.99 | | | | | ( ~ (v1 = 0) & in(all_39_0, all_39_0) = v1) | ( ~ (v0 = 0)
% 143.49/19.99 | | | | & in(all_51_1, all_39_0) = v0))
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | GROUND_INST: instantiating (33) with all_47_1, all_51_1, all_63_1,
% 143.49/19.99 | | | | simplifying with (1), (37), (211) gives:
% 143.49/19.99 | | | | (213) all_63_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 143.49/19.99 | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_47_1,
% 143.49/19.99 | | | | all_51_1) = v0))
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | GROUND_INST: instantiating (5) with empty_set, all_51_1, simplifying
% 143.49/19.99 | | | | with (1), (12), (19) gives:
% 143.49/19.99 | | | | (214) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0)
% 143.49/19.99 | | | | = 0 & $i(v0))
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | DELTA: instantiating (214) with fresh symbol all_225_0 gives:
% 143.49/19.99 | | | | (215) powerset(all_51_1) = all_225_0 & element(empty_set, all_225_0)
% 143.49/19.99 | | | | = 0 & $i(all_225_0)
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | ALPHA: (215) implies:
% 143.49/19.99 | | | | (216) element(empty_set, all_225_0) = 0
% 143.49/19.99 | | | | (217) powerset(all_51_1) = all_225_0
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | BETA: splitting (213) gives:
% 143.49/19.99 | | | |
% 143.49/19.99 | | | | Case 1:
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | (218) all_63_1 = 0
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | REDUCE: (210), (218) imply:
% 143.49/19.99 | | | | | (219) $false
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | CLOSE: (219) is inconsistent.
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | Case 2:
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | (220) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0)
% 143.49/19.99 | | | | | | ( ~ (v0 = 0) & element(all_47_1, all_51_1) = v0))
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | DELTA: instantiating (220) with fresh symbols all_232_0, all_232_1
% 143.49/19.99 | | | | | gives:
% 143.49/19.99 | | | | | (221) (all_232_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_232_1 = 0) &
% 143.49/19.99 | | | | | element(all_47_1, all_51_1) = all_232_1)
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | BETA: splitting (221) gives:
% 143.49/19.99 | | | | |
% 143.49/19.99 | | | | | Case 1:
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | (222) all_232_0 = 0 & empty(all_51_1) = 0
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | ALPHA: (222) implies:
% 143.49/19.99 | | | | | | (223) empty(all_51_1) = 0
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | REF_CLOSE: (4), (24), (41), (223) are inconsistent by sub-proof #23.
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | Case 2:
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | (224) ~ (all_232_1 = 0) & element(all_47_1, all_51_1) =
% 143.49/19.99 | | | | | | all_232_1
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | ALPHA: (224) implies:
% 143.49/19.99 | | | | | | (225) ~ (all_232_1 = 0)
% 143.49/19.99 | | | | | | (226) element(all_47_1, all_51_1) = all_232_1
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | GROUND_INST: instantiating (32) with all_47_1, empty_set, all_51_1,
% 143.49/19.99 | | | | | | all_225_0, all_232_1, simplifying with (1), (12), (37),
% 143.49/19.99 | | | | | | (216), (217), (226) gives:
% 143.49/19.99 | | | | | | (227) all_232_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1,
% 143.49/19.99 | | | | | | empty_set) = v0)
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | BETA: splitting (30) gives:
% 143.49/19.99 | | | | | |
% 143.49/19.99 | | | | | | Case 1:
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | (228) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 143.49/19.99 | | | | | | | all_125_0
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | ALPHA: (228) implies:
% 143.49/19.99 | | | | | | | (229) ~ (all_125_0 = 0)
% 143.49/19.99 | | | | | | | (230) epsilon_connected(all_51_1) = all_125_0
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | REF_CLOSE: (1), (3), (9), (10), (11), (12), (13), (14), (15),
% 143.49/19.99 | | | | | | | (17), (20), (21), (23), (26), (34), (37), (41), (229),
% 143.49/19.99 | | | | | | | (230) are inconsistent by sub-proof #13.
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | Case 2:
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | (231) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) =
% 143.49/19.99 | | | | | | | all_125_1
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | ALPHA: (231) implies:
% 143.49/19.99 | | | | | | | (232) ~ (all_125_1 = 0)
% 143.49/19.99 | | | | | | | (233) epsilon_transitive(all_51_1) = all_125_1
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | BETA: splitting (227) gives:
% 143.49/19.99 | | | | | | |
% 143.49/19.99 | | | | | | | Case 1:
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | (234) all_232_1 = 0
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | REDUCE: (225), (234) imply:
% 143.49/19.99 | | | | | | | | (235) $false
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | CLOSE: (235) is inconsistent.
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | Case 2:
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | (236) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1, empty_set) =
% 143.49/19.99 | | | | | | | | v0)
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | DELTA: instantiating (236) with fresh symbol all_383_0 gives:
% 143.49/19.99 | | | | | | | | (237) ~ (all_383_0 = 0) & in(all_47_1, empty_set) =
% 143.49/19.99 | | | | | | | | all_383_0
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | ALPHA: (237) implies:
% 143.49/19.99 | | | | | | | | (238) ~ (all_383_0 = 0)
% 143.49/19.99 | | | | | | | | (239) in(all_47_1, empty_set) = all_383_0
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | BETA: splitting (212) gives:
% 143.49/19.99 | | | | | | | |
% 143.49/19.99 | | | | | | | | Case 1:
% 143.49/19.99 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | (240) all_60_1 = 0
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | REDUCE: (163), (240) imply:
% 143.49/20.00 | | | | | | | | | (241) $false
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | CLOSE: (241) is inconsistent.
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | Case 2:
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | GROUND_INST: instantiating (40) with empty_set, all_47_1,
% 143.49/20.00 | | | | | | | | | empty_set, all_383_0, simplifying with (12), (31),
% 143.49/20.00 | | | | | | | | | (37), (239) gives:
% 143.49/20.00 | | | | | | | | | (242) all_383_0 = 0 | all_47_1 = empty_set | ? [v0: int] :
% 143.49/20.00 | | | | | | | | | ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 143.49/20.00 | | | | | | | | | in(empty_set, all_47_1) = 0) | ( ~ (v1 = 0) &
% 143.49/20.00 | | | | | | | | | in(empty_set, empty_set) = v1) | ( ~ (v0 = 0) &
% 143.49/20.00 | | | | | | | | | in(all_47_1, empty_set) = v0))
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | GROUND_INST: instantiating (27) with all_51_1, all_125_1,
% 143.49/20.00 | | | | | | | | | simplifying with (1), (233) gives:
% 143.49/20.00 | | | | | | | | | (243) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1
% 143.49/20.00 | | | | | | | | | = 0) & subset(v0, all_51_1) = v1 & in(v0,
% 143.49/20.00 | | | | | | | | | all_51_1) = 0 & $i(v0))
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | BETA: splitting (243) gives:
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | | Case 1:
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | (244) all_125_1 = 0
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | REDUCE: (232), (244) imply:
% 143.49/20.00 | | | | | | | | | | (245) $false
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | CLOSE: (245) is inconsistent.
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | Case 2:
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | (246) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 143.49/20.00 | | | | | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0
% 143.49/20.00 | | | | | | | | | | & $i(v0))
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | DELTA: instantiating (246) with fresh symbols all_561_0,
% 143.49/20.00 | | | | | | | | | | all_561_1 gives:
% 143.49/20.00 | | | | | | | | | | (247) ~ (all_561_0 = 0) & subset(all_561_1, all_51_1) =
% 143.49/20.00 | | | | | | | | | | all_561_0 & in(all_561_1, all_51_1) = 0 &
% 143.49/20.00 | | | | | | | | | | $i(all_561_1)
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | ALPHA: (247) implies:
% 143.49/20.00 | | | | | | | | | | (248) ~ (all_561_0 = 0)
% 143.49/20.00 | | | | | | | | | | (249) $i(all_561_1)
% 143.49/20.00 | | | | | | | | | | (250) in(all_561_1, all_51_1) = 0
% 143.49/20.00 | | | | | | | | | | (251) subset(all_561_1, all_51_1) = all_561_0
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | BETA: splitting (242) gives:
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | Case 1:
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | (252) all_47_1 = empty_set
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | REDUCE: (8), (252) imply:
% 143.49/20.00 | | | | | | | | | | | (253) $false
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | Case 2:
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | (254) all_383_0 = 0 | ? [v0: int] : ? [v1: int] : ?
% 143.49/20.00 | | | | | | | | | | | [v2: int] : ((v2 = 0 & in(empty_set, all_47_1) =
% 143.49/20.00 | | | | | | | | | | | 0) | ( ~ (v1 = 0) & in(empty_set, empty_set) =
% 143.49/20.00 | | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(all_47_1, empty_set) =
% 143.49/20.00 | | | | | | | | | | | v0))
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | BETA: splitting (254) gives:
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | Case 1:
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | (255) all_383_0 = 0
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | REDUCE: (238), (255) imply:
% 143.49/20.00 | | | | | | | | | | | | (256) $false
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | CLOSE: (256) is inconsistent.
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | Case 2:
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_561_1, simplifying with
% 143.49/20.00 | | | | | | | | | | | | (249), (250) gives:
% 143.49/20.00 | | | | | | | | | | | | (257) subset(all_561_1, all_51_1) = 0 &
% 143.49/20.00 | | | | | | | | | | | | ordinal(all_561_1) = 0
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | ALPHA: (257) implies:
% 143.49/20.00 | | | | | | | | | | | | (258) subset(all_561_1, all_51_1) = 0
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_561_0, 0, all_51_1,
% 143.49/20.00 | | | | | | | | | | | | all_561_1, simplifying with (251), (258) gives:
% 143.49/20.00 | | | | | | | | | | | | (259) all_561_0 = 0
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | REDUCE: (248), (259) imply:
% 143.49/20.00 | | | | | | | | | | | | (260) $false
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | | CLOSE: (260) is inconsistent.
% 143.49/20.00 | | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | | End of split
% 143.49/20.00 | | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | | End of split
% 143.49/20.00 | | | | | | | | | |
% 143.49/20.00 | | | | | | | | | End of split
% 143.49/20.00 | | | | | | | | |
% 143.49/20.00 | | | | | | | | End of split
% 143.49/20.00 | | | | | | | |
% 143.49/20.00 | | | | | | | End of split
% 143.49/20.00 | | | | | | |
% 143.49/20.00 | | | | | | End of split
% 143.49/20.00 | | | | | |
% 143.49/20.00 | | | | | End of split
% 143.49/20.00 | | | | |
% 143.49/20.00 | | | | End of split
% 143.49/20.00 | | | |
% 143.49/20.00 | | | End of split
% 143.49/20.00 | | |
% 143.49/20.00 | | End of split
% 143.49/20.00 | |
% 143.49/20.00 | End of split
% 143.49/20.00 |
% 143.49/20.00 End of proof
% 143.49/20.00
% 143.49/20.00 Sub-proof #2 shows that the following formulas are inconsistent:
% 143.49/20.00 ----------------------------------------------------------------
% 143.49/20.00 (1) ~ (all_60_1 = 0)
% 143.49/20.00 (2) $i(empty_set)
% 143.49/20.00 (3) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 143.49/20.00 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 143.49/20.00 (4) empty(empty_set) = 0
% 143.49/20.00 (5) all_60_1 = 0 | all_51_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ?
% 143.49/20.00 [v2: int] : ((v2 = 0 & in(all_51_1, all_39_0) = 0) | ( ~ (v1 = 0) &
% 143.49/20.00 in(all_39_0, all_47_1) = v1) | ( ~ (v0 = 0) & in(all_51_1, all_47_1)
% 143.49/20.00 = v0))
% 143.49/20.00 (6) in(all_47_1, empty_set) = 0
% 143.49/20.00 (7) $i(all_47_1)
% 143.49/20.00 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 143.49/20.00 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 143.49/20.00
% 143.49/20.00 Begin of proof
% 143.49/20.00 |
% 143.49/20.00 | BETA: splitting (5) gives:
% 143.49/20.00 |
% 143.49/20.00 | Case 1:
% 143.49/20.00 | |
% 143.49/20.00 | | (9) all_60_1 = 0
% 143.49/20.00 | |
% 143.49/20.00 | | REDUCE: (1), (9) imply:
% 143.49/20.00 | | (10) $false
% 143.49/20.00 | |
% 143.49/20.00 | | CLOSE: (10) is inconsistent.
% 143.49/20.00 | |
% 143.49/20.00 | Case 2:
% 143.49/20.00 | |
% 143.49/20.00 | |
% 143.49/20.00 | | GROUND_INST: instantiating (3) with all_47_1, empty_set, simplifying with
% 143.49/20.00 | | (2), (6), (7) gives:
% 143.49/20.00 | | (11) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 143.49/20.00 | |
% 143.49/20.00 | | DELTA: instantiating (11) with fresh symbol all_568_0 gives:
% 143.49/20.00 | | (12) ~ (all_568_0 = 0) & empty(empty_set) = all_568_0
% 143.49/20.00 | |
% 143.49/20.00 | | ALPHA: (12) implies:
% 143.49/20.00 | | (13) ~ (all_568_0 = 0)
% 143.49/20.00 | | (14) empty(empty_set) = all_568_0
% 143.49/20.00 | |
% 143.49/20.00 | | GROUND_INST: instantiating (8) with 0, all_568_0, empty_set, simplifying
% 143.49/20.00 | | with (4), (14) gives:
% 143.49/20.00 | | (15) all_568_0 = 0
% 143.49/20.00 | |
% 143.49/20.00 | | REDUCE: (13), (15) imply:
% 143.49/20.00 | | (16) $false
% 143.49/20.00 | |
% 143.49/20.00 | | CLOSE: (16) is inconsistent.
% 143.49/20.00 | |
% 143.49/20.00 | End of split
% 143.49/20.00 |
% 143.49/20.00 End of proof
% 143.49/20.00
% 143.49/20.00 Sub-proof #3 shows that the following formulas are inconsistent:
% 143.49/20.00 ----------------------------------------------------------------
% 143.49/20.00 (1) subset(all_507_1, all_51_1) = 0 & ordinal(all_507_1) = 0
% 143.49/20.00 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 143.49/20.00 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 143.49/20.00 v0))
% 143.49/20.00 (3) subset(all_507_1, all_51_1) = all_507_0
% 143.49/20.00 (4) ~ (all_507_0 = 0)
% 143.49/20.00
% 143.49/20.00 Begin of proof
% 143.49/20.00 |
% 143.49/20.00 | ALPHA: (1) implies:
% 143.49/20.00 | (5) subset(all_507_1, all_51_1) = 0
% 143.49/20.00 |
% 143.49/20.00 | GROUND_INST: instantiating (2) with all_507_0, 0, all_51_1, all_507_1,
% 143.49/20.00 | simplifying with (3), (5) gives:
% 143.49/20.00 | (6) all_507_0 = 0
% 143.49/20.00 |
% 143.49/20.00 | REDUCE: (4), (6) imply:
% 143.49/20.00 | (7) $false
% 143.49/20.00 |
% 143.49/20.00 | CLOSE: (7) is inconsistent.
% 143.49/20.00 |
% 143.49/20.00 End of proof
% 143.49/20.00
% 143.49/20.00 Sub-proof #4 shows that the following formulas are inconsistent:
% 143.49/20.00 ----------------------------------------------------------------
% 143.49/20.00 (1) $i(all_51_1)
% 143.49/20.00 (2) empty(all_51_1) = all_71_2
% 143.49/20.00 (3) ~ (all_232_1 = 0) & in(all_39_0, all_51_1) = all_232_1
% 144.01/20.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2)
% 144.01/20.00 = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) |
% 144.01/20.00 ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0)
% 144.01/20.01 (5) $i(all_39_0)
% 144.01/20.01 (6) powerset(all_51_1) = all_225_0
% 144.01/20.01 (7) ~ (all_71_2 = 0)
% 144.01/20.01 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.01 ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) =
% 144.01/20.01 v0))
% 144.01/20.01 (9) element(all_47_1, all_225_0) = 0
% 144.01/20.01 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.01/20.01 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.01/20.01 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.01/20.01 (11) $i(all_47_1)
% 144.01/20.01 (12) in(all_39_0, all_47_1) = 0
% 144.01/20.01 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.01 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.01/20.01
% 144.01/20.01 Begin of proof
% 144.01/20.01 |
% 144.01/20.01 | ALPHA: (3) implies:
% 144.01/20.01 | (14) ~ (all_232_1 = 0)
% 144.01/20.01 | (15) in(all_39_0, all_51_1) = all_232_1
% 144.01/20.01 |
% 144.01/20.01 | GROUND_INST: instantiating (4) with all_39_0, all_47_1, all_51_1, all_225_0,
% 144.01/20.01 | simplifying with (1), (5), (6), (9), (11), (12) gives:
% 144.01/20.01 | (16) element(all_39_0, all_51_1) = 0
% 144.01/20.01 |
% 144.01/20.01 | GROUND_INST: instantiating (10) with all_39_0, all_51_1, all_232_1,
% 144.01/20.01 | simplifying with (1), (5), (15) gives:
% 144.01/20.01 | (17) all_232_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.01/20.01 | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_39_0, all_51_1)
% 144.01/20.01 | = v0))
% 144.01/20.01 |
% 144.01/20.01 | BETA: splitting (17) gives:
% 144.01/20.01 |
% 144.01/20.01 | Case 1:
% 144.01/20.01 | |
% 144.01/20.01 | | (18) all_232_1 = 0
% 144.01/20.01 | |
% 144.01/20.01 | | REDUCE: (14), (18) imply:
% 144.01/20.01 | | (19) $false
% 144.01/20.01 | |
% 144.01/20.01 | | CLOSE: (19) is inconsistent.
% 144.01/20.01 | |
% 144.01/20.01 | Case 2:
% 144.01/20.01 | |
% 144.01/20.01 | | (20) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0) | ( ~
% 144.01/20.01 | | (v0 = 0) & element(all_39_0, all_51_1) = v0))
% 144.01/20.01 | |
% 144.01/20.01 | | DELTA: instantiating (20) with fresh symbols all_483_0, all_483_1 gives:
% 144.01/20.01 | | (21) (all_483_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_483_1 = 0) &
% 144.01/20.01 | | element(all_39_0, all_51_1) = all_483_1)
% 144.01/20.01 | |
% 144.01/20.01 | | BETA: splitting (21) gives:
% 144.01/20.01 | |
% 144.01/20.01 | | Case 1:
% 144.01/20.01 | | |
% 144.01/20.01 | | | (22) all_483_0 = 0 & empty(all_51_1) = 0
% 144.01/20.01 | | |
% 144.01/20.01 | | | ALPHA: (22) implies:
% 144.01/20.01 | | | (23) empty(all_51_1) = 0
% 144.01/20.01 | | |
% 144.01/20.01 | | | REF_CLOSE: (2), (7), (13), (23) are inconsistent by sub-proof #23.
% 144.01/20.01 | | |
% 144.01/20.01 | | Case 2:
% 144.01/20.01 | | |
% 144.01/20.01 | | | (24) ~ (all_483_1 = 0) & element(all_39_0, all_51_1) = all_483_1
% 144.01/20.01 | | |
% 144.01/20.01 | | | ALPHA: (24) implies:
% 144.01/20.01 | | | (25) ~ (all_483_1 = 0)
% 144.01/20.01 | | | (26) element(all_39_0, all_51_1) = all_483_1
% 144.01/20.01 | | |
% 144.01/20.01 | | | GROUND_INST: instantiating (8) with 0, all_483_1, all_51_1, all_39_0,
% 144.01/20.01 | | | simplifying with (16), (26) gives:
% 144.01/20.01 | | | (27) all_483_1 = 0
% 144.01/20.01 | | |
% 144.01/20.01 | | | REDUCE: (25), (27) imply:
% 144.01/20.01 | | | (28) $false
% 144.01/20.01 | | |
% 144.01/20.01 | | | CLOSE: (28) is inconsistent.
% 144.01/20.01 | | |
% 144.01/20.01 | | End of split
% 144.01/20.01 | |
% 144.01/20.01 | End of split
% 144.01/20.01 |
% 144.01/20.01 End of proof
% 144.01/20.01
% 144.01/20.01 Sub-proof #5 shows that the following formulas are inconsistent:
% 144.01/20.01 ----------------------------------------------------------------
% 144.01/20.01 (1) in(empty_set, all_47_1) = 0
% 144.01/20.01 (2) (all_361_0 = 0 & in(all_47_1, all_225_0) = 0) | (all_361_1 = 0 &
% 144.01/20.01 empty(all_225_0) = 0)
% 144.01/20.01 (3) (all_179_0 = 0 & in(all_39_0, all_49_0) = 0) | (all_179_1 = 0 &
% 144.01/20.01 in(all_49_0, all_39_0) = 0)
% 144.01/20.01 (4) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.01/20.01 all_51_1) = 0 & ordinal(v0) = 0))
% 144.01/20.01 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.01 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.01/20.01 (6) $i(all_39_0)
% 144.01/20.01 (7) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.01/20.01 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.01/20.01 (8) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.01/20.01 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.01/20.01 (9) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.01/20.01 in(all_39_0, all_49_0) = 0)
% 144.01/20.01 (10) ~ (all_125_1 = 0)
% 144.01/20.01 (11) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 144.01/20.01 (12) $i(all_225_0)
% 144.01/20.01 (13) all_49_0 = empty_set
% 144.01/20.01 (14) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 144.01/20.01 all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.01/20.01 (15) $i(all_47_1)
% 144.01/20.01 (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.01 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.01/20.01 v0))
% 144.01/20.01 (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.01 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.01/20.01 (18) (all_362_0 = 0 & in(all_39_0, all_225_0) = 0) | (all_362_1 = 0 &
% 144.01/20.01 empty(all_225_0) = 0)
% 144.01/20.01
% 144.01/20.01 Begin of proof
% 144.01/20.01 |
% 144.01/20.01 | BETA: splitting (14) gives:
% 144.01/20.01 |
% 144.01/20.01 | Case 1:
% 144.01/20.01 | |
% 144.01/20.01 | | (19) all_125_1 = 0
% 144.01/20.01 | |
% 144.01/20.01 | | REDUCE: (10), (19) imply:
% 144.01/20.01 | | (20) $false
% 144.01/20.01 | |
% 144.01/20.01 | | CLOSE: (20) is inconsistent.
% 144.01/20.01 | |
% 144.01/20.01 | Case 2:
% 144.01/20.01 | |
% 144.01/20.01 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_51_1) =
% 144.01/20.01 | | v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.01/20.01 | |
% 144.01/20.01 | | DELTA: instantiating (21) with fresh symbols all_487_0, all_487_1 gives:
% 144.01/20.01 | | (22) ~ (all_487_0 = 0) & subset(all_487_1, all_51_1) = all_487_0 &
% 144.01/20.01 | | in(all_487_1, all_51_1) = 0 & $i(all_487_1)
% 144.01/20.01 | |
% 144.01/20.01 | | ALPHA: (22) implies:
% 144.01/20.01 | | (23) ~ (all_487_0 = 0)
% 144.01/20.01 | | (24) $i(all_487_1)
% 144.01/20.01 | | (25) in(all_487_1, all_51_1) = 0
% 144.01/20.01 | | (26) subset(all_487_1, all_51_1) = all_487_0
% 144.01/20.01 | |
% 144.01/20.01 | | BETA: splitting (2) gives:
% 144.01/20.01 | |
% 144.01/20.01 | | Case 1:
% 144.01/20.01 | | |
% 144.01/20.01 | | | (27) all_361_0 = 0 & in(all_47_1, all_225_0) = 0
% 144.01/20.01 | | |
% 144.01/20.01 | | | ALPHA: (27) implies:
% 144.01/20.01 | | | (28) in(all_47_1, all_225_0) = 0
% 144.01/20.01 | | |
% 144.01/20.01 | | | BETA: splitting (18) gives:
% 144.01/20.01 | | |
% 144.01/20.01 | | | Case 1:
% 144.01/20.01 | | | |
% 144.01/20.01 | | | |
% 144.01/20.02 | | | | GROUND_INST: instantiating (4) with all_487_1, simplifying with (24),
% 144.01/20.02 | | | | (25) gives:
% 144.01/20.02 | | | | (29) subset(all_487_1, all_51_1) = 0 & ordinal(all_487_1) = 0
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | REF_CLOSE: (16), (23), (26), (29) are inconsistent by sub-proof #7.
% 144.01/20.02 | | | |
% 144.01/20.02 | | | Case 2:
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | (30) all_362_1 = 0 & empty(all_225_0) = 0
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | ALPHA: (30) implies:
% 144.01/20.02 | | | | (31) empty(all_225_0) = 0
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 144.01/20.02 | | | | (17), (18), (28), (31) are inconsistent by sub-proof #6.
% 144.01/20.02 | | | |
% 144.01/20.02 | | | End of split
% 144.01/20.02 | | |
% 144.01/20.02 | | Case 2:
% 144.01/20.02 | | |
% 144.01/20.02 | | | (32) all_361_1 = 0 & empty(all_225_0) = 0
% 144.01/20.02 | | |
% 144.01/20.02 | | | ALPHA: (32) implies:
% 144.01/20.02 | | | (33) empty(all_225_0) = 0
% 144.01/20.02 | | |
% 144.01/20.02 | | | BETA: splitting (2) gives:
% 144.01/20.02 | | |
% 144.01/20.02 | | | Case 1:
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | (34) all_361_0 = 0 & in(all_47_1, all_225_0) = 0
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | ALPHA: (34) implies:
% 144.01/20.02 | | | | (35) in(all_47_1, all_225_0) = 0
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 144.01/20.02 | | | | (17), (18), (33), (35) are inconsistent by sub-proof #6.
% 144.01/20.02 | | | |
% 144.01/20.02 | | | Case 2:
% 144.01/20.02 | | | |
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | GROUND_INST: instantiating (4) with all_487_1, simplifying with (24),
% 144.01/20.02 | | | | (25) gives:
% 144.01/20.02 | | | | (36) subset(all_487_1, all_51_1) = 0 & ordinal(all_487_1) = 0
% 144.01/20.02 | | | |
% 144.01/20.02 | | | | REF_CLOSE: (16), (23), (26), (36) are inconsistent by sub-proof #7.
