TSTP Solution File: SEU108+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU108+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n031.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 17:42:32 EDT 2023
% Result : Theorem 111.61s 15.52s
% Output : Proof 202.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU108+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n031.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 15:49:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.72/1.09 Prover 4: Preprocessing ...
% 2.72/1.09 Prover 1: Preprocessing ...
% 2.72/1.13 Prover 0: Preprocessing ...
% 2.72/1.13 Prover 3: Preprocessing ...
% 2.72/1.13 Prover 5: Preprocessing ...
% 2.72/1.13 Prover 2: Preprocessing ...
% 2.72/1.13 Prover 6: Preprocessing ...
% 6.04/1.61 Prover 1: Warning: ignoring some quantifiers
% 6.89/1.66 Prover 2: Proving ...
% 6.89/1.67 Prover 1: Constructing countermodel ...
% 6.89/1.67 Prover 5: Proving ...
% 7.24/1.68 Prover 6: Proving ...
% 7.24/1.70 Prover 4: Warning: ignoring some quantifiers
% 7.24/1.71 Prover 3: Warning: ignoring some quantifiers
% 7.71/1.75 Prover 3: Constructing countermodel ...
% 7.87/1.78 Prover 4: Constructing countermodel ...
% 8.50/1.87 Prover 0: Proving ...
% 72.61/10.34 Prover 2: stopped
% 72.61/10.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 73.11/10.42 Prover 7: Preprocessing ...
% 73.83/10.49 Prover 7: Warning: ignoring some quantifiers
% 73.83/10.50 Prover 7: Constructing countermodel ...
% 74.94/10.64 Prover 7: gave up
% 74.94/10.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 75.35/10.70 Prover 8: Preprocessing ...
% 75.95/10.80 Prover 8: Warning: ignoring some quantifiers
% 75.95/10.82 Prover 8: Constructing countermodel ...
% 99.97/14.00 Prover 5: stopped
% 99.97/14.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 100.62/14.04 Prover 9: Preprocessing ...
% 102.21/14.21 Prover 9: Warning: ignoring some quantifiers
% 102.21/14.22 Prover 9: Constructing countermodel ...
% 111.61/15.52 Prover 3: proved (14881ms)
% 111.61/15.52
% 111.61/15.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 111.61/15.52
% 112.15/15.52 Prover 0: stopped
% 112.15/15.53 Prover 9: stopped
% 112.15/15.53 Prover 6: stopped
% 112.15/15.55 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 112.15/15.55 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 112.15/15.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 112.15/15.55 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 112.48/15.60 Prover 13: Preprocessing ...
% 112.48/15.60 Prover 11: Preprocessing ...
% 112.48/15.60 Prover 10: Preprocessing ...
% 112.48/15.61 Prover 16: Preprocessing ...
% 113.08/15.66 Prover 10: Warning: ignoring some quantifiers
% 113.08/15.66 Prover 10: Constructing countermodel ...
% 113.08/15.67 Prover 13: Warning: ignoring some quantifiers
% 113.08/15.67 Prover 16: Warning: ignoring some quantifiers
% 113.08/15.67 Prover 13: Constructing countermodel ...
% 113.08/15.67 Prover 16: Constructing countermodel ...
% 113.34/15.70 Prover 10: gave up
% 113.34/15.71 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 113.34/15.72 Prover 11: Warning: ignoring some quantifiers
% 113.87/15.77 Prover 11: Constructing countermodel ...
% 113.87/15.77 Prover 13: gave up
% 113.87/15.78 Prover 19: Preprocessing ...
% 114.36/15.83 Prover 19: Warning: ignoring some quantifiers
% 114.36/15.84 Prover 19: Constructing countermodel ...
% 115.61/15.99 Prover 1: stopped
% 133.01/18.91 Prover 19: stopped
% 140.02/20.44 Prover 16: stopped
% 201.11/35.82 Prover 8: Found proof (size 263)
% 201.11/35.82 Prover 8: proved (25136ms)
% 201.11/35.83 Prover 4: stopped
% 201.11/35.84 Prover 11: stopped
% 201.11/35.85
% 201.11/35.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 201.11/35.85
% 201.11/35.86 % SZS output start Proof for theBenchmark
% 201.11/35.87 Assumptions after simplification:
% 201.11/35.87 ---------------------------------
% 201.11/35.87
% 201.11/35.87 (antisymmetry_r2_hidden)
% 201.40/35.89 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ?
