TSTP Solution File: SEU322+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU322+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.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 17:44:04 EDT 2023
% Result : Theorem 21.55s 3.62s
% Output : Proof 97.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU322+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Wed Aug 23 20:21:11 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.14/0.50 ________ _____
% 0.14/0.50 ___ __ \_________(_)________________________________
% 0.14/0.50 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.50 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.50 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.50
% 0.14/0.50 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.50 (2023-06-19)
% 0.14/0.50
% 0.14/0.50 (c) Philipp Rümmer, 2009-2023
% 0.14/0.50 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.50 Amanda Stjerna.
% 0.14/0.50 Free software under BSD-3-Clause.
% 0.14/0.50
% 0.14/0.50 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.50
% 0.14/0.50 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.51 Running up to 7 provers in parallel.
% 0.14/0.53 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.53 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.53 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.53 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.53 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.53 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.55/1.03 Prover 4: Preprocessing ...
% 2.55/1.03 Prover 1: Preprocessing ...
% 2.55/1.07 Prover 5: Preprocessing ...
% 2.55/1.07 Prover 0: Preprocessing ...
% 2.55/1.07 Prover 3: Preprocessing ...
% 2.55/1.07 Prover 2: Preprocessing ...
% 2.55/1.07 Prover 6: Preprocessing ...
% 7.47/1.71 Prover 2: Proving ...
% 7.47/1.71 Prover 5: Proving ...
% 7.47/1.71 Prover 1: Warning: ignoring some quantifiers
% 7.76/1.75 Prover 6: Proving ...
% 7.76/1.76 Prover 1: Constructing countermodel ...
% 7.76/1.76 Prover 3: Warning: ignoring some quantifiers
% 7.76/1.80 Prover 3: Constructing countermodel ...
% 9.25/2.01 Prover 4: Warning: ignoring some quantifiers
% 9.25/2.07 Prover 4: Constructing countermodel ...
% 10.81/2.18 Prover 0: Proving ...
% 10.81/2.23 Prover 3: gave up
% 11.37/2.24 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.58/2.29 Prover 7: Preprocessing ...
% 12.23/2.39 Prover 7: Warning: ignoring some quantifiers
% 12.23/2.41 Prover 7: Constructing countermodel ...
% 21.55/3.61 Prover 0: proved (3102ms)
% 21.55/3.62
% 21.55/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.55/3.62
% 21.55/3.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.55/3.62 Prover 5: stopped
% 21.55/3.62 Prover 2: stopped
% 21.67/3.62 Prover 6: stopped
% 21.67/3.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.67/3.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.67/3.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.67/3.69 Prover 10: Preprocessing ...
% 21.67/3.70 Prover 8: Preprocessing ...
% 22.35/3.71 Prover 13: Preprocessing ...
% 22.35/3.71 Prover 11: Preprocessing ...
% 22.35/3.77 Prover 10: Warning: ignoring some quantifiers
% 22.35/3.78 Prover 10: Constructing countermodel ...
% 22.94/3.82 Prover 13: Warning: ignoring some quantifiers
% 22.94/3.85 Prover 13: Constructing countermodel ...
% 22.94/3.85 Prover 8: Warning: ignoring some quantifiers
% 23.61/3.87 Prover 8: Constructing countermodel ...
% 24.02/4.01 Prover 10: gave up
% 24.66/4.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 24.66/4.07 Prover 16: Preprocessing ...
% 25.23/4.12 Prover 16: Warning: ignoring some quantifiers
% 25.23/4.13 Prover 16: Constructing countermodel ...
% 25.23/4.13 Prover 11: Warning: ignoring some quantifiers
% 25.23/4.14 Prover 11: Constructing countermodel ...
% 30.51/4.81 Prover 8: gave up
% 30.51/4.81 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 30.51/4.90 Prover 19: Preprocessing ...
% 32.17/5.06 Prover 19: Warning: ignoring some quantifiers
% 32.17/5.08 Prover 19: Constructing countermodel ...
% 41.99/6.34 Prover 1: gave up
% 63.95/9.35 Prover 13: stopped
% 66.21/9.49 Prover 19: stopped
% 78.25/11.33 Prover 16: stopped
% 95.98/14.65 Prover 11: Found proof (size 428)
% 95.98/14.65 Prover 11: proved (11029ms)
% 95.98/14.66 Prover 4: stopped
% 95.98/14.66 Prover 7: stopped
% 95.98/14.66
% 95.98/14.66 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 95.98/14.66
% 96.24/14.69 % SZS output start Proof for theBenchmark
% 96.24/14.69 Assumptions after simplification:
% 96.24/14.69 ---------------------------------
% 96.24/14.70
% 96.24/14.70 (d1_struct_0)
% 96.24/14.73 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 96.24/14.73 int] : ? [v3: int] : ? [v4: int] : (( ~ (v2 = 0) & one_sorted_str(v0) =
% 96.24/14.73 v2) | (((v4 = 0 & empty(v1) = 0) | ( ~ (v3 = 0) & empty_carrier(v0) =
% 96.24/14.73 v3)) & ((v3 = 0 & empty_carrier(v0) = 0) | ( ~ (v4 = 0) & empty(v1)
% 96.24/14.73 = v4))))) & ! [v0: $i] : ! [v1: any] : ( ~ (empty_carrier(v0) =
% 96.24/14.73 v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v2 =
% 96.24/14.73 0) & one_sorted_str(v0) = v2) | (( ~ (v1 = 0) | (v4 = 0 &
% 96.24/14.73 the_carrier(v0) = v3 & empty(v3) = 0 & $i(v3))) & (v1 = 0 | ( ~ (v4
% 96.24/14.73 = 0) & the_carrier(v0) = v3 & empty(v3) = v4 & $i(v3)))))) & !
% 96.24/14.73 [v0: $i] : ( ~ (one_sorted_str(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2:
% 96.24/14.73 $i] : ? [v3: int] : (((v3 = 0 & the_carrier(v0) = v2 & empty(v2) = 0 &
% 96.24/14.73 $i(v2)) | ( ~ (v1 = 0) & empty_carrier(v0) = v1)) & ((v1 = 0 &
% 96.24/14.73 empty_carrier(v0) = 0) | ( ~ (v3 = 0) & the_carrier(v0) = v2 &
% 96.24/14.73 empty(v2) = v3 & $i(v2)))))
% 96.24/14.73
% 96.24/14.73 (d1_tops_1)
% 96.24/14.74 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 96.24/14.74 int] : ? [v3: $i] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) =
% 96.24/14.74 v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (interior(v0, v4) = v5) |
% 96.24/14.74 ~ $i(v4) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 96.24/14.74 ((v9 = v5 & topstr_closure(v0, v7) = v8 & subset_complement(v1, v8) =
% 96.24/14.74 v5 & subset_complement(v1, v4) = v7 & $i(v8) & $i(v7) & $i(v5)) |
% 96.24/14.74 ( ~ (v6 = 0) & element(v4, v3) = v6))) & ! [v4: $i] : ! [v5: $i] :
% 96.24/14.74 ( ~ (subset_complement(v1, v4) = v5) | ~ $i(v4) | ? [v6: int] : ?
% 96.24/14.74 [v7: $i] : ? [v8: $i] : ? [v9: $i] : ((v9 = v7 & interior(v0, v4) =
% 96.24/14.74 v7 & topstr_closure(v0, v5) = v8 & subset_complement(v1, v8) = v7
% 96.24/14.74 & $i(v8) & $i(v7)) | ( ~ (v6 = 0) & element(v4, v3) = v6))) & !
% 96.24/14.74 [v4: $i] : ( ~ (element(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6:
% 96.24/14.74 $i] : ? [v7: $i] : (interior(v0, v4) = v5 & topstr_closure(v0, v6)
% 96.24/14.74 = v7 & subset_complement(v1, v7) = v5 & subset_complement(v1, v4) =
% 96.24/14.74 v6 & $i(v7) & $i(v6) & $i(v5)))))) & ! [v0: $i] : ( ~ (top_str(v0)
% 96.24/14.74 = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : (the_carrier(v0) = v1 &
% 96.24/14.74 powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3: $i] : ! [v4: $i] : ( ~
% 96.24/14.74 (interior(v0, v3) = v4) | ~ $i(v3) | ? [v5: int] : ? [v6: $i] : ?
% 96.24/14.74 [v7: $i] : ? [v8: $i] : ((v8 = v4 & topstr_closure(v0, v6) = v7 &
% 96.24/14.74 subset_complement(v1, v7) = v4 & subset_complement(v1, v3) = v6 &
% 96.24/14.74 $i(v7) & $i(v6) & $i(v4)) | ( ~ (v5 = 0) & element(v3, v2) = v5))) &
% 96.24/14.74 ! [v3: $i] : ! [v4: $i] : ( ~ (subset_complement(v1, v3) = v4) | ~
% 96.24/14.74 $i(v3) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ((v8 =
% 96.24/14.74 v6 & interior(v0, v3) = v6 & topstr_closure(v0, v4) = v7 &
% 96.24/14.74 subset_complement(v1, v7) = v6 & $i(v7) & $i(v6)) | ( ~ (v5 = 0) &
% 96.24/14.74 element(v3, v2) = v5))) & ! [v3: $i] : ( ~ (element(v3, v2) = 0) |
% 96.24/14.74 ~ $i(v3) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : (interior(v0, v3) =
% 96.24/14.74 v4 & topstr_closure(v0, v5) = v6 & subset_complement(v1, v6) = v4 &
% 96.24/14.74 subset_complement(v1, v3) = v5 & $i(v6) & $i(v5) & $i(v4)))))
% 96.24/14.74
% 96.24/14.74 (d3_tarski)
% 96.24/14.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 96.24/14.74 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 96.24/14.74 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : !
% 96.24/14.74 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~
% 96.24/14.74 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 &
% 96.24/14.74 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 96.24/14.74 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 96.24/14.74 $i(v0) | in(v2, v1) = 0)
% 96.24/14.74
% 96.24/14.74 (dt_k1_tops_1)
% 96.24/14.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) =
% 96.24/14.74 v2) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ $i(v1) | ~
% 96.24/14.74 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ((v6 = 0 & interior(v0,
% 96.24/14.74 v1) = v5 & element(v5, v3) = 0 & $i(v5)) | ( ~ (v4 = 0) & top_str(v0)
% 96.24/14.74 = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (interior(v0,
% 96.24/14.74 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5:
% 96.24/14.74 $i] : ? [v6: int] : ? [v7: int] : ((v7 = 0 & the_carrier(v0) = v4 &
% 96.24/14.74 powerset(v4) = v5 & element(v2, v5) = 0 & $i(v5) & $i(v4)) | ( ~ (v6 =
% 96.24/14.74 0) & the_carrier(v0) = v4 & powerset(v4) = v5 & element(v1, v5) = v6 &
% 96.24/14.74 $i(v5) & $i(v4)) | ( ~ (v3 = 0) & top_str(v0) = v3)))
% 96.24/14.74
% 96.24/14.75 (dt_k3_subset_1)
% 96.24/14.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 96.24/14.75 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 96.24/14.75 (powerset(v0) = v3 & $i(v3) & ((v5 = 0 & element(v2, v3) = 0) | ( ~ (v4 = 0)
% 96.24/14.75 & element(v1, v3) = v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 96.24/14.75 ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) |
% 96.24/14.75 ? [v3: $i] : (subset_complement(v0, v1) = v3 & element(v3, v2) = 0 &
% 96.24/14.75 $i(v3)))
% 96.24/14.75
% 96.24/14.75 (dt_k6_pre_topc)
% 96.24/14.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (the_carrier(v0) =
% 96.24/14.75 v2) | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ $i(v1) | ~
% 96.24/14.75 $i(v0) | ? [v4: int] : ? [v5: $i] : ? [v6: int] : ((v6 = 0 &
% 96.24/14.75 topstr_closure(v0, v1) = v5 & element(v5, v3) = 0 & $i(v5)) | ( ~ (v4 =
% 96.24/14.75 0) & top_str(v0) = v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (
% 96.24/14.75 ~ (topstr_closure(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 96.24/14.75 [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ((v7 = 0 &
% 96.24/14.75 the_carrier(v0) = v4 & powerset(v4) = v5 & element(v2, v5) = 0 & $i(v5)
% 96.24/14.75 & $i(v4)) | ( ~ (v6 = 0) & the_carrier(v0) = v4 & powerset(v4) = v5 &
% 96.24/14.75 element(v1, v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & top_str(v0) =
% 96.24/14.75 v3)))
% 96.24/14.75
% 96.24/14.75 (dt_l1_pre_topc)
% 96.24/14.75 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (one_sorted_str(v0) = v1) | ~
% 96.24/14.75 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & top_str(v0) = v2)) & ! [v0: $i] : (
% 96.24/14.75 ~ (top_str(v0) = 0) | ~ $i(v0) | one_sorted_str(v0) = 0)
% 96.24/14.75
% 96.24/14.75 (existence_l1_struct_0)
% 96.24/14.75 ? [v0: $i] : (one_sorted_str(v0) = 0 & $i(v0))
% 96.24/14.75
% 96.24/14.75 (fc1_struct_0)
% 96.24/14.75 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ~ $i(v0)
% 96.24/14.75 | ? [v2: int] : ? [v3: $i] : ? [v4: int] : (( ~ (v4 = 0) &
% 96.24/14.75 the_carrier(v0) = v3 & empty(v3) = v4 & $i(v3)) | ( ~ (v2 = 0) &
% 96.24/14.75 one_sorted_str(v0) = v2))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 96.24/14.75 (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ? [v4:
% 96.24/14.75 int] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v4 = 0) & empty(v1) = v4)
% 96.24/14.75 | ( ~ (v3 = 0) & one_sorted_str(v0) = v3))) & ! [v0: $i] : ( ~
% 96.24/14.75 (one_sorted_str(v0) = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3:
% 96.24/14.75 int] : ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) & the_carrier(v0)
% 96.24/14.75 = v2 & empty(v2) = v3 & $i(v2))))
% 96.24/14.75
% 96.24/14.75 (involutiveness_k3_subset_1)
% 96.24/14.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 96.24/14.76 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: $i] : ((v5 =
% 96.24/14.76 v1 & subset_complement(v0, v2) = v1) | ( ~ (v4 = 0) & powerset(v0) = v3
% 96.24/14.76 & element(v1, v3) = v4 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 96.24/14.76 $i] : ( ~ (powerset(v0) = v2) | ~ (element(v1, v2) = 0) | ~ $i(v1) | ~
% 96.24/14.76 $i(v0) | ? [v3: $i] : (subset_complement(v0, v3) = v1 &
% 96.24/14.76 subset_complement(v0, v1) = v3 & $i(v3)))
% 96.24/14.76
% 96.24/14.76 (l40_tops_1)
% 96.24/14.77 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ~ $i(v0)
% 96.24/14.77 | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : (( ~ (v2 = 0) &
% 96.24/14.77 one_sorted_str(v0) = v2) | (the_carrier(v0) = v3 & powerset(v3) = v4 &
% 96.24/14.77 $i(v4) & $i(v3) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: any]
% 96.24/14.77 : ( ~ (subset_complement(v3, v5) = v6) | ~ (in(v7, v6) = v8) | ~
% 96.24/14.77 $i(v7) | ~ $i(v5) | ? [v9: int] : ? [v10: int] : (( ~ (v9 = 0) &
% 96.24/14.77 element(v7, v3) = v9) | ( ~ (v9 = 0) & element(v5, v4) = v9) | ((
% 96.24/14.77 ~ (v8 = 0) | ( ~ (v10 = 0) & in(v7, v5) = v10)) & (v8 = 0 | (v10
% 96.24/14.77 = 0 & in(v7, v5) = 0))))) & ! [v5: $i] : ! [v6: $i] : !
% 96.24/14.77 [v7: $i] : ! [v8: any] : ( ~ (subset_complement(v3, v5) = v6) | ~
% 96.24/14.77 (in(v7, v5) = v8) | ~ $i(v7) | ~ $i(v5) | ? [v9: int] : ? [v10:
% 96.24/14.77 int] : (( ~ (v9 = 0) & element(v7, v3) = v9) | ( ~ (v9 = 0) &
% 96.24/14.77 element(v5, v4) = v9) | (( ~ (v8 = 0) | ( ~ (v10 = 0) & in(v7, v6)
% 96.24/14.77 = v10)) & (v8 = 0 | (v10 = 0 & in(v7, v6) = 0))))) & ! [v5:
% 96.24/14.77 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (subset_complement(v3, v5) = v6)
% 96.24/14.77 | ~ (element(v7, v3) = 0) | ~ $i(v7) | ~ $i(v5) | ? [v8: int] : ?
% 96.24/14.77 [v9: int] : (( ~ (v8 = 0) & element(v5, v4) = v8) | (((v9 = 0 & in(v7,
% 96.24/14.77 v5) = 0) | (v8 = 0 & in(v7, v6) = 0)) & (( ~ (v9 = 0) &
% 96.24/14.77 in(v7, v5) = v9) | ( ~ (v8 = 0) & in(v7, v6) = v8))))) & !
% 96.24/14.77 [v5: $i] : ( ~ (element(v5, v4) = 0) | ~ $i(v5) | ? [v6: $i] :
% 96.24/14.77 (subset_complement(v3, v5) = v6 & $i(v6) & ! [v7: $i] : ! [v8: any]
% 96.24/14.77 : ( ~ (in(v7, v6) = v8) | ~ $i(v7) | ? [v9: int] : ? [v10: int] :
% 96.24/14.77 (( ~ (v9 = 0) & element(v7, v3) = v9) | (( ~ (v8 = 0) | ( ~ (v10 =
% 96.24/14.77 0) & in(v7, v5) = v10)) & (v8 = 0 | (v10 = 0 & in(v7,
% 96.24/14.77 v5) = 0))))) & ! [v7: $i] : ! [v8: any] : ( ~ (in(v7,
% 96.24/14.77 v5) = v8) | ~ $i(v7) | ? [v9: int] : ? [v10: int] : (( ~
% 96.24/14.77 (v9 = 0) & element(v7, v3) = v9) | (( ~ (v8 = 0) | ( ~ (v10 =
% 96.24/14.77 0) & in(v7, v6) = v10)) & (v8 = 0 | (v10 = 0 & in(v7,
% 96.24/14.77 v6) = 0))))) & ! [v7: $i] : ( ~ (element(v7, v3) = 0) |
% 96.24/14.77 ~ $i(v7) | ? [v8: int] : ? [v9: int] : (((v9 = 0 & in(v7, v5) =
% 96.24/14.77 0) | (v8 = 0 & in(v7, v6) = 0)) & (( ~ (v9 = 0) & in(v7, v5)
% 96.24/14.77 = v9) | ( ~ (v8 = 0) & in(v7, v6) = v8))))))))) & ! [v0:
% 96.24/14.77 $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: int] :
% 96.24/14.77 ? [v3: int] : ? [v4: $i] : ((v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0)
% 96.24/14.77 & one_sorted_str(v0) = v3) | (powerset(v1) = v4 & $i(v4) & ! [v5: $i] :
% 96.24/14.77 ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ( ~ (subset_complement(v1,
% 96.24/14.77 v5) = v6) | ~ (in(v7, v6) = v8) | ~ $i(v7) | ~ $i(v5) | ? [v9:
% 96.24/14.77 int] : ? [v10: int] : (( ~ (v9 = 0) & element(v7, v1) = v9) | ( ~
% 96.24/14.77 (v9 = 0) & element(v5, v4) = v9) | (( ~ (v8 = 0) | ( ~ (v10 = 0) &
% 96.24/14.77 in(v7, v5) = v10)) & (v8 = 0 | (v10 = 0 & in(v7, v5) = 0)))))
% 96.24/14.77 & ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: any] : ( ~
% 96.24/14.77 (subset_complement(v1, v5) = v6) | ~ (in(v7, v5) = v8) | ~ $i(v7) |
% 96.24/14.77 ~ $i(v5) | ? [v9: int] : ? [v10: int] : (( ~ (v9 = 0) & element(v7,
% 96.24/14.77 v1) = v9) | ( ~ (v9 = 0) & element(v5, v4) = v9) | (( ~ (v8 = 0)
% 96.24/14.77 | ( ~ (v10 = 0) & in(v7, v6) = v10)) & (v8 = 0 | (v10 = 0 &
% 96.24/14.77 in(v7, v6) = 0))))) & ! [v5: $i] : ! [v6: $i] : ! [v7: $i]
% 96.24/14.77 : ( ~ (subset_complement(v1, v5) = v6) | ~ (element(v7, v1) = 0) | ~
% 96.24/14.77 $i(v7) | ~ $i(v5) | ? [v8: int] : ? [v9: int] : (( ~ (v8 = 0) &
% 96.24/14.77 element(v5, v4) = v8) | (((v9 = 0 & in(v7, v5) = 0) | (v8 = 0 &
% 96.24/14.77 in(v7, v6) = 0)) & (( ~ (v9 = 0) & in(v7, v5) = v9) | ( ~ (v8
% 96.24/14.77 = 0) & in(v7, v6) = v8))))) & ! [v5: $i] : ( ~ (element(v5,
% 96.24/14.77 v4) = 0) | ~ $i(v5) | ? [v6: $i] : (subset_complement(v1, v5) =
% 96.24/14.77 v6 & $i(v6) & ! [v7: $i] : ! [v8: any] : ( ~ (in(v7, v6) = v8) |
% 96.24/14.77 ~ $i(v7) | ? [v9: int] : ? [v10: int] : (( ~ (v9 = 0) &
% 96.24/14.77 element(v7, v1) = v9) | (( ~ (v8 = 0) | ( ~ (v10 = 0) & in(v7,
% 96.24/14.77 v5) = v10)) & (v8 = 0 | (v10 = 0 & in(v7, v5) = 0))))) &
% 96.24/14.77 ! [v7: $i] : ! [v8: any] : ( ~ (in(v7, v5) = v8) | ~ $i(v7) | ?
% 96.24/14.77 [v9: int] : ? [v10: int] : (( ~ (v9 = 0) & element(v7, v1) = v9)
% 96.24/14.77 | (( ~ (v8 = 0) | ( ~ (v10 = 0) & in(v7, v6) = v10)) & (v8 = 0 |
% 96.24/14.77 (v10 = 0 & in(v7, v6) = 0))))) & ! [v7: $i] : ( ~
% 96.24/14.77 (element(v7, v1) = 0) | ~ $i(v7) | ? [v8: int] : ? [v9: int] :
% 96.24/14.77 (((v9 = 0 & in(v7, v5) = 0) | (v8 = 0 & in(v7, v6) = 0)) & (( ~
% 96.24/14.77 (v9 = 0) & in(v7, v5) = v9) | ( ~ (v8 = 0) & in(v7, v6) =
% 96.24/14.77 v8))))))))) & ! [v0: $i] : ( ~ (one_sorted_str(v0) = 0) |
% 96.24/14.77 ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ((v1 = 0 &
% 96.24/14.77 empty_carrier(v0) = 0) | (the_carrier(v0) = v2 & powerset(v2) = v3 &
% 96.24/14.77 $i(v3) & $i(v2) & ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any]
% 96.24/14.77 : ( ~ (subset_complement(v2, v4) = v5) | ~ (in(v6, v5) = v7) | ~
% 96.24/14.77 $i(v6) | ~ $i(v4) | ? [v8: int] : ? [v9: int] : (( ~ (v8 = 0) &
% 96.24/14.77 element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4, v3) = v8) | ((
% 96.24/14.77 ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6, v4) = v9)) & (v7 = 0 | (v9 =
% 96.24/14.77 0 & in(v6, v4) = 0))))) & ! [v4: $i] : ! [v5: $i] : ! [v6:
% 96.24/14.77 $i] : ! [v7: any] : ( ~ (subset_complement(v2, v4) = v5) | ~ (in(v6,
% 96.24/14.77 v4) = v7) | ~ $i(v6) | ~ $i(v4) | ? [v8: int] : ? [v9: int] :
% 96.24/14.77 (( ~ (v8 = 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4, v3)
% 96.24/14.77 = v8) | (( ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6, v5) = v9)) & (v7 = 0
% 96.24/14.77 | (v9 = 0 & in(v6, v5) = 0))))) & ! [v4: $i] : ! [v5: $i] : !