% 144.01/20.02 | | | |
% 144.01/20.02 | | | End of split
% 144.01/20.02 | | |
% 144.01/20.02 | | End of split
% 144.01/20.02 | |
% 144.01/20.02 | End of split
% 144.01/20.02 |
% 144.01/20.02 End of proof
% 144.01/20.02
% 144.01/20.02 Sub-proof #6 shows that the following formulas are inconsistent:
% 144.01/20.02 ----------------------------------------------------------------
% 144.01/20.02 (1) in(empty_set, all_47_1) = 0
% 144.01/20.02 (2) (all_179_0 = 0 & in(all_39_0, all_49_0) = 0) | (all_179_1 = 0 &
% 144.01/20.02 in(all_49_0, all_39_0) = 0)
% 144.01/20.02 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.02 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.01/20.02 (4) $i(all_39_0)
% 144.01/20.02 (5) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.01/20.02 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.01/20.02 (6) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.01/20.02 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.01/20.02 (7) empty(all_225_0) = 0
% 144.01/20.02 (8) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.01/20.02 in(all_39_0, all_49_0) = 0)
% 144.01/20.02 (9) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 144.01/20.02 (10) $i(all_225_0)
% 144.01/20.02 (11) all_49_0 = empty_set
% 144.01/20.02 (12) in(all_47_1, all_225_0) = 0
% 144.01/20.02 (13) $i(all_47_1)
% 144.01/20.02 (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.02 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.01/20.02 (15) (all_362_0 = 0 & in(all_39_0, all_225_0) = 0) | (all_362_1 = 0 &
% 144.01/20.02 empty(all_225_0) = 0)
% 144.01/20.02
% 144.01/20.02 Begin of proof
% 144.01/20.02 |
% 144.01/20.02 | BETA: splitting (15) gives:
% 144.01/20.02 |
% 144.01/20.02 | Case 1:
% 144.01/20.02 | |
% 144.01/20.02 | | (16) all_362_0 = 0 & in(all_39_0, all_225_0) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | ALPHA: (16) implies:
% 144.01/20.02 | | (17) in(all_39_0, all_225_0) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | GROUND_INST: instantiating (9) with all_225_0, simplifying with (7), (10)
% 144.01/20.02 | | gives:
% 144.01/20.02 | | (18) all_225_0 = empty_set
% 144.01/20.02 | |
% 144.01/20.02 | | REDUCE: (7), (18) imply:
% 144.01/20.02 | | (19) empty(empty_set) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | REDUCE: (17), (18) imply:
% 144.01/20.02 | | (20) in(all_39_0, empty_set) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | REDUCE: (10), (18) imply:
% 144.01/20.02 | | (21) $i(empty_set)
% 144.01/20.02 | |
% 144.01/20.02 | | REF_CLOSE: (3), (4), (5), (6), (8), (11), (14), (19), (20), (21) are
% 144.01/20.02 | | inconsistent by sub-proof #14.
% 144.01/20.02 | |
% 144.01/20.02 | Case 2:
% 144.01/20.02 | |
% 144.01/20.02 | | (22) all_362_1 = 0 & empty(all_225_0) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | GROUND_INST: instantiating (9) with all_225_0, simplifying with (7), (10)
% 144.01/20.02 | | gives:
% 144.01/20.02 | | (23) all_225_0 = empty_set
% 144.01/20.02 | |
% 144.01/20.02 | | REDUCE: (7), (23) imply:
% 144.01/20.02 | | (24) empty(empty_set) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | REDUCE: (12), (23) imply:
% 144.01/20.02 | | (25) in(all_47_1, empty_set) = 0
% 144.01/20.02 | |
% 144.01/20.02 | | REDUCE: (10), (23) imply:
% 144.01/20.02 | | (26) $i(empty_set)
% 144.01/20.02 | |
% 144.01/20.02 | | BETA: splitting (2) gives:
% 144.01/20.02 | |
% 144.01/20.02 | | Case 1:
% 144.01/20.02 | | |
% 144.01/20.02 | | | (27) all_179_0 = 0 & in(all_39_0, all_49_0) = 0
% 144.01/20.02 | | |
% 144.01/20.02 | | | ALPHA: (27) implies:
% 144.01/20.02 | | | (28) in(all_39_0, all_49_0) = 0
% 144.01/20.02 | | |
% 144.01/20.02 | | | REDUCE: (11), (28) imply:
% 144.01/20.02 | | | (29) in(all_39_0, empty_set) = 0
% 144.01/20.02 | | |
% 144.01/20.02 | | | REF_CLOSE: (3), (4), (5), (6), (8), (11), (14), (24), (26), (29) are
% 144.01/20.02 | | | inconsistent by sub-proof #14.
% 144.01/20.02 | | |
% 144.01/20.02 | | Case 2:
% 144.01/20.02 | | |
% 144.01/20.02 | | |
% 144.01/20.02 | | | GROUND_INST: instantiating (6) with all_47_1, empty_set, simplifying with
% 144.01/20.02 | | | (1), (13), (26) gives:
% 144.01/20.02 | | | (30) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1, empty_set) = v0)
% 144.01/20.02 | | |
% 144.01/20.02 | | | DELTA: instantiating (30) with fresh symbol all_469_0 gives:
% 144.01/20.02 | | | (31) ~ (all_469_0 = 0) & in(all_47_1, empty_set) = all_469_0
% 144.01/20.02 | | |
% 144.01/20.02 | | | ALPHA: (31) implies:
% 144.01/20.02 | | | (32) ~ (all_469_0 = 0)
% 144.01/20.02 | | | (33) in(all_47_1, empty_set) = all_469_0
% 144.01/20.02 | | |
% 144.01/20.02 | | | GROUND_INST: instantiating (3) with 0, all_469_0, empty_set, all_47_1,
% 144.01/20.02 | | | simplifying with (25), (33) gives:
% 144.01/20.02 | | | (34) all_469_0 = 0
% 144.01/20.02 | | |
% 144.01/20.02 | | | REDUCE: (32), (34) imply:
% 144.01/20.02 | | | (35) $false
% 144.01/20.02 | | |
% 144.01/20.02 | | | CLOSE: (35) is inconsistent.
% 144.01/20.02 | | |
% 144.01/20.02 | | End of split
% 144.01/20.02 | |
% 144.01/20.02 | End of split
% 144.01/20.02 |
% 144.01/20.02 End of proof
% 144.01/20.02
% 144.01/20.02 Sub-proof #7 shows that the following formulas are inconsistent:
% 144.01/20.02 ----------------------------------------------------------------
% 144.01/20.02 (1) subset(all_487_1, all_51_1) = 0 & ordinal(all_487_1) = 0
% 144.01/20.02 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.02 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.01/20.02 v0))
% 144.01/20.02 (3) subset(all_487_1, all_51_1) = all_487_0
% 144.01/20.02 (4) ~ (all_487_0 = 0)
% 144.01/20.02
% 144.01/20.02 Begin of proof
% 144.01/20.02 |
% 144.01/20.02 | ALPHA: (1) implies:
% 144.01/20.02 | (5) subset(all_487_1, all_51_1) = 0
% 144.01/20.02 |
% 144.01/20.02 | GROUND_INST: instantiating (2) with all_487_0, 0, all_51_1, all_487_1,
% 144.01/20.02 | simplifying with (3), (5) gives:
% 144.01/20.02 | (6) all_487_0 = 0
% 144.01/20.02 |
% 144.01/20.02 | REDUCE: (4), (6) imply:
% 144.01/20.02 | (7) $false
% 144.01/20.02 |
% 144.01/20.02 | CLOSE: (7) is inconsistent.
% 144.01/20.02 |
% 144.01/20.02 End of proof
% 144.01/20.02
% 144.01/20.02 Sub-proof #8 shows that the following formulas are inconsistent:
% 144.01/20.02 ----------------------------------------------------------------
% 144.01/20.02 (1) $i(all_51_1)
% 144.01/20.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 144.01/20.02 (ordinal(v0) = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 144.01/20.02 [v3: int] : ? [v4: int] : ((v4 = 0 & in(v1, v0) = 0) | ( ~ (v3 = 0) &
% 144.01/20.02 ordinal(v1) = v3)))
% 144.01/20.02 (3) ~ (all_51_0 = 0)
% 144.01/20.03 (4) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.01/20.03 all_51_1) = 0 & ordinal(v0) = 0))
% 144.01/20.03 (5) element(all_51_1, all_51_1) = all_137_1
% 144.01/20.03 (6) empty(all_51_1) = all_71_2
% 144.01/20.03 (7) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 144.01/20.03 $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 144.01/20.03 $i(v2)))
% 144.01/20.03 (8) (all_162_0 = 0 & in(all_49_0, all_47_1) = 0) | (all_162_1 = 0 &
% 144.01/20.03 in(all_47_1, all_49_0) = 0)
% 144.01/20.03 (9) in(all_39_0, all_51_1) = all_60_1
% 144.01/20.03 (10) ~ (all_47_1 = empty_set)
% 144.01/20.03 (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.03 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.01/20.03 (12) $i(all_39_0)
% 144.01/20.03 (13) (all_175_0 = 0 & in(empty_set, all_39_0) = 0) | (all_175_1 = 0 &
% 144.01/20.03 in(all_39_0, empty_set) = 0)
% 144.01/20.03 (14) $i(empty_set)
% 144.01/20.03 (15) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.01/20.03 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.01/20.03 (16) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.01/20.03 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.01/20.03 (17) empty(empty_set) = 0
% 144.01/20.03 (18) (all_63_0 = 0 & subset(all_47_1, all_51_1) = 0) | ( ~ (all_63_1 = 0) &
% 144.01/20.03 in(all_47_1, all_51_1) = all_63_1)
% 144.01/20.03 (19) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.01/20.03 in(all_39_0, all_49_0) = 0)
% 144.01/20.03 (20) ordinal(all_47_1) = 0
% 144.01/20.03 (21) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 144.01/20.03 (22) subset(empty_set, all_51_1) = 0
% 144.01/20.03 (23) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.01/20.03 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 144.01/20.03 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.01/20.03 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.01/20.03 (24) empty(all_39_0) = all_47_0
% 144.01/20.03 (25) epsilon_connected(all_47_1) = 0
% 144.01/20.03 (26) all_47_1 = all_39_0
% 144.01/20.03 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.01/20.03 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.01/20.03 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.01/20.03 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.01/20.03 = 0) & in(v1, v0) = v4)))
% 144.01/20.03 (28) ~ (all_71_2 = 0)
% 144.01/20.03 (29) (all_61_0 = 0 & subset(empty_set, all_51_1) = 0) | ( ~ (all_61_1 = 0) &
% 144.01/20.03 in(empty_set, all_51_1) = all_61_1)
% 144.01/20.03 (30) all_49_0 = empty_set
% 144.01/20.03 (31) (all_62_0 = 0 & subset(all_49_0, all_51_1) = 0) | ( ~ (all_62_1 = 0) &
% 144.01/20.03 in(all_49_0, all_51_1) = all_62_1)
% 144.01/20.03 (32) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 144.01/20.03 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 144.01/20.03 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 144.01/20.03 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 144.01/20.03 v1) | ~ (powerset(v2) = v0))
% 144.01/20.03 (34) ( ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0) | ( ~
% 144.01/20.03 (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1)
% 144.01/20.03 (35) epsilon_connected(empty_set) = 0
% 144.01/20.03 (36) ~ (all_137_1 = 0)
% 144.01/20.03 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 144.01/20.03 (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~
% 144.01/20.03 (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 144.01/20.03 int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 144.01/20.03 (38) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.03 (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 144.01/20.03 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 144.01/20.03 (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) |
% 144.01/20.03 ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & powerset(v2) =
% 144.01/20.03 v4 & element(v1, v4) = v5 & $i(v4)))
% 144.01/20.03 (40) ordinal(empty_set) = 0
% 144.01/20.03 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.01/20.03 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.01/20.03 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.01/20.03 (42) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.01/20.03 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 144.01/20.03 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.01/20.03 (43) ordinal(all_51_1) = all_51_0
% 144.01/20.03 (44) all_47_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.01/20.03 in(all_39_0, all_47_1) = 0) | (v0 = 0 & in(all_47_1, all_39_0) = 0))
% 144.01/20.03 (45) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~
% 144.01/20.03 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & in(v0, v1) = 0) |
% 144.01/20.03 (v2 = 0 & empty(v1) = 0)))
% 144.01/20.03 (46) $i(all_47_1)
% 144.01/20.03 (47) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.03 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.01/20.03 v0))
% 144.01/20.03 (48) (all_149_0 = 0 & in(empty_set, all_47_1) = 0) | (all_149_1 = 0 &
% 144.01/20.03 in(all_47_1, empty_set) = 0)
% 144.01/20.03 (49) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.01/20.03 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~ $i(v2)
% 144.01/20.03 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.01/20.03 ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.01/20.03 = 0) & in(v1, v0) = v4)))
% 144.01/20.03 (50) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.01/20.03 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.01/20.03 (51) epsilon_connected(all_39_0) = 0
% 144.01/20.03 (52) ~ (all_47_0 = 0)
% 144.01/20.04 (53) (all_60_0 = 0 & subset(all_39_0, all_51_1) = 0) | ( ~ (all_60_1 = 0) &
% 144.01/20.04 in(all_39_0, all_51_1) = all_60_1)
% 144.01/20.04
% 144.01/20.04 Begin of proof
% 144.01/20.04 |
% 144.01/20.04 | BETA: splitting (18) gives:
% 144.01/20.04 |
% 144.01/20.04 | Case 1:
% 144.01/20.04 | |
% 144.01/20.04 | | (54) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 144.01/20.04 | |
% 144.01/20.04 | | ALPHA: (54) implies:
% 144.01/20.04 | | (55) subset(all_47_1, all_51_1) = 0
% 144.01/20.04 | |
% 144.01/20.04 | | REDUCE: (26), (55) imply:
% 144.01/20.04 | | (56) subset(all_39_0, all_51_1) = 0
% 144.01/20.04 | |
% 144.01/20.04 | | REF_CLOSE: (1), (4), (5), (6), (7), (11), (12), (13), (14), (15), (16),
% 144.01/20.04 | | (17), (18), (19), (21), (22), (23), (24), (25), (26), (27), (28),
% 144.01/20.04 | | (30), (32), (33), (34), (36), (37), (41), (42), (45), (46), (47),
% 144.01/20.04 | | (49), (50), (51), (52), (56) are inconsistent by sub-proof #9.
% 144.01/20.04 | |
% 144.01/20.04 | Case 2:
% 144.01/20.04 | |
% 144.01/20.04 | | (57) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) = all_63_1
% 144.01/20.04 | |
% 144.01/20.04 | | ALPHA: (57) implies:
% 144.01/20.04 | | (58) ~ (all_63_1 = 0)
% 144.01/20.04 | | (59) in(all_47_1, all_51_1) = all_63_1
% 144.01/20.04 | |
% 144.01/20.04 | | REDUCE: (26), (59) imply:
% 144.01/20.04 | | (60) in(all_39_0, all_51_1) = all_63_1
% 144.01/20.04 | |
% 144.01/20.04 | | GROUND_INST: instantiating (11) with all_60_1, all_63_1, all_51_1, all_39_0,
% 144.01/20.04 | | simplifying with (9), (60) gives:
% 144.01/20.04 | | (61) all_63_1 = all_60_1
% 144.01/20.04 | |
% 144.01/20.04 | | REDUCE: (58), (61) imply:
% 144.01/20.04 | | (62) ~ (all_60_1 = 0)
% 144.01/20.04 | |
% 144.01/20.04 | | GROUND_INST: instantiating (49) with all_39_0, all_39_0, all_51_1, all_60_1,
% 144.01/20.04 | | simplifying with (1), (9), (12), (51) gives:
% 144.01/20.04 | | (63) all_60_1 = 0 | all_51_1 = all_39_0 | ? [v0: int] : ? [v1: int] :
% 144.01/20.04 | | ? [v2: int] : ((v2 = 0 & in(all_51_1, all_39_0) = 0) | ( ~ (v1 = 0)
% 144.01/20.04 | | & in(all_51_1, all_39_0) = v1) | ( ~ (v0 = 0) & in(all_39_0,
% 144.01/20.04 | | all_39_0) = v0))
% 144.01/20.04 | |
% 144.01/20.04 | | GROUND_INST: instantiating (41) with all_39_0, all_51_1, all_60_1,
% 144.01/20.04 | | simplifying with (1), (9), (12) gives:
% 144.01/20.04 | | (64) all_60_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.01/20.04 | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_39_0,
% 144.01/20.04 | | all_51_1) = v0))
% 144.01/20.04 | |
% 144.01/20.04 | | GROUND_INST: instantiating (7) with empty_set, all_51_1, simplifying with
% 144.01/20.04 | | (1), (14), (22) gives:
% 144.01/20.04 | | (65) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0) = 0
% 144.01/20.04 | | & $i(v0))
% 144.01/20.04 | |
% 144.01/20.04 | | DELTA: instantiating (65) with fresh symbol all_223_0 gives:
% 144.01/20.04 | | (66) powerset(all_51_1) = all_223_0 & element(empty_set, all_223_0) = 0 &
% 144.01/20.04 | | $i(all_223_0)
% 144.01/20.04 | |
% 144.01/20.04 | | ALPHA: (66) implies:
% 144.01/20.04 | | (67) element(empty_set, all_223_0) = 0
% 144.01/20.04 | | (68) powerset(all_51_1) = all_223_0
% 144.01/20.04 | |
% 144.01/20.04 | | BETA: splitting (64) gives:
% 144.01/20.04 | |
% 144.01/20.04 | | Case 1:
% 144.01/20.04 | | |
% 144.01/20.04 | | | (69) all_60_1 = 0
% 144.01/20.04 | | |
% 144.01/20.04 | | | REDUCE: (62), (69) imply:
% 144.01/20.04 | | | (70) $false
% 144.01/20.04 | | |
% 144.01/20.04 | | | CLOSE: (70) is inconsistent.
% 144.01/20.04 | | |
% 144.01/20.04 | | Case 2:
% 144.01/20.04 | | |
% 144.01/20.04 | | | (71) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0) | (
% 144.01/20.04 | | | ~ (v0 = 0) & element(all_39_0, all_51_1) = v0))
% 144.01/20.04 | | |
% 144.01/20.04 | | | DELTA: instantiating (71) with fresh symbols all_230_0, all_230_1 gives:
% 144.01/20.04 | | | (72) (all_230_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_230_1 = 0) &
% 144.01/20.04 | | | element(all_39_0, all_51_1) = all_230_1)
% 144.01/20.04 | | |
% 144.01/20.04 | | | BETA: splitting (72) gives:
% 144.01/20.04 | | |
% 144.01/20.04 | | | Case 1:
% 144.01/20.04 | | | |
% 144.01/20.04 | | | | (73) all_230_0 = 0 & empty(all_51_1) = 0
% 144.01/20.04 | | | |
% 144.01/20.04 | | | | ALPHA: (73) implies:
% 144.01/20.04 | | | | (74) empty(all_51_1) = 0
% 144.27/20.04 | | | |
% 144.27/20.04 | | | | REF_CLOSE: (6), (28), (50), (74) are inconsistent by sub-proof #23.
% 144.27/20.04 | | | |
% 144.27/20.04 | | | Case 2:
% 144.27/20.04 | | | |
% 144.27/20.04 | | | | (75) ~ (all_230_1 = 0) & element(all_39_0, all_51_1) = all_230_1
% 144.27/20.04 | | | |
% 144.27/20.04 | | | | ALPHA: (75) implies:
% 144.27/20.04 | | | | (76) ~ (all_230_1 = 0)
% 144.27/20.04 | | | | (77) element(all_39_0, all_51_1) = all_230_1
% 144.27/20.04 | | | |
% 144.27/20.04 | | | | GROUND_INST: instantiating (37) with all_39_0, empty_set, all_51_1,
% 144.27/20.04 | | | | all_223_0, all_230_1, simplifying with (1), (12), (14),
% 144.27/20.04 | | | | (67), (68), (77) gives:
% 144.27/20.04 | | | | (78) all_230_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0,
% 144.27/20.04 | | | | empty_set) = v0)
% 144.27/20.04 | | | |
% 144.27/20.04 | | | | BETA: splitting (34) gives:
% 144.27/20.04 | | | |
% 144.27/20.04 | | | | Case 1:
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | (79) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | ALPHA: (79) implies:
% 144.27/20.04 | | | | | (80) ~ (all_125_0 = 0)
% 144.27/20.04 | | | | | (81) epsilon_connected(all_51_1) = all_125_0
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | REF_CLOSE: (1), (4), (11), (12), (13), (14), (15), (16), (17), (19),
% 144.27/20.04 | | | | | (23), (25), (27), (30), (42), (46), (50), (80), (81) are
% 144.27/20.04 | | | | | inconsistent by sub-proof #13.
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | Case 2:
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | (82) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | ALPHA: (82) implies:
% 144.27/20.04 | | | | | (83) ~ (all_125_1 = 0)
% 144.27/20.04 | | | | | (84) epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | BETA: splitting (78) gives:
% 144.27/20.04 | | | | |
% 144.27/20.04 | | | | | Case 1:
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | (85) all_230_1 = 0
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | REDUCE: (76), (85) imply:
% 144.27/20.04 | | | | | | (86) $false
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | CLOSE: (86) is inconsistent.
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | Case 2:
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | (87) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, empty_set) = v0)
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | DELTA: instantiating (87) with fresh symbol all_370_0 gives:
% 144.27/20.04 | | | | | | (88) ~ (all_370_0 = 0) & in(all_39_0, empty_set) = all_370_0
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | ALPHA: (88) implies:
% 144.27/20.04 | | | | | | (89) ~ (all_370_0 = 0)
% 144.27/20.04 | | | | | | (90) in(all_39_0, empty_set) = all_370_0
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | BETA: splitting (63) gives:
% 144.27/20.04 | | | | | |
% 144.27/20.04 | | | | | | Case 1:
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | (91) all_60_1 = 0
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | REDUCE: (62), (91) imply:
% 144.27/20.04 | | | | | | | (92) $false
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | CLOSE: (92) is inconsistent.
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | Case 2:
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | GROUND_INST: instantiating (27) with empty_set, empty_set,
% 144.27/20.04 | | | | | | | all_39_0, all_370_0, simplifying with (12), (14),
% 144.27/20.04 | | | | | | | (35), (90) gives:
% 144.27/20.04 | | | | | | | (93) all_370_0 = 0 | all_39_0 = empty_set | ? [v0: int] : ?
% 144.27/20.04 | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(empty_set,
% 144.27/20.04 | | | | | | | all_39_0) = 0) | ( ~ (v1 = 0) & in(all_39_0,
% 144.27/20.04 | | | | | | | empty_set) = v1) | ( ~ (v0 = 0) & in(empty_set,
% 144.27/20.04 | | | | | | | empty_set) = v0))
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | GROUND_INST: instantiating (32) with all_51_1, all_125_1,
% 144.27/20.04 | | | | | | | simplifying with (1), (84) gives:
% 144.27/20.04 | | | | | | | (94) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0)
% 144.27/20.04 | | | | | | | & subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 &
% 144.27/20.04 | | | | | | | $i(v0))
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | BETA: splitting (94) gives:
% 144.27/20.04 | | | | | | |
% 144.27/20.04 | | | | | | | Case 1:
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | (95) all_125_1 = 0
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | REDUCE: (83), (95) imply:
% 144.27/20.04 | | | | | | | | (96) $false
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | CLOSE: (96) is inconsistent.
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | Case 2:
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | (97) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 144.27/20.04 | | | | | | | | all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | DELTA: instantiating (97) with fresh symbols all_469_0,
% 144.27/20.04 | | | | | | | | all_469_1 gives:
% 144.27/20.04 | | | | | | | | (98) ~ (all_469_0 = 0) & subset(all_469_1, all_51_1) =
% 144.27/20.04 | | | | | | | | all_469_0 & in(all_469_1, all_51_1) = 0 & $i(all_469_1)
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | ALPHA: (98) implies:
% 144.27/20.04 | | | | | | | | (99) ~ (all_469_0 = 0)
% 144.27/20.04 | | | | | | | | (100) $i(all_469_1)
% 144.27/20.04 | | | | | | | | (101) in(all_469_1, all_51_1) = 0
% 144.27/20.04 | | | | | | | | (102) subset(all_469_1, all_51_1) = all_469_0
% 144.27/20.04 | | | | | | | |
% 144.27/20.04 | | | | | | | | BETA: splitting (93) gives:
% 144.27/20.04 | | | | | | | |
% 144.27/20.05 | | | | | | | | Case 1:
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | | (103) all_39_0 = empty_set
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11),
% 144.27/20.05 | | | | | | | | | (14), (15), (16), (17), (18), (20), (23), (25),
% 144.27/20.05 | | | | | | | | | (27), (28), (29), (30), (31), (32), (33), (34),
% 144.27/20.05 | | | | | | | | | (35), (36), (37), (38), (39), (40), (41), (42),
% 144.27/20.05 | | | | | | | | | (43), (44), (46), (47), (48), (49), (50), (53),
% 144.27/20.05 | | | | | | | | | (103) are inconsistent by sub-proof #15.
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | Case 2:
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | | (104) all_370_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 144.27/20.05 | | | | | | | | | int] : ((v2 = 0 & in(empty_set, all_39_0) = 0) | (
% 144.27/20.05 | | | | | | | | | ~ (v1 = 0) & in(all_39_0, empty_set) = v1) | ( ~
% 144.27/20.05 | | | | | | | | | (v0 = 0) & in(empty_set, empty_set) = v0))
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | | BETA: splitting (104) gives:
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | | Case 1:
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | (105) all_370_0 = 0
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | REDUCE: (89), (105) imply:
% 144.27/20.05 | | | | | | | | | | (106) $false
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | CLOSE: (106) is inconsistent.