% 201.40/35.89 [v2: int] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 201.40/35.89
% 201.40/35.89 (commutativity_k4_subset_1)
% 201.40/35.89 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v0) =
% 201.40/35.89 v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ $i(v2) | ~
% 201.40/35.90 $i(v1) | ~ $i(v0) | ? [v4: $i] : (subset_union2(v0, v2, v1) = v4 &
% 201.40/35.90 subset_union2(v0, v1, v2) = v4 & $i(v4)))
% 201.40/35.90
% 201.40/35.90 (dt_k4_subset_1)
% 201.40/35.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 201.40/35.90 int] : (v5 = 0 | ~ (subset_union2(v0, v1, v2) = v4) | ~ (powerset(v0) =
% 201.40/35.90 v3) | ~ (element(v4, v3) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 201.40/35.90 [v6: any] : ? [v7: any] : (element(v2, v3) = v7 & element(v1, v3) = v6 & (
% 201.40/35.90 ~ (v7 = 0) | ~ (v6 = 0))))
% 201.40/35.90
% 201.40/35.90 (dt_k6_subset_1)
% 201.40/35.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 201.40/35.90 int] : (v5 = 0 | ~ (subset_difference(v0, v1, v2) = v4) | ~ (powerset(v0)
% 201.40/35.90 = v3) | ~ (element(v4, v3) = v5) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 201.40/35.90 [v6: any] : ? [v7: any] : (element(v2, v3) = v7 & element(v1, v3) = v6 & (
% 201.40/35.90 ~ (v7 = 0) | ~ (v6 = 0))))
% 201.40/35.90
% 201.40/35.90 (fc1_subset_1)
% 201.40/35.90 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: int]
% 201.40/35.90 : ( ~ (v2 = 0) & empty(v1) = v2))
% 201.40/35.90
% 201.40/35.90 (idempotence_k4_subset_1)
% 201.40/35.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v0) =
% 201.40/35.90 v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ $i(v2) | ~
% 201.40/35.90 $i(v1) | ~ $i(v0) | subset_union2(v0, v1, v1) = v1)
% 201.40/35.90
% 201.40/35.90 (rc1_finsub_1)
% 201.40/35.91 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & cap_closed(v0) = 0 &
% 201.40/35.91 diff_closed(v0) = 0 & preboolean(v0) = 0 & cup_closed(v0) = 0 & empty(v0) =
% 201.40/35.91 v1 & $i(v0))
% 201.40/35.91
% 201.40/35.91 (rc1_subset_1)
% 201.40/35.91 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 201.40/35.91 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~
% 201.40/35.91 (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & $i(v3))))
% 201.40/35.91
% 201.40/35.91 (rc2_finset_1)
% 201.40/35.91 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 201.40/35.91 : (relation(v2) = 0 & function(v2) = 0 & one_to_one(v2) = 0 &
% 201.40/35.91 epsilon_transitive(v2) = 0 & epsilon_connected(v2) = 0 & ordinal(v2) = 0 &
% 201.40/35.91 natural(v2) = 0 & element(v2, v1) = 0 & finite(v2) = 0 & empty(v2) = 0 &
% 201.40/35.91 $i(v2)))
% 201.40/35.91
% 201.40/35.91 (rc2_subset_1)
% 201.40/35.91 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 201.40/35.91 : (element(v2, v1) = 0 & empty(v2) = 0 & $i(v2)))
% 201.40/35.91
% 201.40/35.91 (rc2_xboole_0)
% 201.40/35.91 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & empty(v0) = v1 & $i(v0))
% 201.40/35.91
% 201.40/35.91 (rc3_finset_1)
% 201.40/35.92 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 201.40/35.92 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~
% 201.40/35.92 (v4 = 0) & element(v3, v2) = 0 & finite(v3) = 0 & empty(v3) = v4 &
% 201.40/35.92 $i(v3))))
% 201.40/35.92
% 201.40/35.92 (rc4_finset_1)
% 201.40/35.92 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (empty(v0) = v1) | ~ $i(v0) | ?
% 201.40/35.92 [v2: $i] : (powerset(v0) = v2 & $i(v2) & ? [v3: $i] : ? [v4: int] : ( ~
% 201.40/35.92 (v4 = 0) & element(v3, v2) = 0 & finite(v3) = 0 & empty(v3) = v4 &
% 201.40/35.92 $i(v3))))
% 201.40/35.92
% 201.40/35.92 (redefinition_k4_subset_1)
% 201.40/35.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v0) =
% 201.40/35.92 v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ $i(v2) | ~
% 201.40/35.92 $i(v1) | ~ $i(v0) | ? [v4: $i] : (subset_union2(v0, v1, v2) = v4 &
% 201.40/35.92 set_union2(v1, v2) = v4 & $i(v4)))
% 201.40/35.92
% 201.40/35.92 (redefinition_k6_subset_1)
% 201.40/35.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v0) =
% 201.40/35.92 v3) | ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ $i(v2) | ~
% 201.40/35.92 $i(v1) | ~ $i(v0) | ? [v4: $i] : (set_difference(v1, v2) = v4 &
% 201.40/35.92 subset_difference(v0, v1, v2) = v4 & $i(v4)))
% 201.40/35.92
% 201.40/35.92 (t10_finsub_1)
% 201.40/35.93 ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (preboolean(v0) = v1) | ~ $i(v0) |
% 201.40/35.93 ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ?