% 96.24/14.77 [v6: $i] : ( ~ (subset_complement(v2, v4) = v5) | ~ (element(v6, v2) =
% 96.24/14.77 0) | ~ $i(v6) | ~ $i(v4) | ? [v7: int] : ? [v8: int] : (( ~ (v7
% 96.24/14.77 = 0) & element(v4, v3) = v7) | (((v8 = 0 & in(v6, v4) = 0) | (v7
% 96.24/14.78 = 0 & in(v6, v5) = 0)) & (( ~ (v8 = 0) & in(v6, v4) = v8) | (
% 96.24/14.78 ~ (v7 = 0) & in(v6, v5) = v7))))) & ! [v4: $i] : ( ~
% 96.24/14.78 (element(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] :
% 96.24/14.78 (subset_complement(v2, v4) = v5 & $i(v5) & ! [v6: $i] : ! [v7: any]
% 96.24/14.78 : ( ~ (in(v6, v5) = v7) | ~ $i(v6) | ? [v8: int] : ? [v9: int] :
% 96.24/14.78 (( ~ (v8 = 0) & element(v6, v2) = v8) | (( ~ (v7 = 0) | ( ~ (v9 =
% 96.24/14.78 0) & in(v6, v4) = v9)) & (v7 = 0 | (v9 = 0 & in(v6, v4)
% 96.24/14.78 = 0))))) & ! [v6: $i] : ! [v7: any] : ( ~ (in(v6, v4) =
% 96.24/14.78 v7) | ~ $i(v6) | ? [v8: int] : ? [v9: int] : (( ~ (v8 = 0) &
% 96.24/14.78 element(v6, v2) = v8) | (( ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6,
% 96.24/14.78 v5) = v9)) & (v7 = 0 | (v9 = 0 & in(v6, v5) = 0))))) &
% 96.24/14.78 ! [v6: $i] : ( ~ (element(v6, v2) = 0) | ~ $i(v6) | ? [v7: int] :
% 96.24/14.78 ? [v8: int] : (((v8 = 0 & in(v6, v4) = 0) | (v7 = 0 & in(v6, v5) =
% 96.24/14.78 0)) & (( ~ (v8 = 0) & in(v6, v4) = v8) | ( ~ (v7 = 0) &
% 96.24/14.78 in(v6, v5) = v7)))))))))
% 96.24/14.78
% 96.24/14.78 (rc5_struct_0)
% 96.24/14.78 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty_carrier(v0) = v1) | ~ $i(v0)
% 96.24/14.78 | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ?
% 96.24/14.78 [v7: int] : ($i(v5) & ((v6 = 0 & ~ (v7 = 0) & the_carrier(v0) = v3 &
% 96.24/14.78 powerset(v3) = v4 & empty(v5) = v7 & element(v5, v4) = 0 & $i(v4) &
% 96.24/14.78 $i(v3)) | ( ~ (v2 = 0) & one_sorted_str(v0) = v2)))) & ! [v0: $i] :
% 96.24/14.78 ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 96.24/14.78 int] : ? [v4: $i] : ? [v5: $i] : ? [v6: int] : ? [v7: int] : ($i(v5) &
% 96.24/14.78 ((v6 = 0 & ~ (v7 = 0) & powerset(v1) = v4 & empty(v5) = v7 & element(v5,
% 96.24/14.78 v4) = 0 & $i(v4)) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0)
% 96.24/14.78 & one_sorted_str(v0) = v3)))) & ! [v0: $i] : ( ~ (one_sorted_str(v0)
% 96.24/14.78 = 0) | ~ $i(v0) | ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 96.24/14.78 : ? [v5: int] : ? [v6: int] : ($i(v4) & ((v5 = 0 & ~ (v6 = 0) &
% 96.24/14.78 the_carrier(v0) = v2 & powerset(v2) = v3 & empty(v4) = v6 &
% 96.24/14.78 element(v4, v3) = 0 & $i(v3) & $i(v2)) | (v1 = 0 & empty_carrier(v0) =
% 96.24/14.78 0))))
% 96.24/14.78
% 96.24/14.78 (t44_tops_1)
% 96.24/14.78 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 96.24/14.78 int] : ( ~ (v5 = 0) & subset(v4, v3) = v5 & top_str(v0) = 0 & interior(v0,
% 96.24/14.78 v3) = v4 & the_carrier(v0) = v1 & powerset(v1) = v2 & element(v3, v2) = 0
% 96.24/14.78 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 96.24/14.78
% 96.24/14.78 (t48_pre_topc)
% 96.24/14.78 ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ? [v2:
% 96.24/14.78 int] : ? [v3: $i] : (( ~ (v2 = 0) & top_str(v0) = v2) | (powerset(v1) =
% 96.24/14.78 v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (topstr_closure(v0, v4) =
% 96.24/14.78 v5) | ~ $i(v4) | ? [v6: int] : ? [v7: int] : ((v7 = 0 &
% 96.24/14.78 subset(v4, v5) = 0) | ( ~ (v6 = 0) & element(v4, v3) = v6))) & !
% 96.24/14.78 [v4: $i] : ( ~ (element(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] :
% 96.24/14.78 (subset(v4, v5) = 0 & topstr_closure(v0, v4) = v5 & $i(v5)))))) & !
% 96.24/14.78 [v0: $i] : ( ~ (top_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] :
% 96.24/14.78 (the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3: $i] :
% 96.24/14.78 ! [v4: $i] : ( ~ (topstr_closure(v0, v3) = v4) | ~ $i(v3) | ? [v5: int]
% 96.24/14.78 : ? [v6: int] : ((v6 = 0 & subset(v3, v4) = 0) | ( ~ (v5 = 0) &
% 96.24/14.78 element(v3, v2) = v5))) & ! [v3: $i] : ( ~ (element(v3, v2) = 0) |
% 96.24/14.78 ~ $i(v3) | ? [v4: $i] : (subset(v3, v4) = 0 & topstr_closure(v0, v3) =
% 96.24/14.78 v4 & $i(v4)))))
% 96.24/14.78
% 96.24/14.78 (t4_subset)
% 96.24/14.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 96.24/14.79 | ~ (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) =
% 96.24/14.79 v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) &
% 96.24/14.79 in(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int]
% 96.24/14.79 : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 96.24/14.79 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ( ~ (v5 = 0) &
% 96.24/14.79 powerset(v2) = v4 & element(v1, v4) = v5 & $i(v4))) & ! [v0: $i] : !
% 96.24/14.79 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = v3) | ~
% 96.24/14.79 (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~
% 96.24/14.79 $i(v0) | element(v0, v2) = 0)
% 96.24/14.79
% 96.24/14.79 (t54_subset_1)
% 96.24/14.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.79 (subset_complement(v0, v2) = v3) | ~ (in(v1, v3) = 0) | ~ $i(v2) | ~
% 96.24/14.79 $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: int] : ? [v6: int] : (( ~ (v6 =
% 96.24/14.79 0) & in(v1, v2) = v6) | ( ~ (v5 = 0) & powerset(v0) = v4 & element(v2,
% 96.24/14.79 v4) = v5 & $i(v4))))
% 96.24/14.79
% 96.24/14.79 (t5_subset)
% 96.24/14.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) =
% 96.24/14.79 v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0) | ~ $i(v2) | ~
% 96.24/14.79 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & empty(v2) = v4)) & !
% 96.24/14.79 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (empty(v2) = 0) | ~ (in(v0, v1) =
% 96.24/14.79 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 96.24/14.79 (v4 = 0) & powerset(v2) = v3 & element(v1, v3) = v4 & $i(v3)))
% 96.24/14.79
% 96.24/14.79 (function-axioms)
% 96.24/14.80 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 96.24/14.80 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) &
% 96.24/14.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 96.24/14.80 (interior(v3, v2) = v1) | ~ (interior(v3, v2) = v0)) & ! [v0: $i] : !
% 96.24/14.80 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (topstr_closure(v3, v2) =
% 96.24/14.80 v1) | ~ (topstr_closure(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 96.24/14.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 96.24/14.80 (subset_complement(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3,
% 96.24/14.80 v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 96.24/14.80 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3,
% 96.24/14.80 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (top_str(v2) = v1) | ~
% 96.24/14.80 (top_str(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 |
% 96.24/14.80 ~ (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0)) & ! [v0:
% 96.24/14.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 96.24/14.80 ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) = v0)) & ! [v0:
% 96.24/14.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 96.24/14.80 ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0)) & ! [v0: $i] : !
% 96.24/14.80 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 96.24/14.80 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 96.24/14.80 $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0:
% 96.24/14.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 96.24/14.80 ~ (v5_membered(v2) = v1) | ~ (v5_membered(v2) = v0)) & ! [v0:
% 96.24/14.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 96.24/14.80 ~ (natural(v2) = v1) | ~ (natural(v2) = v0)) & ! [v0: MultipleValueBool] :
% 96.24/14.80 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v4_membered(v2) =
% 96.24/14.80 v1) | ~ (v4_membered(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_int_1(v2) = v1) | ~
% 96.24/14.80 (v1_int_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v3_membered(v2) = v1) | ~
% 96.24/14.80 (v3_membered(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_rat_1(v2) = v1) | ~
% 96.24/14.80 (v1_rat_1(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v2_membered(v2) = v1) | ~
% 96.24/14.80 (v2_membered(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xreal_0(v2) = v1) | ~
% 96.24/14.80 (v1_xreal_0(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_membered(v2) = v1) | ~
% 96.24/14.80 (v1_membered(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 96.24/14.80 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (v1_xcmplx_0(v2) = v1) | ~
% 96.24/14.80 (v1_xcmplx_0(v2) = v0))
% 96.24/14.80
% 96.24/14.80 Further assumptions not needed in the proof:
% 96.24/14.80 --------------------------------------------
% 96.24/14.80 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered,
% 96.24/14.80 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 96.24/14.80 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered,
% 96.24/14.80 cc3_membered, cc4_membered, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_l1_struct_0,
% 96.24/14.80 dt_m1_subset_1, dt_u1_struct_0, existence_l1_pre_topc, existence_m1_subset_1,
% 96.24/14.80 fc6_membered, rc1_membered, rc3_struct_0, reflexivity_r1_tarski, t1_subset,
% 96.24/14.80 t2_subset, t3_subset, t6_boole, t7_boole, t8_boole
% 96.24/14.80
% 96.24/14.80 Those formulas are unsatisfiable:
% 96.24/14.80 ---------------------------------
% 96.24/14.80
% 96.24/14.80 Begin of proof
% 96.24/14.80 |
% 96.24/14.80 | ALPHA: (d1_struct_0) implies:
% 96.24/14.81 | (1) ! [v0: $i] : ( ~ (one_sorted_str(v0) = 0) | ~ $i(v0) | ? [v1: int] :
% 96.24/14.81 | ? [v2: $i] : ? [v3: int] : (((v3 = 0 & the_carrier(v0) = v2 &
% 96.24/14.81 | empty(v2) = 0 & $i(v2)) | ( ~ (v1 = 0) & empty_carrier(v0) =
% 96.24/14.81 | v1)) & ((v1 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) &
% 96.24/14.81 | the_carrier(v0) = v2 & empty(v2) = v3 & $i(v2)))))
% 96.24/14.81 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ?
% 96.24/14.81 | [v2: int] : ? [v3: int] : ? [v4: int] : (( ~ (v2 = 0) &
% 96.24/14.81 | one_sorted_str(v0) = v2) | (((v4 = 0 & empty(v1) = 0) | ( ~ (v3 =
% 96.24/14.81 | 0) & empty_carrier(v0) = v3)) & ((v3 = 0 &
% 96.24/14.81 | empty_carrier(v0) = 0) | ( ~ (v4 = 0) & empty(v1) = v4)))))
% 96.24/14.81 |
% 96.24/14.81 | ALPHA: (d1_tops_1) implies:
% 96.24/14.81 | (3) ! [v0: $i] : ( ~ (top_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 96.24/14.81 | $i] : (the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v2) & $i(v1) &
% 96.24/14.81 | ! [v3: $i] : ! [v4: $i] : ( ~ (interior(v0, v3) = v4) | ~ $i(v3)
% 96.24/14.81 | | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ((v8 =
% 96.24/14.81 | v4 & topstr_closure(v0, v6) = v7 & subset_complement(v1, v7)
% 96.24/14.81 | = v4 & subset_complement(v1, v3) = v6 & $i(v7) & $i(v6) &
% 96.24/14.81 | $i(v4)) | ( ~ (v5 = 0) & element(v3, v2) = v5))) & ! [v3:
% 96.24/14.81 | $i] : ! [v4: $i] : ( ~ (subset_complement(v1, v3) = v4) | ~
% 96.24/14.81 | $i(v3) | ? [v5: int] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] :
% 96.24/14.81 | ((v8 = v6 & interior(v0, v3) = v6 & topstr_closure(v0, v4) = v7 &
% 96.24/14.81 | subset_complement(v1, v7) = v6 & $i(v7) & $i(v6)) | ( ~ (v5 =
% 96.24/14.81 | 0) & element(v3, v2) = v5))) & ! [v3: $i] : ( ~
% 96.24/14.81 | (element(v3, v2) = 0) | ~ $i(v3) | ? [v4: $i] : ? [v5: $i] :
% 96.24/14.81 | ? [v6: $i] : (interior(v0, v3) = v4 & topstr_closure(v0, v5) = v6
% 96.24/14.81 | & subset_complement(v1, v6) = v4 & subset_complement(v1, v3) =
% 96.24/14.81 | v5 & $i(v6) & $i(v5) & $i(v4)))))
% 96.24/14.81 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) | ?
% 96.24/14.81 | [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & top_str(v0) = v2) |
% 96.24/14.81 | (powerset(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 96.24/14.81 | (interior(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ? [v7:
% 96.24/14.81 | $i] : ? [v8: $i] : ? [v9: $i] : ((v9 = v5 &
% 96.24/14.81 | topstr_closure(v0, v7) = v8 & subset_complement(v1, v8) =
% 96.24/14.81 | v5 & subset_complement(v1, v4) = v7 & $i(v8) & $i(v7) &
% 96.24/14.81 | $i(v5)) | ( ~ (v6 = 0) & element(v4, v3) = v6))) & ! [v4:
% 96.24/14.81 | $i] : ! [v5: $i] : ( ~ (subset_complement(v1, v4) = v5) | ~
% 96.24/14.81 | $i(v4) | ? [v6: int] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i]
% 96.24/14.81 | : ((v9 = v7 & interior(v0, v4) = v7 & topstr_closure(v0, v5) =
% 96.24/14.81 | v8 & subset_complement(v1, v8) = v7 & $i(v8) & $i(v7)) | (
% 96.24/14.81 | ~ (v6 = 0) & element(v4, v3) = v6))) & ! [v4: $i] : ( ~
% 96.24/14.81 | (element(v4, v3) = 0) | ~ $i(v4) | ? [v5: $i] : ? [v6: $i] :
% 96.24/14.81 | ? [v7: $i] : (interior(v0, v4) = v5 & topstr_closure(v0, v6) =
% 96.24/14.81 | v7 & subset_complement(v1, v7) = v5 & subset_complement(v1,
% 96.24/14.81 | v4) = v6 & $i(v7) & $i(v6) & $i(v5))))))
% 96.24/14.81 |
% 96.24/14.81 | ALPHA: (d3_tarski) implies:
% 96.24/14.82 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 96.24/14.82 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) =
% 96.24/14.82 | 0)
% 96.24/14.82 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 96.24/14.82 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 96.24/14.82 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3)))
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (dt_k1_tops_1) implies:
% 96.24/14.82 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (interior(v0, v1) = v2) |
% 96.24/14.82 | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ?
% 96.24/14.82 | [v6: int] : ? [v7: int] : ((v7 = 0 & the_carrier(v0) = v4 &
% 96.24/14.82 | powerset(v4) = v5 & element(v2, v5) = 0 & $i(v5) & $i(v4)) | ( ~
% 96.24/14.82 | (v6 = 0) & the_carrier(v0) = v4 & powerset(v4) = v5 & element(v1,
% 96.24/14.82 | v5) = v6 & $i(v5) & $i(v4)) | ( ~ (v3 = 0) & top_str(v0) =
% 96.24/14.82 | v3)))
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (dt_k3_subset_1) implies:
% 96.24/14.82 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~
% 96.24/14.82 | (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 96.24/14.82 | (subset_complement(v0, v1) = v3 & element(v3, v2) = 0 & $i(v3)))
% 96.24/14.82 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0,
% 96.24/14.82 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 96.24/14.82 | ? [v5: int] : (powerset(v0) = v3 & $i(v3) & ((v5 = 0 & element(v2,
% 96.24/14.82 | v3) = 0) | ( ~ (v4 = 0) & element(v1, v3) = v4))))
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (dt_k6_pre_topc) implies:
% 96.24/14.82 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.82 | (the_carrier(v0) = v2) | ~ (powerset(v2) = v3) | ~ (element(v1,
% 96.24/14.82 | v3) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ? [v5: $i] :
% 96.24/14.82 | ? [v6: int] : ((v6 = 0 & topstr_closure(v0, v1) = v5 & element(v5,
% 96.24/14.82 | v3) = 0 & $i(v5)) | ( ~ (v4 = 0) & top_str(v0) = v4)))
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (dt_l1_pre_topc) implies:
% 96.24/14.82 | (11) ! [v0: $i] : ( ~ (top_str(v0) = 0) | ~ $i(v0) | one_sorted_str(v0) =
% 96.24/14.82 | 0)
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (fc1_struct_0) implies:
% 96.24/14.82 | (12) ! [v0: $i] : ( ~ (one_sorted_str(v0) = 0) | ~ $i(v0) | ? [v1: int]
% 96.24/14.82 | : ? [v2: $i] : ? [v3: int] : ((v1 = 0 & empty_carrier(v0) = 0) | (
% 96.24/14.82 | ~ (v3 = 0) & the_carrier(v0) = v2 & empty(v2) = v3 & $i(v2))))
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (involutiveness_k3_subset_1) implies:
% 96.24/14.82 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v2) | ~
% 96.24/14.82 | (element(v1, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] :
% 96.24/14.82 | (subset_complement(v0, v3) = v1 & subset_complement(v0, v1) = v3 &
% 96.24/14.82 | $i(v3)))
% 96.24/14.82 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0,
% 96.24/14.82 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 96.24/14.82 | ? [v5: $i] : ((v5 = v1 & subset_complement(v0, v2) = v1) | ( ~ (v4
% 96.24/14.82 | = 0) & powerset(v0) = v3 & element(v1, v3) = v4 & $i(v3))))
% 96.24/14.82 |
% 96.24/14.82 | ALPHA: (l40_tops_1) implies:
% 96.24/14.83 | (15) ! [v0: $i] : ( ~ (one_sorted_str(v0) = 0) | ~ $i(v0) | ? [v1: int]
% 96.24/14.83 | : ? [v2: $i] : ? [v3: $i] : ((v1 = 0 & empty_carrier(v0) = 0) |
% 96.24/14.83 | (the_carrier(v0) = v2 & powerset(v2) = v3 & $i(v3) & $i(v2) & !
% 96.24/14.83 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~
% 96.24/14.83 | (subset_complement(v2, v4) = v5) | ~ (in(v6, v5) = v7) | ~
% 96.24/14.83 | $i(v6) | ~ $i(v4) | ? [v8: int] : ? [v9: int] : (( ~ (v8 =
% 96.24/14.83 | 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4,
% 96.24/14.83 | v3) = v8) | (( ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6, v4) =
% 96.24/14.83 | v9)) & (v7 = 0 | (v9 = 0 & in(v6, v4) = 0))))) & !
% 96.24/14.83 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: any] : ( ~
% 96.24/14.83 | (subset_complement(v2, v4) = v5) | ~ (in(v6, v4) = v7) | ~
% 96.24/14.83 | $i(v6) | ~ $i(v4) | ? [v8: int] : ? [v9: int] : (( ~ (v8 =
% 96.24/14.83 | 0) & element(v6, v2) = v8) | ( ~ (v8 = 0) & element(v4,
% 96.24/14.83 | v3) = v8) | (( ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6, v5) =
% 96.24/14.83 | v9)) & (v7 = 0 | (v9 = 0 & in(v6, v5) = 0))))) & !
% 96.24/14.83 | [v4: $i] : ! [v5: $i] : ! [v6: $i] : ( ~
% 96.24/14.83 | (subset_complement(v2, v4) = v5) | ~ (element(v6, v2) = 0) |
% 96.24/14.83 | ~ $i(v6) | ~ $i(v4) | ? [v7: int] : ? [v8: int] : (( ~ (v7
% 96.24/14.83 | = 0) & element(v4, v3) = v7) | (((v8 = 0 & in(v6, v4) =
% 96.24/14.83 | 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~ (v8 = 0) &
% 96.24/14.83 | in(v6, v4) = v8) | ( ~ (v7 = 0) & in(v6, v5) = v7)))))
% 96.24/14.83 | & ! [v4: $i] : ( ~ (element(v4, v3) = 0) | ~ $i(v4) | ? [v5:
% 96.24/14.83 | $i] : (subset_complement(v2, v4) = v5 & $i(v5) & ! [v6: $i]
% 96.24/14.83 | : ! [v7: any] : ( ~ (in(v6, v5) = v7) | ~ $i(v6) | ? [v8:
% 96.24/14.83 | int] : ? [v9: int] : (( ~ (v8 = 0) & element(v6, v2) =
% 96.24/14.83 | v8) | (( ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6, v4) = v9))
% 96.24/14.83 | & (v7 = 0 | (v9 = 0 & in(v6, v4) = 0))))) & ! [v6:
% 96.24/14.83 | $i] : ! [v7: any] : ( ~ (in(v6, v4) = v7) | ~ $i(v6) |
% 96.24/14.83 | ? [v8: int] : ? [v9: int] : (( ~ (v8 = 0) & element(v6,
% 96.24/14.83 | v2) = v8) | (( ~ (v7 = 0) | ( ~ (v9 = 0) & in(v6,
% 96.24/14.83 | v5) = v9)) & (v7 = 0 | (v9 = 0 & in(v6, v5) =
% 96.24/14.83 | 0))))) & ! [v6: $i] : ( ~ (element(v6, v2) = 0) |
% 96.24/14.83 | ~ $i(v6) | ? [v7: int] : ? [v8: int] : (((v8 = 0 &
% 96.24/14.83 | in(v6, v4) = 0) | (v7 = 0 & in(v6, v5) = 0)) & (( ~
% 96.24/14.83 | (v8 = 0) & in(v6, v4) = v8) | ( ~ (v7 = 0) & in(v6,
% 96.24/14.83 | v5) = v7)))))))))
% 96.24/14.84 | (16) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) |
% 96.24/14.84 | ? [v2: int] : ? [v3: int] : ? [v4: $i] : ((v2 = 0 &
% 96.24/14.84 | empty_carrier(v0) = 0) | ( ~ (v3 = 0) & one_sorted_str(v0) = v3)
% 96.24/14.84 | | (powerset(v1) = v4 & $i(v4) & ! [v5: $i] : ! [v6: $i] : !