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | Case 2:
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | GROUND_INST: instantiating (4) with all_469_1, simplifying with
% 144.27/20.05 | | | | | | | | | | (100), (101) gives:
% 144.27/20.05 | | | | | | | | | | (107) subset(all_469_1, all_51_1) = 0 &
% 144.27/20.05 | | | | | | | | | | ordinal(all_469_1) = 0
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | ALPHA: (107) implies:
% 144.27/20.05 | | | | | | | | | | (108) subset(all_469_1, all_51_1) = 0
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | GROUND_INST: instantiating (47) with all_469_0, 0, all_51_1,
% 144.27/20.05 | | | | | | | | | | all_469_1, simplifying with (102), (108) gives:
% 144.27/20.05 | | | | | | | | | | (109) all_469_0 = 0
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | REDUCE: (99), (109) imply:
% 144.27/20.05 | | | | | | | | | | (110) $false
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | | CLOSE: (110) is inconsistent.
% 144.27/20.05 | | | | | | | | | |
% 144.27/20.05 | | | | | | | | | End of split
% 144.27/20.05 | | | | | | | | |
% 144.27/20.05 | | | | | | | | End of split
% 144.27/20.05 | | | | | | | |
% 144.27/20.05 | | | | | | | End of split
% 144.27/20.05 | | | | | | |
% 144.27/20.05 | | | | | | End of split
% 144.27/20.05 | | | | | |
% 144.27/20.05 | | | | | End of split
% 144.27/20.05 | | | | |
% 144.27/20.05 | | | | End of split
% 144.27/20.05 | | | |
% 144.27/20.05 | | | End of split
% 144.27/20.05 | | |
% 144.27/20.05 | | End of split
% 144.27/20.05 | |
% 144.27/20.05 | End of split
% 144.27/20.05 |
% 144.27/20.05 End of proof
% 144.27/20.05
% 144.27/20.05 Sub-proof #9 shows that the following formulas are inconsistent:
% 144.27/20.05 ----------------------------------------------------------------
% 144.27/20.05 (1) $i(all_51_1)
% 144.27/20.05 (2) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.27/20.05 all_51_1) = 0 & ordinal(v0) = 0))
% 144.27/20.05 (3) element(all_51_1, all_51_1) = all_137_1
% 144.27/20.05 (4) empty(all_51_1) = all_71_2
% 144.27/20.05 (5) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 144.27/20.05 $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 144.27/20.05 $i(v2)))
% 144.27/20.05 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.05 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.27/20.05 (7) $i(all_39_0)
% 144.27/20.05 (8) (all_175_0 = 0 & in(empty_set, all_39_0) = 0) | (all_175_1 = 0 &
% 144.27/20.05 in(all_39_0, empty_set) = 0)
% 144.27/20.05 (9) $i(empty_set)
% 144.27/20.05 (10) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.05 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.27/20.05 (11) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.05 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.27/20.05 (12) empty(empty_set) = 0
% 144.27/20.05 (13) (all_63_0 = 0 & subset(all_47_1, all_51_1) = 0) | ( ~ (all_63_1 = 0) &
% 144.27/20.05 in(all_47_1, all_51_1) = all_63_1)
% 144.27/20.05 (14) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.27/20.05 in(all_39_0, all_49_0) = 0)
% 144.27/20.05 (15) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 144.27/20.05 (16) subset(empty_set, all_51_1) = 0
% 144.27/20.05 (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.27/20.05 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 144.27/20.05 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.27/20.05 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.27/20.05 (18) empty(all_39_0) = all_47_0
% 144.27/20.05 (19) epsilon_connected(all_47_1) = 0
% 144.27/20.05 (20) all_47_1 = all_39_0
% 144.27/20.05 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.27/20.05 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.27/20.05 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.27/20.05 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.27/20.05 = 0) & in(v1, v0) = v4)))
% 144.27/20.05 (22) ~ (all_71_2 = 0)
% 144.27/20.05 (23) all_49_0 = empty_set
% 144.27/20.05 (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 144.27/20.05 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 144.27/20.05 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 144.27/20.05 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 144.27/20.05 v1) | ~ (powerset(v2) = v0))
% 144.27/20.05 (26) ( ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0) | ( ~
% 144.27/20.05 (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1)
% 144.27/20.05 (27) ~ (all_137_1 = 0)
% 144.27/20.05 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 144.27/20.05 (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~
% 144.27/20.05 (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 144.27/20.05 int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 144.27/20.05 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.27/20.05 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.27/20.05 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.27/20.05 (30) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.27/20.05 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 144.27/20.05 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.27/20.05 (31) ! [v0: $i] : ! [v1: $i] : ( ~ (element(v0, v1) = 0) | ~ $i(v1) | ~
% 144.27/20.05 $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & in(v0, v1) = 0) |
% 144.27/20.05 (v2 = 0 & empty(v1) = 0)))
% 144.27/20.05 (32) $i(all_47_1)
% 144.27/20.05 (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.05 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.27/20.05 v0))
% 144.27/20.06 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.27/20.06 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~ $i(v2)
% 144.27/20.06 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.27/20.06 ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.27/20.06 = 0) & in(v1, v0) = v4)))
% 144.27/20.06 (35) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.06 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.27/20.06 (36) subset(all_39_0, all_51_1) = 0
% 144.27/20.06 (37) epsilon_connected(all_39_0) = 0
% 144.27/20.06 (38) ~ (all_47_0 = 0)
% 144.27/20.06
% 144.27/20.06 Begin of proof
% 144.27/20.06 |
% 144.27/20.06 | BETA: splitting (13) gives:
% 144.27/20.06 |
% 144.27/20.06 | Case 1:
% 144.27/20.06 | |
% 144.27/20.06 | | (39) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 144.27/20.06 | |
% 144.27/20.06 | | ALPHA: (39) implies:
% 144.27/20.06 | | (40) subset(all_47_1, all_51_1) = 0
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (5) with empty_set, all_51_1, simplifying with
% 144.27/20.06 | | (1), (9), (16) gives:
% 144.27/20.06 | | (41) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0) = 0
% 144.27/20.06 | | & $i(v0))
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (5) with all_39_0, all_51_1, simplifying with
% 144.27/20.06 | | (1), (7), (36) gives:
% 144.27/20.06 | | (42) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_39_0, v0) = 0 &
% 144.27/20.06 | | $i(v0))
% 144.27/20.06 | |
% 144.27/20.06 | | DELTA: instantiating (42) with fresh symbol all_219_0 gives:
% 144.27/20.06 | | (43) powerset(all_51_1) = all_219_0 & element(all_39_0, all_219_0) = 0 &
% 144.27/20.06 | | $i(all_219_0)
% 144.27/20.06 | |
% 144.27/20.06 | | ALPHA: (43) implies:
% 144.27/20.06 | | (44) element(all_39_0, all_219_0) = 0
% 144.27/20.06 | | (45) powerset(all_51_1) = all_219_0
% 144.27/20.06 | |
% 144.27/20.06 | | DELTA: instantiating (41) with fresh symbol all_221_0 gives:
% 144.27/20.06 | | (46) powerset(all_51_1) = all_221_0 & element(empty_set, all_221_0) = 0 &
% 144.27/20.06 | | $i(all_221_0)
% 144.27/20.06 | |
% 144.27/20.06 | | ALPHA: (46) implies:
% 144.27/20.06 | | (47) powerset(all_51_1) = all_221_0
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (25) with all_219_0, all_221_0, all_51_1,
% 144.27/20.06 | | simplifying with (45), (47) gives:
% 144.27/20.06 | | (48) all_221_0 = all_219_0
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (28) with all_51_1, all_39_0, all_51_1,
% 144.27/20.06 | | all_219_0, all_137_1, simplifying with (1), (3), (7), (44),
% 144.27/20.06 | | (45) gives:
% 144.27/20.06 | | (49) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1, all_39_0)
% 144.27/20.06 | | = v0)
% 144.27/20.06 | |
% 144.27/20.06 | | BETA: splitting (26) gives:
% 144.27/20.06 | |
% 144.27/20.06 | | Case 1:
% 144.27/20.06 | | |
% 144.27/20.06 | | | (50) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 144.27/20.06 | | |
% 144.27/20.06 | | | ALPHA: (50) implies:
% 144.27/20.06 | | | (51) ~ (all_125_0 = 0)
% 144.27/20.06 | | | (52) epsilon_connected(all_51_1) = all_125_0
% 144.27/20.06 | | |
% 144.27/20.06 | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (14), (17),
% 144.27/20.06 | | | (19), (21), (23), (30), (32), (35), (51), (52) are inconsistent
% 144.27/20.06 | | | by sub-proof #13.
% 144.27/20.06 | | |
% 144.27/20.06 | | Case 2:
% 144.27/20.06 | | |
% 144.27/20.06 | | | (53) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.06 | | |
% 144.27/20.06 | | | ALPHA: (53) implies:
% 144.27/20.06 | | | (54) ~ (all_125_1 = 0)
% 144.27/20.06 | | | (55) epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.06 | | |
% 144.27/20.06 | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (14), (18),
% 144.27/20.06 | | | (23), (24), (27), (29), (33), (35), (38), (49), (54), (55) are
% 144.27/20.06 | | | inconsistent by sub-proof #12.
% 144.27/20.06 | | |
% 144.27/20.06 | | End of split
% 144.27/20.06 | |
% 144.27/20.06 | Case 2:
% 144.27/20.06 | |
% 144.27/20.06 | | (56) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) = all_63_1
% 144.27/20.06 | |
% 144.27/20.06 | | ALPHA: (56) implies:
% 144.27/20.06 | | (57) ~ (all_63_1 = 0)
% 144.27/20.06 | | (58) in(all_47_1, all_51_1) = all_63_1
% 144.27/20.06 | |
% 144.27/20.06 | | REDUCE: (20), (58) imply:
% 144.27/20.06 | | (59) in(all_39_0, all_51_1) = all_63_1
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (34) with all_39_0, all_39_0, all_51_1, all_63_1,
% 144.27/20.06 | | simplifying with (1), (7), (37), (59) gives:
% 144.27/20.06 | | (60) all_63_1 = 0 | all_51_1 = all_39_0 | ? [v0: int] : ? [v1: int] :
% 144.27/20.06 | | ? [v2: int] : ((v2 = 0 & in(all_51_1, all_39_0) = 0) | ( ~ (v1 = 0)
% 144.27/20.06 | | & in(all_51_1, all_39_0) = v1) | ( ~ (v0 = 0) & in(all_39_0,
% 144.27/20.06 | | all_39_0) = v0))
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (29) with all_39_0, all_51_1, all_63_1,
% 144.27/20.06 | | simplifying with (1), (7), (59) gives:
% 144.27/20.06 | | (61) all_63_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.27/20.06 | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_39_0,
% 144.27/20.06 | | all_51_1) = v0))
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (5) with empty_set, all_51_1, simplifying with
% 144.27/20.06 | | (1), (9), (16) gives:
% 144.27/20.06 | | (62) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0) = 0
% 144.27/20.06 | | & $i(v0))
% 144.27/20.06 | |
% 144.27/20.06 | | GROUND_INST: instantiating (5) with all_39_0, all_51_1, simplifying with
% 144.27/20.06 | | (1), (7), (36) gives:
% 144.27/20.06 | | (63) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_39_0, v0) = 0 &
% 144.27/20.06 | | $i(v0))
% 144.27/20.06 | |
% 144.27/20.06 | | DELTA: instantiating (63) with fresh symbol all_219_0 gives:
% 144.27/20.06 | | (64) powerset(all_51_1) = all_219_0 & element(all_39_0, all_219_0) = 0 &
% 144.27/20.06 | | $i(all_219_0)
% 144.27/20.06 | |
% 144.27/20.06 | | ALPHA: (64) implies:
% 144.27/20.06 | | (65) element(all_39_0, all_219_0) = 0
% 144.27/20.06 | | (66) powerset(all_51_1) = all_219_0
% 144.27/20.06 | |
% 144.27/20.06 | | DELTA: instantiating (62) with fresh symbol all_221_0 gives:
% 144.27/20.06 | | (67) powerset(all_51_1) = all_221_0 & element(empty_set, all_221_0) = 0 &
% 144.27/20.06 | | $i(all_221_0)
% 144.27/20.06 | |
% 144.27/20.06 | | ALPHA: (67) implies:
% 144.27/20.06 | | (68) $i(all_221_0)
% 144.27/20.06 | | (69) element(empty_set, all_221_0) = 0
% 144.27/20.06 | | (70) powerset(all_51_1) = all_221_0
% 144.27/20.06 | |
% 144.27/20.06 | | BETA: splitting (61) gives:
% 144.27/20.06 | |
% 144.27/20.06 | | Case 1:
% 144.27/20.06 | | |
% 144.27/20.06 | | | (71) all_63_1 = 0
% 144.27/20.06 | | |
% 144.27/20.06 | | | REDUCE: (57), (71) imply:
% 144.27/20.06 | | | (72) $false
% 144.27/20.06 | | |
% 144.27/20.06 | | | CLOSE: (72) is inconsistent.
% 144.27/20.06 | | |
% 144.27/20.06 | | Case 2:
% 144.27/20.06 | | |
% 144.27/20.06 | | | (73) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0) | (
% 144.27/20.06 | | | ~ (v0 = 0) & element(all_39_0, all_51_1) = v0))
% 144.27/20.06 | | |
% 144.27/20.06 | | | DELTA: instantiating (73) with fresh symbols all_229_0, all_229_1 gives:
% 144.27/20.06 | | | (74) (all_229_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_229_1 = 0) &
% 144.27/20.06 | | | element(all_39_0, all_51_1) = all_229_1)
% 144.27/20.06 | | |
% 144.27/20.06 | | | BETA: splitting (74) gives:
% 144.27/20.06 | | |
% 144.27/20.06 | | | Case 1:
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | (75) all_229_0 = 0 & empty(all_51_1) = 0
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | ALPHA: (75) implies:
% 144.27/20.06 | | | | (76) empty(all_51_1) = 0
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | REF_CLOSE: (4), (22), (35), (76) are inconsistent by sub-proof #23.
% 144.27/20.06 | | | |
% 144.27/20.06 | | | Case 2:
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | (77) ~ (all_229_1 = 0) & element(all_39_0, all_51_1) = all_229_1
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | ALPHA: (77) implies:
% 144.27/20.06 | | | | (78) ~ (all_229_1 = 0)
% 144.27/20.06 | | | | (79) element(all_39_0, all_51_1) = all_229_1
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | GROUND_INST: instantiating (25) with all_219_0, all_221_0, all_51_1,
% 144.27/20.06 | | | | simplifying with (66), (70) gives:
% 144.27/20.06 | | | | (80) all_221_0 = all_219_0
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | REDUCE: (69), (80) imply:
% 144.27/20.06 | | | | (81) element(empty_set, all_219_0) = 0
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | REDUCE: (68), (80) imply:
% 144.27/20.06 | | | | (82) $i(all_219_0)
% 144.27/20.06 | | | |
% 144.27/20.06 | | | | GROUND_INST: instantiating (31) with empty_set, all_219_0, simplifying
% 144.27/20.06 | | | | with (9), (81), (82) gives:
% 144.27/20.07 | | | | (83) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(empty_set,
% 144.27/20.07 | | | | all_219_0) = 0) | (v0 = 0 & empty(all_219_0) = 0))
% 144.27/20.07 | | | |
% 144.27/20.07 | | | | GROUND_INST: instantiating (31) with all_39_0, all_219_0, simplifying
% 144.27/20.07 | | | | with (7), (65), (82) gives:
% 144.27/20.07 | | | | (84) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_39_0, all_219_0)
% 144.27/20.07 | | | | = 0) | (v0 = 0 & empty(all_219_0) = 0))
% 144.27/20.07 | | | |
% 144.27/20.07 | | | | GROUND_INST: instantiating (28) with all_39_0, empty_set, all_51_1,
% 144.27/20.07 | | | | all_219_0, all_229_1, simplifying with (1), (7), (9), (66),
% 144.27/20.07 | | | | (79), (81) gives:
% 144.27/20.07 | | | | (85) all_229_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0,
% 144.27/20.07 | | | | empty_set) = v0)
% 144.27/20.07 | | | |
% 144.27/20.07 | | | | DELTA: instantiating (84) with fresh symbols all_353_0, all_353_1 gives:
% 144.27/20.07 | | | | (86) (all_353_0 = 0 & in(all_39_0, all_219_0) = 0) | (all_353_1 = 0 &
% 144.27/20.07 | | | | empty(all_219_0) = 0)
% 144.27/20.07 | | | |
% 144.27/20.07 | | | | DELTA: instantiating (83) with fresh symbols all_354_0, all_354_1 gives:
% 144.27/20.07 | | | | (87) (all_354_0 = 0 & in(empty_set, all_219_0) = 0) | (all_354_1 = 0
% 144.27/20.07 | | | | & empty(all_219_0) = 0)
% 144.27/20.07 | | | |
% 144.27/20.07 | | | | BETA: splitting (26) gives:
% 144.27/20.07 | | | |
% 144.27/20.07 | | | | Case 1:
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | (88) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | ALPHA: (88) implies:
% 144.27/20.07 | | | | | (89) ~ (all_125_0 = 0)
% 144.27/20.07 | | | | | (90) epsilon_connected(all_51_1) = all_125_0
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | REF_CLOSE: (1), (2), (6), (17), (19), (21), (30), (32), (57), (60),
% 144.27/20.07 | | | | | (89), (90) are inconsistent by sub-proof #11.
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | Case 2:
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | (91) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | ALPHA: (91) implies:
% 144.27/20.07 | | | | | (92) ~ (all_125_1 = 0)
% 144.27/20.07 | | | | | (93) epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | BETA: splitting (85) gives:
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | | Case 1:
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | (94) all_229_1 = 0
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | REDUCE: (78), (94) imply:
% 144.27/20.07 | | | | | | (95) $false
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | CLOSE: (95) is inconsistent.
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | Case 2:
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | (96) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, empty_set) = v0)
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | DELTA: instantiating (96) with fresh symbol all_368_0 gives:
% 144.27/20.07 | | | | | | (97) ~ (all_368_0 = 0) & in(all_39_0, empty_set) = all_368_0
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | ALPHA: (97) implies:
% 144.27/20.07 | | | | | | (98) ~ (all_368_0 = 0)
% 144.27/20.07 | | | | | | (99) in(all_39_0, empty_set) = all_368_0
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | BETA: splitting (60) gives:
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | | Case 1:
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | | (100) all_63_1 = 0
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | | REDUCE: (57), (100) imply:
% 144.27/20.07 | | | | | | | (101) $false
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | | CLOSE: (101) is inconsistent.
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | Case 2:
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | | GROUND_INST: instantiating (24) with all_51_1, all_125_1,
% 144.27/20.07 | | | | | | | simplifying with (1), (93) gives:
% 144.27/20.07 | | | | | | | (102) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0)
% 144.27/20.07 | | | | | | | & subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 &
% 144.27/20.07 | | | | | | | $i(v0))
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | | BETA: splitting (102) gives:
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | | Case 1:
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | (103) all_125_1 = 0
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | REDUCE: (92), (103) imply:
% 144.27/20.07 | | | | | | | | (104) $false
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | CLOSE: (104) is inconsistent.
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | Case 2:
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | (105) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 144.27/20.07 | | | | | | | | all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | DELTA: instantiating (105) with fresh symbols all_473_0,
% 144.27/20.07 | | | | | | | | all_473_1 gives:
% 144.27/20.07 | | | | | | | | (106) ~ (all_473_0 = 0) & subset(all_473_1, all_51_1) =
% 144.27/20.07 | | | | | | | | all_473_0 & in(all_473_1, all_51_1) = 0 & $i(all_473_1)
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | ALPHA: (106) implies:
% 144.27/20.07 | | | | | | | | (107) ~ (all_473_0 = 0)
% 144.27/20.07 | | | | | | | | (108) $i(all_473_1)
% 144.27/20.07 | | | | | | | | (109) in(all_473_1, all_51_1) = 0
% 144.27/20.07 | | | | | | | | (110) subset(all_473_1, all_51_1) = all_473_0
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | BETA: splitting (87) gives:
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | | Case 1:
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | | GROUND_INST: instantiating (2) with all_473_1, simplifying with
% 144.27/20.07 | | | | | | | | | (108), (109) gives:
% 144.27/20.07 | | | | | | | | | (111) subset(all_473_1, all_51_1) = 0 & ordinal(all_473_1)
% 144.27/20.07 | | | | | | | | | = 0
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | | REF_CLOSE: (33), (107), (110), (111) are inconsistent by
% 144.27/20.07 | | | | | | | | | sub-proof #10.
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | Case 2:
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | | (112) all_354_1 = 0 & empty(all_219_0) = 0
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | | ALPHA: (112) implies:
% 144.27/20.07 | | | | | | | | | (113) empty(all_219_0) = 0
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | | BETA: splitting (86) gives:
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | | Case 1:
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | (114) all_353_0 = 0 & in(all_39_0, all_219_0) = 0
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | ALPHA: (114) implies:
% 144.27/20.07 | | | | | | | | | | (115) in(all_39_0, all_219_0) = 0
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | GROUND_INST: instantiating (15) with all_219_0, simplifying
% 144.27/20.07 | | | | | | | | | | with (82), (113) gives:
% 144.27/20.07 | | | | | | | | | | (116) all_219_0 = empty_set
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | REDUCE: (115), (116) imply:
% 144.27/20.07 | | | | | | | | | | (117) in(all_39_0, empty_set) = 0
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | GROUND_INST: instantiating (6) with 0, all_368_0, empty_set,
% 144.27/20.07 | | | | | | | | | | all_39_0, simplifying with (99), (117) gives:
% 144.27/20.07 | | | | | | | | | | (118) all_368_0 = 0
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | REDUCE: (98), (118) imply:
% 144.27/20.07 | | | | | | | | | | (119) $false
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | CLOSE: (119) is inconsistent.
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | Case 2:
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | GROUND_INST: instantiating (2) with all_473_1, simplifying with
% 144.27/20.07 | | | | | | | | | | (108), (109) gives:
% 144.27/20.07 | | | | | | | | | | (120) subset(all_473_1, all_51_1) = 0 &
% 144.27/20.07 | | | | | | | | | | ordinal(all_473_1) = 0
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | | REF_CLOSE: (33), (107), (110), (120) are inconsistent by
% 144.27/20.07 | | | | | | | | | | sub-proof #10.
% 144.27/20.07 | | | | | | | | | |
% 144.27/20.07 | | | | | | | | | End of split
% 144.27/20.07 | | | | | | | | |
% 144.27/20.07 | | | | | | | | End of split
% 144.27/20.07 | | | | | | | |
% 144.27/20.07 | | | | | | | End of split
% 144.27/20.07 | | | | | | |
% 144.27/20.07 | | | | | | End of split
% 144.27/20.07 | | | | | |
% 144.27/20.07 | | | | | End of split
% 144.27/20.07 | | | | |
% 144.27/20.07 | | | | End of split
% 144.27/20.07 | | | |
% 144.27/20.07 | | | End of split
% 144.27/20.07 | | |
% 144.27/20.07 | | End of split
% 144.27/20.07 | |
% 144.27/20.07 | End of split
% 144.27/20.07 |
% 144.27/20.07 End of proof
% 144.27/20.07
% 144.27/20.07 Sub-proof #10 shows that the following formulas are inconsistent:
% 144.27/20.07 ----------------------------------------------------------------
% 144.27/20.07 (1) subset(all_473_1, all_51_1) = 0 & ordinal(all_473_1) = 0
% 144.27/20.07 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.07 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.27/20.07 v0))
% 144.27/20.07 (3) subset(all_473_1, all_51_1) = all_473_0
% 144.27/20.07 (4) ~ (all_473_0 = 0)
% 144.27/20.07
% 144.27/20.07 Begin of proof
% 144.27/20.07 |
% 144.27/20.07 | ALPHA: (1) implies:
% 144.27/20.07 | (5) subset(all_473_1, all_51_1) = 0
% 144.27/20.07 |
% 144.27/20.07 | GROUND_INST: instantiating (2) with all_473_0, 0, all_51_1, all_473_1,
% 144.27/20.07 | simplifying with (3), (5) gives:
% 144.27/20.07 | (6) all_473_0 = 0
% 144.27/20.07 |
% 144.27/20.07 | REDUCE: (4), (6) imply:
% 144.27/20.07 | (7) $false
% 144.27/20.07 |
% 144.27/20.07 | CLOSE: (7) is inconsistent.
% 144.27/20.07 |
% 144.27/20.07 End of proof
% 144.27/20.07
% 144.27/20.07 Sub-proof #11 shows that the following formulas are inconsistent:
% 144.27/20.07 ----------------------------------------------------------------
% 144.27/20.07 (1) $i(all_51_1)
% 144.27/20.07 (2) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.27/20.07 all_51_1) = 0 & ordinal(v0) = 0))
% 144.27/20.07 (3) ~ (all_125_0 = 0)
% 144.27/20.07 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.07 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.27/20.07 (5) ~ (all_63_1 = 0)
% 144.27/20.07 (6) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.27/20.07 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] : (
% 144.27/20.07 ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.27/20.07 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.27/20.07 (7) epsilon_connected(all_47_1) = 0
% 144.27/20.08 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.27/20.08 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.27/20.08 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.27/20.08 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.27/20.08 = 0) & in(v1, v0) = v4)))
% 144.27/20.08 (9) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.27/20.08 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int]
% 144.27/20.08 : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.27/20.08 (10) epsilon_connected(all_51_1) = all_125_0
% 144.27/20.08 (11) $i(all_47_1)
% 144.27/20.08 (12) all_63_1 = 0 | all_51_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ?
% 144.27/20.08 [v2: int] : ((v2 = 0 & in(all_51_1, all_39_0) = 0) | ( ~ (v1 = 0) &
% 144.27/20.08 in(all_51_1, all_39_0) = v1) | ( ~ (v0 = 0) & in(all_39_0, all_39_0)
% 144.27/20.08 = v0))
% 144.27/20.08
% 144.27/20.08 Begin of proof
% 144.27/20.08 |
% 144.27/20.08 | BETA: splitting (12) gives:
% 144.27/20.08 |
% 144.27/20.08 | Case 1:
% 144.27/20.08 | |
% 144.27/20.08 | | (13) all_63_1 = 0
% 144.27/20.08 | |
% 144.27/20.08 | | REDUCE: (5), (13) imply:
% 144.27/20.08 | | (14) $false
% 144.27/20.08 | |
% 144.27/20.08 | | CLOSE: (14) is inconsistent.