% 201.40/35.93 [v7: any] : (set_difference(v2, v3) = v6 & set_union2(v2, v3) = v4 & in(v6,
% 201.40/35.93 v0) = v7 & in(v4, v0) = v5 & in(v3, v0) = 0 & in(v2, v0) = 0 & $i(v6) &
% 201.40/35.93 $i(v4) & $i(v3) & $i(v2) & ( ~ (v7 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : (
% 201.40/35.93 ~ (preboolean(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 201.40/35.93 : ! [v4: any] : ( ~ (set_difference(v1, v2) = v3) | ~ (in(v3, v0) = v4) |
% 201.40/35.93 ~ $i(v2) | ~ $i(v1) | ? [v5: any] : ? [v6: any] : ? [v7: $i] : ? [v8:
% 201.40/35.93 any] : (set_union2(v1, v2) = v7 & in(v7, v0) = v8 & in(v2, v0) = v6 &
% 201.40/35.93 in(v1, v0) = v5 & $i(v7) & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 =
% 201.40/35.93 0)))))
% 201.40/35.93
% 201.40/35.93 (t1_subset)
% 201.40/35.93 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) |
% 201.40/35.93 element(v0, v1) = 0)
% 201.40/35.93
% 201.40/35.93 (t20_finsub_1)
% 201.40/35.93 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & powerset(v0) = v1 &
% 201.40/35.93 preboolean(v1) = v2 & $i(v1) & $i(v0))
% 201.40/35.93
% 201.40/35.93 (t2_subset)
% 201.40/35.93 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~
% 201.40/35.93 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (element(v0, v1) = v3 &
% 201.40/35.93 empty(v1) = v4 & ( ~ (v3 = 0) | v4 = 0)))
% 201.40/35.93
% 201.40/35.93 (t6_boole)
% 201.40/35.93 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~
% 201.40/35.93 $i(v0))
% 201.40/35.93
% 201.40/35.93 (t8_boole)
% 201.40/35.94 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)
% 201.40/35.94 | ~ $i(v1) | ~ $i(v0))
% 201.40/35.94
% 201.40/35.94 (function-axioms)
% 201.40/35.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 201.40/35.95 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 201.40/35.95 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 201.40/35.95 [v4: $i] : (v1 = v0 | ~ (subset_union2(v4, v3, v2) = v1) | ~
% 201.40/35.95 (subset_union2(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 201.40/35.95 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 201.40/35.95 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 201.40/35.95 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 201.40/35.95 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 201.40/35.95 ! [v3: $i] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2)
% 201.40/35.95 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 201.40/35.95 $i] : ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 201.40/35.95 v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] :
% 201.40/35.95 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) =
% 201.40/35.95 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 201.40/35.95 $i] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0:
% 201.40/35.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 201.40/35.95 ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: MultipleValueBool]
% 201.40/35.95 : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (one_to_one(v2) =
% 201.40/35.95 v1) | ~ (one_to_one(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 201.40/35.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_transitive(v2) =
% 201.40/35.95 v1) | ~ (epsilon_transitive(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 201.40/35.95 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (epsilon_connected(v2) =
% 201.40/35.95 v1) | ~ (epsilon_connected(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 201.40/35.95 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ordinal(v2) = v1) | ~
% 201.40/35.95 (ordinal(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 201.40/35.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (natural(v2) = v1) | ~
% 201.40/35.95 (natural(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 201.40/35.95 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cap_closed(v2) = v1) | ~
% 201.40/35.95 (cap_closed(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 201.40/35.95 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0:
% 201.40/35.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 201.40/35.95 ~ (diff_closed(v2) = v1) | ~ (diff_closed(v2) = v0)) & ! [v0:
% 201.40/35.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 201.40/35.95 ~ (preboolean(v2) = v1) | ~ (preboolean(v2) = v0)) & ! [v0:
% 201.40/35.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 201.40/35.95 ~ (cup_closed(v2) = v1) | ~ (cup_closed(v2) = v0)) & ! [v0:
% 201.40/35.95 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 201.40/35.95 ~ (finite(v2) = v1) | ~ (finite(v2) = v0)) & ! [v0: MultipleValueBool] :
% 201.40/35.95 ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~
% 201.40/35.95 (empty(v2) = v0)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 201.40/35.95 (subset_difference(v2, v1, v0) = v3 & $i(v3)) & ? [v0: $i] : ? [v1: $i] : ?