% 96.24/14.84 | [v7: $i] : ! [v8: any] : ( ~ (subset_complement(v1, v5) = v6) |
% 96.24/14.84 | ~ (in(v7, v6) = v8) | ~ $i(v7) | ~ $i(v5) | ? [v9: int] :
% 96.24/14.84 | ? [v10: int] : (( ~ (v9 = 0) & element(v7, v1) = v9) | ( ~ (v9
% 96.24/14.84 | = 0) & element(v5, v4) = v9) | (( ~ (v8 = 0) | ( ~ (v10
% 96.24/14.84 | = 0) & in(v7, v5) = v10)) & (v8 = 0 | (v10 = 0 &
% 96.24/14.84 | in(v7, v5) = 0))))) & ! [v5: $i] : ! [v6: $i] : !
% 96.24/14.84 | [v7: $i] : ! [v8: any] : ( ~ (subset_complement(v1, v5) = v6) |
% 96.24/14.84 | ~ (in(v7, v5) = v8) | ~ $i(v7) | ~ $i(v5) | ? [v9: int] :
% 96.24/14.84 | ? [v10: int] : (( ~ (v9 = 0) & element(v7, v1) = v9) | ( ~ (v9
% 96.24/14.84 | = 0) & element(v5, v4) = v9) | (( ~ (v8 = 0) | ( ~ (v10
% 96.24/14.84 | = 0) & in(v7, v6) = v10)) & (v8 = 0 | (v10 = 0 &
% 96.24/14.84 | in(v7, v6) = 0))))) & ! [v5: $i] : ! [v6: $i] : !
% 96.24/14.84 | [v7: $i] : ( ~ (subset_complement(v1, v5) = v6) | ~
% 96.24/14.84 | (element(v7, v1) = 0) | ~ $i(v7) | ~ $i(v5) | ? [v8: int] :
% 96.24/14.84 | ? [v9: int] : (( ~ (v8 = 0) & element(v5, v4) = v8) | (((v9 =
% 96.24/14.84 | 0 & in(v7, v5) = 0) | (v8 = 0 & in(v7, v6) = 0)) & ((
% 96.24/14.84 | ~ (v9 = 0) & in(v7, v5) = v9) | ( ~ (v8 = 0) & in(v7,
% 96.24/14.84 | v6) = v8))))) & ! [v5: $i] : ( ~ (element(v5, v4) =
% 96.24/14.84 | 0) | ~ $i(v5) | ? [v6: $i] : (subset_complement(v1, v5) =
% 96.24/14.84 | v6 & $i(v6) & ! [v7: $i] : ! [v8: any] : ( ~ (in(v7, v6) =
% 96.24/14.84 | v8) | ~ $i(v7) | ? [v9: int] : ? [v10: int] : (( ~
% 96.24/14.84 | (v9 = 0) & element(v7, v1) = v9) | (( ~ (v8 = 0) | ( ~
% 96.24/14.84 | (v10 = 0) & in(v7, v5) = v10)) & (v8 = 0 | (v10 =
% 96.24/14.84 | 0 & in(v7, v5) = 0))))) & ! [v7: $i] : ! [v8:
% 96.24/14.84 | any] : ( ~ (in(v7, v5) = v8) | ~ $i(v7) | ? [v9: int] :
% 96.24/14.84 | ? [v10: int] : (( ~ (v9 = 0) & element(v7, v1) = v9) | ((
% 96.24/14.84 | ~ (v8 = 0) | ( ~ (v10 = 0) & in(v7, v6) = v10)) &
% 96.24/14.84 | (v8 = 0 | (v10 = 0 & in(v7, v6) = 0))))) & ! [v7: $i]
% 96.24/14.84 | : ( ~ (element(v7, v1) = 0) | ~ $i(v7) | ? [v8: int] : ?
% 96.24/14.84 | [v9: int] : (((v9 = 0 & in(v7, v5) = 0) | (v8 = 0 & in(v7,
% 96.24/14.84 | v6) = 0)) & (( ~ (v9 = 0) & in(v7, v5) = v9) | ( ~
% 96.24/14.84 | (v8 = 0) & in(v7, v6) = v8)))))))))
% 96.24/14.84 |
% 96.24/14.84 | ALPHA: (rc5_struct_0) implies:
% 96.24/14.84 | (17) ! [v0: $i] : ( ~ (one_sorted_str(v0) = 0) | ~ $i(v0) | ? [v1: int]
% 96.24/14.84 | : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: int] : ? [v6:
% 96.24/14.84 | int] : ($i(v4) & ((v5 = 0 & ~ (v6 = 0) & the_carrier(v0) = v2 &
% 96.24/14.84 | powerset(v2) = v3 & empty(v4) = v6 & element(v4, v3) = 0 &
% 96.24/14.84 | $i(v3) & $i(v2)) | (v1 = 0 & empty_carrier(v0) = 0))))
% 96.24/14.84 | (18) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) |
% 96.24/14.84 | ? [v2: int] : ? [v3: int] : ? [v4: $i] : ? [v5: $i] : ? [v6:
% 96.24/14.84 | int] : ? [v7: int] : ($i(v5) & ((v6 = 0 & ~ (v7 = 0) &
% 96.24/14.84 | powerset(v1) = v4 & empty(v5) = v7 & element(v5, v4) = 0 &
% 96.24/14.84 | $i(v4)) | (v2 = 0 & empty_carrier(v0) = 0) | ( ~ (v3 = 0) &
% 96.24/14.84 | one_sorted_str(v0) = v3))))
% 96.24/14.84 |
% 96.24/14.84 | ALPHA: (t48_pre_topc) implies:
% 96.24/14.84 | (19) ! [v0: $i] : ( ~ (top_str(v0) = 0) | ~ $i(v0) | ? [v1: $i] : ?
% 96.24/14.84 | [v2: $i] : (the_carrier(v0) = v1 & powerset(v1) = v2 & $i(v2) &
% 96.24/14.84 | $i(v1) & ! [v3: $i] : ! [v4: $i] : ( ~ (topstr_closure(v0, v3) =
% 96.24/14.84 | v4) | ~ $i(v3) | ? [v5: int] : ? [v6: int] : ((v6 = 0 &
% 96.24/14.84 | subset(v3, v4) = 0) | ( ~ (v5 = 0) & element(v3, v2) = v5)))
% 96.24/14.84 | & ! [v3: $i] : ( ~ (element(v3, v2) = 0) | ~ $i(v3) | ? [v4:
% 96.24/14.84 | $i] : (subset(v3, v4) = 0 & topstr_closure(v0, v3) = v4 &
% 96.24/14.84 | $i(v4)))))
% 96.24/14.84 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (the_carrier(v0) = v1) | ~ $i(v0) |
% 96.24/14.84 | ? [v2: int] : ? [v3: $i] : (( ~ (v2 = 0) & top_str(v0) = v2) |
% 96.24/14.84 | (powerset(v1) = v3 & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~
% 96.24/14.84 | (topstr_closure(v0, v4) = v5) | ~ $i(v4) | ? [v6: int] : ?
% 96.24/14.84 | [v7: int] : ((v7 = 0 & subset(v4, v5) = 0) | ( ~ (v6 = 0) &
% 96.24/14.84 | element(v4, v3) = v6))) & ! [v4: $i] : ( ~ (element(v4,
% 96.24/14.84 | v3) = 0) | ~ $i(v4) | ? [v5: $i] : (subset(v4, v5) = 0 &
% 96.24/14.84 | topstr_closure(v0, v4) = v5 & $i(v5))))))
% 96.24/14.84 |
% 96.24/14.84 | ALPHA: (t4_subset) implies:
% 96.24/14.84 | (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.84 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 96.24/14.84 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | element(v0, v2) = 0)
% 96.24/14.84 |
% 96.24/14.84 | ALPHA: (t5_subset) implies:
% 96.24/14.84 | (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.84 | (powerset(v2) = v3) | ~ (element(v1, v3) = 0) | ~ (in(v0, v1) = 0)
% 96.24/14.84 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 96.24/14.84 | empty(v2) = v4))
% 96.24/14.84 |
% 96.24/14.84 | ALPHA: (function-axioms) implies:
% 96.24/14.84 | (23) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 96.24/14.84 | : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 96.24/14.84 | (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2)
% 96.24/14.84 | = v1) | ~ (powerset(v2) = v0))
% 96.24/14.84 | (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 96.24/14.84 | : (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) =
% 96.24/14.84 | v0))
% 96.24/14.84 | (26) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 96.24/14.84 | : (v1 = v0 | ~ (one_sorted_str(v2) = v1) | ~ (one_sorted_str(v2) =
% 96.24/14.84 | v0))
% 96.24/14.84 | (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 96.24/14.84 | (the_carrier(v2) = v1) | ~ (the_carrier(v2) = v0))
% 96.24/14.85 | (28) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 96.24/14.85 | : (v1 = v0 | ~ (top_str(v2) = v1) | ~ (top_str(v2) = v0))
% 96.24/14.85 | (29) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 96.24/14.85 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 96.24/14.85 | v0))
% 96.24/14.85 | (30) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 96.24/14.85 | : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 96.24/14.85 | v2) = v0))
% 96.24/14.85 | (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 96.24/14.85 | (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) =
% 96.24/14.85 | v0))
% 96.24/14.85 | (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 96.24/14.85 | (topstr_closure(v3, v2) = v1) | ~ (topstr_closure(v3, v2) = v0))
% 96.24/14.85 |
% 96.24/14.85 | DELTA: instantiating (existence_l1_struct_0) with fresh symbol all_42_0 gives:
% 96.24/14.85 | (33) one_sorted_str(all_42_0) = 0 & $i(all_42_0)
% 96.24/14.85 |
% 96.24/14.85 | ALPHA: (33) implies:
% 96.24/14.85 | (34) $i(all_42_0)
% 96.24/14.85 | (35) one_sorted_str(all_42_0) = 0
% 96.24/14.85 |
% 96.24/14.85 | DELTA: instantiating (t44_tops_1) with fresh symbols all_51_0, all_51_1,
% 96.24/14.85 | all_51_2, all_51_3, all_51_4, all_51_5 gives:
% 96.24/14.85 | (36) ~ (all_51_0 = 0) & subset(all_51_1, all_51_2) = all_51_0 &
% 96.24/14.85 | top_str(all_51_5) = 0 & interior(all_51_5, all_51_2) = all_51_1 &
% 96.24/14.85 | the_carrier(all_51_5) = all_51_4 & powerset(all_51_4) = all_51_3 &
% 96.24/14.85 | element(all_51_2, all_51_3) = 0 & $i(all_51_1) & $i(all_51_2) &
% 96.24/14.85 | $i(all_51_3) & $i(all_51_4) & $i(all_51_5)
% 96.24/14.85 |
% 96.24/14.85 | ALPHA: (36) implies:
% 96.24/14.85 | (37) ~ (all_51_0 = 0)
% 96.24/14.85 | (38) $i(all_51_5)
% 96.24/14.85 | (39) $i(all_51_4)
% 96.24/14.85 | (40) $i(all_51_2)
% 96.24/14.85 | (41) $i(all_51_1)
% 96.24/14.85 | (42) element(all_51_2, all_51_3) = 0
% 96.24/14.85 | (43) powerset(all_51_4) = all_51_3
% 96.24/14.85 | (44) the_carrier(all_51_5) = all_51_4
% 96.24/14.85 | (45) interior(all_51_5, all_51_2) = all_51_1
% 96.24/14.85 | (46) top_str(all_51_5) = 0
% 96.24/14.85 | (47) subset(all_51_1, all_51_2) = all_51_0
% 96.24/14.85 |
% 96.24/14.85 | GROUND_INST: instantiating (13) with all_51_4, all_51_2, all_51_3, simplifying
% 96.24/14.85 | with (39), (40), (42), (43) gives:
% 96.24/14.85 | (48) ? [v0: $i] : (subset_complement(all_51_4, v0) = all_51_2 &
% 96.24/14.85 | subset_complement(all_51_4, all_51_2) = v0 & $i(v0))
% 96.24/14.85 |
% 96.24/14.85 | GROUND_INST: instantiating (8) with all_51_4, all_51_2, all_51_3, simplifying
% 96.24/14.85 | with (39), (40), (42), (43) gives:
% 96.24/14.85 | (49) ? [v0: $i] : (subset_complement(all_51_4, all_51_2) = v0 &
% 96.24/14.85 | element(v0, all_51_3) = 0 & $i(v0))
% 96.24/14.85 |
% 96.24/14.85 | GROUND_INST: instantiating (1) with all_42_0, simplifying with (34), (35)
% 96.24/14.85 | gives:
% 96.24/14.85 | (50) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (((v2 = 0 &
% 96.24/14.85 | the_carrier(all_42_0) = v1 & empty(v1) = 0 & $i(v1)) | ( ~ (v0 =
% 96.24/14.85 | 0) & empty_carrier(all_42_0) = v0)) & ((v0 = 0 &
% 96.24/14.85 | empty_carrier(all_42_0) = 0) | ( ~ (v2 = 0) &
% 96.24/14.85 | the_carrier(all_42_0) = v1 & empty(v1) = v2 & $i(v1))))
% 96.24/14.85 |
% 96.24/14.85 | GROUND_INST: instantiating (18) with all_51_5, all_51_4, simplifying with
% 96.24/14.85 | (38), (44) gives:
% 96.24/14.85 | (51) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ? [v3: $i] : ? [v4: int]
% 96.24/14.85 | : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5 = 0) & powerset(all_51_4)
% 96.24/14.85 | = v2 & empty(v3) = v5 & element(v3, v2) = 0 & $i(v2)) | (v0 = 0
% 96.24/14.85 | & empty_carrier(all_51_5) = 0) | ( ~ (v1 = 0) &
% 96.24/14.85 | one_sorted_str(all_51_5) = v1)))
% 96.24/14.85 |
% 96.24/14.85 | GROUND_INST: instantiating (16) with all_51_5, all_51_4, simplifying with
% 96.24/14.85 | (38), (44) gives:
% 96.24/14.86 | (52) ? [v0: int] : ? [v1: int] : ? [v2: $i] : ((v0 = 0 &
% 96.24/14.86 | empty_carrier(all_51_5) = 0) | ( ~ (v1 = 0) &
% 96.24/14.86 | one_sorted_str(all_51_5) = v1) | (powerset(all_51_4) = v2 & $i(v2)
% 96.24/14.86 | & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : ( ~
% 96.24/14.86 | (subset_complement(all_51_4, v3) = v4) | ~ (in(v5, v4) = v6) |
% 96.24/14.86 | ~ $i(v5) | ~ $i(v3) | ? [v7: int] : ? [v8: int] : (( ~ (v7 =
% 96.24/14.86 | 0) & element(v5, all_51_4) = v7) | ( ~ (v7 = 0) &
% 96.24/14.86 | element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v8 = 0) &
% 96.24/14.86 | in(v5, v3) = v8)) & (v6 = 0 | (v8 = 0 & in(v5, v3) =
% 96.24/14.86 | 0))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : !
% 96.24/14.86 | [v6: any] : ( ~ (subset_complement(all_51_4, v3) = v4) | ~
% 96.24/14.86 | (in(v5, v3) = v6) | ~ $i(v5) | ~ $i(v3) | ? [v7: int] : ?
% 96.24/14.86 | [v8: int] : (( ~ (v7 = 0) & element(v5, all_51_4) = v7) | ( ~
% 96.24/14.86 | (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 = 0) | ( ~ (v8 =
% 96.24/14.86 | 0) & in(v5, v4) = v8)) & (v6 = 0 | (v8 = 0 & in(v5,
% 96.24/14.86 | v4) = 0))))) & ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 96.24/14.86 | : ( ~ (subset_complement(all_51_4, v3) = v4) | ~ (element(v5,
% 96.24/14.86 | all_51_4) = 0) | ~ $i(v5) | ~ $i(v3) | ? [v6: int] : ?
% 96.24/14.86 | [v7: int] : (( ~ (v6 = 0) & element(v3, v2) = v6) | (((v7 = 0 &
% 96.24/14.86 | in(v5, v3) = 0) | (v6 = 0 & in(v5, v4) = 0)) & (( ~ (v7
% 96.24/14.86 | = 0) & in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) =
% 96.24/14.86 | v6))))) & ! [v3: $i] : ( ~ (element(v3, v2) = 0) | ~
% 96.24/14.86 | $i(v3) | ? [v4: $i] : (subset_complement(all_51_4, v3) = v4 &
% 96.24/14.86 | $i(v4) & ! [v5: $i] : ! [v6: any] : ( ~ (in(v5, v4) = v6) |
% 96.24/14.86 | ~ $i(v5) | ? [v7: int] : ? [v8: int] : (( ~ (v7 = 0) &
% 96.24/14.86 | element(v5, all_51_4) = v7) | (( ~ (v6 = 0) | ( ~ (v8 =
% 96.24/14.86 | 0) & in(v5, v3) = v8)) & (v6 = 0 | (v8 = 0 &
% 96.24/14.86 | in(v5, v3) = 0))))) & ! [v5: $i] : ! [v6: any] : (
% 96.24/14.86 | ~ (in(v5, v3) = v6) | ~ $i(v5) | ? [v7: int] : ? [v8:
% 96.24/14.86 | int] : (( ~ (v7 = 0) & element(v5, all_51_4) = v7) | (( ~
% 96.24/14.86 | (v6 = 0) | ( ~ (v8 = 0) & in(v5, v4) = v8)) & (v6 = 0
% 96.24/14.86 | | (v8 = 0 & in(v5, v4) = 0))))) & ! [v5: $i] : ( ~
% 96.24/14.86 | (element(v5, all_51_4) = 0) | ~ $i(v5) | ? [v6: int] : ?
% 96.24/14.86 | [v7: int] : (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 & in(v5,
% 96.24/14.86 | v4) = 0)) & (( ~ (v7 = 0) & in(v5, v3) = v7) | ( ~
% 96.24/14.86 | (v6 = 0) & in(v5, v4) = v6))))))))
% 96.24/14.86 |
% 96.24/14.86 | GROUND_INST: instantiating (2) with all_51_5, all_51_4, simplifying with (38),
% 96.24/14.86 | (44) gives:
% 96.24/14.86 | (53) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ (v0 = 0) &
% 96.24/14.86 | one_sorted_str(all_51_5) = v0) | (((v2 = 0 & empty(all_51_4) = 0)
% 96.24/14.86 | | ( ~ (v1 = 0) & empty_carrier(all_51_5) = v1)) & ((v1 = 0 &
% 96.24/14.86 | empty_carrier(all_51_5) = 0) | ( ~ (v2 = 0) & empty(all_51_4)
% 96.24/14.86 | = v2))))
% 96.24/14.86 |
% 96.24/14.86 | GROUND_INST: instantiating (4) with all_51_5, all_51_4, simplifying with (38),
% 96.24/14.86 | (44) gives:
% 96.24/14.86 | (54) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & top_str(all_51_5) = v0) |
% 96.24/14.86 | (powerset(all_51_4) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.86 | (interior(all_51_5, v2) = v3) | ~ $i(v2) | ? [v4: int] : ?
% 96.24/14.86 | [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v3 &
% 96.24/14.86 | topstr_closure(all_51_5, v5) = v6 &
% 96.24/14.86 | subset_complement(all_51_4, v6) = v3 &
% 96.24/14.86 | subset_complement(all_51_4, v2) = v5 & $i(v6) & $i(v5) &
% 96.24/14.86 | $i(v3)) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2:
% 96.24/14.86 | $i] : ! [v3: $i] : ( ~ (subset_complement(all_51_4, v2) = v3) |
% 96.24/14.86 | ~ $i(v2) | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7:
% 96.24/14.86 | $i] : ((v7 = v5 & interior(all_51_5, v2) = v5 &
% 96.24/14.86 | topstr_closure(all_51_5, v3) = v6 &
% 96.24/14.86 | subset_complement(all_51_4, v6) = v5 & $i(v6) & $i(v5)) | (
% 96.24/14.86 | ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2: $i] : ( ~
% 96.24/14.86 | (element(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] :
% 96.24/14.86 | ? [v5: $i] : (interior(all_51_5, v2) = v3 &
% 96.24/14.86 | topstr_closure(all_51_5, v4) = v5 &
% 96.24/14.86 | subset_complement(all_51_4, v5) = v3 &
% 96.24/14.86 | subset_complement(all_51_4, v2) = v4 & $i(v5) & $i(v4) &
% 96.24/14.86 | $i(v3)))))
% 96.24/14.86 |
% 96.24/14.86 | GROUND_INST: instantiating (20) with all_51_5, all_51_4, simplifying with
% 96.24/14.86 | (38), (44) gives:
% 96.24/14.86 | (55) ? [v0: int] : ? [v1: $i] : (( ~ (v0 = 0) & top_str(all_51_5) = v0) |
% 96.24/14.86 | (powerset(all_51_4) = v1 & $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.86 | (topstr_closure(all_51_5, v2) = v3) | ~ $i(v2) | ? [v4: int] :
% 96.24/14.86 | ? [v5: int] : ((v5 = 0 & subset(v2, v3) = 0) | ( ~ (v4 = 0) &
% 96.24/14.86 | element(v2, v1) = v4))) & ! [v2: $i] : ( ~ (element(v2, v1)
% 96.24/14.86 | = 0) | ~ $i(v2) | ? [v3: $i] : (subset(v2, v3) = 0 &
% 96.24/14.86 | topstr_closure(all_51_5, v2) = v3 & $i(v3)))))
% 96.24/14.86 |
% 96.24/14.86 | GROUND_INST: instantiating (7) with all_51_5, all_51_2, all_51_1, simplifying
% 96.24/14.86 | with (38), (40), (45) gives:
% 96.24/14.87 | (56) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: int]
% 96.24/14.87 | : ((v4 = 0 & the_carrier(all_51_5) = v1 & powerset(v1) = v2 &
% 96.24/14.87 | element(all_51_1, v2) = 0 & $i(v2) & $i(v1)) | ( ~ (v3 = 0) &
% 96.24/14.87 | the_carrier(all_51_5) = v1 & powerset(v1) = v2 & element(all_51_2,
% 96.24/14.87 | v2) = v3 & $i(v2) & $i(v1)) | ( ~ (v0 = 0) & top_str(all_51_5) =
% 96.24/14.87 | v0))
% 96.24/14.87 |
% 96.24/14.87 | GROUND_INST: instantiating (11) with all_51_5, simplifying with (38), (46)
% 96.24/14.87 | gives:
% 96.24/14.87 | (57) one_sorted_str(all_51_5) = 0
% 96.24/14.87 |
% 96.24/14.87 | GROUND_INST: instantiating (3) with all_51_5, simplifying with (38), (46)
% 96.24/14.87 | gives:
% 96.24/14.87 | (58) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_51_5) = v0 & powerset(v0)
% 96.24/14.87 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.87 | (interior(all_51_5, v2) = v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 96.24/14.87 | $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v3 &
% 96.24/14.87 | topstr_closure(all_51_5, v5) = v6 & subset_complement(v0, v6)
% 96.24/14.87 | = v3 & subset_complement(v0, v2) = v5 & $i(v6) & $i(v5) &
% 96.24/14.87 | $i(v3)) | ( ~ (v4 = 0) & element(v2, v1) = v4))) & ! [v2: $i]
% 96.24/14.87 | : ! [v3: $i] : ( ~ (subset_complement(v0, v2) = v3) | ~ $i(v2) |
% 96.24/14.87 | ? [v4: int] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ((v7 = v5
% 96.24/14.87 | & interior(all_51_5, v2) = v5 & topstr_closure(all_51_5, v3) =
% 96.24/14.87 | v6 & subset_complement(v0, v6) = v5 & $i(v6) & $i(v5)) | ( ~
% 96.24/14.87 | (v4 = 0) & element(v2, v1) = v4))) & ! [v2: $i] : ( ~
% 96.24/14.87 | (element(v2, v1) = 0) | ~ $i(v2) | ? [v3: $i] : ? [v4: $i] : ?