% 144.27/20.08 | |
% 144.27/20.08 | Case 2:
% 144.27/20.08 | |
% 144.27/20.08 | |
% 144.27/20.08 | | GROUND_INST: instantiating (6) with all_51_1, all_125_0, simplifying with
% 144.27/20.08 | | (1), (10) gives:
% 144.27/20.08 | | (15) all_125_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 144.27/20.08 | | int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3
% 144.27/20.08 | | & in(v1, all_51_1) = 0 & in(v0, v1) = v2 & in(v0, all_51_1) = 0 &
% 144.27/20.08 | | $i(v1) & $i(v0))
% 144.27/20.08 | |
% 144.27/20.08 | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (11), (15) are inconsistent by
% 144.27/20.08 | | sub-proof #22.
% 144.27/20.08 | |
% 144.27/20.08 | End of split
% 144.27/20.08 |
% 144.27/20.08 End of proof
% 144.27/20.08
% 144.27/20.08 Sub-proof #12 shows that the following formulas are inconsistent:
% 144.27/20.08 ----------------------------------------------------------------
% 144.27/20.08 (1) $i(all_51_1)
% 144.27/20.08 (2) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.27/20.08 all_51_1) = 0 & ordinal(v0) = 0))
% 144.27/20.08 (3) epsilon_transitive(all_51_1) = all_125_1
% 144.27/20.08 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.08 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.27/20.08 (5) $i(all_39_0)
% 144.27/20.08 (6) (all_175_0 = 0 & in(empty_set, all_39_0) = 0) | (all_175_1 = 0 &
% 144.27/20.08 in(all_39_0, empty_set) = 0)
% 144.27/20.08 (7) $i(empty_set)
% 144.27/20.08 (8) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.08 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.27/20.08 (9) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.08 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.27/20.08 (10) empty(empty_set) = 0
% 144.27/20.08 (11) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.27/20.08 in(all_39_0, all_49_0) = 0)
% 144.27/20.08 (12) ~ (all_125_1 = 0)
% 144.27/20.08 (13) empty(all_39_0) = all_47_0
% 144.27/20.08 (14) all_49_0 = empty_set
% 144.27/20.08 (15) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 144.27/20.08 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 144.27/20.08 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 144.27/20.08 (16) ~ (all_137_1 = 0)
% 144.27/20.08 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.27/20.08 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.27/20.08 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.27/20.08 (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.08 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.27/20.08 v0))
% 144.27/20.08 (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.08 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.27/20.08 (20) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1, all_39_0) =
% 144.27/20.08 v0)
% 144.27/20.08 (21) ~ (all_47_0 = 0)
% 144.27/20.08
% 144.27/20.08 Begin of proof
% 144.27/20.08 |
% 144.27/20.08 | BETA: splitting (20) gives:
% 144.27/20.08 |
% 144.27/20.08 | Case 1:
% 144.27/20.08 | |
% 144.27/20.08 | | (22) all_137_1 = 0
% 144.27/20.08 | |
% 144.27/20.08 | | REDUCE: (16), (22) imply:
% 144.27/20.08 | | (23) $false
% 144.27/20.08 | |
% 144.27/20.08 | | CLOSE: (23) is inconsistent.
% 144.27/20.08 | |
% 144.27/20.08 | Case 2:
% 144.27/20.08 | |
% 144.27/20.08 | | (24) ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1, all_39_0) = v0)
% 144.27/20.08 | |
% 144.27/20.08 | | DELTA: instantiating (24) with fresh symbol all_373_0 gives:
% 144.27/20.08 | | (25) ~ (all_373_0 = 0) & in(all_51_1, all_39_0) = all_373_0
% 144.27/20.08 | |
% 144.27/20.08 | | ALPHA: (25) implies:
% 144.27/20.08 | | (26) ~ (all_373_0 = 0)
% 144.27/20.08 | | (27) in(all_51_1, all_39_0) = all_373_0
% 144.27/20.08 | |
% 144.27/20.08 | | BETA: splitting (6) gives:
% 144.27/20.08 | |
% 144.27/20.08 | | Case 1:
% 144.27/20.08 | | |
% 144.27/20.08 | | |
% 144.27/20.08 | | | GROUND_INST: instantiating (17) with all_51_1, all_39_0, all_373_0,
% 144.27/20.08 | | | simplifying with (1), (5), (27) gives:
% 144.27/20.08 | | | (28) all_373_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.27/20.08 | | | empty(all_39_0) = 0) | ( ~ (v0 = 0) & element(all_51_1,
% 144.27/20.08 | | | all_39_0) = v0))
% 144.27/20.08 | | |
% 144.27/20.08 | | | GROUND_INST: instantiating (15) with all_51_1, all_125_1, simplifying with
% 144.27/20.08 | | | (1), (3) gives:
% 144.27/20.08 | | | (29) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 144.27/20.08 | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.27/20.08 | | |
% 144.27/20.08 | | | BETA: splitting (29) gives:
% 144.27/20.08 | | |
% 144.27/20.08 | | | Case 1:
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | (30) all_125_1 = 0
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | REDUCE: (12), (30) imply:
% 144.27/20.08 | | | | (31) $false
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | CLOSE: (31) is inconsistent.
% 144.27/20.08 | | | |
% 144.27/20.08 | | | Case 2:
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_51_1)
% 144.27/20.08 | | | | = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | DELTA: instantiating (32) with fresh symbols all_453_0, all_453_1 gives:
% 144.27/20.08 | | | | (33) ~ (all_453_0 = 0) & subset(all_453_1, all_51_1) = all_453_0 &
% 144.27/20.08 | | | | in(all_453_1, all_51_1) = 0 & $i(all_453_1)
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | ALPHA: (33) implies:
% 144.27/20.08 | | | | (34) ~ (all_453_0 = 0)
% 144.27/20.08 | | | | (35) $i(all_453_1)
% 144.27/20.08 | | | | (36) in(all_453_1, all_51_1) = 0
% 144.27/20.08 | | | | (37) subset(all_453_1, all_51_1) = all_453_0
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | BETA: splitting (28) gives:
% 144.27/20.08 | | | |
% 144.27/20.08 | | | | Case 1:
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | (38) all_373_0 = 0
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | REDUCE: (26), (38) imply:
% 144.27/20.08 | | | | | (39) $false
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | CLOSE: (39) is inconsistent.
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | Case 2:
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | (40) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_39_0) = 0)
% 144.27/20.08 | | | | | | ( ~ (v0 = 0) & element(all_51_1, all_39_0) = v0))
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | DELTA: instantiating (40) with fresh symbols all_458_0, all_458_1
% 144.27/20.08 | | | | | gives:
% 144.27/20.08 | | | | | (41) (all_458_0 = 0 & empty(all_39_0) = 0) | ( ~ (all_458_1 = 0) &
% 144.27/20.08 | | | | | element(all_51_1, all_39_0) = all_458_1)
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | BETA: splitting (41) gives:
% 144.27/20.08 | | | | |
% 144.27/20.08 | | | | | Case 1:
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | (42) all_458_0 = 0 & empty(all_39_0) = 0
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | ALPHA: (42) implies:
% 144.27/20.08 | | | | | | (43) empty(all_39_0) = 0
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | GROUND_INST: instantiating (19) with all_47_0, 0, all_39_0,
% 144.27/20.08 | | | | | | simplifying with (13), (43) gives:
% 144.27/20.08 | | | | | | (44) all_47_0 = 0
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | REDUCE: (21), (44) imply:
% 144.27/20.08 | | | | | | (45) $false
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | CLOSE: (45) is inconsistent.
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | Case 2:
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | GROUND_INST: instantiating (2) with all_453_1, simplifying with
% 144.27/20.08 | | | | | | (35), (36) gives:
% 144.27/20.08 | | | | | | (46) subset(all_453_1, all_51_1) = 0 & ordinal(all_453_1) = 0
% 144.27/20.08 | | | | | |
% 144.27/20.08 | | | | | | ALPHA: (46) implies:
% 144.27/20.09 | | | | | | (47) subset(all_453_1, all_51_1) = 0
% 144.27/20.09 | | | | | |
% 144.27/20.09 | | | | | | GROUND_INST: instantiating (18) with all_453_0, 0, all_51_1,
% 144.27/20.09 | | | | | | all_453_1, simplifying with (37), (47) gives:
% 144.27/20.09 | | | | | | (48) all_453_0 = 0
% 144.27/20.09 | | | | | |
% 144.27/20.09 | | | | | | REDUCE: (34), (48) imply:
% 144.27/20.09 | | | | | | (49) $false
% 144.27/20.09 | | | | | |
% 144.27/20.09 | | | | | | CLOSE: (49) is inconsistent.
% 144.27/20.09 | | | | | |
% 144.27/20.09 | | | | | End of split
% 144.27/20.09 | | | | |
% 144.27/20.09 | | | | End of split
% 144.27/20.09 | | | |
% 144.27/20.09 | | | End of split
% 144.27/20.09 | | |
% 144.27/20.09 | | Case 2:
% 144.27/20.09 | | |
% 144.27/20.09 | | | (50) all_175_1 = 0 & in(all_39_0, empty_set) = 0
% 144.27/20.09 | | |
% 144.27/20.09 | | | ALPHA: (50) implies:
% 144.27/20.09 | | | (51) in(all_39_0, empty_set) = 0
% 144.27/20.09 | | |
% 144.27/20.09 | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (14), (19), (51) are
% 144.27/20.09 | | | inconsistent by sub-proof #14.
% 144.27/20.09 | | |
% 144.27/20.09 | | End of split
% 144.27/20.09 | |
% 144.27/20.09 | End of split
% 144.27/20.09 |
% 144.27/20.09 End of proof
% 144.27/20.09
% 144.27/20.09 Sub-proof #13 shows that the following formulas are inconsistent:
% 144.27/20.09 ----------------------------------------------------------------
% 144.27/20.09 (1) $i(all_51_1)
% 144.27/20.09 (2) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.27/20.09 all_51_1) = 0 & ordinal(v0) = 0))
% 144.27/20.09 (3) ~ (all_125_0 = 0)
% 144.27/20.09 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.09 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.27/20.09 (5) $i(all_39_0)
% 144.27/20.09 (6) (all_175_0 = 0 & in(empty_set, all_39_0) = 0) | (all_175_1 = 0 &
% 144.27/20.09 in(all_39_0, empty_set) = 0)
% 144.27/20.09 (7) $i(empty_set)
% 144.27/20.09 (8) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.09 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.27/20.09 (9) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.09 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.27/20.09 (10) empty(empty_set) = 0
% 144.27/20.09 (11) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.27/20.09 in(all_39_0, all_49_0) = 0)
% 144.27/20.09 (12) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.27/20.09 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 144.27/20.09 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.27/20.09 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.27/20.09 (13) epsilon_connected(all_47_1) = 0
% 144.27/20.09 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.27/20.09 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.27/20.09 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.27/20.09 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.27/20.09 = 0) & in(v1, v0) = v4)))
% 144.27/20.09 (15) all_49_0 = empty_set
% 144.27/20.09 (16) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.27/20.09 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 144.27/20.09 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.27/20.09 (17) epsilon_connected(all_51_1) = all_125_0
% 144.27/20.09 (18) $i(all_47_1)
% 144.27/20.09 (19) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.09 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.27/20.09
% 144.27/20.09 Begin of proof
% 144.27/20.09 |
% 144.27/20.09 | BETA: splitting (6) gives:
% 144.27/20.09 |
% 144.27/20.09 | Case 1:
% 144.27/20.09 | |
% 144.27/20.09 | |
% 144.27/20.09 | | GROUND_INST: instantiating (12) with all_51_1, all_125_0, simplifying with
% 144.27/20.09 | | (1), (17) gives:
% 144.27/20.09 | | (20) all_125_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 144.27/20.09 | | int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3
% 144.27/20.09 | | & in(v1, all_51_1) = 0 & in(v0, v1) = v2 & in(v0, all_51_1) = 0 &
% 144.27/20.09 | | $i(v1) & $i(v0))
% 144.27/20.09 | |
% 144.27/20.09 | | REF_CLOSE: (2), (3), (4), (13), (14), (16), (18), (20) are inconsistent by
% 144.27/20.09 | | sub-proof #22.
% 144.27/20.09 | |
% 144.27/20.09 | Case 2:
% 144.27/20.09 | |
% 144.27/20.09 | | (21) all_175_1 = 0 & in(all_39_0, empty_set) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | ALPHA: (21) implies:
% 144.27/20.09 | | (22) in(all_39_0, empty_set) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (15), (19), (22) are
% 144.27/20.09 | | inconsistent by sub-proof #14.
% 144.27/20.09 | |
% 144.27/20.09 | End of split
% 144.27/20.09 |
% 144.27/20.09 End of proof
% 144.27/20.09
% 144.27/20.09 Sub-proof #14 shows that the following formulas are inconsistent:
% 144.27/20.09 ----------------------------------------------------------------
% 144.27/20.09 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.09 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.27/20.09 (2) $i(all_39_0)
% 144.27/20.09 (3) $i(empty_set)
% 144.27/20.09 (4) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.09 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.27/20.09 (5) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.09 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.27/20.09 (6) empty(empty_set) = 0
% 144.27/20.09 (7) (all_183_0 = 0 & in(all_49_0, all_39_0) = 0) | (all_183_1 = 0 &
% 144.27/20.09 in(all_39_0, all_49_0) = 0)
% 144.27/20.09 (8) all_49_0 = empty_set
% 144.27/20.09 (9) in(all_39_0, empty_set) = 0
% 144.27/20.09 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.09 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.27/20.09
% 144.27/20.09 Begin of proof
% 144.27/20.09 |
% 144.27/20.09 | BETA: splitting (7) gives:
% 144.27/20.09 |
% 144.27/20.09 | Case 1:
% 144.27/20.09 | |
% 144.27/20.09 | | (11) all_183_0 = 0 & in(all_49_0, all_39_0) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | ALPHA: (11) implies:
% 144.27/20.09 | | (12) in(all_49_0, all_39_0) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | REDUCE: (8), (12) imply:
% 144.27/20.09 | | (13) in(empty_set, all_39_0) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | GROUND_INST: instantiating (5) with all_39_0, empty_set, simplifying with
% 144.27/20.09 | | (2), (3), (13) gives:
% 144.27/20.09 | | (14) ? [v0: int] : ( ~ (v0 = 0) & in(all_39_0, empty_set) = v0)
% 144.27/20.09 | |
% 144.27/20.09 | | DELTA: instantiating (14) with fresh symbol all_441_0 gives:
% 144.27/20.09 | | (15) ~ (all_441_0 = 0) & in(all_39_0, empty_set) = all_441_0
% 144.27/20.09 | |
% 144.27/20.09 | | ALPHA: (15) implies:
% 144.27/20.09 | | (16) ~ (all_441_0 = 0)
% 144.27/20.09 | | (17) in(all_39_0, empty_set) = all_441_0
% 144.27/20.09 | |
% 144.27/20.09 | | GROUND_INST: instantiating (1) with 0, all_441_0, empty_set, all_39_0,
% 144.27/20.09 | | simplifying with (9), (17) gives:
% 144.27/20.09 | | (18) all_441_0 = 0
% 144.27/20.09 | |
% 144.27/20.09 | | REDUCE: (16), (18) imply:
% 144.27/20.09 | | (19) $false
% 144.27/20.09 | |
% 144.27/20.09 | | CLOSE: (19) is inconsistent.
% 144.27/20.09 | |
% 144.27/20.09 | Case 2:
% 144.27/20.09 | |
% 144.27/20.09 | | (20) all_183_1 = 0 & in(all_39_0, all_49_0) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | ALPHA: (20) implies:
% 144.27/20.09 | | (21) in(all_39_0, all_49_0) = 0
% 144.27/20.09 | |
% 144.27/20.09 | | GROUND_INST: instantiating (4) with all_39_0, empty_set, simplifying with
% 144.27/20.09 | | (2), (3), (9) gives:
% 144.27/20.09 | | (22) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 144.27/20.09 | |
% 144.27/20.09 | | DELTA: instantiating (22) with fresh symbol all_441_0 gives:
% 144.27/20.09 | | (23) ~ (all_441_0 = 0) & empty(empty_set) = all_441_0
% 144.27/20.09 | |
% 144.27/20.09 | | ALPHA: (23) implies:
% 144.27/20.09 | | (24) ~ (all_441_0 = 0)
% 144.27/20.09 | | (25) empty(empty_set) = all_441_0
% 144.27/20.09 | |
% 144.27/20.10 | | GROUND_INST: instantiating (10) with 0, all_441_0, empty_set, simplifying
% 144.27/20.10 | | with (6), (25) gives:
% 144.27/20.10 | | (26) all_441_0 = 0
% 144.27/20.10 | |
% 144.27/20.10 | | REDUCE: (24), (26) imply:
% 144.27/20.10 | | (27) $false
% 144.27/20.10 | |
% 144.27/20.10 | | CLOSE: (27) is inconsistent.
% 144.27/20.10 | |
% 144.27/20.10 | End of split
% 144.27/20.10 |
% 144.27/20.10 End of proof
% 144.27/20.10
% 144.27/20.10 Sub-proof #15 shows that the following formulas are inconsistent:
% 144.27/20.10 ----------------------------------------------------------------
% 144.27/20.10 (1) $i(all_51_1)
% 144.27/20.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 144.27/20.10 (ordinal(v0) = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 144.27/20.10 [v3: int] : ? [v4: int] : ((v4 = 0 & in(v1, v0) = 0) | ( ~ (v3 = 0) &
% 144.27/20.10 ordinal(v1) = v3)))
% 144.27/20.10 (3) ~ (all_51_0 = 0)
% 144.27/20.10 (4) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.27/20.10 all_51_1) = 0 & ordinal(v0) = 0))
% 144.27/20.10 (5) element(all_51_1, all_51_1) = all_137_1
% 144.27/20.10 (6) empty(all_51_1) = all_71_2
% 144.27/20.10 (7) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 144.27/20.10 $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 144.27/20.10 $i(v2)))
% 144.27/20.10 (8) (all_162_0 = 0 & in(all_49_0, all_47_1) = 0) | (all_162_1 = 0 &
% 144.27/20.10 in(all_47_1, all_49_0) = 0)
% 144.27/20.10 (9) ~ (all_47_1 = empty_set)
% 144.27/20.10 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.10 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.27/20.10 (11) $i(empty_set)
% 144.27/20.10 (12) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.10 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.27/20.10 (13) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.27/20.10 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.27/20.10 (14) empty(empty_set) = 0
% 144.27/20.10 (15) (all_63_0 = 0 & subset(all_47_1, all_51_1) = 0) | ( ~ (all_63_1 = 0) &
% 144.27/20.10 in(all_47_1, all_51_1) = all_63_1)
% 144.27/20.10 (16) ordinal(all_47_1) = 0
% 144.27/20.10 (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.27/20.10 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 144.27/20.10 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.27/20.10 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.27/20.10 (18) epsilon_connected(all_47_1) = 0
% 144.27/20.10 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.27/20.10 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.27/20.10 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.27/20.10 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.27/20.10 = 0) & in(v1, v0) = v4)))
% 144.27/20.10 (20) ~ (all_71_2 = 0)
% 144.27/20.10 (21) (all_61_0 = 0 & subset(empty_set, all_51_1) = 0) | ( ~ (all_61_1 = 0) &
% 144.27/20.10 in(empty_set, all_51_1) = all_61_1)
% 144.27/20.10 (22) all_49_0 = empty_set
% 144.27/20.10 (23) (all_62_0 = 0 & subset(all_49_0, all_51_1) = 0) | ( ~ (all_62_1 = 0) &
% 144.27/20.10 in(all_49_0, all_51_1) = all_62_1)
% 144.27/20.10 (24) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 144.27/20.10 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 144.27/20.10 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 144.27/20.10 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 144.27/20.10 v1) | ~ (powerset(v2) = v0))
% 144.27/20.10 (26) ( ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0) | ( ~
% 144.27/20.10 (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1)
% 144.27/20.10 (27) epsilon_connected(empty_set) = 0
% 144.27/20.10 (28) ~ (all_137_1 = 0)
% 144.27/20.10 (29) all_39_0 = empty_set
% 144.27/20.10 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 144.27/20.10 (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~
% 144.27/20.10 (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 144.27/20.10 int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 144.27/20.10 (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.10 (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 144.27/20.10 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 144.27/20.10 (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) |
% 144.27/20.10 ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) & powerset(v2) =
% 144.27/20.10 v4 & element(v1, v4) = v5 & $i(v4)))
% 144.27/20.10 (33) ordinal(empty_set) = 0
% 144.27/20.10 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.27/20.10 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.27/20.10 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.27/20.10 (35) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.27/20.10 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 144.27/20.10 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.27/20.10 (36) ordinal(all_51_1) = all_51_0
% 144.27/20.10 (37) all_47_1 = all_39_0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.27/20.10 in(all_39_0, all_47_1) = 0) | (v0 = 0 & in(all_47_1, all_39_0) = 0))
% 144.27/20.10 (38) $i(all_47_1)
% 144.27/20.10 (39) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.10 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.27/20.10 v0))
% 144.27/20.10 (40) (all_149_0 = 0 & in(empty_set, all_47_1) = 0) | (all_149_1 = 0 &
% 144.27/20.10 in(all_47_1, empty_set) = 0)
% 144.27/20.10 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.27/20.10 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~ $i(v2)
% 144.27/20.10 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.27/20.10 ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.27/20.10 = 0) & in(v1, v0) = v4)))
% 144.27/20.10 (42) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.27/20.10 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.27/20.10 (43) (all_60_0 = 0 & subset(all_39_0, all_51_1) = 0) | ( ~ (all_60_1 = 0) &
% 144.27/20.10 in(all_39_0, all_51_1) = all_60_1)
% 144.27/20.10
% 144.27/20.10 Begin of proof
% 144.27/20.10 |
% 144.27/20.10 | BETA: splitting (37) gives:
% 144.27/20.10 |
% 144.27/20.10 | Case 1:
% 144.27/20.10 | |
% 144.27/20.10 | | (44) all_47_1 = all_39_0
% 144.27/20.10 | |
% 144.27/20.10 | | COMBINE_EQS: (29), (44) imply:
% 144.27/20.10 | | (45) all_47_1 = empty_set
% 144.27/20.10 | |
% 144.27/20.10 | | REDUCE: (9), (45) imply:
% 144.27/20.11 | | (46) $false
% 144.27/20.11 | |
% 144.27/20.11 | | CLOSE: (46) is inconsistent.
% 144.27/20.11 | |
% 144.27/20.11 | Case 2:
% 144.27/20.11 | |
% 144.27/20.11 | | (47) ~ (all_47_1 = all_39_0)
% 144.27/20.11 | | (48) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_39_0, all_47_1) = 0)
% 144.27/20.11 | | | (v0 = 0 & in(all_47_1, all_39_0) = 0))
% 144.27/20.11 | |
% 144.27/20.11 | | DELTA: instantiating (48) with fresh symbols all_181_0, all_181_1 gives:
% 144.27/20.11 | | (49) (all_181_0 = 0 & in(all_39_0, all_47_1) = 0) | (all_181_1 = 0 &
% 144.27/20.11 | | in(all_47_1, all_39_0) = 0)
% 144.27/20.11 | |
% 144.27/20.11 | | BETA: splitting (21) gives:
% 144.27/20.11 | |
% 144.27/20.11 | | Case 1:
% 144.27/20.11 | | |
% 144.27/20.11 | | | (50) all_61_0 = 0 & subset(empty_set, all_51_1) = 0
% 144.27/20.11 | | |
% 144.27/20.11 | | | ALPHA: (50) implies:
% 144.27/20.11 | | | (51) subset(empty_set, all_51_1) = 0
% 144.27/20.11 | | |
% 144.27/20.11 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 144.27/20.11 | | | (14), (15), (16), (17), (18), (19), (20), (22), (24), (25),
% 144.27/20.11 | | | (26), (28), (29), (30), (34), (35), (38), (39), (41), (42),
% 144.27/20.11 | | | (49), (51) are inconsistent by sub-proof #18.
% 144.27/20.11 | | |
% 144.27/20.11 | | Case 2:
% 144.27/20.11 | | |
% 144.27/20.11 | | | (52) ~ (all_61_1 = 0) & in(empty_set, all_51_1) = all_61_1
% 144.27/20.11 | | |
% 144.27/20.11 | | | ALPHA: (52) implies:
% 144.27/20.11 | | | (53) ~ (all_61_1 = 0)
% 144.27/20.11 | | | (54) in(empty_set, all_51_1) = all_61_1
% 144.27/20.11 | | |
% 144.27/20.11 | | | BETA: splitting (43) gives:
% 144.27/20.11 | | |
% 144.27/20.11 | | | Case 1:
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | (55) all_60_0 = 0 & subset(all_39_0, all_51_1) = 0
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | ALPHA: (55) implies:
% 144.27/20.11 | | | | (56) subset(all_39_0, all_51_1) = 0
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | REDUCE: (29), (56) imply:
% 144.27/20.11 | | | | (57) subset(empty_set, all_51_1) = 0
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 144.27/20.11 | | | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (24),
% 144.27/20.11 | | | | (25), (26), (28), (29), (30), (34), (35), (38), (39), (41),
% 144.27/20.11 | | | | (42), (49), (57) are inconsistent by sub-proof #18.