% 96.24/14.87 | [v5: $i] : (interior(all_51_5, v2) = v3 & topstr_closure(all_51_5,
% 96.24/14.87 | v4) = v5 & subset_complement(v0, v5) = v3 &
% 96.24/14.87 | subset_complement(v0, v2) = v4 & $i(v5) & $i(v4) & $i(v3))))
% 96.24/14.87 |
% 96.24/14.87 | GROUND_INST: instantiating (19) with all_51_5, simplifying with (38), (46)
% 96.24/14.87 | gives:
% 96.24/14.87 | (59) ? [v0: $i] : ? [v1: $i] : (the_carrier(all_51_5) = v0 & powerset(v0)
% 96.24/14.87 | = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ! [v3: $i] : ( ~
% 96.24/14.87 | (topstr_closure(all_51_5, v2) = v3) | ~ $i(v2) | ? [v4: int] :
% 96.24/14.87 | ? [v5: int] : ((v5 = 0 & subset(v2, v3) = 0) | ( ~ (v4 = 0) &
% 96.24/14.87 | element(v2, v1) = v4))) & ! [v2: $i] : ( ~ (element(v2, v1) =
% 96.24/14.87 | 0) | ~ $i(v2) | ? [v3: $i] : (subset(v2, v3) = 0 &
% 96.24/14.87 | topstr_closure(all_51_5, v2) = v3 & $i(v3))))
% 96.24/14.87 |
% 96.24/14.87 | GROUND_INST: instantiating (6) with all_51_1, all_51_2, all_51_0, simplifying
% 96.24/14.87 | with (40), (41), (47) gives:
% 96.24/14.87 | (60) all_51_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0,
% 96.24/14.87 | all_51_1) = 0 & in(v0, all_51_2) = v1 & $i(v0))
% 96.24/14.87 |
% 96.24/14.87 | DELTA: instantiating (49) with fresh symbol all_59_0 gives:
% 96.24/14.87 | (61) subset_complement(all_51_4, all_51_2) = all_59_0 & element(all_59_0,
% 96.24/14.87 | all_51_3) = 0 & $i(all_59_0)
% 96.24/14.87 |
% 96.24/14.87 | ALPHA: (61) implies:
% 96.24/14.87 | (62) element(all_59_0, all_51_3) = 0
% 96.24/14.87 | (63) subset_complement(all_51_4, all_51_2) = all_59_0
% 96.24/14.87 |
% 96.24/14.87 | DELTA: instantiating (48) with fresh symbol all_61_0 gives:
% 96.24/14.87 | (64) subset_complement(all_51_4, all_61_0) = all_51_2 &
% 96.24/14.87 | subset_complement(all_51_4, all_51_2) = all_61_0 & $i(all_61_0)
% 96.24/14.87 |
% 96.24/14.87 | ALPHA: (64) implies:
% 96.24/14.87 | (65) subset_complement(all_51_4, all_51_2) = all_61_0
% 96.24/14.87 |
% 96.24/14.87 | DELTA: instantiating (53) with fresh symbols all_90_0, all_90_1, all_90_2
% 96.24/14.87 | gives:
% 96.24/14.87 | (66) ( ~ (all_90_2 = 0) & one_sorted_str(all_51_5) = all_90_2) |
% 96.24/14.87 | (((all_90_0 = 0 & empty(all_51_4) = 0) | ( ~ (all_90_1 = 0) &
% 96.24/14.87 | empty_carrier(all_51_5) = all_90_1)) & ((all_90_1 = 0 &
% 96.24/14.87 | empty_carrier(all_51_5) = 0) | ( ~ (all_90_0 = 0) &
% 96.24/14.87 | empty(all_51_4) = all_90_0)))
% 96.24/14.87 |
% 96.24/14.87 | DELTA: instantiating (51) with fresh symbols all_107_0, all_107_1, all_107_2,
% 96.24/14.87 | all_107_3, all_107_4, all_107_5 gives:
% 96.24/14.87 | (67) $i(all_107_2) & ((all_107_1 = 0 & ~ (all_107_0 = 0) &
% 96.24/14.87 | powerset(all_51_4) = all_107_3 & empty(all_107_2) = all_107_0 &
% 96.24/14.87 | element(all_107_2, all_107_3) = 0 & $i(all_107_3)) | (all_107_5 =
% 96.24/14.87 | 0 & empty_carrier(all_51_5) = 0) | ( ~ (all_107_4 = 0) &
% 96.24/14.87 | one_sorted_str(all_51_5) = all_107_4))
% 96.24/14.87 |
% 96.24/14.87 | ALPHA: (67) implies:
% 96.24/14.87 | (68) (all_107_1 = 0 & ~ (all_107_0 = 0) & powerset(all_51_4) = all_107_3 &
% 96.24/14.87 | empty(all_107_2) = all_107_0 & element(all_107_2, all_107_3) = 0 &
% 96.24/14.87 | $i(all_107_3)) | (all_107_5 = 0 & empty_carrier(all_51_5) = 0) | ( ~
% 96.24/14.87 | (all_107_4 = 0) & one_sorted_str(all_51_5) = all_107_4)
% 96.24/14.87 |
% 96.24/14.87 | DELTA: instantiating (50) with fresh symbols all_111_0, all_111_1, all_111_2
% 96.24/14.87 | gives:
% 96.24/14.87 | (69) ((all_111_0 = 0 & the_carrier(all_42_0) = all_111_1 & empty(all_111_1)
% 96.24/14.87 | = 0 & $i(all_111_1)) | ( ~ (all_111_2 = 0) &
% 96.24/14.87 | empty_carrier(all_42_0) = all_111_2)) & ((all_111_2 = 0 &
% 96.24/14.87 | empty_carrier(all_42_0) = 0) | ( ~ (all_111_0 = 0) &
% 96.24/14.87 | the_carrier(all_42_0) = all_111_1 & empty(all_111_1) = all_111_0 &
% 96.24/14.87 | $i(all_111_1)))
% 96.24/14.87 |
% 96.24/14.87 | ALPHA: (69) implies:
% 96.24/14.87 | (70) (all_111_2 = 0 & empty_carrier(all_42_0) = 0) | ( ~ (all_111_0 = 0) &
% 96.24/14.87 | the_carrier(all_42_0) = all_111_1 & empty(all_111_1) = all_111_0 &
% 96.24/14.87 | $i(all_111_1))
% 96.24/14.87 | (71) (all_111_0 = 0 & the_carrier(all_42_0) = all_111_1 & empty(all_111_1)
% 96.24/14.87 | = 0 & $i(all_111_1)) | ( ~ (all_111_2 = 0) & empty_carrier(all_42_0)
% 96.24/14.87 | = all_111_2)
% 96.24/14.87 |
% 96.24/14.87 | DELTA: instantiating (56) with fresh symbols all_123_0, all_123_1, all_123_2,
% 96.24/14.87 | all_123_3, all_123_4 gives:
% 96.24/14.87 | (72) (all_123_0 = 0 & the_carrier(all_51_5) = all_123_3 &
% 96.24/14.87 | powerset(all_123_3) = all_123_2 & element(all_51_1, all_123_2) = 0 &
% 96.24/14.87 | $i(all_123_2) & $i(all_123_3)) | ( ~ (all_123_1 = 0) &
% 96.24/14.88 | the_carrier(all_51_5) = all_123_3 & powerset(all_123_3) = all_123_2
% 96.24/14.88 | & element(all_51_2, all_123_2) = all_123_1 & $i(all_123_2) &
% 96.24/14.88 | $i(all_123_3)) | ( ~ (all_123_4 = 0) & top_str(all_51_5) =
% 96.24/14.88 | all_123_4)
% 96.24/14.88 |
% 96.24/14.88 | DELTA: instantiating (59) with fresh symbols all_127_0, all_127_1 gives:
% 96.24/14.88 | (73) the_carrier(all_51_5) = all_127_1 & powerset(all_127_1) = all_127_0 &
% 96.24/14.88 | $i(all_127_0) & $i(all_127_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 96.24/14.88 | (topstr_closure(all_51_5, v0) = v1) | ~ $i(v0) | ? [v2: int] : ?
% 96.24/14.88 | [v3: int] : ((v3 = 0 & subset(v0, v1) = 0) | ( ~ (v2 = 0) &
% 96.24/14.88 | element(v0, all_127_0) = v2))) & ! [v0: $i] : ( ~ (element(v0,
% 96.24/14.88 | all_127_0) = 0) | ~ $i(v0) | ? [v1: $i] : (subset(v0, v1) = 0
% 96.24/14.88 | & topstr_closure(all_51_5, v0) = v1 & $i(v1)))
% 96.24/14.88 |
% 96.24/14.88 | ALPHA: (73) implies:
% 96.24/14.88 | (74) powerset(all_127_1) = all_127_0
% 96.24/14.88 | (75) the_carrier(all_51_5) = all_127_1
% 96.24/14.88 | (76) ! [v0: $i] : ! [v1: $i] : ( ~ (topstr_closure(all_51_5, v0) = v1) |
% 96.24/14.88 | ~ $i(v0) | ? [v2: int] : ? [v3: int] : ((v3 = 0 & subset(v0, v1) =
% 96.24/14.88 | 0) | ( ~ (v2 = 0) & element(v0, all_127_0) = v2)))
% 96.24/14.88 |
% 96.24/14.88 | DELTA: instantiating (55) with fresh symbols all_130_0, all_130_1 gives:
% 96.24/14.88 | (77) ( ~ (all_130_1 = 0) & top_str(all_51_5) = all_130_1) |
% 96.24/14.88 | (powerset(all_51_4) = all_130_0 & $i(all_130_0) & ! [v0: $i] : !
% 96.24/14.88 | [v1: $i] : ( ~ (topstr_closure(all_51_5, v0) = v1) | ~ $i(v0) | ?
% 96.24/14.88 | [v2: int] : ? [v3: int] : ((v3 = 0 & subset(v0, v1) = 0) | ( ~
% 96.24/14.88 | (v2 = 0) & element(v0, all_130_0) = v2))) & ! [v0: $i] : ( ~
% 96.24/14.88 | (element(v0, all_130_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 96.24/14.88 | (subset(v0, v1) = 0 & topstr_closure(all_51_5, v0) = v1 &
% 96.24/14.88 | $i(v1))))
% 96.24/14.88 |
% 96.24/14.88 | DELTA: instantiating (54) with fresh symbols all_137_0, all_137_1 gives:
% 96.24/14.88 | (78) ( ~ (all_137_1 = 0) & top_str(all_51_5) = all_137_1) |
% 96.24/14.88 | (powerset(all_51_4) = all_137_0 & $i(all_137_0) & ! [v0: $i] : !
% 96.24/14.88 | [v1: $i] : ( ~ (interior(all_51_5, v0) = v1) | ~ $i(v0) | ? [v2:
% 96.24/14.88 | int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v1 &
% 96.24/14.88 | topstr_closure(all_51_5, v3) = v4 &
% 96.24/14.88 | subset_complement(all_51_4, v4) = v1 &
% 96.24/14.88 | subset_complement(all_51_4, v0) = v3 & $i(v4) & $i(v3) &
% 96.24/14.88 | $i(v1)) | ( ~ (v2 = 0) & element(v0, all_137_0) = v2))) & !
% 96.24/14.88 | [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_51_4, v0) = v1)
% 96.24/14.88 | | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 96.24/14.88 | $i] : ((v5 = v3 & interior(all_51_5, v0) = v3 &
% 96.24/14.88 | topstr_closure(all_51_5, v1) = v4 &
% 96.24/14.88 | subset_complement(all_51_4, v4) = v3 & $i(v4) & $i(v3)) | ( ~
% 96.24/14.88 | (v2 = 0) & element(v0, all_137_0) = v2))) & ! [v0: $i] : ( ~
% 96.24/14.88 | (element(v0, all_137_0) = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2:
% 96.24/14.88 | $i] : ? [v3: $i] : (interior(all_51_5, v0) = v1 &
% 96.24/14.88 | topstr_closure(all_51_5, v2) = v3 & subset_complement(all_51_4,
% 96.24/14.88 | v3) = v1 & subset_complement(all_51_4, v0) = v2 & $i(v3) &
% 96.24/14.88 | $i(v2) & $i(v1))))
% 96.24/14.88 |
% 96.24/14.88 | DELTA: instantiating (58) with fresh symbols all_141_0, all_141_1 gives:
% 96.24/14.88 | (79) the_carrier(all_51_5) = all_141_1 & powerset(all_141_1) = all_141_0 &
% 96.24/14.88 | $i(all_141_0) & $i(all_141_1) & ! [v0: $i] : ! [v1: $i] : ( ~
% 96.24/14.88 | (interior(all_51_5, v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3:
% 96.24/14.88 | $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v1 &
% 96.24/14.88 | topstr_closure(all_51_5, v3) = v4 & subset_complement(all_141_1,
% 96.24/14.88 | v4) = v1 & subset_complement(all_141_1, v0) = v3 & $i(v4) &
% 96.24/14.88 | $i(v3) & $i(v1)) | ( ~ (v2 = 0) & element(v0, all_141_0) = v2)))
% 96.24/14.88 | & ! [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_141_1, v0) =
% 96.24/14.88 | v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ?
% 96.24/14.88 | [v5: $i] : ((v5 = v3 & interior(all_51_5, v0) = v3 &
% 96.24/14.88 | topstr_closure(all_51_5, v1) = v4 & subset_complement(all_141_1,
% 96.24/14.88 | v4) = v3 & $i(v4) & $i(v3)) | ( ~ (v2 = 0) & element(v0,
% 96.24/14.88 | all_141_0) = v2))) & ! [v0: $i] : ( ~ (element(v0, all_141_0)
% 96.24/14.88 | = 0) | ~ $i(v0) | ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 96.24/14.88 | (interior(all_51_5, v0) = v1 & topstr_closure(all_51_5, v2) = v3 &
% 96.24/14.88 | subset_complement(all_141_1, v3) = v1 &
% 96.24/14.88 | subset_complement(all_141_1, v0) = v2 & $i(v3) & $i(v2) & $i(v1)))
% 96.24/14.88 |
% 96.24/14.88 | ALPHA: (79) implies:
% 96.24/14.88 | (80) powerset(all_141_1) = all_141_0
% 96.24/14.88 | (81) the_carrier(all_51_5) = all_141_1
% 96.24/14.88 | (82) ! [v0: $i] : ! [v1: $i] : ( ~ (interior(all_51_5, v0) = v1) | ~
% 96.24/14.88 | $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] :
% 96.24/14.88 | ((v5 = v1 & topstr_closure(all_51_5, v3) = v4 &
% 96.24/14.88 | subset_complement(all_141_1, v4) = v1 &
% 96.24/14.88 | subset_complement(all_141_1, v0) = v3 & $i(v4) & $i(v3) &
% 96.24/14.88 | $i(v1)) | ( ~ (v2 = 0) & element(v0, all_141_0) = v2)))
% 96.24/14.88 |
% 96.24/14.88 | GROUND_INST: instantiating (82) with all_51_2, all_51_1, simplifying with
% 96.24/14.88 | (40), (45) gives:
% 96.24/14.89 | (83) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3 =
% 96.24/14.89 | all_51_1 & topstr_closure(all_51_5, v1) = v2 &
% 96.24/14.89 | subset_complement(all_141_1, v2) = all_51_1 &
% 96.24/14.89 | subset_complement(all_141_1, all_51_2) = v1 & $i(v2) & $i(v1) &
% 96.24/14.89 | $i(all_51_1)) | ( ~ (v0 = 0) & element(all_51_2, all_141_0) = v0))
% 96.24/14.89 |
% 96.24/14.89 | DELTA: instantiating (52) with fresh symbols all_166_0, all_166_1, all_166_2
% 96.24/14.89 | gives:
% 96.24/14.89 | (84) (all_166_2 = 0 & empty_carrier(all_51_5) = 0) | ( ~ (all_166_1 = 0) &
% 96.24/14.89 | one_sorted_str(all_51_5) = all_166_1) | (powerset(all_51_4) =
% 96.24/14.89 | all_166_0 & $i(all_166_0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 96.24/14.89 | : ! [v3: any] : ( ~ (subset_complement(all_51_4, v0) = v1) | ~
% 96.24/14.89 | (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 96.24/14.89 | int] : (( ~ (v4 = 0) & element(v2, all_51_4) = v4) | ( ~ (v4 =
% 96.24/14.89 | 0) & element(v0, all_166_0) = v4) | (( ~ (v3 = 0) | ( ~ (v5
% 96.24/14.89 | = 0) & in(v2, v0) = v5)) & (v3 = 0 | (v5 = 0 & in(v2,
% 96.24/14.89 | v0) = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 96.24/14.89 | ! [v3: any] : ( ~ (subset_complement(all_51_4, v0) = v1) | ~
% 96.24/14.89 | (in(v2, v0) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int] : ? [v5:
% 96.24/14.89 | int] : (( ~ (v4 = 0) & element(v2, all_51_4) = v4) | ( ~ (v4 =
% 96.24/14.89 | 0) & element(v0, all_166_0) = v4) | (( ~ (v3 = 0) | ( ~ (v5
% 96.24/14.89 | = 0) & in(v2, v1) = v5)) & (v3 = 0 | (v5 = 0 & in(v2,
% 96.24/14.89 | v1) = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 96.24/14.89 | ( ~ (subset_complement(all_51_4, v0) = v1) | ~ (element(v2,
% 96.24/14.89 | all_51_4) = 0) | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ?
% 96.24/14.89 | [v4: int] : (( ~ (v3 = 0) & element(v0, all_166_0) = v3) | (((v4 =
% 96.24/14.89 | 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & (( ~
% 96.24/14.89 | (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2, v1) =
% 96.24/14.89 | v3))))) & ! [v0: $i] : ( ~ (element(v0, all_166_0) = 0) |
% 96.24/14.89 | ~ $i(v0) | ? [v1: $i] : (subset_complement(all_51_4, v0) = v1 &
% 96.24/14.89 | $i(v1) & ! [v2: $i] : ! [v3: any] : ( ~ (in(v2, v1) = v3) | ~
% 96.24/14.89 | $i(v2) | ? [v4: int] : ? [v5: int] : (( ~ (v4 = 0) &
% 96.24/14.89 | element(v2, all_51_4) = v4) | (( ~ (v3 = 0) | ( ~ (v5 = 0)
% 96.24/14.89 | & in(v2, v0) = v5)) & (v3 = 0 | (v5 = 0 & in(v2, v0) =
% 96.24/14.89 | 0))))) & ! [v2: $i] : ! [v3: any] : ( ~ (in(v2, v0)
% 96.24/14.89 | = v3) | ~ $i(v2) | ? [v4: int] : ? [v5: int] : (( ~ (v4 =
% 96.24/14.89 | 0) & element(v2, all_51_4) = v4) | (( ~ (v3 = 0) | ( ~
% 96.24/14.89 | (v5 = 0) & in(v2, v1) = v5)) & (v3 = 0 | (v5 = 0 &
% 96.24/14.89 | in(v2, v1) = 0))))) & ! [v2: $i] : ( ~ (element(v2,
% 96.24/14.89 | all_51_4) = 0) | ~ $i(v2) | ? [v3: int] : ? [v4: int] :
% 96.24/14.89 | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) = 0)) & ((
% 96.24/14.89 | ~ (v4 = 0) & in(v2, v0) = v4) | ( ~ (v3 = 0) & in(v2,
% 96.24/14.89 | v1) = v3)))))))
% 96.24/14.89 |
% 96.24/14.89 | DELTA: instantiating (83) with fresh symbols all_173_0, all_173_1, all_173_2,
% 96.24/14.89 | all_173_3 gives:
% 96.24/14.89 | (85) (all_173_0 = all_51_1 & topstr_closure(all_51_5, all_173_2) =
% 96.24/14.89 | all_173_1 & subset_complement(all_141_1, all_173_1) = all_51_1 &
% 96.24/14.89 | subset_complement(all_141_1, all_51_2) = all_173_2 & $i(all_173_1) &
% 96.24/14.89 | $i(all_173_2) & $i(all_51_1)) | ( ~ (all_173_3 = 0) &
% 96.24/14.89 | element(all_51_2, all_141_0) = all_173_3)
% 96.24/14.89 |
% 96.24/14.89 | BETA: splitting (77) gives:
% 96.24/14.89 |
% 96.24/14.89 | Case 1:
% 96.24/14.89 | |
% 96.24/14.89 | | (86) ~ (all_130_1 = 0) & top_str(all_51_5) = all_130_1
% 96.24/14.89 | |
% 96.24/14.89 | | ALPHA: (86) implies:
% 96.24/14.89 | | (87) ~ (all_130_1 = 0)
% 96.24/14.89 | | (88) top_str(all_51_5) = all_130_1
% 96.24/14.89 | |
% 96.24/14.89 | | GROUND_INST: instantiating (28) with 0, all_130_1, all_51_5, simplifying
% 96.24/14.89 | | with (46), (88) gives:
% 96.24/14.89 | | (89) all_130_1 = 0
% 96.24/14.89 | |
% 96.24/14.89 | | REDUCE: (87), (89) imply:
% 96.24/14.89 | | (90) $false
% 96.24/14.89 | |
% 96.24/14.89 | | CLOSE: (90) is inconsistent.
% 96.24/14.89 | |
% 96.24/14.89 | Case 2:
% 96.24/14.89 | |
% 96.24/14.89 | | (91) powerset(all_51_4) = all_130_0 & $i(all_130_0) & ! [v0: $i] : !
% 96.24/14.89 | | [v1: $i] : ( ~ (topstr_closure(all_51_5, v0) = v1) | ~ $i(v0) | ?
% 96.24/14.89 | | [v2: int] : ? [v3: int] : ((v3 = 0 & subset(v0, v1) = 0) | ( ~
% 96.24/14.89 | | (v2 = 0) & element(v0, all_130_0) = v2))) & ! [v0: $i] : ( ~
% 96.24/14.89 | | (element(v0, all_130_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 96.24/14.89 | | (subset(v0, v1) = 0 & topstr_closure(all_51_5, v0) = v1 & $i(v1)))
% 96.24/14.89 | |
% 96.24/14.89 | | ALPHA: (91) implies:
% 96.24/14.89 | | (92) powerset(all_51_4) = all_130_0
% 96.24/14.89 | |
% 96.24/14.89 | | BETA: splitting (60) gives:
% 96.24/14.89 | |
% 96.24/14.89 | | Case 1:
% 96.24/14.89 | | |
% 96.24/14.89 | | | (93) all_51_0 = 0
% 96.24/14.89 | | |
% 96.24/14.89 | | | REDUCE: (37), (93) imply:
% 96.24/14.89 | | | (94) $false
% 96.24/14.89 | | |
% 96.24/14.89 | | | CLOSE: (94) is inconsistent.
% 96.24/14.89 | | |
% 96.24/14.89 | | Case 2:
% 96.24/14.89 | | |
% 96.24/14.90 | | | (95) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_51_1) = 0 &
% 96.24/14.90 | | | in(v0, all_51_2) = v1 & $i(v0))
% 96.24/14.90 | | |
% 96.24/14.90 | | | DELTA: instantiating (95) with fresh symbols all_251_0, all_251_1 gives:
% 96.24/14.90 | | | (96) ~ (all_251_0 = 0) & in(all_251_1, all_51_1) = 0 & in(all_251_1,
% 96.24/14.90 | | | all_51_2) = all_251_0 & $i(all_251_1)
% 96.24/14.90 | | |
% 96.24/14.90 | | | ALPHA: (96) implies:
% 96.24/14.90 | | | (97) ~ (all_251_0 = 0)
% 96.24/14.90 | | | (98) $i(all_251_1)
% 96.24/14.90 | | | (99) in(all_251_1, all_51_2) = all_251_0
% 96.24/14.90 | | | (100) in(all_251_1, all_51_1) = 0
% 96.24/14.90 | | |
% 96.24/14.90 | | | BETA: splitting (78) gives:
% 96.24/14.90 | | |
% 96.24/14.90 | | | Case 1:
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | (101) ~ (all_137_1 = 0) & top_str(all_51_5) = all_137_1
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | ALPHA: (101) implies:
% 96.24/14.90 | | | | (102) ~ (all_137_1 = 0)
% 96.24/14.90 | | | | (103) top_str(all_51_5) = all_137_1
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (28) with 0, all_137_1, all_51_5, simplifying
% 96.24/14.90 | | | | with (46), (103) gives:
% 96.24/14.90 | | | | (104) all_137_1 = 0
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | REDUCE: (102), (104) imply:
% 96.24/14.90 | | | | (105) $false
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | CLOSE: (105) is inconsistent.