% 144.27/20.11 | | | |
% 144.27/20.11 | | | Case 2:
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | (58) ~ (all_60_1 = 0) & in(all_39_0, all_51_1) = all_60_1
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | ALPHA: (58) implies:
% 144.27/20.11 | | | | (59) in(all_39_0, all_51_1) = all_60_1
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | REDUCE: (29), (59) imply:
% 144.27/20.11 | | | | (60) in(empty_set, all_51_1) = all_60_1
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | GROUND_INST: instantiating (10) with all_61_1, all_60_1, all_51_1,
% 144.27/20.11 | | | | empty_set, simplifying with (54), (60) gives:
% 144.27/20.11 | | | | (61) all_61_1 = all_60_1
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | REDUCE: (53), (61) imply:
% 144.27/20.11 | | | | (62) ~ (all_60_1 = 0)
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | BETA: splitting (23) gives:
% 144.27/20.11 | | | |
% 144.27/20.11 | | | | Case 1:
% 144.27/20.11 | | | | |
% 144.27/20.11 | | | | | (63) all_62_0 = 0 & subset(all_49_0, all_51_1) = 0
% 144.27/20.11 | | | | |
% 144.27/20.11 | | | | | ALPHA: (63) implies:
% 144.27/20.11 | | | | | (64) subset(all_49_0, all_51_1) = 0
% 144.27/20.11 | | | | |
% 144.27/20.11 | | | | | REDUCE: (22), (64) imply:
% 144.27/20.11 | | | | | (65) subset(empty_set, all_51_1) = 0
% 144.27/20.11 | | | | |
% 144.27/20.11 | | | | | BETA: splitting (15) gives:
% 144.27/20.11 | | | | |
% 144.27/20.11 | | | | | Case 1:
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | (66) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | ALPHA: (66) implies:
% 144.27/20.11 | | | | | | (67) subset(all_47_1, all_51_1) = 0
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | GROUND_INST: instantiating (41) with all_47_1, empty_set, all_51_1,
% 144.27/20.11 | | | | | | all_60_1, simplifying with (1), (11), (18), (38), (60)
% 144.27/20.11 | | | | | | gives:
% 144.27/20.11 | | | | | | (68) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ? [v1:
% 144.27/20.11 | | | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, empty_set) =
% 144.27/20.11 | | | | | | 0) | ( ~ (v1 = 0) & in(all_51_1, all_47_1) = v1) | ( ~
% 144.27/20.11 | | | | | | (v0 = 0) & in(empty_set, all_47_1) = v0))
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | GROUND_INST: instantiating (41) with empty_set, empty_set, all_51_1,
% 144.27/20.11 | | | | | | all_60_1, simplifying with (1), (11), (27), (60) gives:
% 144.27/20.11 | | | | | | (69) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ? [v1:
% 144.27/20.11 | | | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, empty_set) =
% 144.27/20.11 | | | | | | 0) | ( ~ (v1 = 0) & in(all_51_1, empty_set) = v1) | ( ~
% 144.27/20.11 | | | | | | (v0 = 0) & in(empty_set, empty_set) = v0))
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | GROUND_INST: instantiating (34) with empty_set, all_51_1, all_60_1,
% 144.27/20.11 | | | | | | simplifying with (1), (11), (60) gives:
% 144.27/20.11 | | | | | | (70) all_60_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.27/20.11 | | | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(empty_set,
% 144.27/20.11 | | | | | | all_51_1) = v0))
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | GROUND_INST: instantiating (7) with empty_set, all_51_1, simplifying
% 144.27/20.11 | | | | | | with (1), (11), (65) gives:
% 144.27/20.11 | | | | | | (71) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set,
% 144.27/20.11 | | | | | | v0) = 0 & $i(v0))
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | GROUND_INST: instantiating (7) with all_47_1, all_51_1, simplifying
% 144.27/20.11 | | | | | | with (1), (38), (67) gives:
% 144.27/20.11 | | | | | | (72) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_47_1,
% 144.27/20.11 | | | | | | v0) = 0 & $i(v0))
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | DELTA: instantiating (72) with fresh symbol all_223_0 gives:
% 144.27/20.11 | | | | | | (73) powerset(all_51_1) = all_223_0 & element(all_47_1,
% 144.27/20.11 | | | | | | all_223_0) = 0 & $i(all_223_0)
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | ALPHA: (73) implies:
% 144.27/20.11 | | | | | | (74) element(all_47_1, all_223_0) = 0
% 144.27/20.11 | | | | | | (75) powerset(all_51_1) = all_223_0
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | DELTA: instantiating (71) with fresh symbol all_225_0 gives:
% 144.27/20.11 | | | | | | (76) powerset(all_51_1) = all_225_0 & element(empty_set,
% 144.27/20.11 | | | | | | all_225_0) = 0 & $i(all_225_0)
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | ALPHA: (76) implies:
% 144.27/20.11 | | | | | | (77) powerset(all_51_1) = all_225_0
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | BETA: splitting (70) gives:
% 144.27/20.11 | | | | | |
% 144.27/20.11 | | | | | | Case 1:
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | (78) all_60_1 = 0
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | REDUCE: (62), (78) imply:
% 144.27/20.11 | | | | | | | (79) $false
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | CLOSE: (79) is inconsistent.
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | Case 2:
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | (80) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) =
% 144.27/20.11 | | | | | | | 0) | ( ~ (v0 = 0) & element(empty_set, all_51_1) =
% 144.27/20.11 | | | | | | | v0))
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | DELTA: instantiating (80) with fresh symbols all_233_0, all_233_1
% 144.27/20.11 | | | | | | | gives:
% 144.27/20.11 | | | | | | | (81) (all_233_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_233_1 =
% 144.27/20.11 | | | | | | | 0) & element(empty_set, all_51_1) = all_233_1)
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | BETA: splitting (81) gives:
% 144.27/20.11 | | | | | | |
% 144.27/20.11 | | | | | | | Case 1:
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | (82) all_233_0 = 0 & empty(all_51_1) = 0
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | ALPHA: (82) implies:
% 144.27/20.11 | | | | | | | | (83) empty(all_51_1) = 0
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | GROUND_INST: instantiating (42) with all_71_2, 0, all_51_1,
% 144.27/20.11 | | | | | | | | simplifying with (6), (83) gives:
% 144.27/20.11 | | | | | | | | (84) all_71_2 = 0
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | REDUCE: (20), (84) imply:
% 144.27/20.11 | | | | | | | | (85) $false
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | CLOSE: (85) is inconsistent.
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | Case 2:
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | (86) ~ (all_233_1 = 0) & element(empty_set, all_51_1) =
% 144.27/20.11 | | | | | | | | all_233_1
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | ALPHA: (86) implies:
% 144.27/20.11 | | | | | | | | (87) ~ (all_233_1 = 0)
% 144.27/20.11 | | | | | | | | (88) element(empty_set, all_51_1) = all_233_1
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | GROUND_INST: instantiating (25) with all_223_0, all_225_0,
% 144.27/20.11 | | | | | | | | all_51_1, simplifying with (75), (77) gives:
% 144.27/20.11 | | | | | | | | (89) all_225_0 = all_223_0
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | GROUND_INST: instantiating (30) with empty_set, all_47_1,
% 144.27/20.11 | | | | | | | | all_51_1, all_223_0, all_233_1, simplifying with
% 144.27/20.11 | | | | | | | | (1), (11), (38), (74), (75), (88) gives:
% 144.27/20.11 | | | | | | | | (90) all_233_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 144.27/20.11 | | | | | | | | in(empty_set, all_47_1) = v0)
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | BETA: splitting (90) gives:
% 144.27/20.11 | | | | | | | |
% 144.27/20.11 | | | | | | | | Case 1:
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | | (91) all_233_1 = 0
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | | REDUCE: (87), (91) imply:
% 144.27/20.11 | | | | | | | | | (92) $false
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | | CLOSE: (92) is inconsistent.
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | Case 2:
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | | (93) ? [v0: int] : ( ~ (v0 = 0) & in(empty_set, all_47_1)
% 144.27/20.11 | | | | | | | | | = v0)
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | | DELTA: instantiating (93) with fresh symbol all_372_0 gives:
% 144.27/20.11 | | | | | | | | | (94) ~ (all_372_0 = 0) & in(empty_set, all_47_1) =
% 144.27/20.11 | | | | | | | | | all_372_0
% 144.27/20.11 | | | | | | | | |
% 144.27/20.11 | | | | | | | | | ALPHA: (94) implies:
% 144.27/20.11 | | | | | | | | | (95) ~ (all_372_0 = 0)
% 144.27/20.12 | | | | | | | | | (96) in(empty_set, all_47_1) = all_372_0
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | | BETA: splitting (40) gives:
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | | Case 1:
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | (97) all_149_0 = 0 & in(empty_set, all_47_1) = 0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | ALPHA: (97) implies:
% 144.27/20.12 | | | | | | | | | | (98) in(empty_set, all_47_1) = 0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_372_0, all_47_1,
% 144.27/20.12 | | | | | | | | | | empty_set, simplifying with (96), (98) gives:
% 144.27/20.12 | | | | | | | | | | (99) all_372_0 = 0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | REDUCE: (95), (99) imply:
% 144.27/20.12 | | | | | | | | | | (100) $false
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | CLOSE: (100) is inconsistent.
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | Case 2:
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | (101) all_149_1 = 0 & in(all_47_1, empty_set) = 0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | ALPHA: (101) implies:
% 144.27/20.12 | | | | | | | | | | (102) in(all_47_1, empty_set) = 0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | REF_CLOSE: (3), (11), (12), (14), (31), (33), (36), (38),
% 144.27/20.12 | | | | | | | | | | (42), (62), (68), (69), (102) are inconsistent by
% 144.27/20.12 | | | | | | | | | | sub-proof #16.
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | End of split
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | End of split
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | End of split
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | End of split
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | Case 2:
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | (103) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) = all_63_1
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | ALPHA: (103) implies:
% 144.27/20.12 | | | | | | (104) ~ (all_63_1 = 0)
% 144.27/20.12 | | | | | | (105) in(all_47_1, all_51_1) = all_63_1
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | GROUND_INST: instantiating (41) with all_47_1, empty_set, all_51_1,
% 144.27/20.12 | | | | | | all_60_1, simplifying with (1), (11), (18), (38), (60)
% 144.27/20.12 | | | | | | gives:
% 144.27/20.12 | | | | | | (106) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ?
% 144.27/20.12 | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_51_1,
% 144.27/20.12 | | | | | | empty_set) = 0) | ( ~ (v1 = 0) & in(all_51_1,
% 144.27/20.12 | | | | | | all_47_1) = v1) | ( ~ (v0 = 0) & in(empty_set,
% 144.27/20.12 | | | | | | all_47_1) = v0))
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | GROUND_INST: instantiating (41) with empty_set, empty_set, all_51_1,
% 144.27/20.12 | | | | | | all_60_1, simplifying with (1), (11), (27), (60) gives:
% 144.27/20.12 | | | | | | (107) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ?
% 144.27/20.12 | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_51_1,
% 144.27/20.12 | | | | | | empty_set) = 0) | ( ~ (v1 = 0) & in(all_51_1,
% 144.27/20.12 | | | | | | empty_set) = v1) | ( ~ (v0 = 0) & in(empty_set,
% 144.27/20.12 | | | | | | empty_set) = v0))
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | GROUND_INST: instantiating (19) with all_47_1, all_51_1, all_47_1,
% 144.27/20.12 | | | | | | all_63_1, simplifying with (1), (18), (38), (105)
% 144.27/20.12 | | | | | | gives:
% 144.27/20.12 | | | | | | (108) all_63_1 = 0 | all_51_1 = all_47_1 | ? [v0: int] : ? [v1:
% 144.27/20.12 | | | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, all_47_1) =
% 144.27/20.12 | | | | | | 0) | ( ~ (v1 = 0) & in(all_47_1, all_47_1) = v1) | ( ~
% 144.27/20.12 | | | | | | (v0 = 0) & in(all_51_1, all_47_1) = v0))
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | GROUND_INST: instantiating (41) with empty_set, all_47_1, all_51_1,
% 144.27/20.12 | | | | | | all_63_1, simplifying with (1), (11), (27), (38), (105)
% 144.27/20.12 | | | | | | gives:
% 144.27/20.12 | | | | | | (109) all_63_1 = 0 | all_51_1 = all_47_1 | ? [v0: int] : ? [v1:
% 144.27/20.12 | | | | | | int] : ? [v2: int] : ((v2 = 0 & in(all_51_1, all_47_1) =
% 144.27/20.12 | | | | | | 0) | ( ~ (v1 = 0) & in(all_51_1, empty_set) = v1) | ( ~
% 144.27/20.12 | | | | | | (v0 = 0) & in(all_47_1, empty_set) = v0))
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | GROUND_INST: instantiating (34) with all_47_1, all_51_1, all_63_1,
% 144.27/20.12 | | | | | | simplifying with (1), (38), (105) gives:
% 144.27/20.12 | | | | | | (110) all_63_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.27/20.12 | | | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_47_1,
% 144.27/20.12 | | | | | | all_51_1) = v0))
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | GROUND_INST: instantiating (7) with empty_set, all_51_1, simplifying
% 144.27/20.12 | | | | | | with (1), (11), (65) gives:
% 144.27/20.12 | | | | | | (111) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set,
% 144.27/20.12 | | | | | | v0) = 0 & $i(v0))
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | DELTA: instantiating (111) with fresh symbol all_219_0 gives:
% 144.27/20.12 | | | | | | (112) powerset(all_51_1) = all_219_0 & element(empty_set,
% 144.27/20.12 | | | | | | all_219_0) = 0 & $i(all_219_0)
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | ALPHA: (112) implies:
% 144.27/20.12 | | | | | | (113) element(empty_set, all_219_0) = 0
% 144.27/20.12 | | | | | | (114) powerset(all_51_1) = all_219_0
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | BETA: splitting (110) gives:
% 144.27/20.12 | | | | | |
% 144.27/20.12 | | | | | | Case 1:
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | (115) all_63_1 = 0
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | REDUCE: (104), (115) imply:
% 144.27/20.12 | | | | | | | (116) $false
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | CLOSE: (116) is inconsistent.
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | Case 2:
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | (117) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1)
% 144.27/20.12 | | | | | | | = 0) | ( ~ (v0 = 0) & element(all_47_1, all_51_1) =
% 144.27/20.12 | | | | | | | v0))
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | DELTA: instantiating (117) with fresh symbols all_230_0, all_230_1
% 144.27/20.12 | | | | | | | gives:
% 144.27/20.12 | | | | | | | (118) (all_230_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_230_1 =
% 144.27/20.12 | | | | | | | 0) & element(all_47_1, all_51_1) = all_230_1)
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | BETA: splitting (118) gives:
% 144.27/20.12 | | | | | | |
% 144.27/20.12 | | | | | | | Case 1:
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | (119) all_230_0 = 0 & empty(all_51_1) = 0
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | ALPHA: (119) implies:
% 144.27/20.12 | | | | | | | | (120) empty(all_51_1) = 0
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | REF_CLOSE: (6), (20), (42), (120) are inconsistent by sub-proof
% 144.27/20.12 | | | | | | | | #23.
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | Case 2:
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | (121) ~ (all_230_1 = 0) & element(all_47_1, all_51_1) =
% 144.27/20.12 | | | | | | | | all_230_1
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | ALPHA: (121) implies:
% 144.27/20.12 | | | | | | | | (122) ~ (all_230_1 = 0)
% 144.27/20.12 | | | | | | | | (123) element(all_47_1, all_51_1) = all_230_1
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | GROUND_INST: instantiating (30) with all_51_1, empty_set,
% 144.27/20.12 | | | | | | | | all_51_1, all_219_0, all_137_1, simplifying with
% 144.27/20.12 | | | | | | | | (1), (5), (11), (113), (114) gives:
% 144.27/20.12 | | | | | | | | (124) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 144.27/20.12 | | | | | | | | in(all_51_1, empty_set) = v0)
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | GROUND_INST: instantiating (30) with all_47_1, empty_set,
% 144.27/20.12 | | | | | | | | all_51_1, all_219_0, all_230_1, simplifying with
% 144.27/20.12 | | | | | | | | (1), (11), (38), (113), (114), (123) gives:
% 144.27/20.12 | | | | | | | | (125) all_230_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) &
% 144.27/20.12 | | | | | | | | in(all_47_1, empty_set) = v0)
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | BETA: splitting (26) gives:
% 144.27/20.12 | | | | | | | |
% 144.27/20.12 | | | | | | | | Case 1:
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | | (126) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 144.27/20.12 | | | | | | | | | all_125_0
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | | ALPHA: (126) implies:
% 144.27/20.12 | | | | | | | | | (127) ~ (all_125_0 = 0)
% 144.27/20.12 | | | | | | | | | (128) epsilon_connected(all_51_1) = all_125_0
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | | BETA: splitting (125) gives:
% 144.27/20.12 | | | | | | | | |
% 144.27/20.12 | | | | | | | | | Case 1:
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | (129) all_230_1 = 0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | REDUCE: (122), (129) imply:
% 144.27/20.12 | | | | | | | | | | (130) $false
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | CLOSE: (130) is inconsistent.
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | Case 2:
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | (131) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1,
% 144.27/20.12 | | | | | | | | | | empty_set) = v0)
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | DELTA: instantiating (131) with fresh symbol all_354_0
% 144.27/20.12 | | | | | | | | | | gives:
% 144.27/20.12 | | | | | | | | | | (132) ~ (all_354_0 = 0) & in(all_47_1, empty_set) =
% 144.27/20.12 | | | | | | | | | | all_354_0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | ALPHA: (132) implies:
% 144.27/20.12 | | | | | | | | | | (133) ~ (all_354_0 = 0)
% 144.27/20.12 | | | | | | | | | | (134) in(all_47_1, empty_set) = all_354_0
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | BETA: splitting (124) gives:
% 144.27/20.12 | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | Case 1:
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | (135) all_137_1 = 0
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | REDUCE: (28), (135) imply:
% 144.27/20.12 | | | | | | | | | | | (136) $false
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | Case 2:
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | (137) ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1,
% 144.27/20.12 | | | | | | | | | | | empty_set) = v0)
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | DELTA: instantiating (137) with fresh symbol all_359_0
% 144.27/20.12 | | | | | | | | | | | gives:
% 144.27/20.12 | | | | | | | | | | | (138) ~ (all_359_0 = 0) & in(all_51_1, empty_set) =
% 144.27/20.12 | | | | | | | | | | | all_359_0
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | ALPHA: (138) implies:
% 144.27/20.12 | | | | | | | | | | | (139) ~ (all_359_0 = 0)
% 144.27/20.12 | | | | | | | | | | | (140) in(all_51_1, empty_set) = all_359_0
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | BETA: splitting (40) gives:
% 144.27/20.12 | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | Case 1:
% 144.27/20.12 | | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | | (141) all_149_0 = 0 & in(empty_set, all_47_1) = 0
% 144.27/20.12 | | | | | | | | | | | |
% 144.27/20.12 | | | | | | | | | | | | ALPHA: (141) implies:
% 144.27/20.12 | | | | | | | | | | | | (142) in(empty_set, all_47_1) = 0
% 144.27/20.12 | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | BETA: splitting (106) gives:
% 144.27/20.13 | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | (143) all_51_1 = empty_set
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | REDUCE: (36), (143) imply:
% 144.27/20.13 | | | | | | | | | | | | | (144) ordinal(empty_set) = all_51_0
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | REF_CLOSE: (3), (31), (33), (144) are inconsistent by
% 144.27/20.13 | | | | | | | | | | | | | sub-proof #17.
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | (145) all_60_1 = 0 | ? [v0: int] : ? [v1: int] : ?
% 144.27/20.13 | | | | | | | | | | | | | [v2: int] : ((v2 = 0 & in(all_51_1, empty_set) =
% 144.27/20.13 | | | | | | | | | | | | | 0) | ( ~ (v1 = 0) & in(all_51_1, all_47_1) =
% 144.27/20.13 | | | | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(empty_set, all_47_1) =
% 144.27/20.13 | | | | | | | | | | | | | v0))
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | BETA: splitting (145) gives:
% 144.27/20.13 | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | (146) all_60_1 = 0
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | REDUCE: (62), (146) imply:
% 144.27/20.13 | | | | | | | | | | | | | | (147) $false
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | (148) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2
% 144.27/20.13 | | | | | | | | | | | | | | = 0 & in(all_51_1, empty_set) = 0) | ( ~ (v1 =
% 144.27/20.13 | | | | | | | | | | | | | | 0) & in(all_51_1, all_47_1) = v1) | ( ~ (v0
% 144.27/20.13 | | | | | | | | | | | | | | = 0) & in(empty_set, all_47_1) = v0))
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | DELTA: instantiating (148) with fresh symbols all_409_0,
% 144.27/20.13 | | | | | | | | | | | | | | all_409_1, all_409_2 gives:
% 144.27/20.13 | | | | | | | | | | | | | | (149) (all_409_0 = 0 & in(all_51_1, empty_set) = 0) | (
% 144.27/20.13 | | | | | | | | | | | | | | ~ (all_409_1 = 0) & in(all_51_1, all_47_1) =
% 144.27/20.13 | | | | | | | | | | | | | | all_409_1) | ( ~ (all_409_2 = 0) & in(empty_set,
% 144.27/20.13 | | | | | | | | | | | | | | all_47_1) = all_409_2)
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 144.27/20.13 | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | (150) all_409_0 = 0 & in(all_51_1, empty_set) = 0
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 144.27/20.13 | | | | | | | | | | | | | | | (151) in(all_51_1, empty_set) = 0
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_359_0, 0, empty_set,
% 144.27/20.13 | | | | | | | | | | | | | | | all_51_1, simplifying with (140), (151) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | (152) all_359_0 = 0
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | REDUCE: (139), (152) imply:
% 144.27/20.13 | | | | | | | | | | | | | | | (153) $false
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | (154) ( ~ (all_409_1 = 0) & in(all_51_1, all_47_1) =
% 144.27/20.13 | | | | | | | | | | | | | | | all_409_1) | ( ~ (all_409_2 = 0) & in(empty_set,
% 144.27/20.13 | | | | | | | | | | | | | | | all_47_1) = all_409_2)
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 144.27/20.13 | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | (155) ~ (all_409_1 = 0) & in(all_51_1, all_47_1) =
% 144.27/20.13 | | | | | | | | | | | | | | | | all_409_1
% 144.27/20.13 | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 144.27/20.13 | | | | | | | | | | | | | | | | (156) ~ (all_409_1 = 0)
% 144.27/20.13 | | | | | | | | | | | | | | | | (157) in(all_51_1, all_47_1) = all_409_1
% 144.27/20.13 | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | (158) all_63_1 = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | REDUCE: (104), (158) imply:
% 144.27/20.13 | | | | | | | | | | | | | | | | | (159) $false
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | (160) all_51_1 = all_47_1 | ? [v0: int] : ? [v1: int]
% 144.27/20.13 | | | | | | | | | | | | | | | | | : ? [v2: int] : ((v2 = 0 & in(all_51_1, all_47_1)
% 144.27/20.13 | | | | | | | | | | | | | | | | | = 0) | ( ~ (v1 = 0) & in(all_51_1, empty_set)
% 144.27/20.13 | | | | | | | | | | | | | | | | | = v1) | ( ~ (v0 = 0) & in(all_47_1, empty_set)
% 144.27/20.13 | | | | | | | | | | | | | | | | | = v0))
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (161) all_63_1 = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | REDUCE: (104), (161) imply:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (162) $false
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with empty_set, empty_set,
% 144.27/20.13 | | | | | | | | | | | | | | | | | | all_47_1, all_354_0, simplifying with (11), (27),
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (38), (134) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (163) all_354_0 = 0 | all_47_1 = empty_set | ? [v0:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | in(empty_set, all_47_1) = 0) | ( ~ (v1 = 0) &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | in(all_47_1, empty_set) = v1) | ( ~ (v0 = 0) &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | in(empty_set, empty_set) = v0))
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (19) with all_47_1, all_47_1,
% 144.27/20.13 | | | | | | | | | | | | | | | | | | all_51_1, all_409_1, simplifying with (1), (18),
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (38), (157) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (164) all_409_1 = 0 | all_51_1 = all_47_1 | ? [v0: int]
% 144.27/20.13 | | | | | | | | | | | | | | | | | | : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | in(all_47_1, all_51_1) = 0) | ( ~ (v1 = 0) &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | in(all_51_1, all_47_1) = v1) | ( ~ (v0 = 0) &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | in(all_47_1, all_47_1) = v0))
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (17) with all_51_1, all_125_0,
% 144.27/20.13 | | | | | | | | | | | | | | | | | | simplifying with (1), (128) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | (165) all_125_0 = 0 | ? [v0: $i] : ? [v1: $i] : ?
% 144.27/20.13 | | | | | | | | | | | | | | | | | | [v2: int] : ? [v3: int] : ( ~ (v3 = 0) & ~ (v2 =
% 144.27/20.13 | | | | | | | | | | | | | | | | | | 0) & ~ (v1 = v0) & in(v1, v0) = v3 & in(v1,
% 144.27/20.13 | | | | | | | | | | | | | | | | | | all_51_1) = 0 & in(v0, v1) = v2 & in(v0,
% 144.27/20.13 | | | | | | | | | | | | | | | | | | all_51_1) = 0 & $i(v1) & $i(v0))
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | (166) all_47_1 = empty_set
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | REDUCE: (9), (166) imply:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | (167) $false
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | (168) all_354_0 = 0 | ? [v0: int] : ? [v1: int] : ?
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | [v2: int] : ((v2 = 0 & in(empty_set, all_47_1) =
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | 0) | ( ~ (v1 = 0) & in(all_47_1, empty_set) =
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(empty_set, empty_set)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | = v0))
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (169) all_125_0 = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (169) imply:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (170) $false
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (171) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | & in(v1, v0) = v3 & in(v1, all_51_1) = 0 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | in(v0, v1) = v2 & in(v0, all_51_1) = 0 & $i(v1)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | & $i(v0))
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (171) with fresh symbols all_501_0,
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | all_501_1, all_501_2, all_501_3 gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (172) ~ (all_501_0 = 0) & ~ (all_501_1 = 0) & ~
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (all_501_2 = all_501_3) & in(all_501_2, all_501_3)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | = all_501_0 & in(all_501_2, all_51_1) = 0 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | in(all_501_3, all_501_2) = all_501_1 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | in(all_501_3, all_51_1) = 0 & $i(all_501_2) &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | $i(all_501_3)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (173) ~ (all_501_2 = all_501_3)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (174) ~ (all_501_1 = 0)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (175) ~ (all_501_0 = 0)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (176) $i(all_501_3)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (177) $i(all_501_2)
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (178) in(all_501_3, all_51_1) = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (179) in(all_501_3, all_501_2) = all_501_1
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (180) in(all_501_2, all_51_1) = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | (181) in(all_501_2, all_501_3) = all_501_0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (182) all_354_0 = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (182) imply:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (183) $false
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_501_3, simplifying with
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (176), (178) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (184) subset(all_501_3, all_51_1) = 0 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | ordinal(all_501_3) = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (185) ordinal(all_501_3) = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_501_2, simplifying with
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (177), (180) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (186) subset(all_501_2, all_51_1) = 0 &
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | ordinal(all_501_2) = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | (187) ordinal(all_501_2) = 0
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.13 | | | | | | | | | | | | | | | | | | | | | | (188) all_51_1 = all_47_1
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (188) imply:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | (189) ordinal(all_47_1) = all_51_0
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with 0, all_51_0, all_47_1,
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | simplifying with (16), (189) gives:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | (190) all_51_0 = 0
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3), (190) imply:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | (191) $false
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (191) is inconsistent.