% 96.24/14.90 | | | |
% 96.24/14.90 | | | Case 2:
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | (106) powerset(all_51_4) = all_137_0 & $i(all_137_0) & ! [v0: $i] :
% 96.24/14.90 | | | | ! [v1: $i] : ( ~ (interior(all_51_5, v0) = v1) | ~ $i(v0) | ?
% 96.24/14.90 | | | | [v2: int] : ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 =
% 96.24/14.90 | | | | v1 & topstr_closure(all_51_5, v3) = v4 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v4) = v1 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v0) = v3 & $i(v4) & $i(v3) &
% 96.24/14.90 | | | | $i(v1)) | ( ~ (v2 = 0) & element(v0, all_137_0) = v2))) &
% 96.24/14.90 | | | | ! [v0: $i] : ! [v1: $i] : ( ~ (subset_complement(all_51_4,
% 96.24/14.90 | | | | v0) = v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ?
% 96.24/14.90 | | | | [v4: $i] : ? [v5: $i] : ((v5 = v3 & interior(all_51_5, v0) =
% 96.24/14.90 | | | | v3 & topstr_closure(all_51_5, v1) = v4 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v4) = v3 & $i(v4) & $i(v3)) |
% 96.24/14.90 | | | | ( ~ (v2 = 0) & element(v0, all_137_0) = v2))) & ! [v0: $i]
% 96.24/14.90 | | | | : ( ~ (element(v0, all_137_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 96.24/14.90 | | | | ? [v2: $i] : ? [v3: $i] : (interior(all_51_5, v0) = v1 &
% 96.24/14.90 | | | | topstr_closure(all_51_5, v2) = v3 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v3) = v1 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v0) = v2 & $i(v3) & $i(v2) &
% 96.24/14.90 | | | | $i(v1)))
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | ALPHA: (106) implies:
% 96.24/14.90 | | | | (107) powerset(all_51_4) = all_137_0
% 96.24/14.90 | | | | (108) ! [v0: $i] : ! [v1: $i] : ( ~ (interior(all_51_5, v0) = v1) |
% 96.24/14.90 | | | | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: $i] : ?
% 96.24/14.90 | | | | [v5: $i] : ((v5 = v1 & topstr_closure(all_51_5, v3) = v4 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v4) = v1 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v0) = v3 & $i(v4) & $i(v3) &
% 96.24/14.90 | | | | $i(v1)) | ( ~ (v2 = 0) & element(v0, all_137_0) = v2)))
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (108) with all_51_2, all_51_1, simplifying
% 96.24/14.90 | | | | with (40), (45) gives:
% 96.24/14.90 | | | | (109) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ((v3
% 96.24/14.90 | | | | = all_51_1 & topstr_closure(all_51_5, v1) = v2 &
% 96.24/14.90 | | | | subset_complement(all_51_4, v2) = all_51_1 &
% 96.24/14.90 | | | | subset_complement(all_51_4, all_51_2) = v1 & $i(v2) &
% 96.24/14.90 | | | | $i(v1) & $i(all_51_1)) | ( ~ (v0 = 0) & element(all_51_2,
% 96.24/14.90 | | | | all_137_0) = v0))
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | DELTA: instantiating (109) with fresh symbols all_280_0, all_280_1,
% 96.24/14.90 | | | | all_280_2, all_280_3 gives:
% 96.24/14.90 | | | | (110) (all_280_0 = all_51_1 & topstr_closure(all_51_5, all_280_2) =
% 96.24/14.90 | | | | all_280_1 & subset_complement(all_51_4, all_280_1) = all_51_1
% 96.24/14.90 | | | | & subset_complement(all_51_4, all_51_2) = all_280_2 &
% 96.24/14.90 | | | | $i(all_280_1) & $i(all_280_2) & $i(all_51_1)) | ( ~
% 96.24/14.90 | | | | (all_280_3 = 0) & element(all_51_2, all_137_0) = all_280_3)
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (24) with all_51_3, all_137_0, all_51_4,
% 96.24/14.90 | | | | simplifying with (43), (107) gives:
% 96.24/14.90 | | | | (111) all_137_0 = all_51_3
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (24) with all_130_0, all_137_0, all_51_4,
% 96.24/14.90 | | | | simplifying with (92), (107) gives:
% 96.24/14.90 | | | | (112) all_137_0 = all_130_0
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (27) with all_51_4, all_141_1, all_51_5,
% 96.24/14.90 | | | | simplifying with (44), (81) gives:
% 96.24/14.90 | | | | (113) all_141_1 = all_51_4
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (27) with all_127_1, all_141_1, all_51_5,
% 96.24/14.90 | | | | simplifying with (75), (81) gives:
% 96.24/14.90 | | | | (114) all_141_1 = all_127_1
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | GROUND_INST: instantiating (31) with all_59_0, all_61_0, all_51_2,
% 96.24/14.90 | | | | all_51_4, simplifying with (63), (65) gives:
% 96.24/14.90 | | | | (115) all_61_0 = all_59_0
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | COMBINE_EQS: (113), (114) imply:
% 96.24/14.90 | | | | (116) all_127_1 = all_51_4
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | COMBINE_EQS: (111), (112) imply:
% 96.24/14.90 | | | | (117) all_130_0 = all_51_3
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | SIMP: (117) implies:
% 96.24/14.90 | | | | (118) all_130_0 = all_51_3
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | REDUCE: (80), (113) imply:
% 96.24/14.90 | | | | (119) powerset(all_51_4) = all_141_0
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | REDUCE: (74), (116) imply:
% 96.24/14.90 | | | | (120) powerset(all_51_4) = all_127_0
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | BETA: splitting (110) gives:
% 96.24/14.90 | | | |
% 96.24/14.90 | | | | Case 1:
% 96.24/14.90 | | | | |
% 96.24/14.90 | | | | | (121) all_280_0 = all_51_1 & topstr_closure(all_51_5, all_280_2) =
% 96.24/14.90 | | | | | all_280_1 & subset_complement(all_51_4, all_280_1) = all_51_1
% 96.24/14.90 | | | | | & subset_complement(all_51_4, all_51_2) = all_280_2 &
% 96.24/14.90 | | | | | $i(all_280_1) & $i(all_280_2) & $i(all_51_1)
% 96.24/14.90 | | | | |
% 96.24/14.90 | | | | | ALPHA: (121) implies:
% 96.24/14.90 | | | | | (122) $i(all_280_1)
% 96.24/14.90 | | | | | (123) subset_complement(all_51_4, all_51_2) = all_280_2
% 96.24/14.90 | | | | | (124) subset_complement(all_51_4, all_280_1) = all_51_1
% 96.24/14.90 | | | | | (125) topstr_closure(all_51_5, all_280_2) = all_280_1
% 96.24/14.90 | | | | |
% 96.24/14.90 | | | | | GROUND_INST: instantiating (24) with all_51_3, all_141_0, all_51_4,
% 96.24/14.90 | | | | | simplifying with (43), (119) gives:
% 96.24/14.91 | | | | | (126) all_141_0 = all_51_3
% 96.24/14.91 | | | | |
% 96.24/14.91 | | | | | GROUND_INST: instantiating (24) with all_127_0, all_141_0, all_51_4,
% 96.24/14.91 | | | | | simplifying with (119), (120) gives:
% 96.24/14.91 | | | | | (127) all_141_0 = all_127_0
% 96.24/14.91 | | | | |
% 97.09/14.91 | | | | | GROUND_INST: instantiating (31) with all_59_0, all_280_2, all_51_2,
% 97.09/14.91 | | | | | all_51_4, simplifying with (63), (123) gives:
% 97.09/14.91 | | | | | (128) all_280_2 = all_59_0
% 97.09/14.91 | | | | |
% 97.09/14.91 | | | | | COMBINE_EQS: (126), (127) imply:
% 97.09/14.91 | | | | | (129) all_127_0 = all_51_3
% 97.09/14.91 | | | | |
% 97.09/14.91 | | | | | SIMP: (129) implies:
% 97.09/14.91 | | | | | (130) all_127_0 = all_51_3
% 97.09/14.91 | | | | |
% 97.09/14.91 | | | | | REDUCE: (125), (128) imply:
% 97.09/14.91 | | | | | (131) topstr_closure(all_51_5, all_59_0) = all_280_1
% 97.09/14.91 | | | | |
% 97.09/14.91 | | | | | BETA: splitting (85) gives:
% 97.09/14.91 | | | | |
% 97.09/14.91 | | | | | Case 1:
% 97.09/14.91 | | | | | |
% 97.09/14.91 | | | | | | (132) all_173_0 = all_51_1 & topstr_closure(all_51_5, all_173_2)
% 97.09/14.91 | | | | | | = all_173_1 & subset_complement(all_141_1, all_173_1) =
% 97.09/14.91 | | | | | | all_51_1 & subset_complement(all_141_1, all_51_2) =
% 97.09/14.91 | | | | | | all_173_2 & $i(all_173_1) & $i(all_173_2) & $i(all_51_1)
% 97.09/14.91 | | | | | |
% 97.09/14.91 | | | | | | ALPHA: (132) implies:
% 97.09/14.91 | | | | | | (133) $i(all_173_2)
% 97.09/14.91 | | | | | | (134) subset_complement(all_141_1, all_51_2) = all_173_2
% 97.09/14.91 | | | | | | (135) topstr_closure(all_51_5, all_173_2) = all_173_1
% 97.09/14.91 | | | | | |
% 97.09/14.91 | | | | | | REDUCE: (113), (134) imply:
% 97.09/14.91 | | | | | | (136) subset_complement(all_51_4, all_51_2) = all_173_2
% 97.09/14.91 | | | | | |
% 97.09/14.91 | | | | | | BETA: splitting (72) gives:
% 97.09/14.91 | | | | | |
% 97.09/14.91 | | | | | | Case 1:
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | (137) all_123_0 = 0 & the_carrier(all_51_5) = all_123_3 &
% 97.09/14.91 | | | | | | | powerset(all_123_3) = all_123_2 & element(all_51_1,
% 97.09/14.91 | | | | | | | all_123_2) = 0 & $i(all_123_2) & $i(all_123_3)
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | ALPHA: (137) implies:
% 97.09/14.91 | | | | | | | (138) $i(all_123_3)
% 97.09/14.91 | | | | | | | (139) element(all_51_1, all_123_2) = 0
% 97.09/14.91 | | | | | | | (140) powerset(all_123_3) = all_123_2
% 97.09/14.91 | | | | | | | (141) the_carrier(all_51_5) = all_123_3
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (27) with all_51_4, all_123_3,
% 97.09/14.91 | | | | | | | all_51_5, simplifying with (44), (141) gives:
% 97.09/14.91 | | | | | | | (142) all_123_3 = all_51_4
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (31) with all_59_0, all_173_2,
% 97.09/14.91 | | | | | | | all_51_2, all_51_4, simplifying with (63), (136)
% 97.09/14.91 | | | | | | | gives:
% 97.09/14.91 | | | | | | | (143) all_173_2 = all_59_0
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | REDUCE: (135), (143) imply:
% 97.09/14.91 | | | | | | | (144) topstr_closure(all_51_5, all_59_0) = all_173_1
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | REDUCE: (140), (142) imply:
% 97.09/14.91 | | | | | | | (145) powerset(all_51_4) = all_123_2
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | REDUCE: (133), (143) imply:
% 97.09/14.91 | | | | | | | (146) $i(all_59_0)
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (24) with all_51_3, all_123_2,
% 97.09/14.91 | | | | | | | all_51_4, simplifying with (43), (145) gives:
% 97.09/14.91 | | | | | | | (147) all_123_2 = all_51_3
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (32) with all_280_1, all_173_1,
% 97.09/14.91 | | | | | | | all_59_0, all_51_5, simplifying with (131), (144)
% 97.09/14.91 | | | | | | | gives:
% 97.09/14.91 | | | | | | | (148) all_280_1 = all_173_1
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | REDUCE: (124), (148) imply:
% 97.09/14.91 | | | | | | | (149) subset_complement(all_51_4, all_173_1) = all_51_1
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | REDUCE: (139), (147) imply:
% 97.09/14.91 | | | | | | | (150) element(all_51_1, all_51_3) = 0
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | REDUCE: (122), (148) imply:
% 97.09/14.91 | | | | | | | (151) $i(all_173_1)
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (21) with all_251_1, all_51_1,
% 97.09/14.91 | | | | | | | all_51_4, all_51_3, simplifying with (39), (41),
% 97.09/14.91 | | | | | | | (43), (98), (100), (150) gives:
% 97.09/14.91 | | | | | | | (152) element(all_251_1, all_51_4) = 0
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (22) with all_251_1, all_51_1,
% 97.09/14.91 | | | | | | | all_51_4, all_51_3, simplifying with (39), (41),
% 97.09/14.91 | | | | | | | (43), (98), (100), (150) gives:
% 97.09/14.91 | | | | | | | (153) ? [v0: int] : ( ~ (v0 = 0) & empty(all_51_4) = v0)
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (13) with all_51_4, all_51_1, all_51_3,
% 97.09/14.91 | | | | | | | simplifying with (39), (41), (43), (150) gives:
% 97.09/14.91 | | | | | | | (154) ? [v0: $i] : (subset_complement(all_51_4, v0) = all_51_1
% 97.09/14.91 | | | | | | | & subset_complement(all_51_4, all_51_1) = v0 & $i(v0))
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (8) with all_51_4, all_51_1, all_51_3,
% 97.09/14.91 | | | | | | | simplifying with (39), (41), (43), (150) gives:
% 97.09/14.91 | | | | | | | (155) ? [v0: $i] : (subset_complement(all_51_4, all_51_1) = v0
% 97.09/14.91 | | | | | | | & element(v0, all_51_3) = 0 & $i(v0))
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (10) with all_51_5, all_59_0, all_51_4,
% 97.09/14.91 | | | | | | | all_51_3, simplifying with (38), (43), (44), (62),
% 97.09/14.91 | | | | | | | (146) gives:
% 97.09/14.91 | | | | | | | (156) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 97.09/14.91 | | | | | | | topstr_closure(all_51_5, all_59_0) = v1 & element(v1,
% 97.09/14.91 | | | | | | | all_51_3) = 0 & $i(v1)) | ( ~ (v0 = 0) &
% 97.09/14.91 | | | | | | | top_str(all_51_5) = v0))
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (17) with all_51_5, simplifying with
% 97.09/14.91 | | | | | | | (38), (57) gives:
% 97.09/14.91 | | | | | | | (157) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 97.09/14.91 | | | | | | | ? [v4: int] : ? [v5: int] : ($i(v3) & ((v4 = 0 & ~ (v5
% 97.09/14.91 | | | | | | | = 0) & the_carrier(all_51_5) = v1 & powerset(v1)
% 97.09/14.91 | | | | | | | = v2 & empty(v3) = v5 & element(v3, v2) = 0 &
% 97.09/14.91 | | | | | | | $i(v2) & $i(v1)) | (v0 = 0 &
% 97.09/14.91 | | | | | | | empty_carrier(all_51_5) = 0)))
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (1) with all_51_5, simplifying with
% 97.09/14.91 | | | | | | | (38), (57) gives:
% 97.09/14.91 | | | | | | | (158) ? [v0: int] : ? [v1: $i] : ? [v2: int] : (((v2 = 0 &
% 97.09/14.91 | | | | | | | the_carrier(all_51_5) = v1 & empty(v1) = 0 &
% 97.09/14.91 | | | | | | | $i(v1)) | ( ~ (v0 = 0) & empty_carrier(all_51_5) =
% 97.09/14.91 | | | | | | | v0)) & ((v0 = 0 & empty_carrier(all_51_5) = 0) | (
% 97.09/14.91 | | | | | | | ~ (v2 = 0) & the_carrier(all_51_5) = v1 & empty(v1)
% 97.09/14.91 | | | | | | | = v2 & $i(v1))))
% 97.09/14.91 | | | | | | |
% 97.09/14.91 | | | | | | | GROUND_INST: instantiating (12) with all_51_5, simplifying with
% 97.09/14.91 | | | | | | | (38), (57) gives:
% 97.09/14.92 | | | | | | | (159) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v0 = 0 &
% 97.09/14.92 | | | | | | | empty_carrier(all_51_5) = 0) | ( ~ (v2 = 0) &
% 97.09/14.92 | | | | | | | the_carrier(all_51_5) = v1 & empty(v1) = v2 &
% 97.09/14.92 | | | | | | | $i(v1)))
% 97.09/14.92 | | | | | | |
% 97.09/14.92 | | | | | | | GROUND_INST: instantiating (15) with all_51_5, simplifying with
% 97.09/14.92 | | | | | | | (38), (57) gives:
% 97.09/14.92 | | | | | | | (160) ? [v0: int] : ? [v1: $i] : ? [v2: $i] : ((v0 = 0 &
% 97.09/14.92 | | | | | | | empty_carrier(all_51_5) = 0) | (the_carrier(all_51_5)
% 97.09/14.92 | | | | | | | = v1 & powerset(v1) = v2 & $i(v2) & $i(v1) & ! [v3:
% 97.09/14.92 | | | | | | | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (
% 97.09/14.92 | | | | | | | ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v4)
% 97.09/14.92 | | | | | | | = v6) | ~ $i(v5) | ~ $i(v3) | ? [v7: int] : ?
% 97.09/14.92 | | | | | | | [v8: int] : (( ~ (v7 = 0) & element(v5, v1) = v7) |
% 97.09/14.92 | | | | | | | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 =
% 97.09/14.92 | | | | | | | 0) | ( ~ (v8 = 0) & in(v5, v3) = v8)) & (v6
% 97.09/14.92 | | | | | | | = 0 | (v8 = 0 & in(v5, v3) = 0))))) & ! [v3:
% 97.09/14.92 | | | | | | | $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: any] : (
% 97.09/14.92 | | | | | | | ~ (subset_complement(v1, v3) = v4) | ~ (in(v5, v3)
% 97.09/14.92 | | | | | | | = v6) | ~ $i(v5) | ~ $i(v3) | ? [v7: int] : ?
% 97.09/14.92 | | | | | | | [v8: int] : (( ~ (v7 = 0) & element(v5, v1) = v7) |
% 97.09/14.92 | | | | | | | ( ~ (v7 = 0) & element(v3, v2) = v7) | (( ~ (v6 =
% 97.09/14.92 | | | | | | | 0) | ( ~ (v8 = 0) & in(v5, v4) = v8)) & (v6
% 97.09/14.92 | | | | | | | = 0 | (v8 = 0 & in(v5, v4) = 0))))) & ! [v3:
% 97.09/14.92 | | | | | | | $i] : ! [v4: $i] : ! [v5: $i] : ( ~
% 97.09/14.92 | | | | | | | (subset_complement(v1, v3) = v4) | ~ (element(v5,
% 97.09/14.92 | | | | | | | v1) = 0) | ~ $i(v5) | ~ $i(v3) | ? [v6: int]
% 97.09/14.92 | | | | | | | : ? [v7: int] : (( ~ (v6 = 0) & element(v3, v2) =
% 97.09/14.92 | | | | | | | v6) | (((v7 = 0 & in(v5, v3) = 0) | (v6 = 0 &
% 97.09/14.92 | | | | | | | in(v5, v4) = 0)) & (( ~ (v7 = 0) & in(v5,
% 97.09/14.92 | | | | | | | v3) = v7) | ( ~ (v6 = 0) & in(v5, v4) =
% 97.09/14.92 | | | | | | | v6))))) & ! [v3: $i] : ( ~ (element(v3,
% 97.09/14.92 | | | | | | | v2) = 0) | ~ $i(v3) | ? [v4: $i] :
% 97.09/14.92 | | | | | | | (subset_complement(v1, v3) = v4 & $i(v4) & ! [v5:
% 97.09/14.92 | | | | | | | $i] : ! [v6: any] : ( ~ (in(v5, v4) = v6) | ~
% 97.09/14.92 | | | | | | | $i(v5) | ? [v7: int] : ? [v8: int] : (( ~ (v7
% 97.09/14.92 | | | | | | | = 0) & element(v5, v1) = v7) | (( ~ (v6 =
% 97.09/14.92 | | | | | | | 0) | ( ~ (v8 = 0) & in(v5, v3) = v8)) &
% 97.09/14.92 | | | | | | | (v6 = 0 | (v8 = 0 & in(v5, v3) = 0))))) &
% 97.09/14.92 | | | | | | | ! [v5: $i] : ! [v6: any] : ( ~ (in(v5, v3) = v6)
% 97.09/14.92 | | | | | | | | ~ $i(v5) | ? [v7: int] : ? [v8: int] : ((
% 97.09/14.92 | | | | | | | ~ (v7 = 0) & element(v5, v1) = v7) | (( ~
% 97.09/14.92 | | | | | | | (v6 = 0) | ( ~ (v8 = 0) & in(v5, v4) =
% 97.09/14.92 | | | | | | | v8)) & (v6 = 0 | (v8 = 0 & in(v5, v4) =
% 97.09/14.92 | | | | | | | 0))))) & ! [v5: $i] : ( ~ (element(v5,
% 97.09/14.92 | | | | | | | v1) = 0) | ~ $i(v5) | ? [v6: int] : ?