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_51_1 = all_47_1)
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | (193) all_409_1 = 0
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (193) imply:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | (194) $false
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (194) is inconsistent.
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | (195) all_51_1 = all_47_1 | ? [v0: int] : ? [v1: int]
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | : ? [v2: int] : ((v2 = 0 & in(all_47_1, all_51_1)
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | = 0) | ( ~ (v1 = 0) & in(all_51_1, all_47_1) =
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(all_47_1, all_47_1) =
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | v0))
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | | (196) all_51_1 = all_47_1
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (196) imply:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | | (197) $false
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (197) is inconsistent.
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (35) with all_501_2, all_501_3,
% 144.27/20.14 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (176), (177), (185), (187) gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | (198) all_501_2 = all_501_3 | ? [v0: int] : ? [v1:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | int] : ((v1 = 0 & in(all_501_3, all_501_2) = 0)
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | (v0 = 0 & in(all_501_2, all_501_3) = 0))
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_501_2 = all_501_3
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (173), (199) imply:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | (200) $false
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | (201) ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | in(all_501_3, all_501_2) = 0) | (v0 = 0 &
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | in(all_501_2, all_501_3) = 0))
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | DELTA: instantiating (201) with fresh symbols all_830_0,
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | all_830_1 gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | (202) (all_830_0 = 0 & in(all_501_3, all_501_2) = 0) |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | (all_830_1 = 0 & in(all_501_2, all_501_3) = 0)
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_830_0 = 0 & in(all_501_3, all_501_2) = 0
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) in(all_501_3, all_501_2) = 0
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_501_1, 0, all_501_2,
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | all_501_3, simplifying with (179), (204) gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_501_1 = 0
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (174), (205) imply:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (206) $false
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (206) is inconsistent.
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_830_1 = 0 & in(all_501_2, all_501_3) = 0
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (208) in(all_501_2, all_501_3) = 0
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with all_501_0, 0, all_501_3,
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | all_501_2, simplifying with (181), (208) gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_501_0 = 0
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (209) imply:
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (210) $false
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (210) is inconsistent.
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | (211) ~ (all_409_2 = 0) & in(empty_set, all_47_1) =
% 144.68/20.14 | | | | | | | | | | | | | | | | all_409_2
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 144.68/20.14 | | | | | | | | | | | | | | | | (212) ~ (all_409_2 = 0)
% 144.68/20.14 | | | | | | | | | | | | | | | | (213) in(empty_set, all_47_1) = all_409_2
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_409_2, all_47_1,
% 144.68/20.14 | | | | | | | | | | | | | | | | empty_set, simplifying with (142), (213) gives:
% 144.68/20.14 | | | | | | | | | | | | | | | | (214) all_409_2 = 0
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | REDUCE: (212), (214) imply:
% 144.68/20.14 | | | | | | | | | | | | | | | | (215) $false
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | | CLOSE: (215) is inconsistent.
% 144.68/20.14 | | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | (216) all_149_1 = 0 & in(all_47_1, empty_set) = 0
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | ALPHA: (216) implies:
% 144.68/20.14 | | | | | | | | | | | | (217) in(all_47_1, empty_set) = 0
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | REF_CLOSE: (3), (11), (12), (14), (31), (33), (36), (38),
% 144.68/20.14 | | | | | | | | | | | | (42), (62), (106), (107), (217) are inconsistent
% 144.68/20.14 | | | | | | | | | | | | by sub-proof #16.
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | End of split
% 144.68/20.14 | | | | | | | | |
% 144.68/20.14 | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | |
% 144.68/20.14 | | | | | | | | | (218) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) =
% 144.68/20.14 | | | | | | | | | all_125_1
% 144.68/20.14 | | | | | | | | |
% 144.68/20.14 | | | | | | | | | ALPHA: (218) implies:
% 144.68/20.14 | | | | | | | | | (219) ~ (all_125_1 = 0)
% 144.68/20.14 | | | | | | | | | (220) epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.14 | | | | | | | | |
% 144.68/20.14 | | | | | | | | | BETA: splitting (125) gives:
% 144.68/20.14 | | | | | | | | |
% 144.68/20.14 | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | (221) all_230_1 = 0
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | REDUCE: (122), (221) imply:
% 144.68/20.14 | | | | | | | | | | (222) $false
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | CLOSE: (222) is inconsistent.
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | (223) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1,
% 144.68/20.14 | | | | | | | | | | empty_set) = v0)
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | DELTA: instantiating (223) with fresh symbol all_349_0
% 144.68/20.14 | | | | | | | | | | gives:
% 144.68/20.14 | | | | | | | | | | (224) ~ (all_349_0 = 0) & in(all_47_1, empty_set) =
% 144.68/20.14 | | | | | | | | | | all_349_0
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | ALPHA: (224) implies:
% 144.68/20.14 | | | | | | | | | | (225) ~ (all_349_0 = 0)
% 144.68/20.14 | | | | | | | | | | (226) in(all_47_1, empty_set) = all_349_0
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | BETA: splitting (108) gives:
% 144.68/20.14 | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | (227) all_63_1 = 0
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | REDUCE: (104), (227) imply:
% 144.68/20.14 | | | | | | | | | | | (228) $false
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | CLOSE: (228) is inconsistent.
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | GROUND_INST: instantiating (41) with all_47_1, all_47_1,
% 144.68/20.14 | | | | | | | | | | | empty_set, all_349_0, simplifying with (11), (18),
% 144.68/20.14 | | | | | | | | | | | (38), (226) gives:
% 144.68/20.14 | | | | | | | | | | | (229) all_349_0 = 0 | all_47_1 = empty_set | ? [v0:
% 144.68/20.14 | | | | | | | | | | | int] : ? [v1: int] : ? [v2: int] : ((v2 = 0 &
% 144.68/20.14 | | | | | | | | | | | in(empty_set, all_47_1) = 0) | ( ~ (v1 = 0) &
% 144.68/20.14 | | | | | | | | | | | in(empty_set, all_47_1) = v1) | ( ~ (v0 = 0) &
% 144.68/20.14 | | | | | | | | | | | in(all_47_1, all_47_1) = v0))
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | GROUND_INST: instantiating (24) with all_51_1, all_125_1,
% 144.68/20.14 | | | | | | | | | | | simplifying with (1), (220) gives:
% 144.68/20.14 | | | | | | | | | | | (230) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 144.68/20.14 | | | | | | | | | | | (v1 = 0) & subset(v0, all_51_1) = v1 & in(v0,
% 144.68/20.14 | | | | | | | | | | | all_51_1) = 0 & $i(v0))
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | BETA: splitting (230) gives:
% 144.68/20.14 | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | (231) all_125_1 = 0
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | REDUCE: (219), (231) imply:
% 144.68/20.14 | | | | | | | | | | | | (232) $false
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | CLOSE: (232) is inconsistent.
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | (233) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 144.68/20.14 | | | | | | | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0
% 144.68/20.14 | | | | | | | | | | | | & $i(v0))
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | DELTA: instantiating (233) with fresh symbols all_472_0,
% 144.68/20.14 | | | | | | | | | | | | all_472_1 gives:
% 144.68/20.14 | | | | | | | | | | | | (234) ~ (all_472_0 = 0) & subset(all_472_1, all_51_1) =
% 144.68/20.14 | | | | | | | | | | | | all_472_0 & in(all_472_1, all_51_1) = 0 &
% 144.68/20.14 | | | | | | | | | | | | $i(all_472_1)
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | ALPHA: (234) implies:
% 144.68/20.14 | | | | | | | | | | | | (235) ~ (all_472_0 = 0)
% 144.68/20.14 | | | | | | | | | | | | (236) $i(all_472_1)
% 144.68/20.14 | | | | | | | | | | | | (237) in(all_472_1, all_51_1) = 0
% 144.68/20.14 | | | | | | | | | | | | (238) subset(all_472_1, all_51_1) = all_472_0
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | BETA: splitting (229) gives:
% 144.68/20.14 | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | (239) all_47_1 = empty_set
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | REDUCE: (9), (239) imply:
% 144.68/20.14 | | | | | | | | | | | | | (240) $false
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | Case 2:
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | (241) all_349_0 = 0 | ? [v0: int] : ? [v1: int] : ?
% 144.68/20.14 | | | | | | | | | | | | | [v2: int] : ((v2 = 0 & in(empty_set, all_47_1) =
% 144.68/20.14 | | | | | | | | | | | | | 0) | ( ~ (v1 = 0) & in(empty_set, all_47_1) =
% 144.68/20.14 | | | | | | | | | | | | | v1) | ( ~ (v0 = 0) & in(all_47_1, all_47_1) =
% 144.68/20.14 | | | | | | | | | | | | | v0))
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | BETA: splitting (241) gives:
% 144.68/20.14 | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | Case 1:
% 144.68/20.14 | | | | | | | | | | | | | |
% 144.68/20.14 | | | | | | | | | | | | | | (242) all_349_0 = 0
% 144.68/20.14 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | REDUCE: (225), (242) imply:
% 144.68/20.15 | | | | | | | | | | | | | | (243) $false
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | CLOSE: (243) is inconsistent.
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | Case 2:
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_472_1, simplifying with
% 144.68/20.15 | | | | | | | | | | | | | | (236), (237) gives:
% 144.68/20.15 | | | | | | | | | | | | | | (244) subset(all_472_1, all_51_1) = 0 &
% 144.68/20.15 | | | | | | | | | | | | | | ordinal(all_472_1) = 0
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | ALPHA: (244) implies:
% 144.68/20.15 | | | | | | | | | | | | | | (245) subset(all_472_1, all_51_1) = 0
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_472_0, 0, all_51_1,
% 144.68/20.15 | | | | | | | | | | | | | | all_472_1, simplifying with (238), (245) gives:
% 144.68/20.15 | | | | | | | | | | | | | | (246) all_472_0 = 0
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | REDUCE: (235), (246) imply:
% 144.68/20.15 | | | | | | | | | | | | | | (247) $false
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | | CLOSE: (247) is inconsistent.
% 144.68/20.15 | | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | | End of split
% 144.68/20.15 | | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | | End of split
% 144.68/20.15 | | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | | End of split
% 144.68/20.15 | | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | End of split
% 144.68/20.15 | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | End of split
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | End of split
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | End of split
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | End of split
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | End of split
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | Case 2:
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | | (248) ~ (all_62_1 = 0) & in(all_49_0, all_51_1) = all_62_1
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | | ALPHA: (248) implies:
% 144.68/20.15 | | | | | (249) ~ (all_62_1 = 0)
% 144.68/20.15 | | | | | (250) in(all_49_0, all_51_1) = all_62_1
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | | REDUCE: (22), (250) imply:
% 144.68/20.15 | | | | | (251) in(empty_set, all_51_1) = all_62_1
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | | GROUND_INST: instantiating (10) with all_60_1, all_62_1, all_51_1,
% 144.68/20.15 | | | | | empty_set, simplifying with (60), (251) gives:
% 144.68/20.15 | | | | | (252) all_62_1 = all_60_1
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | | BETA: splitting (15) gives:
% 144.68/20.15 | | | | |
% 144.68/20.15 | | | | | Case 1:
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | (253) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | ALPHA: (253) implies:
% 144.68/20.15 | | | | | | (254) subset(all_47_1, all_51_1) = 0
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | GROUND_INST: instantiating (7) with all_47_1, all_51_1, simplifying
% 144.68/20.15 | | | | | | with (1), (38), (254) gives:
% 144.68/20.15 | | | | | | (255) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_47_1,
% 144.68/20.15 | | | | | | v0) = 0 & $i(v0))
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | DELTA: instantiating (255) with fresh symbol all_227_0 gives:
% 144.68/20.15 | | | | | | (256) powerset(all_51_1) = all_227_0 & element(all_47_1,
% 144.68/20.15 | | | | | | all_227_0) = 0 & $i(all_227_0)
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | ALPHA: (256) implies:
% 144.68/20.15 | | | | | | (257) element(all_47_1, all_227_0) = 0
% 144.68/20.15 | | | | | | (258) powerset(all_51_1) = all_227_0
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | GROUND_INST: instantiating (30) with all_51_1, all_47_1, all_51_1,
% 144.68/20.15 | | | | | | all_227_0, all_137_1, simplifying with (1), (5), (38),
% 144.68/20.15 | | | | | | (257), (258) gives:
% 144.68/20.15 | | | | | | (259) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1,
% 144.68/20.15 | | | | | | all_47_1) = v0)
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | BETA: splitting (26) gives:
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | Case 1:
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | (260) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 144.68/20.15 | | | | | | | all_125_0
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | ALPHA: (260) implies:
% 144.68/20.15 | | | | | | | (261) ~ (all_125_0 = 0)
% 144.68/20.15 | | | | | | | (262) epsilon_connected(all_51_1) = all_125_0
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | REF_CLOSE: (1), (4), (8), (10), (11), (12), (13), (14), (17),
% 144.68/20.15 | | | | | | | (18), (19), (22), (29), (35), (38), (42), (49), (261),
% 144.68/20.15 | | | | | | | (262) are inconsistent by sub-proof #20.
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | Case 2:
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | (263) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) =
% 144.68/20.15 | | | | | | | all_125_1
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | ALPHA: (263) implies:
% 144.68/20.15 | | | | | | | (264) ~ (all_125_1 = 0)
% 144.68/20.15 | | | | | | | (265) epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | REF_CLOSE: (1), (4), (10), (11), (12), (13), (14), (24), (28),
% 144.68/20.15 | | | | | | | (29), (34), (38), (39), (42), (49), (259), (264), (265)
% 144.68/20.15 | | | | | | | are inconsistent by sub-proof #19.
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | End of split
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | Case 2:
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | GROUND_INST: instantiating (41) with all_47_1, empty_set, all_51_1,
% 144.68/20.15 | | | | | | all_60_1, simplifying with (1), (11), (18), (38), (60)
% 144.68/20.15 | | | | | | gives:
% 144.68/20.15 | | | | | | (266) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ?
% 144.68/20.15 | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_51_1,
% 144.68/20.15 | | | | | | empty_set) = 0) | ( ~ (v1 = 0) & in(all_51_1,
% 144.68/20.15 | | | | | | all_47_1) = v1) | ( ~ (v0 = 0) & in(empty_set,
% 144.68/20.15 | | | | | | all_47_1) = v0))
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | GROUND_INST: instantiating (41) with empty_set, empty_set, all_51_1,
% 144.68/20.15 | | | | | | all_60_1, simplifying with (1), (11), (27), (60) gives:
% 144.68/20.15 | | | | | | (267) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ?
% 144.68/20.15 | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(all_51_1,
% 144.68/20.15 | | | | | | empty_set) = 0) | ( ~ (v1 = 0) & in(all_51_1,
% 144.68/20.15 | | | | | | empty_set) = v1) | ( ~ (v0 = 0) & in(empty_set,
% 144.68/20.15 | | | | | | empty_set) = v0))
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | GROUND_INST: instantiating (34) with empty_set, all_51_1, all_60_1,
% 144.68/20.15 | | | | | | simplifying with (1), (11), (60) gives:
% 144.68/20.15 | | | | | | (268) all_60_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.68/20.15 | | | | | | empty(all_51_1) = 0) | ( ~ (v0 = 0) &
% 144.68/20.15 | | | | | | element(empty_set, all_51_1) = v0))
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | BETA: splitting (268) gives:
% 144.68/20.15 | | | | | |
% 144.68/20.15 | | | | | | Case 1:
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | (269) all_60_1 = 0
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | REDUCE: (62), (269) imply:
% 144.68/20.15 | | | | | | | (270) $false
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | CLOSE: (270) is inconsistent.
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | Case 2:
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | (271) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1)
% 144.68/20.15 | | | | | | | = 0) | ( ~ (v0 = 0) & element(empty_set, all_51_1) =
% 144.68/20.15 | | | | | | | v0))
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | DELTA: instantiating (271) with fresh symbols all_233_0, all_233_1
% 144.68/20.15 | | | | | | | gives:
% 144.68/20.15 | | | | | | | (272) (all_233_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_233_1 =
% 144.68/20.15 | | | | | | | 0) & element(empty_set, all_51_1) = all_233_1)
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | BETA: splitting (272) gives:
% 144.68/20.15 | | | | | | |
% 144.68/20.15 | | | | | | | Case 1:
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | (273) all_233_0 = 0 & empty(all_51_1) = 0
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | ALPHA: (273) implies:
% 144.68/20.15 | | | | | | | | (274) empty(all_51_1) = 0
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | REF_CLOSE: (6), (20), (42), (274) are inconsistent by sub-proof
% 144.68/20.15 | | | | | | | | #23.
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | Case 2:
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | (275) ~ (all_233_1 = 0) & element(empty_set, all_51_1) =
% 144.68/20.15 | | | | | | | | all_233_1
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | ALPHA: (275) implies:
% 144.68/20.15 | | | | | | | | (276) ~ (all_233_1 = 0)
% 144.68/20.15 | | | | | | | | (277) element(empty_set, all_51_1) = all_233_1
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | BETA: splitting (26) gives:
% 144.68/20.15 | | | | | | | |
% 144.68/20.15 | | | | | | | | Case 1:
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | (278) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) =
% 144.68/20.15 | | | | | | | | | all_125_0
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | ALPHA: (278) implies:
% 144.68/20.15 | | | | | | | | | (279) ~ (all_125_0 = 0)
% 144.68/20.15 | | | | | | | | | (280) epsilon_connected(all_51_1) = all_125_0
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | REF_CLOSE: (1), (4), (8), (10), (11), (12), (13), (14), (17),
% 144.68/20.15 | | | | | | | | | (18), (19), (22), (29), (35), (38), (42), (49),
% 144.68/20.15 | | | | | | | | | (279), (280) are inconsistent by sub-proof #20.
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | Case 2:
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | (281) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) =
% 144.68/20.15 | | | | | | | | | all_125_1
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | ALPHA: (281) implies:
% 144.68/20.15 | | | | | | | | | (282) ~ (all_125_1 = 0)
% 144.68/20.15 | | | | | | | | | (283) epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | BETA: splitting (40) gives:
% 144.68/20.15 | | | | | | | | |
% 144.68/20.15 | | | | | | | | | Case 1:
% 144.68/20.15 | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | (284) all_149_0 = 0 & in(empty_set, all_47_1) = 0
% 144.68/20.15 | | | | | | | | | |
% 144.68/20.15 | | | | | | | | | | ALPHA: (284) implies:
% 144.68/20.15 | | | | | | | | | | (285) in(empty_set, all_47_1) = 0
% 144.68/20.15 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | GROUND_INST: instantiating (32) with empty_set, all_47_1,
% 144.68/20.16 | | | | | | | | | | all_51_1, all_233_1, simplifying with (1), (11),
% 144.68/20.16 | | | | | | | | | | (38), (277), (285) gives:
% 144.68/20.16 | | | | | | | | | | (286) all_233_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 144.68/20.16 | | | | | | | | | | (v1 = 0) & powerset(all_51_1) = v0 &
% 144.68/20.16 | | | | | | | | | | element(all_47_1, v0) = v1 & $i(v0))
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | GROUND_INST: instantiating (24) with all_51_1, all_125_1,
% 144.68/20.16 | | | | | | | | | | simplifying with (1), (283) gives:
% 144.68/20.16 | | | | | | | | | | (287) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~
% 144.68/20.16 | | | | | | | | | | (v1 = 0) & subset(v0, all_51_1) = v1 & in(v0,
% 144.68/20.16 | | | | | | | | | | all_51_1) = 0 & $i(v0))
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | BETA: splitting (287) gives:
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | Case 1:
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | (288) all_125_1 = 0
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | REDUCE: (282), (288) imply:
% 144.68/20.16 | | | | | | | | | | | (289) $false
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | Case 2:
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | (290) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 144.68/20.16 | | | | | | | | | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0
% 144.68/20.16 | | | | | | | | | | | & $i(v0))
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | DELTA: instantiating (290) with fresh symbols all_470_0,
% 144.68/20.16 | | | | | | | | | | | all_470_1 gives:
% 144.68/20.16 | | | | | | | | | | | (291) ~ (all_470_0 = 0) & subset(all_470_1, all_51_1) =
% 144.68/20.16 | | | | | | | | | | | all_470_0 & in(all_470_1, all_51_1) = 0 &
% 144.68/20.16 | | | | | | | | | | | $i(all_470_1)
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | ALPHA: (291) implies:
% 144.68/20.16 | | | | | | | | | | | (292) ~ (all_470_0 = 0)
% 144.68/20.16 | | | | | | | | | | | (293) $i(all_470_1)
% 144.68/20.16 | | | | | | | | | | | (294) in(all_470_1, all_51_1) = 0
% 144.68/20.16 | | | | | | | | | | | (295) subset(all_470_1, all_51_1) = all_470_0
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | BETA: splitting (286) gives:
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | Case 1:
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | (296) all_233_1 = 0
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | REDUCE: (276), (296) imply:
% 144.68/20.16 | | | | | | | | | | | | (297) $false
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | Case 2:
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | GROUND_INST: instantiating (4) with all_470_1, simplifying with
% 144.68/20.16 | | | | | | | | | | | | (293), (294) gives:
% 144.68/20.16 | | | | | | | | | | | | (298) subset(all_470_1, all_51_1) = 0 &
% 144.68/20.16 | | | | | | | | | | | | ordinal(all_470_1) = 0
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | ALPHA: (298) implies:
% 144.68/20.16 | | | | | | | | | | | | (299) subset(all_470_1, all_51_1) = 0
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | GROUND_INST: instantiating (39) with all_470_0, 0, all_51_1,
% 144.68/20.16 | | | | | | | | | | | | all_470_1, simplifying with (295), (299) gives:
% 144.68/20.16 | | | | | | | | | | | | (300) all_470_0 = 0
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | REDUCE: (292), (300) imply:
% 144.68/20.16 | | | | | | | | | | | | (301) $false
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | | CLOSE: (301) is inconsistent.
% 144.68/20.16 | | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | | End of split
% 144.68/20.16 | | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | End of split
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | Case 2:
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | (302) all_149_1 = 0 & in(all_47_1, empty_set) = 0
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | ALPHA: (302) implies:
% 144.68/20.16 | | | | | | | | | | (303) in(all_47_1, empty_set) = 0
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | | REF_CLOSE: (3), (11), (12), (14), (31), (33), (36), (38),
% 144.68/20.16 | | | | | | | | | | (42), (62), (266), (267), (303) are inconsistent
% 144.68/20.16 | | | | | | | | | | by sub-proof #16.
% 144.68/20.16 | | | | | | | | | |
% 144.68/20.16 | | | | | | | | | End of split
% 144.68/20.16 | | | | | | | | |
% 144.68/20.16 | | | | | | | | End of split
% 144.68/20.16 | | | | | | | |
% 144.68/20.16 | | | | | | | End of split
% 144.68/20.16 | | | | | | |
% 144.68/20.16 | | | | | | End of split
% 144.68/20.16 | | | | | |
% 144.68/20.16 | | | | | End of split
% 144.68/20.16 | | | | |
% 144.68/20.16 | | | | End of split
% 144.68/20.16 | | | |
% 144.68/20.16 | | | End of split
% 144.68/20.16 | | |
% 144.68/20.16 | | End of split
% 144.68/20.16 | |
% 144.68/20.16 | End of split
% 144.68/20.16 |
% 144.68/20.16 End of proof
% 144.68/20.16
% 144.68/20.16 Sub-proof #16 shows that the following formulas are inconsistent:
% 144.68/20.16 ----------------------------------------------------------------
% 144.68/20.16 (1) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ? [v1: int] : ?
% 144.68/20.16 [v2: int] : ((v2 = 0 & in(all_51_1, empty_set) = 0) | ( ~ (v1 = 0) &
% 144.68/20.16 in(all_51_1, all_47_1) = v1) | ( ~ (v0 = 0) & in(empty_set, all_47_1)
% 144.68/20.16 = v0))
% 144.68/20.16 (2) ~ (all_51_0 = 0)
% 144.68/20.16 (3) ~ (all_60_1 = 0)
% 144.68/20.16 (4) $i(empty_set)
% 144.68/20.16 (5) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.68/20.16 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.68/20.16 (6) empty(empty_set) = 0
% 144.68/20.16 (7) all_60_1 = 0 | all_51_1 = empty_set | ? [v0: int] : ? [v1: int] : ?
% 144.68/20.16 [v2: int] : ((v2 = 0 & in(all_51_1, empty_set) = 0) | ( ~ (v1 = 0) &
% 144.68/20.16 in(all_51_1, empty_set) = v1) | ( ~ (v0 = 0) & in(empty_set,
% 144.68/20.16 empty_set) = v0))
% 144.68/20.16 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.16 (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 144.68/20.16 (9) ordinal(empty_set) = 0
% 144.68/20.16 (10) in(all_47_1, empty_set) = 0
% 144.68/20.16 (11) ordinal(all_51_1) = all_51_0
% 144.68/20.16 (12) $i(all_47_1)
% 144.68/20.16 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.16 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.68/20.16
% 144.68/20.16 Begin of proof
% 144.68/20.16 |
% 144.68/20.16 | BETA: splitting (7) gives:
% 144.68/20.16 |
% 144.68/20.16 | Case 1:
% 144.68/20.16 | |
% 144.68/20.16 | | (14) all_51_1 = empty_set
% 144.68/20.16 | |
% 144.68/20.16 | | REDUCE: (11), (14) imply:
% 144.68/20.16 | | (15) ordinal(empty_set) = all_51_0
% 144.68/20.16 | |
% 144.68/20.16 | | REF_CLOSE: (2), (8), (9), (15) are inconsistent by sub-proof #17.
% 144.68/20.16 | |
% 144.68/20.16 | Case 2:
% 144.68/20.16 | |
% 144.68/20.16 | | (16) ~ (all_51_1 = empty_set)
% 144.68/20.16 | |
% 144.68/20.16 | | BETA: splitting (1) gives:
% 144.68/20.16 | |
% 144.68/20.16 | | Case 1:
% 144.68/20.16 | | |
% 144.68/20.16 | | | (17) all_51_1 = empty_set
% 144.68/20.16 | | |
% 144.68/20.16 | | | REDUCE: (16), (17) imply:
% 144.68/20.16 | | | (18) $false
% 144.68/20.16 | | |
% 144.68/20.16 | | | CLOSE: (18) is inconsistent.
% 144.68/20.16 | | |
% 144.68/20.16 | | Case 2:
% 144.68/20.16 | | |
% 144.68/20.16 | | | (19) all_60_1 = 0 | ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 =
% 144.68/20.16 | | | 0 & in(all_51_1, empty_set) = 0) | ( ~ (v1 = 0) & in(all_51_1,
% 144.68/20.16 | | | all_47_1) = v1) | ( ~ (v0 = 0) & in(empty_set, all_47_1) =
% 144.68/20.16 | | | v0))
% 144.68/20.16 | | |
% 144.68/20.16 | | | BETA: splitting (19) gives:
% 144.68/20.16 | | |
% 144.68/20.16 | | | Case 1:
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | (20) all_60_1 = 0
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | REDUCE: (3), (20) imply:
% 144.68/20.16 | | | | (21) $false
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | CLOSE: (21) is inconsistent.
% 144.68/20.16 | | | |
% 144.68/20.16 | | | Case 2:
% 144.68/20.16 | | | |
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | GROUND_INST: instantiating (5) with all_47_1, empty_set, simplifying
% 144.68/20.16 | | | | with (4), (10), (12) gives:
% 144.68/20.16 | | | | (22) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | DELTA: instantiating (22) with fresh symbol all_463_0 gives:
% 144.68/20.16 | | | | (23) ~ (all_463_0 = 0) & empty(empty_set) = all_463_0
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | ALPHA: (23) implies:
% 144.68/20.16 | | | | (24) ~ (all_463_0 = 0)
% 144.68/20.16 | | | | (25) empty(empty_set) = all_463_0
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | GROUND_INST: instantiating (13) with 0, all_463_0, empty_set,
% 144.68/20.16 | | | | simplifying with (6), (25) gives:
% 144.68/20.16 | | | | (26) all_463_0 = 0
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | REDUCE: (24), (26) imply:
% 144.68/20.16 | | | | (27) $false
% 144.68/20.16 | | | |
% 144.68/20.16 | | | | CLOSE: (27) is inconsistent.
% 144.68/20.16 | | | |
% 144.68/20.16 | | | End of split
% 144.68/20.16 | | |
% 144.68/20.16 | | End of split
% 144.68/20.16 | |
% 144.68/20.16 | End of split
% 144.68/20.16 |
% 144.68/20.16 End of proof
% 144.68/20.16
% 144.68/20.16 Sub-proof #17 shows that the following formulas are inconsistent:
% 144.68/20.16 ----------------------------------------------------------------
% 144.68/20.16 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.16 (v1 = v0 | ~ (ordinal(v2) = v1) | ~ (ordinal(v2) = v0))
% 144.68/20.16 (2) ordinal(empty_set) = all_51_0
% 144.68/20.16 (3) ordinal(empty_set) = 0
% 144.68/20.16 (4) ~ (all_51_0 = 0)
% 144.68/20.16
% 144.68/20.16 Begin of proof
% 144.68/20.16 |
% 144.68/20.16 | GROUND_INST: instantiating (1) with 0, all_51_0, empty_set, simplifying with
% 144.68/20.16 | (2), (3) gives:
% 144.68/20.16 | (5) all_51_0 = 0
% 144.68/20.16 |
% 144.68/20.16 | REDUCE: (4), (5) imply:
% 144.68/20.16 | (6) $false
% 144.68/20.16 |
% 144.68/20.16 | CLOSE: (6) is inconsistent.
% 144.68/20.16 |
% 144.68/20.16 End of proof
% 144.68/20.16
% 144.68/20.16 Sub-proof #18 shows that the following formulas are inconsistent:
% 144.68/20.16 ----------------------------------------------------------------
% 144.68/20.16 (1) $i(all_51_1)
% 144.68/20.16 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | v1 = v0 | ~
% 144.68/20.16 (ordinal(v0) = 0) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 144.68/20.16 [v3: int] : ? [v4: int] : ((v4 = 0 & in(v1, v0) = 0) | ( ~ (v3 = 0) &
% 144.68/20.16 ordinal(v1) = v3)))
% 144.68/20.16 (3) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.68/20.16 all_51_1) = 0 & ordinal(v0) = 0))
% 144.68/20.17 (4) element(all_51_1, all_51_1) = all_137_1
% 144.68/20.17 (5) empty(all_51_1) = all_71_2
% 144.68/20.17 (6) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 144.68/20.17 $i(v0) | ? [v2: $i] : (powerset(v1) = v2 & element(v0, v2) = 0 &
% 144.68/20.17 $i(v2)))
% 144.68/20.17 (7) (all_162_0 = 0 & in(all_49_0, all_47_1) = 0) | (all_162_1 = 0 &
% 144.68/20.17 in(all_47_1, all_49_0) = 0)
% 144.68/20.17 (8) ~ (all_47_1 = empty_set)
% 144.68/20.17 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.17 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.68/20.17 (10) $i(empty_set)
% 144.68/20.17 (11) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.68/20.17 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.68/20.17 (12) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.68/20.17 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.68/20.17 (13) empty(empty_set) = 0
% 144.68/20.17 (14) (all_63_0 = 0 & subset(all_47_1, all_51_1) = 0) | ( ~ (all_63_1 = 0) &
% 144.68/20.17 in(all_47_1, all_51_1) = all_63_1)
% 144.68/20.17 (15) ordinal(all_47_1) = 0
% 144.68/20.17 (16) subset(empty_set, all_51_1) = 0
% 144.68/20.17 (17) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.68/20.17 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 144.68/20.17 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.68/20.17 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.68/20.17 (18) epsilon_connected(all_47_1) = 0
% 144.68/20.17 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.68/20.17 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.68/20.17 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.68/20.17 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.68/20.17 = 0) & in(v1, v0) = v4)))
% 144.68/20.17 (20) ~ (all_71_2 = 0)
% 144.68/20.17 (21) all_49_0 = empty_set
% 144.68/20.17 (22) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 144.68/20.17 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 144.68/20.17 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 144.68/20.17 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 144.68/20.17 v1) | ~ (powerset(v2) = v0))
% 144.68/20.17 (24) ( ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0) | ( ~
% 144.68/20.17 (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1)
% 144.68/20.17 (25) ~ (all_137_1 = 0)
% 144.68/20.17 (26) all_39_0 = empty_set
% 144.68/20.17 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 144.68/20.17 (v4 = 0 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~
% 144.68/20.17 (element(v0, v2) = v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 144.68/20.17 int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 144.68/20.17 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.68/20.17 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.68/20.17 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.68/20.17 (29) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.68/20.17 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 144.68/20.17 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.68/20.17 (30) $i(all_47_1)
% 144.68/20.17 (31) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.17 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.68/20.17 v0))
% 144.68/20.17 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.68/20.17 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v1, v2) = v3) | ~ $i(v2)
% 144.68/20.17 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.68/20.17 ((v6 = 0 & in(v2, v1) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.68/20.17 = 0) & in(v1, v0) = v4)))
% 144.68/20.17 (33) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.17 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.68/20.17 (34) (all_181_0 = 0 & in(all_39_0, all_47_1) = 0) | (all_181_1 = 0 &
% 144.68/20.17 in(all_47_1, all_39_0) = 0)
% 144.68/20.17
% 144.68/20.17 Begin of proof
% 144.68/20.17 |
% 144.68/20.17 | BETA: splitting (14) gives:
% 144.68/20.17 |
% 144.68/20.17 | Case 1:
% 144.68/20.17 | |
% 144.68/20.17 | | (35) all_63_0 = 0 & subset(all_47_1, all_51_1) = 0
% 144.68/20.17 | |
% 144.68/20.17 | | ALPHA: (35) implies:
% 144.68/20.17 | | (36) subset(all_47_1, all_51_1) = 0
% 144.68/20.17 | |
% 144.68/20.17 | | GROUND_INST: instantiating (6) with empty_set, all_51_1, simplifying with
% 144.68/20.17 | | (1), (10), (16) gives:
% 144.68/20.17 | | (37) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0) = 0
% 144.68/20.17 | | & $i(v0))
% 144.68/20.17 | |
% 144.68/20.17 | | GROUND_INST: instantiating (6) with all_47_1, all_51_1, simplifying with
% 144.68/20.17 | | (1), (30), (36) gives:
% 144.68/20.17 | | (38) ? [v0: $i] : (powerset(all_51_1) = v0 & element(all_47_1, v0) = 0 &
% 144.68/20.17 | | $i(v0))
% 144.68/20.17 | |
% 144.68/20.17 | | DELTA: instantiating (38) with fresh symbol all_219_0 gives:
% 144.68/20.17 | | (39) powerset(all_51_1) = all_219_0 & element(all_47_1, all_219_0) = 0 &
% 144.68/20.17 | | $i(all_219_0)
% 144.68/20.17 | |
% 144.68/20.17 | | ALPHA: (39) implies:
% 144.68/20.17 | | (40) element(all_47_1, all_219_0) = 0
% 144.68/20.17 | | (41) powerset(all_51_1) = all_219_0
% 144.68/20.17 | |
% 144.68/20.17 | | DELTA: instantiating (37) with fresh symbol all_221_0 gives:
% 144.68/20.17 | | (42) powerset(all_51_1) = all_221_0 & element(empty_set, all_221_0) = 0 &
% 144.68/20.17 | | $i(all_221_0)
% 144.68/20.17 | |
% 144.68/20.17 | | ALPHA: (42) implies:
% 144.68/20.17 | | (43) powerset(all_51_1) = all_221_0
% 144.68/20.17 | |
% 144.68/20.17 | | GROUND_INST: instantiating (23) with all_219_0, all_221_0, all_51_1,
% 144.68/20.17 | | simplifying with (41), (43) gives:
% 144.68/20.17 | | (44) all_221_0 = all_219_0
% 144.68/20.17 | |
% 144.68/20.17 | | GROUND_INST: instantiating (27) with all_51_1, all_47_1, all_51_1,
% 144.68/20.17 | | all_219_0, all_137_1, simplifying with (1), (4), (30), (40),
% 144.68/20.17 | | (41) gives:
% 144.68/20.17 | | (45) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1, all_47_1)
% 144.68/20.17 | | = v0)
% 144.68/20.17 | |
% 144.68/20.17 | | BETA: splitting (24) gives:
% 144.68/20.17 | |
% 144.68/20.17 | | Case 1:
% 144.68/20.17 | | |
% 144.68/20.17 | | | (46) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 144.68/20.17 | | |
% 144.68/20.17 | | | ALPHA: (46) implies:
% 144.68/20.17 | | | (47) ~ (all_125_0 = 0)
% 144.68/20.17 | | | (48) epsilon_connected(all_51_1) = all_125_0
% 144.68/20.17 | | |
% 144.68/20.18 | | | REF_CLOSE: (1), (3), (7), (9), (10), (11), (12), (13), (17), (18), (19),
% 144.68/20.18 | | | (21), (26), (29), (30), (33), (34), (47), (48) are inconsistent
% 144.68/20.18 | | | by sub-proof #20.
% 144.68/20.18 | | |
% 144.68/20.18 | | Case 2:
% 144.68/20.18 | | |
% 144.68/20.18 | | | (49) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.18 | | |
% 144.68/20.18 | | | ALPHA: (49) implies:
% 144.68/20.18 | | | (50) ~ (all_125_1 = 0)
% 144.68/20.18 | | | (51) epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.18 | | |
% 144.68/20.18 | | | REF_CLOSE: (1), (3), (9), (10), (11), (12), (13), (22), (25), (26), (28),
% 144.68/20.18 | | | (30), (31), (33), (34), (45), (50), (51) are inconsistent by
% 144.68/20.18 | | | sub-proof #19.
% 144.68/20.18 | | |
% 144.68/20.18 | | End of split
% 144.68/20.18 | |
% 144.68/20.18 | Case 2:
% 144.68/20.18 | |
% 144.68/20.18 | | (52) ~ (all_63_1 = 0) & in(all_47_1, all_51_1) = all_63_1
% 144.68/20.18 | |
% 144.68/20.18 | | ALPHA: (52) implies:
% 144.68/20.18 | | (53) ~ (all_63_1 = 0)
% 144.68/20.18 | | (54) in(all_47_1, all_51_1) = all_63_1
% 144.68/20.18 | |
% 144.68/20.18 | | GROUND_INST: instantiating (2) with all_47_1, all_51_1, all_63_1,
% 144.68/20.18 | | simplifying with (1), (15), (30), (54) gives:
% 144.68/20.18 | | (55) all_63_1 = 0 | all_51_1 = all_47_1 | ? [v0: int] : ? [v1: int] :
% 144.68/20.18 | | ((v1 = 0 & in(all_51_1, all_47_1) = 0) | ( ~ (v0 = 0) &
% 144.68/20.18 | | ordinal(all_51_1) = v0))
% 144.68/20.18 | |
% 144.68/20.18 | | GROUND_INST: instantiating (28) with all_47_1, all_51_1, all_63_1,
% 144.68/20.18 | | simplifying with (1), (30), (54) gives:
% 144.68/20.18 | | (56) all_63_1 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.68/20.18 | | empty(all_51_1) = 0) | ( ~ (v0 = 0) & element(all_47_1,
% 144.68/20.18 | | all_51_1) = v0))
% 144.68/20.18 | |
% 144.68/20.18 | | GROUND_INST: instantiating (6) with empty_set, all_51_1, simplifying with
% 144.68/20.18 | | (1), (10), (16) gives:
% 144.68/20.18 | | (57) ? [v0: $i] : (powerset(all_51_1) = v0 & element(empty_set, v0) = 0
% 144.68/20.18 | | & $i(v0))
% 144.68/20.18 | |
% 144.68/20.18 | | DELTA: instantiating (57) with fresh symbol all_219_0 gives:
% 144.68/20.18 | | (58) powerset(all_51_1) = all_219_0 & element(empty_set, all_219_0) = 0 &
% 144.68/20.18 | | $i(all_219_0)
% 144.68/20.18 | |
% 144.68/20.18 | | ALPHA: (58) implies:
% 144.68/20.18 | | (59) element(empty_set, all_219_0) = 0
% 144.68/20.18 | | (60) powerset(all_51_1) = all_219_0
% 144.68/20.18 | |
% 144.68/20.18 | | BETA: splitting (56) gives:
% 144.68/20.18 | |
% 144.68/20.18 | | Case 1:
% 144.68/20.18 | | |
% 144.68/20.18 | | | (61) all_63_1 = 0
% 144.68/20.18 | | |
% 144.68/20.18 | | | REDUCE: (53), (61) imply:
% 144.68/20.18 | | | (62) $false
% 144.68/20.18 | | |
% 144.68/20.18 | | | CLOSE: (62) is inconsistent.
% 144.68/20.18 | | |
% 144.68/20.18 | | Case 2:
% 144.68/20.18 | | |
% 144.68/20.18 | | | (63) ? [v0: int] : ? [v1: int] : ((v1 = 0 & empty(all_51_1) = 0) | (
% 144.68/20.18 | | | ~ (v0 = 0) & element(all_47_1, all_51_1) = v0))
% 144.68/20.18 | | |
% 144.68/20.18 | | | DELTA: instantiating (63) with fresh symbols all_226_0, all_226_1 gives:
% 144.68/20.18 | | | (64) (all_226_0 = 0 & empty(all_51_1) = 0) | ( ~ (all_226_1 = 0) &
% 144.68/20.18 | | | element(all_47_1, all_51_1) = all_226_1)
% 144.68/20.18 | | |
% 144.68/20.18 | | | BETA: splitting (64) gives:
% 144.68/20.18 | | |
% 144.68/20.18 | | | Case 1:
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | (65) all_226_0 = 0 & empty(all_51_1) = 0
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | ALPHA: (65) implies:
% 144.68/20.18 | | | | (66) empty(all_51_1) = 0
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | REF_CLOSE: (5), (20), (33), (66) are inconsistent by sub-proof #23.
% 144.68/20.18 | | | |
% 144.68/20.18 | | | Case 2:
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | (67) ~ (all_226_1 = 0) & element(all_47_1, all_51_1) = all_226_1
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | ALPHA: (67) implies:
% 144.68/20.18 | | | | (68) ~ (all_226_1 = 0)
% 144.68/20.18 | | | | (69) element(all_47_1, all_51_1) = all_226_1
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | GROUND_INST: instantiating (27) with all_47_1, empty_set, all_51_1,
% 144.68/20.18 | | | | all_219_0, all_226_1, simplifying with (1), (10), (30),
% 144.68/20.18 | | | | (59), (60), (69) gives:
% 144.68/20.18 | | | | (70) all_226_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1,
% 144.68/20.18 | | | | empty_set) = v0)
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | BETA: splitting (24) gives:
% 144.68/20.18 | | | |
% 144.68/20.18 | | | | Case 1:
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | (71) ~ (all_125_0 = 0) & epsilon_connected(all_51_1) = all_125_0
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | ALPHA: (71) implies:
% 144.68/20.18 | | | | | (72) ~ (all_125_0 = 0)
% 144.68/20.18 | | | | | (73) epsilon_connected(all_51_1) = all_125_0
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | REF_CLOSE: (1), (3), (7), (9), (10), (11), (12), (13), (17), (18),
% 144.68/20.18 | | | | | (19), (21), (26), (29), (30), (33), (34), (72), (73) are
% 144.68/20.18 | | | | | inconsistent by sub-proof #20.
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | Case 2:
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | (74) ~ (all_125_1 = 0) & epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | ALPHA: (74) implies:
% 144.68/20.18 | | | | | (75) ~ (all_125_1 = 0)
% 144.68/20.18 | | | | | (76) epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | BETA: splitting (70) gives:
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | | Case 1:
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | (77) all_226_1 = 0
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | REDUCE: (68), (77) imply:
% 144.68/20.18 | | | | | | (78) $false
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | CLOSE: (78) is inconsistent.
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | Case 2:
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | (79) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1, empty_set) = v0)
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | DELTA: instantiating (79) with fresh symbol all_347_0 gives:
% 144.68/20.18 | | | | | | (80) ~ (all_347_0 = 0) & in(all_47_1, empty_set) = all_347_0
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | ALPHA: (80) implies:
% 144.68/20.18 | | | | | | (81) ~ (all_347_0 = 0)
% 144.68/20.18 | | | | | | (82) in(all_47_1, empty_set) = all_347_0
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | BETA: splitting (55) gives:
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | | Case 1:
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | (83) all_63_1 = 0
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | REDUCE: (53), (83) imply:
% 144.68/20.18 | | | | | | | (84) $false
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | CLOSE: (84) is inconsistent.
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | Case 2:
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | GROUND_INST: instantiating (32) with all_47_1, all_47_1,
% 144.68/20.18 | | | | | | | empty_set, all_347_0, simplifying with (10), (18),
% 144.68/20.18 | | | | | | | (30), (82) gives:
% 144.68/20.18 | | | | | | | (85) all_347_0 = 0 | all_47_1 = empty_set | ? [v0: int] : ?
% 144.68/20.18 | | | | | | | [v1: int] : ? [v2: int] : ((v2 = 0 & in(empty_set,
% 144.68/20.18 | | | | | | | all_47_1) = 0) | ( ~ (v1 = 0) & in(empty_set,
% 144.68/20.18 | | | | | | | all_47_1) = v1) | ( ~ (v0 = 0) & in(all_47_1,
% 144.68/20.18 | | | | | | | all_47_1) = v0))
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | GROUND_INST: instantiating (22) with all_51_1, all_125_1,
% 144.68/20.18 | | | | | | | simplifying with (1), (76) gives:
% 144.68/20.18 | | | | | | | (86) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0)
% 144.68/20.18 | | | | | | | & subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 &
% 144.68/20.18 | | | | | | | $i(v0))
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | BETA: splitting (86) gives:
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | | Case 1:
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | (87) all_125_1 = 0
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | REDUCE: (75), (87) imply:
% 144.68/20.18 | | | | | | | | (88) $false
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | CLOSE: (88) is inconsistent.
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | Case 2:
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | (89) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0,
% 144.68/20.18 | | | | | | | | all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | DELTA: instantiating (89) with fresh symbols all_434_0,
% 144.68/20.18 | | | | | | | | all_434_1 gives:
% 144.68/20.18 | | | | | | | | (90) ~ (all_434_0 = 0) & subset(all_434_1, all_51_1) =
% 144.68/20.18 | | | | | | | | all_434_0 & in(all_434_1, all_51_1) = 0 & $i(all_434_1)
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | ALPHA: (90) implies:
% 144.68/20.18 | | | | | | | | (91) ~ (all_434_0 = 0)
% 144.68/20.18 | | | | | | | | (92) $i(all_434_1)
% 144.68/20.18 | | | | | | | | (93) in(all_434_1, all_51_1) = 0
% 144.68/20.18 | | | | | | | | (94) subset(all_434_1, all_51_1) = all_434_0
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | BETA: splitting (85) gives:
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | | Case 1:
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | | (95) all_47_1 = empty_set
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | | REDUCE: (8), (95) imply:
% 144.68/20.18 | | | | | | | | | (96) $false
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | | CLOSE: (96) is inconsistent.
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | Case 2:
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | | (97) all_347_0 = 0 | ? [v0: int] : ? [v1: int] : ? [v2:
% 144.68/20.18 | | | | | | | | | int] : ((v2 = 0 & in(empty_set, all_47_1) = 0) | ( ~
% 144.68/20.18 | | | | | | | | | (v1 = 0) & in(empty_set, all_47_1) = v1) | ( ~ (v0
% 144.68/20.18 | | | | | | | | | = 0) & in(all_47_1, all_47_1) = v0))
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | | BETA: splitting (97) gives:
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | | Case 1:
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | (98) all_347_0 = 0
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | REDUCE: (81), (98) imply:
% 144.68/20.18 | | | | | | | | | | (99) $false
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | CLOSE: (99) is inconsistent.
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | Case 2:
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | GROUND_INST: instantiating (3) with all_434_1, simplifying with
% 144.68/20.18 | | | | | | | | | | (92), (93) gives:
% 144.68/20.18 | | | | | | | | | | (100) subset(all_434_1, all_51_1) = 0 &
% 144.68/20.18 | | | | | | | | | | ordinal(all_434_1) = 0
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | ALPHA: (100) implies:
% 144.68/20.18 | | | | | | | | | | (101) subset(all_434_1, all_51_1) = 0
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | GROUND_INST: instantiating (31) with all_434_0, 0, all_51_1,
% 144.68/20.18 | | | | | | | | | | all_434_1, simplifying with (94), (101) gives:
% 144.68/20.18 | | | | | | | | | | (102) all_434_0 = 0
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | REDUCE: (91), (102) imply:
% 144.68/20.18 | | | | | | | | | | (103) $false
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | | CLOSE: (103) is inconsistent.
% 144.68/20.18 | | | | | | | | | |
% 144.68/20.18 | | | | | | | | | End of split
% 144.68/20.18 | | | | | | | | |
% 144.68/20.18 | | | | | | | | End of split
% 144.68/20.18 | | | | | | | |
% 144.68/20.18 | | | | | | | End of split
% 144.68/20.18 | | | | | | |
% 144.68/20.18 | | | | | | End of split
% 144.68/20.18 | | | | | |
% 144.68/20.18 | | | | | End of split
% 144.68/20.18 | | | | |
% 144.68/20.18 | | | | End of split
% 144.68/20.18 | | | |
% 144.68/20.18 | | | End of split
% 144.68/20.18 | | |
% 144.68/20.18 | | End of split
% 144.68/20.19 | |
% 144.68/20.19 | End of split
% 144.68/20.19 |
% 144.68/20.19 End of proof
% 144.68/20.19
% 144.68/20.19 Sub-proof #19 shows that the following formulas are inconsistent:
% 144.68/20.19 ----------------------------------------------------------------
% 144.68/20.19 (1) $i(all_51_1)
% 144.68/20.19 (2) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.68/20.19 all_51_1) = 0 & ordinal(v0) = 0))
% 144.68/20.19 (3) epsilon_transitive(all_51_1) = all_125_1
% 144.68/20.19 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.19 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.68/20.19 (5) $i(empty_set)
% 144.68/20.19 (6) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.68/20.19 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.68/20.19 (7) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.68/20.19 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.68/20.19 (8) empty(empty_set) = 0
% 144.68/20.19 (9) ~ (all_125_1 = 0)
% 144.68/20.19 (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_transitive(v0) = v1)
% 144.68/20.19 | ~ $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & subset(v2,
% 144.68/20.19 v0) = v3 & in(v2, v0) = 0 & $i(v2)))
% 144.68/20.19 (11) ~ (all_137_1 = 0)
% 144.68/20.19 (12) all_39_0 = empty_set
% 144.68/20.19 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 144.68/20.19 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((v4 = 0
% 144.68/20.19 & empty(v1) = 0) | ( ~ (v3 = 0) & element(v0, v1) = v3)))
% 144.68/20.19 (14) all_137_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1, all_47_1) =
% 144.68/20.19 v0)
% 144.68/20.19 (15) $i(all_47_1)
% 144.68/20.19 (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.19 ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) =
% 144.68/20.19 v0))
% 144.68/20.19 (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.19 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.68/20.19 (18) (all_181_0 = 0 & in(all_39_0, all_47_1) = 0) | (all_181_1 = 0 &
% 144.68/20.19 in(all_47_1, all_39_0) = 0)
% 144.68/20.19
% 144.68/20.19 Begin of proof
% 144.68/20.19 |
% 144.68/20.19 | BETA: splitting (14) gives:
% 144.68/20.19 |
% 144.68/20.19 | Case 1:
% 144.68/20.19 | |
% 144.68/20.19 | | (19) all_137_1 = 0
% 144.68/20.19 | |
% 144.68/20.19 | | REDUCE: (11), (19) imply:
% 144.68/20.19 | | (20) $false
% 144.68/20.19 | |
% 144.68/20.19 | | CLOSE: (20) is inconsistent.