% 97.09/14.92 | | | | | | | [v7: int] : (((v7 = 0 & in(v5, v3) = 0) | (v6 =
% 97.09/14.92 | | | | | | | 0 & in(v5, v4) = 0)) & (( ~ (v7 = 0) &
% 97.09/14.92 | | | | | | | in(v5, v3) = v7) | ( ~ (v6 = 0) & in(v5,
% 97.09/14.92 | | | | | | | v4) = v6))))))))
% 97.09/14.92 | | | | | | |
% 97.09/14.92 | | | | | | | GROUND_INST: instantiating (t54_subset_1) with all_51_4,
% 97.09/14.92 | | | | | | | all_251_1, all_173_1, all_51_1, simplifying with
% 97.09/14.92 | | | | | | | (39), (98), (100), (149), (151) gives:
% 97.09/14.92 | | | | | | | (161) ? [v0: $i] : ? [v1: int] : ? [v2: int] : (( ~ (v2 = 0)
% 97.09/14.92 | | | | | | | & in(all_251_1, all_173_1) = v2) | ( ~ (v1 = 0) &
% 97.09/14.92 | | | | | | | powerset(all_51_4) = v0 & element(all_173_1, v0) = v1
% 97.09/14.92 | | | | | | | & $i(v0)))
% 97.09/14.92 | | | | | | |
% 97.09/14.92 | | | | | | | GROUND_INST: instantiating (9) with all_51_4, all_173_1, all_51_1,
% 97.09/14.92 | | | | | | | simplifying with (39), (149), (151) gives:
% 97.34/14.92 | | | | | | | (162) ? [v0: $i] : ? [v1: int] : ? [v2: int] :
% 97.34/14.92 | | | | | | | (powerset(all_51_4) = v0 & $i(v0) & ((v2 = 0 &
% 97.34/14.92 | | | | | | | element(all_51_1, v0) = 0) | ( ~ (v1 = 0) &
% 97.34/14.92 | | | | | | | element(all_173_1, v0) = v1)))
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | GROUND_INST: instantiating (14) with all_51_4, all_173_1,
% 97.34/14.92 | | | | | | | all_51_1, simplifying with (39), (149), (151) gives:
% 97.34/14.92 | | | | | | | (163) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 =
% 97.34/14.92 | | | | | | | all_173_1 & subset_complement(all_51_4, all_51_1) =
% 97.34/14.92 | | | | | | | all_173_1) | ( ~ (v1 = 0) & powerset(all_51_4) = v0 &
% 97.34/14.92 | | | | | | | element(all_173_1, v0) = v1 & $i(v0)))
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | GROUND_INST: instantiating (76) with all_59_0, all_173_1,
% 97.34/14.92 | | | | | | | simplifying with (144), (146) gives:
% 97.34/14.92 | | | | | | | (164) ? [v0: int] : ? [v1: int] : ((v1 = 0 & subset(all_59_0,
% 97.34/14.92 | | | | | | | all_173_1) = 0) | ( ~ (v0 = 0) & element(all_59_0,
% 97.34/14.92 | | | | | | | all_127_0) = v0))
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | DELTA: instantiating (153) with fresh symbol all_338_0 gives:
% 97.34/14.92 | | | | | | | (165) ~ (all_338_0 = 0) & empty(all_51_4) = all_338_0
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | ALPHA: (165) implies:
% 97.34/14.92 | | | | | | | (166) ~ (all_338_0 = 0)
% 97.34/14.92 | | | | | | | (167) empty(all_51_4) = all_338_0
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | DELTA: instantiating (155) with fresh symbol all_350_0 gives:
% 97.34/14.92 | | | | | | | (168) subset_complement(all_51_4, all_51_1) = all_350_0 &
% 97.34/14.92 | | | | | | | element(all_350_0, all_51_3) = 0 & $i(all_350_0)
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | ALPHA: (168) implies:
% 97.34/14.92 | | | | | | | (169) element(all_350_0, all_51_3) = 0
% 97.34/14.92 | | | | | | | (170) subset_complement(all_51_4, all_51_1) = all_350_0
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | DELTA: instantiating (154) with fresh symbol all_354_0 gives:
% 97.34/14.92 | | | | | | | (171) subset_complement(all_51_4, all_354_0) = all_51_1 &
% 97.34/14.92 | | | | | | | subset_complement(all_51_4, all_51_1) = all_354_0 &
% 97.34/14.92 | | | | | | | $i(all_354_0)
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | ALPHA: (171) implies:
% 97.34/14.92 | | | | | | | (172) subset_complement(all_51_4, all_51_1) = all_354_0
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | DELTA: instantiating (164) with fresh symbols all_372_0, all_372_1
% 97.34/14.92 | | | | | | | gives:
% 97.34/14.92 | | | | | | | (173) (all_372_0 = 0 & subset(all_59_0, all_173_1) = 0) | ( ~
% 97.34/14.92 | | | | | | | (all_372_1 = 0) & element(all_59_0, all_127_0) =
% 97.34/14.92 | | | | | | | all_372_1)
% 97.34/14.92 | | | | | | |
% 97.34/14.92 | | | | | | | DELTA: instantiating (156) with fresh symbols all_381_0,
% 97.34/14.92 | | | | | | | all_381_1, all_381_2 gives:
% 97.34/14.93 | | | | | | | (174) (all_381_0 = 0 & topstr_closure(all_51_5, all_59_0) =
% 97.34/14.93 | | | | | | | all_381_1 & element(all_381_1, all_51_3) = 0 &
% 97.34/14.93 | | | | | | | $i(all_381_1)) | ( ~ (all_381_2 = 0) &
% 97.34/14.93 | | | | | | | top_str(all_51_5) = all_381_2)
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (163) with fresh symbols all_393_0,
% 97.34/14.93 | | | | | | | all_393_1, all_393_2 gives:
% 97.34/14.93 | | | | | | | (175) (all_393_0 = all_173_1 & subset_complement(all_51_4,
% 97.34/14.93 | | | | | | | all_51_1) = all_173_1) | ( ~ (all_393_1 = 0) &
% 97.34/14.93 | | | | | | | powerset(all_51_4) = all_393_2 & element(all_173_1,
% 97.34/14.93 | | | | | | | all_393_2) = all_393_1 & $i(all_393_2))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (162) with fresh symbols all_394_0,
% 97.34/14.93 | | | | | | | all_394_1, all_394_2 gives:
% 97.34/14.93 | | | | | | | (176) powerset(all_51_4) = all_394_2 & $i(all_394_2) &
% 97.34/14.93 | | | | | | | ((all_394_0 = 0 & element(all_51_1, all_394_2) = 0) | ( ~
% 97.34/14.93 | | | | | | | (all_394_1 = 0) & element(all_173_1, all_394_2) =
% 97.34/14.93 | | | | | | | all_394_1))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | ALPHA: (176) implies:
% 97.34/14.93 | | | | | | | (177) powerset(all_51_4) = all_394_2
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (159) with fresh symbols all_397_0,
% 97.34/14.93 | | | | | | | all_397_1, all_397_2 gives:
% 97.34/14.93 | | | | | | | (178) (all_397_2 = 0 & empty_carrier(all_51_5) = 0) | ( ~
% 97.34/14.93 | | | | | | | (all_397_0 = 0) & the_carrier(all_51_5) = all_397_1 &
% 97.34/14.93 | | | | | | | empty(all_397_1) = all_397_0 & $i(all_397_1))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (161) with fresh symbols all_398_0,
% 97.34/14.93 | | | | | | | all_398_1, all_398_2 gives:
% 97.34/14.93 | | | | | | | (179) ( ~ (all_398_0 = 0) & in(all_251_1, all_173_1) =
% 97.34/14.93 | | | | | | | all_398_0) | ( ~ (all_398_1 = 0) & powerset(all_51_4) =
% 97.34/14.93 | | | | | | | all_398_2 & element(all_173_1, all_398_2) = all_398_1 &
% 97.34/14.93 | | | | | | | $i(all_398_2))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (157) with fresh symbols all_507_0,
% 97.34/14.93 | | | | | | | all_507_1, all_507_2, all_507_3, all_507_4, all_507_5
% 97.34/14.93 | | | | | | | gives:
% 97.34/14.93 | | | | | | | (180) $i(all_507_2) & ((all_507_1 = 0 & ~ (all_507_0 = 0) &
% 97.34/14.93 | | | | | | | the_carrier(all_51_5) = all_507_4 &
% 97.34/14.93 | | | | | | | powerset(all_507_4) = all_507_3 & empty(all_507_2) =
% 97.34/14.93 | | | | | | | all_507_0 & element(all_507_2, all_507_3) = 0 &
% 97.34/14.93 | | | | | | | $i(all_507_3) & $i(all_507_4)) | (all_507_5 = 0 &
% 97.34/14.93 | | | | | | | empty_carrier(all_51_5) = 0))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | ALPHA: (180) implies:
% 97.34/14.93 | | | | | | | (181) (all_507_1 = 0 & ~ (all_507_0 = 0) &
% 97.34/14.93 | | | | | | | the_carrier(all_51_5) = all_507_4 & powerset(all_507_4)
% 97.34/14.93 | | | | | | | = all_507_3 & empty(all_507_2) = all_507_0 &
% 97.34/14.93 | | | | | | | element(all_507_2, all_507_3) = 0 & $i(all_507_3) &
% 97.34/14.93 | | | | | | | $i(all_507_4)) | (all_507_5 = 0 &
% 97.34/14.93 | | | | | | | empty_carrier(all_51_5) = 0)
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (158) with fresh symbols all_509_0,
% 97.34/14.93 | | | | | | | all_509_1, all_509_2 gives:
% 97.34/14.93 | | | | | | | (182) ((all_509_0 = 0 & the_carrier(all_51_5) = all_509_1 &
% 97.34/14.93 | | | | | | | empty(all_509_1) = 0 & $i(all_509_1)) | ( ~
% 97.34/14.93 | | | | | | | (all_509_2 = 0) & empty_carrier(all_51_5) =
% 97.34/14.93 | | | | | | | all_509_2)) & ((all_509_2 = 0 &
% 97.34/14.93 | | | | | | | empty_carrier(all_51_5) = 0) | ( ~ (all_509_0 = 0) &
% 97.34/14.93 | | | | | | | the_carrier(all_51_5) = all_509_1 & empty(all_509_1)
% 97.34/14.93 | | | | | | | = all_509_0 & $i(all_509_1)))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | ALPHA: (182) implies:
% 97.34/14.93 | | | | | | | (183) (all_509_2 = 0 & empty_carrier(all_51_5) = 0) | ( ~
% 97.34/14.93 | | | | | | | (all_509_0 = 0) & the_carrier(all_51_5) = all_509_1 &
% 97.34/14.93 | | | | | | | empty(all_509_1) = all_509_0 & $i(all_509_1))
% 97.34/14.93 | | | | | | | (184) (all_509_0 = 0 & the_carrier(all_51_5) = all_509_1 &
% 97.34/14.93 | | | | | | | empty(all_509_1) = 0 & $i(all_509_1)) | ( ~ (all_509_2
% 97.34/14.93 | | | | | | | = 0) & empty_carrier(all_51_5) = all_509_2)
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | DELTA: instantiating (160) with fresh symbols all_571_0,
% 97.34/14.93 | | | | | | | all_571_1, all_571_2 gives:
% 97.34/14.93 | | | | | | | (185) (all_571_2 = 0 & empty_carrier(all_51_5) = 0) |
% 97.34/14.93 | | | | | | | (the_carrier(all_51_5) = all_571_1 & powerset(all_571_1)
% 97.34/14.93 | | | | | | | = all_571_0 & $i(all_571_0) & $i(all_571_1) & ! [v0:
% 97.34/14.93 | | | | | | | $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 97.34/14.93 | | | | | | | (subset_complement(all_571_1, v0) = v1) | ~ (in(v2,
% 97.34/14.93 | | | | | | | v1) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int]
% 97.34/14.93 | | | | | | | : ? [v5: int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.93 | | | | | | | all_571_1) = v4) | ( ~ (v4 = 0) & element(v0,
% 97.34/14.93 | | | | | | | all_571_0) = v4) | (( ~ (v3 = 0) | ( ~ (v5 = 0)
% 97.34/14.93 | | | | | | | & in(v2, v0) = v5)) & (v3 = 0 | (v5 = 0 &
% 97.34/14.93 | | | | | | | in(v2, v0) = 0))))) & ! [v0: $i] : ! [v1:
% 97.34/14.93 | | | | | | | $i] : ! [v2: $i] : ! [v3: any] : ( ~
% 97.34/14.93 | | | | | | | (subset_complement(all_571_1, v0) = v1) | ~ (in(v2,
% 97.34/14.93 | | | | | | | v0) = v3) | ~ $i(v2) | ~ $i(v0) | ? [v4: int]
% 97.34/14.93 | | | | | | | : ? [v5: int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.93 | | | | | | | all_571_1) = v4) | ( ~ (v4 = 0) & element(v0,
% 97.34/14.93 | | | | | | | all_571_0) = v4) | (( ~ (v3 = 0) | ( ~ (v5 = 0)
% 97.34/14.93 | | | | | | | & in(v2, v1) = v5)) & (v3 = 0 | (v5 = 0 &
% 97.34/14.93 | | | | | | | in(v2, v1) = 0))))) & ! [v0: $i] : ! [v1:
% 97.34/14.93 | | | | | | | $i] : ! [v2: $i] : ( ~ (subset_complement(all_571_1,
% 97.34/14.93 | | | | | | | v0) = v1) | ~ (element(v2, all_571_1) = 0) | ~
% 97.34/14.93 | | | | | | | $i(v2) | ~ $i(v0) | ? [v3: int] : ? [v4: int] : ((
% 97.34/14.93 | | | | | | | ~ (v3 = 0) & element(v0, all_571_0) = v3) | (((v4
% 97.34/14.93 | | | | | | | = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1)
% 97.34/14.93 | | | | | | | = 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | (
% 97.34/14.93 | | | | | | | ~ (v3 = 0) & in(v2, v1) = v3))))) & ! [v0:
% 97.34/14.93 | | | | | | | $i] : ( ~ (element(v0, all_571_0) = 0) | ~ $i(v0) |
% 97.34/14.93 | | | | | | | ? [v1: $i] : (subset_complement(all_571_1, v0) = v1 &
% 97.34/14.93 | | | | | | | $i(v1) & ! [v2: $i] : ! [v3: any] : ( ~ (in(v2,
% 97.34/14.93 | | | | | | | v1) = v3) | ~ $i(v2) | ? [v4: int] : ?
% 97.34/14.93 | | | | | | | [v5: int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.93 | | | | | | | all_571_1) = v4) | (( ~ (v3 = 0) | ( ~ (v5
% 97.34/14.93 | | | | | | | = 0) & in(v2, v0) = v5)) & (v3 = 0 |
% 97.34/14.93 | | | | | | | (v5 = 0 & in(v2, v0) = 0))))) & ! [v2: $i]
% 97.34/14.93 | | | | | | | : ! [v3: any] : ( ~ (in(v2, v0) = v3) | ~ $i(v2)
% 97.34/14.93 | | | | | | | | ? [v4: int] : ? [v5: int] : (( ~ (v4 = 0) &
% 97.34/14.93 | | | | | | | element(v2, all_571_1) = v4) | (( ~ (v3 = 0)
% 97.34/14.93 | | | | | | | | ( ~ (v5 = 0) & in(v2, v1) = v5)) & (v3 =
% 97.34/14.93 | | | | | | | 0 | (v5 = 0 & in(v2, v1) = 0))))) & ! [v2:
% 97.34/14.93 | | | | | | | $i] : ( ~ (element(v2, all_571_1) = 0) | ~
% 97.34/14.93 | | | | | | | $i(v2) | ? [v3: int] : ? [v4: int] : (((v4 = 0
% 97.34/14.93 | | | | | | | & in(v2, v0) = 0) | (v3 = 0 & in(v2, v1) =
% 97.34/14.93 | | | | | | | 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4) | (
% 97.34/14.93 | | | | | | | ~ (v3 = 0) & in(v2, v1) = v3)))))))
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | BETA: splitting (66) gives:
% 97.34/14.93 | | | | | | |
% 97.34/14.93 | | | | | | | Case 1:
% 97.34/14.93 | | | | | | | |
% 97.34/14.93 | | | | | | | | (186) ~ (all_90_2 = 0) & one_sorted_str(all_51_5) = all_90_2
% 97.34/14.93 | | | | | | | |
% 97.34/14.93 | | | | | | | | ALPHA: (186) implies:
% 97.34/14.93 | | | | | | | | (187) ~ (all_90_2 = 0)
% 97.34/14.93 | | | | | | | | (188) one_sorted_str(all_51_5) = all_90_2
% 97.34/14.93 | | | | | | | |
% 97.34/14.93 | | | | | | | | GROUND_INST: instantiating (26) with 0, all_90_2, all_51_5,
% 97.34/14.93 | | | | | | | | simplifying with (57), (188) gives:
% 97.34/14.94 | | | | | | | | (189) all_90_2 = 0
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | | REDUCE: (187), (189) imply:
% 97.34/14.94 | | | | | | | | (190) $false
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | | CLOSE: (190) is inconsistent.
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | Case 2:
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | | (191) ((all_90_0 = 0 & empty(all_51_4) = 0) | ( ~ (all_90_1 =
% 97.34/14.94 | | | | | | | | 0) & empty_carrier(all_51_5) = all_90_1)) &
% 97.34/14.94 | | | | | | | | ((all_90_1 = 0 & empty_carrier(all_51_5) = 0) | ( ~
% 97.34/14.94 | | | | | | | | (all_90_0 = 0) & empty(all_51_4) = all_90_0))
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | | ALPHA: (191) implies:
% 97.34/14.94 | | | | | | | | (192) (all_90_0 = 0 & empty(all_51_4) = 0) | ( ~ (all_90_1 =
% 97.34/14.94 | | | | | | | | 0) & empty_carrier(all_51_5) = all_90_1)
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | | BETA: splitting (173) gives:
% 97.34/14.94 | | | | | | | |
% 97.34/14.94 | | | | | | | | Case 1:
% 97.34/14.94 | | | | | | | | |
% 97.34/14.94 | | | | | | | | | (193) all_372_0 = 0 & subset(all_59_0, all_173_1) = 0
% 97.34/14.94 | | | | | | | | |
% 97.34/14.94 | | | | | | | | | ALPHA: (193) implies:
% 97.34/14.94 | | | | | | | | | (194) subset(all_59_0, all_173_1) = 0
% 97.34/14.94 | | | | | | | | |
% 97.34/14.94 | | | | | | | | | BETA: splitting (174) gives:
% 97.34/14.94 | | | | | | | | |
% 97.34/14.94 | | | | | | | | | Case 1:
% 97.34/14.94 | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | (195) all_381_0 = 0 & topstr_closure(all_51_5, all_59_0)
% 97.34/14.94 | | | | | | | | | | = all_381_1 & element(all_381_1, all_51_3) = 0 &
% 97.34/14.94 | | | | | | | | | | $i(all_381_1)
% 97.34/14.94 | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | ALPHA: (195) implies:
% 97.34/14.94 | | | | | | | | | | (196) $i(all_381_1)
% 97.34/14.94 | | | | | | | | | | (197) element(all_381_1, all_51_3) = 0
% 97.34/14.94 | | | | | | | | | | (198) topstr_closure(all_51_5, all_59_0) = all_381_1
% 97.34/14.94 | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | BETA: splitting (184) gives:
% 97.34/14.94 | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | Case 1:
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | (199) all_509_0 = 0 & the_carrier(all_51_5) = all_509_1
% 97.34/14.94 | | | | | | | | | | | & empty(all_509_1) = 0 & $i(all_509_1)
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | ALPHA: (199) implies:
% 97.34/14.94 | | | | | | | | | | | (200) all_509_0 = 0
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | BETA: splitting (192) gives:
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | Case 1:
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | (201) all_90_0 = 0 & empty(all_51_4) = 0
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | ALPHA: (201) implies:
% 97.34/14.94 | | | | | | | | | | | | (202) empty(all_51_4) = 0
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | REF_CLOSE: (23), (166), (167), (202) are inconsistent by
% 97.34/14.94 | | | | | | | | | | | | sub-proof #4.
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | Case 2:
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | (203) ~ (all_90_1 = 0) & empty_carrier(all_51_5) =
% 97.34/14.94 | | | | | | | | | | | | all_90_1
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | ALPHA: (203) implies:
% 97.34/14.94 | | | | | | | | | | | | (204) ~ (all_90_1 = 0)
% 97.34/14.94 | | | | | | | | | | | | (205) empty_carrier(all_51_5) = all_90_1
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | BETA: splitting (183) gives:
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | Case 1:
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | (206) all_509_2 = 0 & empty_carrier(all_51_5) = 0
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | ALPHA: (206) implies:
% 97.34/14.94 | | | | | | | | | | | | | (207) empty_carrier(all_51_5) = 0
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_90_1, all_51_5,
% 97.34/14.94 | | | | | | | | | | | | | simplifying with (205), (207) gives:
% 97.34/14.94 | | | | | | | | | | | | | (208) all_90_1 = 0
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | REDUCE: (204), (208) imply:
% 97.34/14.94 | | | | | | | | | | | | | (209) $false
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | Case 2:
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | (210) ~ (all_509_0 = 0) & the_carrier(all_51_5) =
% 97.34/14.94 | | | | | | | | | | | | | all_509_1 & empty(all_509_1) = all_509_0 &
% 97.34/14.94 | | | | | | | | | | | | | $i(all_509_1)
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | ALPHA: (210) implies:
% 97.34/14.94 | | | | | | | | | | | | | (211) ~ (all_509_0 = 0)
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | REDUCE: (200), (211) imply:
% 97.34/14.94 | | | | | | | | | | | | | (212) $false
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | | CLOSE: (212) is inconsistent.
% 97.34/14.94 | | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | End of split
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | End of split
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | Case 2:
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | (213) ~ (all_509_2 = 0) & empty_carrier(all_51_5) =
% 97.34/14.94 | | | | | | | | | | | all_509_2
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | ALPHA: (213) implies:
% 97.34/14.94 | | | | | | | | | | | (214) empty_carrier(all_51_5) = all_509_2
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | BETA: splitting (84) gives:
% 97.34/14.94 | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | Case 1:
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | (215) all_166_2 = 0 & empty_carrier(all_51_5) = 0
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | ALPHA: (215) implies:
% 97.34/14.94 | | | | | | | | | | | | (216) empty_carrier(all_51_5) = 0
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | | REF_CLOSE: (23), (25), (166), (167), (192), (214), (216) are
% 97.34/14.94 | | | | | | | | | | | | inconsistent by sub-proof #2.
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.94 | | | | | | | | | | | Case 2:
% 97.34/14.94 | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | (217) ( ~ (all_166_1 = 0) & one_sorted_str(all_51_5) =
% 97.34/14.95 | | | | | | | | | | | | all_166_1) | (powerset(all_51_4) = all_166_0 &
% 97.34/14.95 | | | | | | | | | | | | $i(all_166_0) & ! [v0: $i] : ! [v1: $i] : !
% 97.34/14.95 | | | | | | | | | | | | [v2: $i] : ! [v3: any] : ( ~
% 97.34/14.95 | | | | | | | | | | | | (subset_complement(all_51_4, v0) = v1) | ~
% 97.34/14.95 | | | | | | | | | | | | (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v0) | ?
% 97.34/14.95 | | | | | | | | | | | | [v4: int] : ? [v5: int] : (( ~ (v4 = 0) &
% 97.34/14.95 | | | | | | | | | | | | element(v2, all_51_4) = v4) | ( ~ (v4 = 0)
% 97.34/14.95 | | | | | | | | | | | | & element(v0, all_166_0) = v4) | (( ~ (v3
% 97.34/14.95 | | | | | | | | | | | | = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 97.34/14.95 | | | | | | | | | | | | v5)) & (v3 = 0 | (v5 = 0 & in(v2, v0)
% 97.34/14.95 | | | | | | | | | | | | = 0))))) & ! [v0: $i] : ! [v1: $i] :
% 97.34/14.95 | | | | | | | | | | | | ! [v2: $i] : ! [v3: any] : ( ~
% 97.34/14.95 | | | | | | | | | | | | (subset_complement(all_51_4, v0) = v1) | ~
% 97.34/14.95 | | | | | | | | | | | | (in(v2, v0) = v3) | ~ $i(v2) | ~ $i(v0) | ?
% 97.34/14.95 | | | | | | | | | | | | [v4: int] : ? [v5: int] : (( ~ (v4 = 0) &
% 97.34/14.95 | | | | | | | | | | | | element(v2, all_51_4) = v4) | ( ~ (v4 = 0)
% 97.34/14.95 | | | | | | | | | | | | & element(v0, all_166_0) = v4) | (( ~ (v3
% 97.34/14.95 | | | | | | | | | | | | = 0) | ( ~ (v5 = 0) & in(v2, v1) =
% 97.34/14.95 | | | | | | | | | | | | v5)) & (v3 = 0 | (v5 = 0 & in(v2, v1)
% 97.34/14.95 | | | | | | | | | | | | = 0))))) & ! [v0: $i] : ! [v1: $i] :
% 97.34/14.95 | | | | | | | | | | | | ! [v2: $i] : ( ~ (subset_complement(all_51_4,
% 97.34/14.95 | | | | | | | | | | | | v0) = v1) | ~ (element(v2, all_51_4) = 0)
% 97.34/14.95 | | | | | | | | | | | | | ~ $i(v2) | ~ $i(v0) | ? [v3: int] : ?
% 97.34/14.95 | | | | | | | | | | | | [v4: int] : (( ~ (v3 = 0) & element(v0,
% 97.34/14.95 | | | | | | | | | | | | all_166_0) = v3) | (((v4 = 0 & in(v2,
% 97.34/14.95 | | | | | | | | | | | | v0) = 0) | (v3 = 0 & in(v2, v1) =
% 97.34/14.95 | | | | | | | | | | | | 0)) & (( ~ (v4 = 0) & in(v2, v0) = v4)
% 97.34/14.95 | | | | | | | | | | | | | ( ~ (v3 = 0) & in(v2, v1) = v3))))) &
% 97.34/14.95 | | | | | | | | | | | | ! [v0: $i] : ( ~ (element(v0, all_166_0) = 0) |
% 97.34/14.95 | | | | | | | | | | | | ~ $i(v0) | ? [v1: $i] :
% 97.34/14.95 | | | | | | | | | | | | (subset_complement(all_51_4, v0) = v1 & $i(v1)
% 97.34/14.95 | | | | | | | | | | | | & ! [v2: $i] : ! [v3: any] : ( ~ (in(v2,
% 97.34/14.95 | | | | | | | | | | | | v1) = v3) | ~ $i(v2) | ? [v4: int] :
% 97.34/14.95 | | | | | | | | | | | | ? [v5: int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.95 | | | | | | | | | | | | all_51_4) = v4) | (( ~ (v3 = 0) | (
% 97.34/14.95 | | | | | | | | | | | | ~ (v5 = 0) & in(v2, v0) = v5)) &
% 97.34/14.95 | | | | | | | | | | | | (v3 = 0 | (v5 = 0 & in(v2, v0) =
% 97.34/14.95 | | | | | | | | | | | | 0))))) & ! [v2: $i] : ! [v3:
% 97.34/14.95 | | | | | | | | | | | | any] : ( ~ (in(v2, v0) = v3) | ~ $i(v2) |
% 97.34/14.95 | | | | | | | | | | | | ? [v4: int] : ? [v5: int] : (( ~ (v4 =
% 97.34/14.95 | | | | | | | | | | | | 0) & element(v2, all_51_4) = v4) |
% 97.34/14.95 | | | | | | | | | | | | (( ~ (v3 = 0) | ( ~ (v5 = 0) & in(v2,
% 97.34/14.95 | | | | | | | | | | | | v1) = v5)) & (v3 = 0 | (v5 = 0 &
% 97.34/14.95 | | | | | | | | | | | | in(v2, v1) = 0))))) & ! [v2: $i]
% 97.34/14.95 | | | | | | | | | | | | : ( ~ (element(v2, all_51_4) = 0) | ~
% 97.34/14.95 | | | | | | | | | | | | $i(v2) | ? [v3: int] : ? [v4: int] :
% 97.34/14.95 | | | | | | | | | | | | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 &
% 97.34/14.95 | | | | | | | | | | | | in(v2, v1) = 0)) & (( ~ (v4 = 0) &
% 97.34/14.95 | | | | | | | | | | | | in(v2, v0) = v4) | ( ~ (v3 = 0) &
% 97.34/14.95 | | | | | | | | | | | | in(v2, v1) = v3)))))))
% 97.34/14.95 | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | BETA: splitting (217) gives:
% 97.34/14.95 | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | Case 1:
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | (218) ~ (all_166_1 = 0) & one_sorted_str(all_51_5) =
% 97.34/14.95 | | | | | | | | | | | | | all_166_1
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | ALPHA: (218) implies:
% 97.34/14.95 | | | | | | | | | | | | | (219) ~ (all_166_1 = 0)
% 97.34/14.95 | | | | | | | | | | | | | (220) one_sorted_str(all_51_5) = all_166_1
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_166_1, all_51_5,
% 97.34/14.95 | | | | | | | | | | | | | simplifying with (57), (220) gives:
% 97.34/14.95 | | | | | | | | | | | | | (221) all_166_1 = 0
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | REDUCE: (219), (221) imply:
% 97.34/14.95 | | | | | | | | | | | | | (222) $false
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | CLOSE: (222) is inconsistent.
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | Case 2:
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | (223) powerset(all_51_4) = all_166_0 & $i(all_166_0) &
% 97.34/14.95 | | | | | | | | | | | | | ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 97.34/14.95 | | | | | | | | | | | | | any] : ( ~ (subset_complement(all_51_4, v0) =
% 97.34/14.95 | | | | | | | | | | | | | v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~
% 97.34/14.95 | | | | | | | | | | | | | $i(v0) | ? [v4: int] : ? [v5: int] : (( ~ (v4
% 97.34/14.95 | | | | | | | | | | | | | = 0) & element(v2, all_51_4) = v4) | ( ~
% 97.34/14.95 | | | | | | | | | | | | | (v4 = 0) & element(v0, all_166_0) = v4) | ((
% 97.34/14.95 | | | | | | | | | | | | | ~ (v3 = 0) | ( ~ (v5 = 0) & in(v2, v0) =
% 97.34/14.95 | | | | | | | | | | | | | v5)) & (v3 = 0 | (v5 = 0 & in(v2, v0) =
% 97.34/14.95 | | | | | | | | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : !
% 97.34/14.95 | | | | | | | | | | | | | [v2: $i] : ! [v3: any] : ( ~
% 97.34/14.95 | | | | | | | | | | | | | (subset_complement(all_51_4, v0) = v1) | ~
% 97.34/14.95 | | | | | | | | | | | | | (in(v2, v0) = v3) | ~ $i(v2) | ~ $i(v0) | ?
% 97.34/14.95 | | | | | | | | | | | | | [v4: int] : ? [v5: int] : (( ~ (v4 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | element(v2, all_51_4) = v4) | ( ~ (v4 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | element(v0, all_166_0) = v4) | (( ~ (v3 = 0)
% 97.34/14.95 | | | | | | | | | | | | | | ( ~ (v5 = 0) & in(v2, v1) = v5)) & (v3 =
% 97.34/14.95 | | | | | | | | | | | | | 0 | (v5 = 0 & in(v2, v1) = 0))))) & !
% 97.34/14.95 | | | | | | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 97.34/14.95 | | | | | | | | | | | | | (subset_complement(all_51_4, v0) = v1) | ~
% 97.34/14.95 | | | | | | | | | | | | | (element(v2, all_51_4) = 0) | ~ $i(v2) | ~
% 97.34/14.95 | | | | | | | | | | | | | $i(v0) | ? [v3: int] : ? [v4: int] : (( ~ (v3
% 97.34/14.95 | | | | | | | | | | | | | = 0) & element(v0, all_166_0) = v3) |
% 97.34/14.95 | | | | | | | | | | | | | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2,
% 97.34/14.95 | | | | | | | | | | | | | v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0)
% 97.34/14.95 | | | | | | | | | | | | | = v4) | ( ~ (v3 = 0) & in(v2, v1) =
% 97.34/14.95 | | | | | | | | | | | | | v3))))) & ! [v0: $i] : ( ~ (element(v0,
% 97.34/14.95 | | | | | | | | | | | | | all_166_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 97.34/14.95 | | | | | | | | | | | | | (subset_complement(all_51_4, v0) = v1 & $i(v1) &
% 97.34/14.95 | | | | | | | | | | | | | ! [v2: $i] : ! [v3: any] : ( ~ (in(v2, v1) =
% 97.34/14.95 | | | | | | | | | | | | | v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 97.34/14.95 | | | | | | | | | | | | | int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.95 | | | | | | | | | | | | | all_51_4) = v4) | (( ~ (v3 = 0) | ( ~
% 97.34/14.95 | | | | | | | | | | | | | (v5 = 0) & in(v2, v0) = v5)) & (v3 =
% 97.34/14.95 | | | | | | | | | | | | | 0 | (v5 = 0 & in(v2, v0) = 0))))) & !
% 97.34/14.95 | | | | | | | | | | | | | [v2: $i] : ! [v3: any] : ( ~ (in(v2, v0) =
% 97.34/14.95 | | | | | | | | | | | | | v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 97.34/14.95 | | | | | | | | | | | | | int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.95 | | | | | | | | | | | | | all_51_4) = v4) | (( ~ (v3 = 0) | ( ~
% 97.34/14.95 | | | | | | | | | | | | | (v5 = 0) & in(v2, v1) = v5)) & (v3 =
% 97.34/14.95 | | | | | | | | | | | | | 0 | (v5 = 0 & in(v2, v1) = 0))))) & !
% 97.34/14.95 | | | | | | | | | | | | | [v2: $i] : ( ~ (element(v2, all_51_4) = 0) |
% 97.34/14.95 | | | | | | | | | | | | | ~ $i(v2) | ? [v3: int] : ? [v4: int] :
% 97.34/14.95 | | | | | | | | | | | | | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 &
% 97.34/14.95 | | | | | | | | | | | | | in(v2, v1) = 0)) & (( ~ (v4 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | in(v2, v0) = v4) | ( ~ (v3 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | in(v2, v1) = v3))))))
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | ALPHA: (223) implies:
% 97.34/14.95 | | | | | | | | | | | | | (224) powerset(all_51_4) = all_166_0
% 97.34/14.95 | | | | | | | | | | | | | (225) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 97.34/14.95 | | | | | | | | | | | | | any] : ( ~ (subset_complement(all_51_4, v0) =
% 97.34/14.95 | | | | | | | | | | | | | v1) | ~ (in(v2, v0) = v3) | ~ $i(v2) | ~
% 97.34/14.95 | | | | | | | | | | | | | $i(v0) | ? [v4: int] : ? [v5: int] : (( ~ (v4
% 97.34/14.95 | | | | | | | | | | | | | = 0) & element(v2, all_51_4) = v4) | ( ~
% 97.34/14.95 | | | | | | | | | | | | | (v4 = 0) & element(v0, all_166_0) = v4) | ((
% 97.34/14.95 | | | | | | | | | | | | | ~ (v3 = 0) | ( ~ (v5 = 0) & in(v2, v1) =
% 97.34/14.95 | | | | | | | | | | | | | v5)) & (v3 = 0 | (v5 = 0 & in(v2, v1) =
% 97.34/14.95 | | | | | | | | | | | | | 0)))))
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | GROUND_INST: instantiating (225) with all_51_2, all_59_0,
% 97.34/14.95 | | | | | | | | | | | | | all_251_1, all_251_0, simplifying with (40), (63),
% 97.34/14.95 | | | | | | | | | | | | | (98), (99) gives:
% 97.34/14.95 | | | | | | | | | | | | | (226) ? [v0: int] : ? [v1: int] : (( ~ (v0 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | element(all_251_1, all_51_4) = v0) | ( ~ (v0 =
% 97.34/14.95 | | | | | | | | | | | | | 0) & element(all_51_2, all_166_0) = v0) | ((
% 97.34/14.95 | | | | | | | | | | | | | ~ (all_251_0 = 0) | ( ~ (v1 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | in(all_251_1, all_59_0) = v1)) &
% 97.34/14.95 | | | | | | | | | | | | | (all_251_0 = 0 | (v1 = 0 & in(all_251_1,
% 97.34/14.95 | | | | | | | | | | | | | all_59_0) = 0))))
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | DELTA: instantiating (226) with fresh symbols all_664_0,
% 97.34/14.95 | | | | | | | | | | | | | all_664_1 gives:
% 97.34/14.95 | | | | | | | | | | | | | (227) ( ~ (all_664_1 = 0) & element(all_251_1, all_51_4)
% 97.34/14.95 | | | | | | | | | | | | | = all_664_1) | ( ~ (all_664_1 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | element(all_51_2, all_166_0) = all_664_1) | (( ~
% 97.34/14.95 | | | | | | | | | | | | | (all_251_0 = 0) | ( ~ (all_664_0 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | in(all_251_1, all_59_0) = all_664_0)) &
% 97.34/14.95 | | | | | | | | | | | | | (all_251_0 = 0 | (all_664_0 = 0 & in(all_251_1,
% 97.34/14.95 | | | | | | | | | | | | | all_59_0) = 0)))
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | BETA: splitting (68) gives:
% 97.34/14.95 | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | Case 1:
% 97.34/14.95 | | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | | (228) all_107_1 = 0 & ~ (all_107_0 = 0) &
% 97.34/14.95 | | | | | | | | | | | | | | powerset(all_51_4) = all_107_3 & empty(all_107_2)
% 97.34/14.95 | | | | | | | | | | | | | | = all_107_0 & element(all_107_2, all_107_3) = 0 &
% 97.34/14.95 | | | | | | | | | | | | | | $i(all_107_3)
% 97.34/14.95 | | | | | | | | | | | | | |
% 97.34/14.95 | | | | | | | | | | | | | | ALPHA: (228) implies:
% 97.34/14.96 | | | | | | | | | | | | | | (229) powerset(all_51_4) = all_107_3
% 97.34/14.96 | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 97.34/14.96 | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | Case 1:
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | (230) all_90_0 = 0 & empty(all_51_4) = 0
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 97.34/14.96 | | | | | | | | | | | | | | | (231) empty(all_51_4) = 0
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | REF_CLOSE: (23), (166), (167), (231) are inconsistent by
% 97.34/14.96 | | | | | | | | | | | | | | | sub-proof #4.
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | Case 2:
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | (232) ~ (all_90_1 = 0) & empty_carrier(all_51_5) =
% 97.34/14.96 | | | | | | | | | | | | | | | all_90_1
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 97.34/14.96 | | | | | | | | | | | | | | | (233) ~ (all_90_1 = 0)
% 97.34/14.96 | | | | | | | | | | | | | | | (234) empty_carrier(all_51_5) = all_90_1
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 97.34/14.96 | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | Case 1:
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | (235) all_571_2 = 0 & empty_carrier(all_51_5) = 0
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 97.34/14.96 | | | | | | | | | | | | | | | | (236) empty_carrier(all_51_5) = 0
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | REF_CLOSE: (25), (214), (233), (234), (236) are inconsistent
% 97.34/14.96 | | | | | | | | | | | | | | | | by sub-proof #3.
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | Case 2:
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | (237) the_carrier(all_51_5) = all_571_1 &
% 97.34/14.96 | | | | | | | | | | | | | | | | powerset(all_571_1) = all_571_0 & $i(all_571_0) &
% 97.34/14.96 | | | | | | | | | | | | | | | | $i(all_571_1) & ! [v0: $i] : ! [v1: $i] : !
% 97.34/14.96 | | | | | | | | | | | | | | | | [v2: $i] : ! [v3: any] : ( ~
% 97.34/14.96 | | | | | | | | | | | | | | | | (subset_complement(all_571_1, v0) = v1) | ~
% 97.34/14.96 | | | | | | | | | | | | | | | | (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v0) | ?
% 97.34/14.96 | | | | | | | | | | | | | | | | [v4: int] : ? [v5: int] : (( ~ (v4 = 0) &
% 97.34/14.96 | | | | | | | | | | | | | | | | element(v2, all_571_1) = v4) | ( ~ (v4 = 0)
% 97.34/14.96 | | | | | | | | | | | | | | | | & element(v0, all_571_0) = v4) | (( ~ (v3 =
% 97.34/14.96 | | | | | | | | | | | | | | | | 0) | ( ~ (v5 = 0) & in(v2, v0) = v5)) &
% 97.34/14.96 | | | | | | | | | | | | | | | | (v3 = 0 | (v5 = 0 & in(v2, v0) = 0))))) & !
% 97.34/14.96 | | | | | | | | | | | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 97.34/14.96 | | | | | | | | | | | | | | | | any] : ( ~ (subset_complement(all_571_1, v0) =
% 97.34/14.96 | | | | | | | | | | | | | | | | v1) | ~ (in(v2, v0) = v3) | ~ $i(v2) | ~
% 97.34/14.96 | | | | | | | | | | | | | | | | $i(v0) | ? [v4: int] : ? [v5: int] : (( ~ (v4
% 97.34/14.96 | | | | | | | | | | | | | | | | = 0) & element(v2, all_571_1) = v4) | ( ~
% 97.34/14.96 | | | | | | | | | | | | | | | | (v4 = 0) & element(v0, all_571_0) = v4) | ((
% 97.34/14.96 | | | | | | | | | | | | | | | | ~ (v3 = 0) | ( ~ (v5 = 0) & in(v2, v1) =
% 97.34/14.96 | | | | | | | | | | | | | | | | v5)) & (v3 = 0 | (v5 = 0 & in(v2, v1) =
% 97.34/14.96 | | | | | | | | | | | | | | | | 0))))) & ! [v0: $i] : ! [v1: $i] : !
% 97.34/14.96 | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (subset_complement(all_571_1, v0) =
% 97.34/14.96 | | | | | | | | | | | | | | | | v1) | ~ (element(v2, all_571_1) = 0) | ~
% 97.34/14.96 | | | | | | | | | | | | | | | | $i(v2) | ~ $i(v0) | ? [v3: int] : ? [v4: int]
% 97.34/14.96 | | | | | | | | | | | | | | | | : (( ~ (v3 = 0) & element(v0, all_571_0) = v3) |
% 97.34/14.96 | | | | | | | | | | | | | | | | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 & in(v2,
% 97.34/14.96 | | | | | | | | | | | | | | | | v1) = 0)) & (( ~ (v4 = 0) & in(v2, v0)
% 97.34/14.96 | | | | | | | | | | | | | | | | = v4) | ( ~ (v3 = 0) & in(v2, v1) =
% 97.34/14.96 | | | | | | | | | | | | | | | | v3))))) & ! [v0: $i] : ( ~ (element(v0,
% 97.34/14.96 | | | | | | | | | | | | | | | | all_571_0) = 0) | ~ $i(v0) | ? [v1: $i] :
% 97.34/14.96 | | | | | | | | | | | | | | | | (subset_complement(all_571_1, v0) = v1 & $i(v1)
% 97.34/14.96 | | | | | | | | | | | | | | | | & ! [v2: $i] : ! [v3: any] : ( ~ (in(v2, v1)
% 97.34/14.96 | | | | | | | | | | | | | | | | = v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 97.34/14.96 | | | | | | | | | | | | | | | | int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.96 | | | | | | | | | | | | | | | | all_571_1) = v4) | (( ~ (v3 = 0) | ( ~
% 97.34/14.96 | | | | | | | | | | | | | | | | (v5 = 0) & in(v2, v0) = v5)) & (v3 =
% 97.34/14.96 | | | | | | | | | | | | | | | | 0 | (v5 = 0 & in(v2, v0) = 0))))) & !
% 97.34/14.96 | | | | | | | | | | | | | | | | [v2: $i] : ! [v3: any] : ( ~ (in(v2, v0) =
% 97.34/14.96 | | | | | | | | | | | | | | | | v3) | ~ $i(v2) | ? [v4: int] : ? [v5:
% 97.34/14.96 | | | | | | | | | | | | | | | | int] : (( ~ (v4 = 0) & element(v2,
% 97.34/14.96 | | | | | | | | | | | | | | | | all_571_1) = v4) | (( ~ (v3 = 0) | ( ~
% 97.34/14.96 | | | | | | | | | | | | | | | | (v5 = 0) & in(v2, v1) = v5)) & (v3 =
% 97.34/14.96 | | | | | | | | | | | | | | | | 0 | (v5 = 0 & in(v2, v1) = 0))))) & !
% 97.34/14.96 | | | | | | | | | | | | | | | | [v2: $i] : ( ~ (element(v2, all_571_1) = 0) |
% 97.34/14.96 | | | | | | | | | | | | | | | | ~ $i(v2) | ? [v3: int] : ? [v4: int] :
% 97.34/14.96 | | | | | | | | | | | | | | | | (((v4 = 0 & in(v2, v0) = 0) | (v3 = 0 &
% 97.34/14.96 | | | | | | | | | | | | | | | | in(v2, v1) = 0)) & (( ~ (v4 = 0) &
% 97.34/14.96 | | | | | | | | | | | | | | | | in(v2, v0) = v4) | ( ~ (v3 = 0) &
% 97.34/14.96 | | | | | | | | | | | | | | | | in(v2, v1) = v3))))))
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | ALPHA: (237) implies:
% 97.34/14.96 | | | | | | | | | | | | | | | | (238) powerset(all_571_1) = all_571_0
% 97.34/14.96 | | | | | | | | | | | | | | | | (239) the_carrier(all_51_5) = all_571_1
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 97.34/14.96 | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | Case 1:
% 97.34/14.96 | | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | | (240) all_507_1 = 0 & ~ (all_507_0 = 0) &
% 97.34/14.96 | | | | | | | | | | | | | | | | | the_carrier(all_51_5) = all_507_4 &
% 97.34/14.96 | | | | | | | | | | | | | | | | | powerset(all_507_4) = all_507_3 & empty(all_507_2)
% 97.34/14.96 | | | | | | | | | | | | | | | | | = all_507_0 & element(all_507_2, all_507_3) = 0 &
% 97.34/14.96 | | | | | | | | | | | | | | | | | $i(all_507_3) & $i(all_507_4)
% 97.34/14.96 | | | | | | | | | | | | | | | | |
% 97.34/14.96 | | | | | | | | | | | | | | | | | ALPHA: (240) implies:
% 97.53/14.96 | | | | | | | | | | | | | | | | | (241) powerset(all_507_4) = all_507_3
% 97.53/14.96 | | | | | | | | | | | | | | | | | (242) the_carrier(all_51_5) = all_507_4
% 97.53/14.96 | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 97.53/14.96 | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | (243) all_509_2 = 0 & empty_carrier(all_51_5) = 0
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 97.53/14.96 | | | | | | | | | | | | | | | | | | (244) empty_carrier(all_51_5) = 0
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (214), (233), (234), (244) are inconsistent
% 97.53/14.96 | | | | | | | | | | | | | | | | | | by sub-proof #3.
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | (245) ~ (all_509_0 = 0) & the_carrier(all_51_5) =
% 97.53/14.96 | | | | | | | | | | | | | | | | | | all_509_1 & empty(all_509_1) = all_509_0 &
% 97.53/14.96 | | | | | | | | | | | | | | | | | | $i(all_509_1)
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 97.53/14.96 | | | | | | | | | | | | | | | | | | (246) the_carrier(all_51_5) = all_509_1
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 97.53/14.96 | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.96 | | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | (247) all_397_2 = 0 & empty_carrier(all_51_5) = 0
% 97.53/14.96 | | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | (248) empty_carrier(all_51_5) = 0
% 97.53/14.96 | | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (214), (233), (234), (248) are inconsistent
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | by sub-proof #3.