% 144.68/20.19 | |
% 144.68/20.19 | Case 2:
% 144.68/20.19 | |
% 144.68/20.19 | | (21) ? [v0: int] : ( ~ (v0 = 0) & in(all_51_1, all_47_1) = v0)
% 144.68/20.19 | |
% 144.68/20.19 | | DELTA: instantiating (21) with fresh symbol all_346_0 gives:
% 144.68/20.19 | | (22) ~ (all_346_0 = 0) & in(all_51_1, all_47_1) = all_346_0
% 144.68/20.19 | |
% 144.68/20.19 | | ALPHA: (22) implies:
% 144.68/20.19 | | (23) ~ (all_346_0 = 0)
% 144.68/20.19 | | (24) in(all_51_1, all_47_1) = all_346_0
% 144.68/20.19 | |
% 144.68/20.19 | | BETA: splitting (18) gives:
% 144.68/20.19 | |
% 144.68/20.19 | | Case 1:
% 144.68/20.19 | | |
% 144.68/20.19 | | |
% 144.68/20.19 | | | GROUND_INST: instantiating (13) with all_51_1, all_47_1, all_346_0,
% 144.68/20.19 | | | simplifying with (1), (15), (24) gives:
% 144.68/20.19 | | | (25) all_346_0 = 0 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.68/20.19 | | | empty(all_47_1) = 0) | ( ~ (v0 = 0) & element(all_51_1,
% 144.68/20.19 | | | all_47_1) = v0))
% 144.68/20.19 | | |
% 144.68/20.19 | | | GROUND_INST: instantiating (10) with all_51_1, all_125_1, simplifying with
% 144.68/20.19 | | | (1), (3) gives:
% 144.68/20.19 | | | (26) all_125_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 144.68/20.19 | | | subset(v0, all_51_1) = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.68/20.19 | | |
% 144.68/20.19 | | | BETA: splitting (26) gives:
% 144.68/20.19 | | |
% 144.68/20.19 | | | Case 1:
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | (27) all_125_1 = 0
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | REDUCE: (9), (27) imply:
% 144.68/20.19 | | | | (28) $false
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | CLOSE: (28) is inconsistent.
% 144.68/20.19 | | | |
% 144.68/20.19 | | | Case 2:
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_51_1)
% 144.68/20.19 | | | | = v1 & in(v0, all_51_1) = 0 & $i(v0))
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | DELTA: instantiating (29) with fresh symbols all_414_0, all_414_1 gives:
% 144.68/20.19 | | | | (30) ~ (all_414_0 = 0) & subset(all_414_1, all_51_1) = all_414_0 &
% 144.68/20.19 | | | | in(all_414_1, all_51_1) = 0 & $i(all_414_1)
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | ALPHA: (30) implies:
% 144.68/20.19 | | | | (31) ~ (all_414_0 = 0)
% 144.68/20.19 | | | | (32) $i(all_414_1)
% 144.68/20.19 | | | | (33) in(all_414_1, all_51_1) = 0
% 144.68/20.19 | | | | (34) subset(all_414_1, all_51_1) = all_414_0
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | BETA: splitting (25) gives:
% 144.68/20.19 | | | |
% 144.68/20.19 | | | | Case 1:
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | (35) all_346_0 = 0
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | REDUCE: (23), (35) imply:
% 144.68/20.19 | | | | | (36) $false
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | CLOSE: (36) is inconsistent.
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | Case 2:
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | GROUND_INST: instantiating (2) with all_414_1, simplifying with (32),
% 144.68/20.19 | | | | | (33) gives:
% 144.68/20.19 | | | | | (37) subset(all_414_1, all_51_1) = 0 & ordinal(all_414_1) = 0
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | ALPHA: (37) implies:
% 144.68/20.19 | | | | | (38) subset(all_414_1, all_51_1) = 0
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | GROUND_INST: instantiating (16) with all_414_0, 0, all_51_1,
% 144.68/20.19 | | | | | all_414_1, simplifying with (34), (38) gives:
% 144.68/20.19 | | | | | (39) all_414_0 = 0
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | REDUCE: (31), (39) imply:
% 144.68/20.19 | | | | | (40) $false
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | | CLOSE: (40) is inconsistent.
% 144.68/20.19 | | | | |
% 144.68/20.19 | | | | End of split
% 144.68/20.19 | | | |
% 144.68/20.19 | | | End of split
% 144.68/20.19 | | |
% 144.68/20.19 | | Case 2:
% 144.68/20.19 | | |
% 144.68/20.19 | | | (41) all_181_1 = 0 & in(all_47_1, all_39_0) = 0
% 144.68/20.19 | | |
% 144.68/20.19 | | | ALPHA: (41) implies:
% 144.68/20.19 | | | (42) in(all_47_1, all_39_0) = 0
% 144.68/20.19 | | |
% 144.68/20.19 | | | REDUCE: (12), (42) imply:
% 144.68/20.19 | | | (43) in(all_47_1, empty_set) = 0
% 144.68/20.19 | | |
% 144.68/20.19 | | | REF_CLOSE: (4), (5), (6), (7), (8), (12), (15), (17), (18), (43) are
% 144.68/20.19 | | | inconsistent by sub-proof #21.
% 144.68/20.19 | | |
% 144.68/20.19 | | End of split
% 144.68/20.19 | |
% 144.68/20.19 | End of split
% 144.68/20.19 |
% 144.68/20.19 End of proof
% 144.68/20.19
% 144.68/20.19 Sub-proof #20 shows that the following formulas are inconsistent:
% 144.68/20.19 ----------------------------------------------------------------
% 144.68/20.19 (1) $i(all_51_1)
% 144.68/20.19 (2) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.68/20.19 all_51_1) = 0 & ordinal(v0) = 0))
% 144.68/20.19 (3) (all_162_0 = 0 & in(all_49_0, all_47_1) = 0) | (all_162_1 = 0 &
% 144.68/20.19 in(all_47_1, all_49_0) = 0)
% 144.68/20.19 (4) ~ (all_125_0 = 0)
% 144.68/20.19 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.68/20.19 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.92/20.20 (6) $i(empty_set)
% 144.92/20.20 (7) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.92/20.20 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.92/20.20 (8) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.92/20.20 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.92/20.20 (9) empty(empty_set) = 0
% 144.92/20.20 (10) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (epsilon_connected(v0) = v1) |
% 144.92/20.20 ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 144.92/20.20 ( ~ (v5 = 0) & ~ (v4 = 0) & ~ (v3 = v2) & in(v3, v2) = v5 & in(v3,
% 144.92/20.20 v0) = 0 & in(v2, v3) = v4 & in(v2, v0) = 0 & $i(v3) & $i(v2)))
% 144.92/20.20 (11) epsilon_connected(all_47_1) = 0
% 144.92/20.20 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.92/20.20 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.92/20.20 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.92/20.20 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.92/20.20 = 0) & in(v1, v0) = v4)))
% 144.92/20.20 (13) all_49_0 = empty_set
% 144.92/20.20 (14) all_39_0 = empty_set
% 144.92/20.20 (15) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.92/20.20 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 144.92/20.20 int] : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.92/20.20 (16) epsilon_connected(all_51_1) = all_125_0
% 144.92/20.20 (17) $i(all_47_1)
% 144.92/20.20 (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.92/20.20 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.92/20.20 (19) (all_181_0 = 0 & in(all_39_0, all_47_1) = 0) | (all_181_1 = 0 &
% 144.92/20.20 in(all_47_1, all_39_0) = 0)
% 144.92/20.20
% 144.92/20.20 Begin of proof
% 144.92/20.20 |
% 144.92/20.20 | BETA: splitting (3) gives:
% 144.92/20.20 |
% 144.92/20.20 | Case 1:
% 144.92/20.20 | |
% 144.92/20.20 | |
% 144.92/20.20 | | GROUND_INST: instantiating (10) with all_51_1, all_125_0, simplifying with
% 144.92/20.20 | | (1), (16) gives:
% 144.92/20.20 | | (20) all_125_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3:
% 144.92/20.20 | | int] : ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3
% 144.92/20.20 | | & in(v1, all_51_1) = 0 & in(v0, v1) = v2 & in(v0, all_51_1) = 0 &
% 144.92/20.20 | | $i(v1) & $i(v0))
% 144.92/20.20 | |
% 144.92/20.20 | | REF_CLOSE: (2), (4), (5), (11), (12), (15), (17), (20) are inconsistent by
% 144.92/20.20 | | sub-proof #22.
% 144.92/20.20 | |
% 144.92/20.20 | Case 2:
% 144.92/20.20 | |
% 144.92/20.20 | | (21) all_162_1 = 0 & in(all_47_1, all_49_0) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | ALPHA: (21) implies:
% 144.92/20.20 | | (22) in(all_47_1, all_49_0) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | REDUCE: (13), (22) imply:
% 144.92/20.20 | | (23) in(all_47_1, empty_set) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | REF_CLOSE: (5), (6), (7), (8), (9), (14), (17), (18), (19), (23) are
% 144.92/20.20 | | inconsistent by sub-proof #21.
% 144.92/20.20 | |
% 144.92/20.20 | End of split
% 144.92/20.20 |
% 144.92/20.20 End of proof
% 144.92/20.20
% 144.92/20.20 Sub-proof #21 shows that the following formulas are inconsistent:
% 144.92/20.20 ----------------------------------------------------------------
% 144.92/20.20 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.92/20.20 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.92/20.20 (2) $i(empty_set)
% 144.92/20.20 (3) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.92/20.20 | ? [v2: int] : ( ~ (v2 = 0) & empty(v1) = v2))
% 144.92/20.20 (4) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0)
% 144.92/20.20 | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 144.92/20.20 (5) empty(empty_set) = 0
% 144.92/20.20 (6) all_39_0 = empty_set
% 144.92/20.20 (7) in(all_47_1, empty_set) = 0
% 144.92/20.20 (8) $i(all_47_1)
% 144.92/20.20 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.92/20.20 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.92/20.20 (10) (all_181_0 = 0 & in(all_39_0, all_47_1) = 0) | (all_181_1 = 0 &
% 144.92/20.20 in(all_47_1, all_39_0) = 0)
% 144.92/20.20
% 144.92/20.20 Begin of proof
% 144.92/20.20 |
% 144.92/20.20 | BETA: splitting (10) gives:
% 144.92/20.20 |
% 144.92/20.20 | Case 1:
% 144.92/20.20 | |
% 144.92/20.20 | | (11) all_181_0 = 0 & in(all_39_0, all_47_1) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | ALPHA: (11) implies:
% 144.92/20.20 | | (12) in(all_39_0, all_47_1) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | REDUCE: (6), (12) imply:
% 144.92/20.20 | | (13) in(empty_set, all_47_1) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | GROUND_INST: instantiating (4) with all_47_1, empty_set, simplifying with
% 144.92/20.20 | | (2), (8), (13) gives:
% 144.92/20.20 | | (14) ? [v0: int] : ( ~ (v0 = 0) & in(all_47_1, empty_set) = v0)
% 144.92/20.20 | |
% 144.92/20.20 | | DELTA: instantiating (14) with fresh symbol all_402_0 gives:
% 144.92/20.20 | | (15) ~ (all_402_0 = 0) & in(all_47_1, empty_set) = all_402_0
% 144.92/20.20 | |
% 144.92/20.20 | | ALPHA: (15) implies:
% 144.92/20.20 | | (16) ~ (all_402_0 = 0)
% 144.92/20.20 | | (17) in(all_47_1, empty_set) = all_402_0
% 144.92/20.20 | |
% 144.92/20.20 | | GROUND_INST: instantiating (1) with 0, all_402_0, empty_set, all_47_1,
% 144.92/20.20 | | simplifying with (7), (17) gives:
% 144.92/20.20 | | (18) all_402_0 = 0
% 144.92/20.20 | |
% 144.92/20.20 | | REDUCE: (16), (18) imply:
% 144.92/20.20 | | (19) $false
% 144.92/20.20 | |
% 144.92/20.20 | | CLOSE: (19) is inconsistent.
% 144.92/20.20 | |
% 144.92/20.20 | Case 2:
% 144.92/20.20 | |
% 144.92/20.20 | | (20) all_181_1 = 0 & in(all_47_1, all_39_0) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | ALPHA: (20) implies:
% 144.92/20.20 | | (21) in(all_47_1, all_39_0) = 0
% 144.92/20.20 | |
% 144.92/20.20 | | GROUND_INST: instantiating (3) with all_47_1, empty_set, simplifying with
% 144.92/20.20 | | (2), (7), (8) gives:
% 144.92/20.20 | | (22) ? [v0: int] : ( ~ (v0 = 0) & empty(empty_set) = v0)
% 144.92/20.20 | |
% 144.92/20.20 | | DELTA: instantiating (22) with fresh symbol all_402_0 gives:
% 144.92/20.20 | | (23) ~ (all_402_0 = 0) & empty(empty_set) = all_402_0
% 144.92/20.20 | |
% 144.92/20.20 | | ALPHA: (23) implies:
% 144.92/20.20 | | (24) ~ (all_402_0 = 0)
% 144.92/20.20 | | (25) empty(empty_set) = all_402_0
% 144.92/20.20 | |
% 144.92/20.20 | | GROUND_INST: instantiating (9) with 0, all_402_0, empty_set, simplifying
% 144.92/20.20 | | with (5), (25) gives:
% 144.92/20.20 | | (26) all_402_0 = 0
% 144.92/20.20 | |
% 144.92/20.20 | | REDUCE: (24), (26) imply:
% 144.92/20.20 | | (27) $false
% 144.92/20.20 | |
% 144.92/20.20 | | CLOSE: (27) is inconsistent.
% 144.92/20.20 | |
% 144.92/20.20 | End of split
% 144.92/20.20 |
% 144.92/20.20 End of proof
% 144.92/20.20
% 144.92/20.20 Sub-proof #22 shows that the following formulas are inconsistent:
% 144.92/20.20 ----------------------------------------------------------------
% 144.92/20.20 (1) ! [v0: $i] : ( ~ (in(v0, all_51_1) = 0) | ~ $i(v0) | (subset(v0,
% 144.92/20.20 all_51_1) = 0 & ordinal(v0) = 0))
% 144.92/20.20 (2) ~ (all_125_0 = 0)
% 144.92/20.20 (3) all_125_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] :
% 144.92/20.20 ( ~ (v3 = 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3 & in(v1,
% 144.92/20.20 all_51_1) = 0 & in(v0, v1) = v2 & in(v0, all_51_1) = 0 & $i(v1) &
% 144.92/20.20 $i(v0))
% 144.92/20.20 (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.92/20.20 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 144.92/20.20 (5) epsilon_connected(all_47_1) = 0
% 144.92/20.20 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | v2 =
% 144.92/20.20 v1 | ~ (epsilon_connected(v0) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2)
% 144.92/20.20 | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: int] : ? [v6: int] :
% 144.92/20.20 ((v6 = 0 & in(v1, v2) = 0) | ( ~ (v5 = 0) & in(v2, v0) = v5) | ( ~ (v4
% 144.92/20.20 = 0) & in(v1, v0) = v4)))
% 144.92/20.20 (7) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (ordinal(v1) = 0) | ~
% 144.92/20.20 (ordinal(v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int]
% 144.92/20.20 : ((v3 = 0 & in(v1, v0) = 0) | (v2 = 0 & in(v0, v1) = 0)))
% 144.92/20.20 (8) $i(all_47_1)
% 144.92/20.20
% 144.92/20.20 Begin of proof
% 144.92/20.20 |
% 144.92/20.20 | BETA: splitting (3) gives:
% 144.92/20.20 |
% 144.92/20.20 | Case 1:
% 144.92/20.20 | |
% 144.92/20.20 | | (9) all_125_0 = 0
% 144.92/20.20 | |
% 144.92/20.20 | | REDUCE: (2), (9) imply:
% 144.92/20.20 | | (10) $false
% 144.92/20.20 | |
% 144.92/20.20 | | CLOSE: (10) is inconsistent.
% 144.92/20.20 | |
% 144.92/20.20 | Case 2:
% 144.92/20.20 | |
% 144.92/20.21 | | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ? [v3: int] : ( ~ (v3 =
% 144.92/20.21 | | 0) & ~ (v2 = 0) & ~ (v1 = v0) & in(v1, v0) = v3 & in(v1,
% 144.92/20.21 | | all_51_1) = 0 & in(v0, v1) = v2 & in(v0, all_51_1) = 0 & $i(v1)
% 144.92/20.21 | | & $i(v0))
% 144.92/20.21 | |
% 144.92/20.21 | | DELTA: instantiating (11) with fresh symbols all_418_0, all_418_1,
% 144.92/20.21 | | all_418_2, all_418_3 gives:
% 144.92/20.21 | | (12) ~ (all_418_0 = 0) & ~ (all_418_1 = 0) & ~ (all_418_2 = all_418_3)
% 144.92/20.21 | | & in(all_418_2, all_418_3) = all_418_0 & in(all_418_2, all_51_1) = 0
% 144.92/20.21 | | & in(all_418_3, all_418_2) = all_418_1 & in(all_418_3, all_51_1) = 0
% 144.92/20.21 | | & $i(all_418_2) & $i(all_418_3)
% 144.92/20.21 | |
% 144.92/20.21 | | ALPHA: (12) implies:
% 144.92/20.21 | | (13) ~ (all_418_2 = all_418_3)
% 144.92/20.21 | | (14) ~ (all_418_1 = 0)
% 144.92/20.21 | | (15) ~ (all_418_0 = 0)
% 144.92/20.21 | | (16) $i(all_418_3)
% 144.92/20.21 | | (17) $i(all_418_2)
% 144.92/20.21 | | (18) in(all_418_3, all_51_1) = 0
% 144.92/20.21 | | (19) in(all_418_3, all_418_2) = all_418_1
% 144.92/20.21 | | (20) in(all_418_2, all_51_1) = 0
% 144.92/20.21 | | (21) in(all_418_2, all_418_3) = all_418_0
% 144.92/20.21 | |
% 144.92/20.21 | | GROUND_INST: instantiating (1) with all_418_3, simplifying with (16), (18)
% 144.92/20.21 | | gives:
% 144.92/20.21 | | (22) subset(all_418_3, all_51_1) = 0 & ordinal(all_418_3) = 0
% 144.92/20.21 | |
% 144.92/20.21 | | ALPHA: (22) implies:
% 144.92/20.21 | | (23) ordinal(all_418_3) = 0
% 144.92/20.21 | |
% 144.92/20.21 | | GROUND_INST: instantiating (1) with all_418_2, simplifying with (17), (20)
% 144.92/20.21 | | gives:
% 144.92/20.21 | | (24) subset(all_418_2, all_51_1) = 0 & ordinal(all_418_2) = 0
% 144.92/20.21 | |
% 144.92/20.21 | | ALPHA: (24) implies:
% 144.92/20.21 | | (25) ordinal(all_418_2) = 0
% 144.92/20.21 | |
% 144.92/20.21 | | GROUND_INST: instantiating (6) with all_47_1, all_418_3, all_418_2,
% 144.92/20.21 | | all_418_0, simplifying with (5), (8), (16), (17), (21) gives:
% 144.92/20.21 | | (26) all_418_0 = 0 | all_418_2 = all_418_3 | ? [v0: int] : ? [v1: int]
% 144.92/20.21 | | : ? [v2: int] : ((v2 = 0 & in(all_418_3, all_418_2) = 0) | ( ~ (v1
% 144.92/20.21 | | = 0) & in(all_418_2, all_47_1) = v1) | ( ~ (v0 = 0) &
% 144.92/20.21 | | in(all_418_3, all_47_1) = v0))
% 144.92/20.21 | |
% 144.92/20.21 | | BETA: splitting (26) gives:
% 144.92/20.21 | |
% 144.92/20.21 | | Case 1:
% 144.92/20.21 | | |
% 144.92/20.21 | | | (27) all_418_0 = 0
% 144.92/20.21 | | |
% 144.92/20.21 | | | REDUCE: (15), (27) imply:
% 144.92/20.21 | | | (28) $false
% 144.92/20.21 | | |
% 144.92/20.21 | | | CLOSE: (28) is inconsistent.
% 144.92/20.21 | | |
% 144.92/20.21 | | Case 2:
% 144.92/20.21 | | |
% 144.92/20.21 | | | (29) all_418_2 = all_418_3 | ? [v0: int] : ? [v1: int] : ? [v2: int]
% 144.92/20.21 | | | : ((v2 = 0 & in(all_418_3, all_418_2) = 0) | ( ~ (v1 = 0) &
% 144.92/20.21 | | | in(all_418_2, all_47_1) = v1) | ( ~ (v0 = 0) & in(all_418_3,
% 144.92/20.21 | | | all_47_1) = v0))
% 144.92/20.21 | | |
% 144.92/20.21 | | | BETA: splitting (29) gives:
% 144.92/20.21 | | |
% 144.92/20.21 | | | Case 1:
% 144.92/20.21 | | | |
% 144.92/20.21 | | | | (30) all_418_2 = all_418_3
% 144.92/20.21 | | | |
% 144.92/20.21 | | | | REDUCE: (13), (30) imply:
% 144.92/20.21 | | | | (31) $false
% 144.92/20.21 | | | |
% 144.92/20.21 | | | | CLOSE: (31) is inconsistent.
% 144.92/20.21 | | | |
% 144.92/20.21 | | | Case 2:
% 144.92/20.21 | | | |
% 144.92/20.21 | | | |
% 144.92/20.21 | | | | GROUND_INST: instantiating (7) with all_418_2, all_418_3, simplifying
% 144.92/20.21 | | | | with (16), (17), (23), (25) gives:
% 144.92/20.21 | | | | (32) all_418_2 = all_418_3 | ? [v0: int] : ? [v1: int] : ((v1 = 0 &
% 144.92/20.21 | | | | in(all_418_3, all_418_2) = 0) | (v0 = 0 & in(all_418_2,
% 144.92/20.21 | | | | all_418_3) = 0))
% 144.92/20.21 | | | |
% 144.92/20.21 | | | | BETA: splitting (32) gives:
% 144.92/20.21 | | | |
% 144.92/20.21 | | | | Case 1:
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | (33) all_418_2 = all_418_3
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | REDUCE: (13), (33) imply:
% 144.92/20.21 | | | | | (34) $false
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | CLOSE: (34) is inconsistent.
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | Case 2:
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | (35) ? [v0: int] : ? [v1: int] : ((v1 = 0 & in(all_418_3,
% 144.92/20.21 | | | | | all_418_2) = 0) | (v0 = 0 & in(all_418_2, all_418_3) =
% 144.92/20.21 | | | | | 0))
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | DELTA: instantiating (35) with fresh symbols all_606_0, all_606_1
% 144.92/20.21 | | | | | gives:
% 144.92/20.21 | | | | | (36) (all_606_0 = 0 & in(all_418_3, all_418_2) = 0) | (all_606_1 =
% 144.92/20.21 | | | | | 0 & in(all_418_2, all_418_3) = 0)
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | BETA: splitting (36) gives:
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | | Case 1:
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | (37) all_606_0 = 0 & in(all_418_3, all_418_2) = 0
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | ALPHA: (37) implies:
% 144.92/20.21 | | | | | | (38) in(all_418_3, all_418_2) = 0
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | GROUND_INST: instantiating (4) with all_418_1, 0, all_418_2,
% 144.92/20.21 | | | | | | all_418_3, simplifying with (19), (38) gives:
% 144.92/20.21 | | | | | | (39) all_418_1 = 0
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | REDUCE: (14), (39) imply:
% 144.92/20.21 | | | | | | (40) $false
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | CLOSE: (40) is inconsistent.
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | Case 2:
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | (41) all_606_1 = 0 & in(all_418_2, all_418_3) = 0
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | ALPHA: (41) implies:
% 144.92/20.21 | | | | | | (42) in(all_418_2, all_418_3) = 0
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | GROUND_INST: instantiating (4) with all_418_0, 0, all_418_3,
% 144.92/20.21 | | | | | | all_418_2, simplifying with (21), (42) gives:
% 144.92/20.21 | | | | | | (43) all_418_0 = 0
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | REDUCE: (15), (43) imply:
% 144.92/20.21 | | | | | | (44) $false
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | | CLOSE: (44) is inconsistent.
% 144.92/20.21 | | | | | |
% 144.92/20.21 | | | | | End of split
% 144.92/20.21 | | | | |
% 144.92/20.21 | | | | End of split
% 144.92/20.21 | | | |
% 144.92/20.21 | | | End of split
% 144.92/20.21 | | |
% 144.92/20.21 | | End of split
% 144.92/20.21 | |
% 144.92/20.21 | End of split
% 144.92/20.21 |
% 144.92/20.21 End of proof
% 144.92/20.21
% 144.92/20.21 Sub-proof #23 shows that the following formulas are inconsistent:
% 144.92/20.21 ----------------------------------------------------------------
% 144.92/20.21 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 144.92/20.21 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 144.92/20.21 (2) empty(all_51_1) = all_71_2
% 144.92/20.21 (3) empty(all_51_1) = 0
% 144.92/20.21 (4) ~ (all_71_2 = 0)
% 144.92/20.21
% 144.92/20.21 Begin of proof
% 144.92/20.21 |
% 144.92/20.21 | GROUND_INST: instantiating (1) with all_71_2, 0, all_51_1, simplifying with
% 144.92/20.21 | (2), (3) gives:
% 144.92/20.21 | (5) all_71_2 = 0
% 144.92/20.21 |
% 144.92/20.21 | REDUCE: (4), (5) imply:
% 144.92/20.21 | (6) $false
% 144.92/20.21 |
% 144.92/20.21 | CLOSE: (6) is inconsistent.
% 144.92/20.21 |
% 144.92/20.21 End of proof
% 144.92/20.21 % SZS output end Proof for theBenchmark
% 144.92/20.21
% 144.92/20.21 19596ms
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