% 97.53/14.96 | | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.96 | | | | | | | | | | | | | | | | | | |
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | (249) ~ (all_397_0 = 0) & the_carrier(all_51_5) =
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | all_397_1 & empty(all_397_1) = all_397_0 &
% 97.53/14.96 | | | | | | | | | | | | | | | | | | | $i(all_397_1)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (250) the_carrier(all_51_5) = all_397_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_51_3, all_166_0,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (43), (224) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (251) all_166_0 = all_51_3
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_166_0, all_394_2,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (177), (224) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (252) all_394_2 = all_166_0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_107_3, all_394_2,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (177), (229) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (253) all_394_2 = all_107_3
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_397_1, all_507_4,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_5, simplifying with (242), (250) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (254) all_507_4 = all_397_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_51_4, all_571_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_5, simplifying with (44), (239) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (255) all_571_1 = all_51_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_509_1, all_571_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_5, simplifying with (239), (246) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (256) all_571_1 = all_509_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (27) with all_507_4, all_571_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_5, simplifying with (239), (242) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (257) all_571_1 = all_507_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_350_0, all_354_0,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_51_1, all_51_4, simplifying with (170), (172)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (258) all_354_0 = all_350_0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (32) with all_173_1, all_381_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | all_59_0, all_51_5, simplifying with (144), (198)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (259) all_381_1 = all_173_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (255), (256) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (260) all_509_1 = all_51_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (256), (257) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (261) all_509_1 = all_507_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (261) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (262) all_507_4 = all_51_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (263) all_507_4 = all_51_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (254), (263) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (264) all_397_1 = all_51_4
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (252), (253) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (265) all_166_0 = all_107_3
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | SIMP: (265) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (266) all_166_0 = all_107_3
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (251), (266) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (267) all_107_3 = all_51_3
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | REDUCE: (238), (255) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (268) powerset(all_51_4) = all_571_0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | REDUCE: (241), (263) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (269) powerset(all_51_4) = all_507_3
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | REDUCE: (197), (259) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | (270) element(all_173_1, all_51_3) = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | (271) ~ (all_398_0 = 0) & in(all_251_1, all_173_1) =
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | all_398_0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | (272) ~ (all_398_0 = 0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | (273) in(all_251_1, all_173_1) = all_398_0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (274) ~ (all_664_1 = 0) & element(all_251_1, all_51_4)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | = all_664_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (274) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (275) ~ (all_664_1 = 0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (276) element(all_251_1, all_51_4) = all_664_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_664_1, all_51_4,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | all_251_1, simplifying with (152), (276) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (277) all_664_1 = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (277) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (278) $false
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | CLOSE: (278) is inconsistent.
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (279) ( ~ (all_664_1 = 0) & element(all_51_2, all_166_0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | = all_664_1) | (( ~ (all_251_0 = 0) | ( ~
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | (all_664_0 = 0) & in(all_251_1, all_59_0) =
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | all_664_0)) & (all_251_0 = 0 | (all_664_0 =
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | 0 & in(all_251_1, all_59_0) = 0)))
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (280) ~ (all_664_1 = 0) & element(all_51_2, all_166_0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | = all_664_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (281) ~ (all_664_1 = 0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (282) element(all_51_2, all_166_0) = all_664_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (251), (282) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (283) element(all_51_2, all_51_3) = all_664_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_664_1, all_51_3,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | all_51_2, simplifying with (42), (283) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (284) all_664_1 = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (281), (284) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (285) $false
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (285) is inconsistent.
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (286) ( ~ (all_251_0 = 0) | ( ~ (all_664_0 = 0) &
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | in(all_251_1, all_59_0) = all_664_0)) &
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (all_251_0 = 0 | (all_664_0 = 0 & in(all_251_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | all_59_0) = 0))
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | (287) all_251_0 = 0 | (all_664_0 = 0 & in(all_251_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | all_59_0) = 0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | (288) all_251_0 = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (97), (288) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | (289) $false
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (289) is inconsistent.
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | (290) all_664_0 = 0 & in(all_251_1, all_59_0) = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | (291) in(all_251_1, all_59_0) = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | (292) all_111_0 = 0 & the_carrier(all_42_0) = all_111_1
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | & empty(all_111_1) = 0 & $i(all_111_1)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | (293) all_111_0 = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_59_0, all_173_1,
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | all_251_1, simplifying with (98), (146), (151),
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (194), (291) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (294) in(all_251_1, all_173_1) = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (272), (273), (294) are inconsistent by
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (295) ~ (all_111_0 = 0) & the_carrier(all_42_0) =
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | all_111_1 & empty(all_111_1) = all_111_0 &
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_111_1)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (296) ~ (all_111_0 = 0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (293), (296) imply:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (297) $false
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | (298) ~ (all_111_2 = 0) & empty_carrier(all_42_0) =
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | all_111_2
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | (299) ~ (all_111_2 = 0)
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | (300) empty_carrier(all_42_0) = all_111_2
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_111_2 = 0 & empty_carrier(all_42_0) = 0
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 97.53/14.97 | | | | | | | | | | | | | | | | | | | | | | | | | (302) empty_carrier(all_42_0) = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_111_2, all_42_0,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (300), (302) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_111_2 = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (299), (303) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | (304) $false
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (304) is inconsistent.
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (5) with all_59_0, all_173_1,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | all_251_1, simplifying with (98), (146), (151),
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | (194), (291) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | (305) in(all_251_1, all_173_1) = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (272), (273), (305) are inconsistent by
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | (306) ~ (all_398_1 = 0) & powerset(all_51_4) =
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | all_398_2 & element(all_173_1, all_398_2) =
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | all_398_1 & $i(all_398_2)
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | (307) ~ (all_398_1 = 0)
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | (308) element(all_173_1, all_398_2) = all_398_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | (309) powerset(all_51_4) = all_398_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | Case 1:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (310) all_393_0 = all_173_1 &
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | subset_complement(all_51_4, all_51_1) = all_173_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (311) subset_complement(all_51_4, all_51_1) = all_173_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_51_3, all_571_0,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (43), (268) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (312) all_571_0 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_507_3, all_571_0,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (268), (269) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (313) all_571_0 = all_507_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_398_2, all_571_0,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (268), (309) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (314) all_571_0 = all_398_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with all_350_0, all_173_1,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_1, all_51_4, simplifying with (170), (311)
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (315) all_350_0 = all_173_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (314) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (316) all_507_3 = all_398_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (312), (313) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (317) all_507_3 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (316), (317) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (318) all_398_2 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (308), (318) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (319) element(all_173_1, all_51_3) = all_398_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_398_1, all_51_3,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_173_1, simplifying with (270), (319) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (320) all_398_1 = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (307), (320) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (321) $false
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | CLOSE: (321) is inconsistent.
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (322) ~ (all_393_1 = 0) & powerset(all_51_4) =
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_393_2 & element(all_173_1, all_393_2) =
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_393_1 & $i(all_393_2)
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (323) ~ (all_393_1 = 0)
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (324) element(all_173_1, all_393_2) = all_393_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (325) powerset(all_51_4) = all_393_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_51_3, all_507_3,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (43), (269) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (326) all_507_3 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_398_2, all_507_3,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (269), (309) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (327) all_507_3 = all_398_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_507_3, all_571_0,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (268), (269) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (328) all_571_0 = all_507_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (24) with all_393_2, all_571_0,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_4, simplifying with (268), (325) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (329) all_571_0 = all_393_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (329) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (330) all_507_3 = all_393_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (330) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (331) all_507_3 = all_393_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (326), (327) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (332) all_398_2 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (327), (331) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (333) all_398_2 = all_393_2
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (333) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (334) all_393_2 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | SIMP: (334) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (335) all_393_2 = all_51_3
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (308), (332) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (336) element(all_173_1, all_51_3) = all_398_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (324), (335) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (337) element(all_173_1, all_51_3) = all_393_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_398_1, all_51_3,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_173_1, simplifying with (270), (336) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (338) all_398_1 = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (30) with all_393_1, all_398_1,
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | all_51_3, all_173_1, simplifying with (336), (337)
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | gives:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (339) all_398_1 = all_393_1
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (338), (339) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (340) all_393_1 = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | REDUCE: (323), (340) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | (341) $false
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | | CLOSE: (341) is inconsistent.
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | (342) all_507_5 = 0 & empty_carrier(all_51_5) = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | | | (343) empty_carrier(all_51_5) = 0
% 97.53/14.98 | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (214), (233), (234), (343) are inconsistent
% 97.53/14.98 | | | | | | | | | | | | | | | | | by sub-proof #3.
% 97.53/14.98 | | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | (344) (all_107_5 = 0 & empty_carrier(all_51_5) = 0) | (
% 97.53/14.98 | | | | | | | | | | | | | | ~ (all_107_4 = 0) & one_sorted_str(all_51_5) =
% 97.53/14.98 | | | | | | | | | | | | | | all_107_4)
% 97.53/14.98 | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 97.53/14.98 | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | Case 1:
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | (345) all_107_5 = 0 & empty_carrier(all_51_5) = 0
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | ALPHA: (345) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | (346) empty_carrier(all_51_5) = 0
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | REF_CLOSE: (23), (25), (166), (167), (192), (214), (346) are
% 97.53/14.98 | | | | | | | | | | | | | | | inconsistent by sub-proof #2.
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | (347) ~ (all_107_4 = 0) & one_sorted_str(all_51_5) =
% 97.53/14.98 | | | | | | | | | | | | | | | all_107_4
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | ALPHA: (347) implies:
% 97.53/14.98 | | | | | | | | | | | | | | | (348) ~ (all_107_4 = 0)
% 97.53/14.98 | | | | | | | | | | | | | | | (349) one_sorted_str(all_51_5) = all_107_4
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | GROUND_INST: instantiating (26) with 0, all_107_4, all_51_5,
% 97.53/14.98 | | | | | | | | | | | | | | | simplifying with (57), (349) gives:
% 97.53/14.98 | | | | | | | | | | | | | | | (350) all_107_4 = 0
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | REDUCE: (348), (350) imply:
% 97.53/14.98 | | | | | | | | | | | | | | | (351) $false
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | | CLOSE: (351) is inconsistent.
% 97.53/14.98 | | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | End of split
% 97.53/14.98 | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | Case 2:
% 97.53/14.98 | | | | | | | | | |
% 97.53/14.98 | | | | | | | | | | (352) ~ (all_381_2 = 0) & top_str(all_51_5) = all_381_2
% 97.53/14.98 | | | | | | | | | |
% 97.53/14.99 | | | | | | | | | | ALPHA: (352) implies:
% 97.53/14.99 | | | | | | | | | | (353) ~ (all_381_2 = 0)
% 97.53/14.99 | | | | | | | | | | (354) top_str(all_51_5) = all_381_2
% 97.53/14.99 | | | | | | | | | |
% 97.53/14.99 | | | | | | | | | | GROUND_INST: instantiating (28) with 0, all_381_2, all_51_5,
% 97.53/14.99 | | | | | | | | | | simplifying with (46), (354) gives:
% 97.53/14.99 | | | | | | | | | | (355) all_381_2 = 0
% 97.53/14.99 | | | | | | | | | |
% 97.53/14.99 | | | | | | | | | | REDUCE: (353), (355) imply:
% 97.53/14.99 | | | | | | | | | | (356) $false
% 97.53/14.99 | | | | | | | | | |
% 97.53/14.99 | | | | | | | | | | CLOSE: (356) is inconsistent.
% 97.53/14.99 | | | | | | | | | |
% 97.53/14.99 | | | | | | | | | End of split
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | Case 2:
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | | (357) ~ (all_372_1 = 0) & element(all_59_0, all_127_0) =
% 97.53/14.99 | | | | | | | | | all_372_1
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | | ALPHA: (357) implies:
% 97.53/14.99 | | | | | | | | | (358) ~ (all_372_1 = 0)
% 97.53/14.99 | | | | | | | | | (359) element(all_59_0, all_127_0) = all_372_1
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | | REDUCE: (130), (359) imply:
% 97.53/14.99 | | | | | | | | | (360) element(all_59_0, all_51_3) = all_372_1
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | | GROUND_INST: instantiating (30) with 0, all_372_1, all_51_3,
% 97.53/14.99 | | | | | | | | | all_59_0, simplifying with (62), (360) gives:
% 97.53/14.99 | | | | | | | | | (361) all_372_1 = 0
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | | REDUCE: (358), (361) imply:
% 97.53/14.99 | | | | | | | | | (362) $false
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | | CLOSE: (362) is inconsistent.
% 97.53/14.99 | | | | | | | | |
% 97.53/14.99 | | | | | | | | End of split
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | End of split
% 97.53/14.99 | | | | | | |
% 97.53/14.99 | | | | | | Case 2:
% 97.53/14.99 | | | | | | |
% 97.53/14.99 | | | | | | | (363) ( ~ (all_123_1 = 0) & the_carrier(all_51_5) = all_123_3 &
% 97.53/14.99 | | | | | | | powerset(all_123_3) = all_123_2 & element(all_51_2,
% 97.53/14.99 | | | | | | | all_123_2) = all_123_1 & $i(all_123_2) &
% 97.53/14.99 | | | | | | | $i(all_123_3)) | ( ~ (all_123_4 = 0) &
% 97.53/14.99 | | | | | | | top_str(all_51_5) = all_123_4)
% 97.53/14.99 | | | | | | |
% 97.53/14.99 | | | | | | | BETA: splitting (363) gives:
% 97.53/14.99 | | | | | | |
% 97.53/14.99 | | | | | | | Case 1:
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | (364) ~ (all_123_1 = 0) & the_carrier(all_51_5) = all_123_3
% 97.53/14.99 | | | | | | | | & powerset(all_123_3) = all_123_2 & element(all_51_2,
% 97.53/14.99 | | | | | | | | all_123_2) = all_123_1 & $i(all_123_2) &
% 97.53/14.99 | | | | | | | | $i(all_123_3)
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | ALPHA: (364) implies:
% 97.53/14.99 | | | | | | | | (365) ~ (all_123_1 = 0)
% 97.53/14.99 | | | | | | | | (366) element(all_51_2, all_123_2) = all_123_1
% 97.53/14.99 | | | | | | | | (367) powerset(all_123_3) = all_123_2
% 97.53/14.99 | | | | | | | | (368) the_carrier(all_51_5) = all_123_3
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | GROUND_INST: instantiating (27) with all_51_4, all_123_3,
% 97.53/14.99 | | | | | | | | all_51_5, simplifying with (44), (368) gives:
% 97.53/14.99 | | | | | | | | (369) all_123_3 = all_51_4
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | REDUCE: (367), (369) imply:
% 97.53/14.99 | | | | | | | | (370) powerset(all_51_4) = all_123_2
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | GROUND_INST: instantiating (24) with all_51_3, all_123_2,
% 97.53/14.99 | | | | | | | | all_51_4, simplifying with (43), (370) gives:
% 97.53/14.99 | | | | | | | | (371) all_123_2 = all_51_3
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | REDUCE: (366), (371) imply:
% 97.53/14.99 | | | | | | | | (372) element(all_51_2, all_51_3) = all_123_1
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | GROUND_INST: instantiating (30) with 0, all_123_1, all_51_3,
% 97.53/14.99 | | | | | | | | all_51_2, simplifying with (42), (372) gives:
% 97.53/14.99 | | | | | | | | (373) all_123_1 = 0
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | REDUCE: (365), (373) imply:
% 97.53/14.99 | | | | | | | | (374) $false
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | CLOSE: (374) is inconsistent.
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | Case 2:
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | (375) ~ (all_123_4 = 0) & top_str(all_51_5) = all_123_4
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | ALPHA: (375) implies:
% 97.53/14.99 | | | | | | | | (376) ~ (all_123_4 = 0)
% 97.53/14.99 | | | | | | | | (377) top_str(all_51_5) = all_123_4
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | GROUND_INST: instantiating (28) with 0, all_123_4, all_51_5,
% 97.53/14.99 | | | | | | | | simplifying with (46), (377) gives:
% 97.53/14.99 | | | | | | | | (378) all_123_4 = 0
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | REDUCE: (376), (378) imply:
% 97.53/14.99 | | | | | | | | (379) $false
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | | CLOSE: (379) is inconsistent.
% 97.53/14.99 | | | | | | | |
% 97.53/14.99 | | | | | | | End of split
% 97.53/14.99 | | | | | | |
% 97.53/14.99 | | | | | | End of split
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | Case 2:
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | | (380) ~ (all_173_3 = 0) & element(all_51_2, all_141_0) =
% 97.53/14.99 | | | | | | all_173_3
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | | ALPHA: (380) implies:
% 97.53/14.99 | | | | | | (381) ~ (all_173_3 = 0)
% 97.53/14.99 | | | | | | (382) element(all_51_2, all_141_0) = all_173_3
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | | REDUCE: (126), (382) imply:
% 97.53/14.99 | | | | | | (383) element(all_51_2, all_51_3) = all_173_3
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | | GROUND_INST: instantiating (30) with 0, all_173_3, all_51_3,
% 97.53/14.99 | | | | | | all_51_2, simplifying with (42), (383) gives:
% 97.53/14.99 | | | | | | (384) all_173_3 = 0
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | | REDUCE: (381), (384) imply:
% 97.53/14.99 | | | | | | (385) $false
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | | CLOSE: (385) is inconsistent.
% 97.53/14.99 | | | | | |
% 97.53/14.99 | | | | | End of split
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | Case 2:
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | | (386) ~ (all_280_3 = 0) & element(all_51_2, all_137_0) = all_280_3
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | | ALPHA: (386) implies:
% 97.53/14.99 | | | | | (387) ~ (all_280_3 = 0)
% 97.53/14.99 | | | | | (388) element(all_51_2, all_137_0) = all_280_3
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | | REDUCE: (111), (388) imply:
% 97.53/14.99 | | | | | (389) element(all_51_2, all_51_3) = all_280_3
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | | GROUND_INST: instantiating (30) with 0, all_280_3, all_51_3, all_51_2,
% 97.53/14.99 | | | | | simplifying with (42), (389) gives:
% 97.53/14.99 | | | | | (390) all_280_3 = 0
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | | REDUCE: (387), (390) imply:
% 97.53/14.99 | | | | | (391) $false
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | | CLOSE: (391) is inconsistent.
% 97.53/14.99 | | | | |
% 97.53/14.99 | | | | End of split
% 97.53/14.99 | | | |
% 97.53/14.99 | | | End of split
% 97.53/14.99 | | |
% 97.53/14.99 | | End of split
% 97.53/14.99 | |
% 97.53/14.99 | End of split
% 97.53/14.99 |
% 97.53/14.99 End of proof
% 97.53/14.99
% 97.53/14.99 Sub-proof #1 shows that the following formulas are inconsistent:
% 97.53/14.99 ----------------------------------------------------------------
% 97.53/14.99 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 97.53/14.99 ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 97.53/14.99 (2) in(all_251_1, all_173_1) = all_398_0
% 97.53/14.99 (3) in(all_251_1, all_173_1) = 0
% 97.53/14.99 (4) ~ (all_398_0 = 0)
% 97.53/14.99
% 97.53/14.99 Begin of proof
% 97.53/14.99 |
% 97.53/14.99 | GROUND_INST: instantiating (1) with all_398_0, 0, all_173_1, all_251_1,
% 97.53/14.99 | simplifying with (2), (3) gives:
% 97.53/14.99 | (5) all_398_0 = 0
% 97.53/14.99 |
% 97.53/14.99 | REDUCE: (4), (5) imply:
% 97.53/14.99 | (6) $false
% 97.53/14.99 |
% 97.53/14.99 | CLOSE: (6) is inconsistent.
% 97.53/14.99 |
% 97.53/14.99 End of proof
% 97.53/14.99
% 97.53/14.99 Sub-proof #2 shows that the following formulas are inconsistent:
% 97.53/14.99 ----------------------------------------------------------------
% 97.53/14.99 (1) empty_carrier(all_51_5) = 0
% 97.53/14.99 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 97.53/14.99 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 97.53/14.99 (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 97.53/14.99 (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0))
% 97.53/14.99 (4) ~ (all_338_0 = 0)
% 97.53/14.99 (5) empty(all_51_4) = all_338_0
% 97.53/14.99 (6) (all_90_0 = 0 & empty(all_51_4) = 0) | ( ~ (all_90_1 = 0) &
% 97.53/14.99 empty_carrier(all_51_5) = all_90_1)
% 97.53/15.00 (7) empty_carrier(all_51_5) = all_509_2
% 97.53/15.00
% 97.53/15.00 Begin of proof
% 97.53/15.00 |
% 97.53/15.00 | BETA: splitting (6) gives:
% 97.53/15.00 |
% 97.53/15.00 | Case 1:
% 97.53/15.00 | |
% 97.53/15.00 | | (8) all_90_0 = 0 & empty(all_51_4) = 0
% 97.53/15.00 | |
% 97.53/15.00 | | ALPHA: (8) implies:
% 97.53/15.00 | | (9) empty(all_51_4) = 0
% 97.53/15.00 | |
% 97.53/15.00 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #4.
% 97.53/15.00 | |
% 97.53/15.00 | Case 2:
% 97.53/15.00 | |
% 97.53/15.00 | | (10) ~ (all_90_1 = 0) & empty_carrier(all_51_5) = all_90_1
% 97.53/15.00 | |
% 97.53/15.00 | | ALPHA: (10) implies:
% 97.53/15.00 | | (11) ~ (all_90_1 = 0)
% 97.53/15.00 | | (12) empty_carrier(all_51_5) = all_90_1
% 97.53/15.00 | |
% 97.53/15.00 | | REF_CLOSE: (1), (3), (7), (11), (12) are inconsistent by sub-proof #3.
% 97.53/15.00 | |
% 97.53/15.00 | End of split
% 97.53/15.00 |
% 97.53/15.00 End of proof
% 97.53/15.00
% 97.53/15.00 Sub-proof #3 shows that the following formulas are inconsistent:
% 97.53/15.00 ----------------------------------------------------------------
% 97.53/15.00 (1) empty_carrier(all_51_5) = 0
% 97.53/15.00 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 97.53/15.00 (v1 = v0 | ~ (empty_carrier(v2) = v1) | ~ (empty_carrier(v2) = v0))
% 97.53/15.00 (3) ~ (all_90_1 = 0)
% 97.53/15.00 (4) empty_carrier(all_51_5) = all_90_1
% 97.53/15.00 (5) empty_carrier(all_51_5) = all_509_2
% 97.53/15.00
% 97.53/15.00 Begin of proof
% 97.53/15.00 |
% 97.53/15.00 | GROUND_INST: instantiating (2) with all_90_1, all_509_2, all_51_5, simplifying
% 97.53/15.00 | with (4), (5) gives:
% 97.53/15.00 | (6) all_509_2 = all_90_1
% 97.53/15.00 |
% 97.53/15.00 | GROUND_INST: instantiating (2) with 0, all_509_2, all_51_5, simplifying with
% 97.53/15.00 | (1), (5) gives:
% 97.53/15.00 | (7) all_509_2 = 0
% 97.53/15.00 |
% 97.53/15.00 | COMBINE_EQS: (6), (7) imply:
% 97.53/15.00 | (8) all_90_1 = 0
% 97.53/15.00 |
% 97.53/15.00 | SIMP: (8) implies:
% 97.53/15.00 | (9) all_90_1 = 0
% 97.53/15.00 |
% 97.53/15.00 | REDUCE: (3), (9) imply:
% 97.53/15.00 | (10) $false
% 97.53/15.00 |
% 97.53/15.00 | CLOSE: (10) is inconsistent.
% 97.53/15.00 |
% 97.53/15.00 End of proof
% 97.53/15.00
% 97.53/15.00 Sub-proof #4 shows that the following formulas are inconsistent:
% 97.53/15.00 ----------------------------------------------------------------
% 97.53/15.00 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 97.53/15.00 (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 97.53/15.00 (2) empty(all_51_4) = all_338_0
% 97.53/15.00 (3) empty(all_51_4) = 0
% 97.53/15.00 (4) ~ (all_338_0 = 0)
% 97.53/15.00
% 97.53/15.00 Begin of proof
% 97.53/15.00 |
% 97.53/15.00 | GROUND_INST: instantiating (1) with 0, all_338_0, all_51_4, simplifying with
% 97.53/15.00 | (2), (3) gives:
% 97.53/15.00 | (5) all_338_0 = 0
% 97.53/15.00 |
% 97.53/15.00 | REDUCE: (4), (5) imply:
% 97.53/15.00 | (6) $false
% 97.53/15.00 |
% 97.53/15.00 | CLOSE: (6) is inconsistent.
% 97.53/15.00 |
% 97.53/15.00 End of proof
% 97.53/15.00 % SZS output end Proof for theBenchmark
% 97.53/15.00
% 97.53/15.00 14500ms
%------------------------------------------------------------------------------