% 201.40/35.95 [v2: $i] : ? [v3: $i] : (subset_union2(v2, v1, v0) = v3 & $i(v3)) & ? [v0:
% 201.40/35.95 $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (subset(v1, v0) = v2) & ?
% 201.40/35.95 [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (element(v1, v0) = v2) &
% 201.40/35.95 ? [v0: $i] : ? [v1: $i] : ? [v2: MultipleValueBool] : (in(v1, v0) = v2) &
% 201.40/35.95 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_difference(v1, v0) = v2 &
% 201.40/35.95 $i(v2)) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (set_union2(v1, v0) = v2
% 201.40/35.95 & $i(v2)) & ? [v0: $i] : ? [v1: MultipleValueBool] : (relation(v0) = v1) &
% 201.40/35.95 ? [v0: $i] : ? [v1: MultipleValueBool] : (function(v0) = v1) & ? [v0: $i] :
% 201.40/35.95 ? [v1: MultipleValueBool] : (one_to_one(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (epsilon_transitive(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (epsilon_connected(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (ordinal(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (natural(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (cap_closed(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (diff_closed(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (preboolean(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (cup_closed(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (finite(v0) = v1) & ? [v0: $i] : ? [v1:
% 201.40/35.95 MultipleValueBool] : (empty(v0) = v1) & ? [v0: $i] : ? [v1: $i] :
% 201.40/35.95 (powerset(v0) = v1 & $i(v1))
% 201.40/35.95
% 201.40/35.95 Further assumptions not needed in the proof:
% 201.40/35.95 --------------------------------------------
% 201.40/35.95 cc1_finset_1, cc1_finsub_1, cc2_finset_1, cc2_finsub_1,
% 201.40/35.95 commutativity_k2_xboole_0, existence_m1_subset_1, fc12_finset_1, fc1_xboole_0,
% 201.40/35.95 fc2_xboole_0, fc3_xboole_0, fc9_finset_1, idempotence_k2_xboole_0, rc1_finset_1,
% 201.40/35.95 rc1_xboole_0, reflexivity_r1_tarski, t1_boole, t3_boole, t3_subset, t4_boole,
% 201.40/35.95 t4_subset, t5_subset, t7_boole
% 201.40/35.95
% 201.40/35.95 Those formulas are unsatisfiable:
% 201.40/35.95 ---------------------------------
% 201.40/35.95
% 201.40/35.95 Begin of proof
% 201.40/35.95 |
% 201.40/35.95 | ALPHA: (t10_finsub_1) implies:
% 201.40/35.96 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (preboolean(v0) = v1) | ~
% 201.40/35.96 | $i(v0) | ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: any] : ?
% 201.40/35.96 | [v6: $i] : ? [v7: any] : (set_difference(v2, v3) = v6 &
% 201.40/35.96 | set_union2(v2, v3) = v4 & in(v6, v0) = v7 & in(v4, v0) = v5 &
% 201.40/35.96 | in(v3, v0) = 0 & in(v2, v0) = 0 & $i(v6) & $i(v4) & $i(v3) & $i(v2)
% 201.40/35.96 | & ( ~ (v7 = 0) | ~ (v5 = 0))))
% 201.40/35.96 |
% 201.40/35.96 | ALPHA: (t6_boole) implies:
% 201.40/35.96 | (2) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0))
% 201.40/35.96 |
% 201.40/35.96 | ALPHA: (function-axioms) implies:
% 201.40/35.96 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 201.40/35.96 | (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 201.40/35.96 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 201.40/35.96 | ! [v3: $i] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3,
% 201.40/35.96 | v2) = v0))
% 201.40/35.96 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 201.40/35.96 | (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 201.40/35.96 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 201.40/35.96 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 201.40/35.96 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 201.40/35.96 | (v1 = v0 | ~ (subset_union2(v4, v3, v2) = v1) | ~ (subset_union2(v4,
% 201.40/35.96 | v3, v2) = v0))
% 201.40/35.96 |
% 201.40/35.96 | DELTA: instantiating (rc2_xboole_0) with fresh symbols all_83_0, all_83_1
% 201.40/35.96 | gives:
% 201.40/35.96 | (8) ~ (all_83_0 = 0) & empty(all_83_1) = all_83_0 & $i(all_83_1)
% 201.40/35.96 |
% 201.40/35.96 | ALPHA: (8) implies:
% 201.40/35.96 | (9) ~ (all_83_0 = 0)
% 201.40/35.96 | (10) $i(all_83_1)
% 201.40/35.96 | (11) empty(all_83_1) = all_83_0
% 201.79/35.96 |
% 201.79/35.96 | DELTA: instantiating (t20_finsub_1) with fresh symbols all_91_0, all_91_1,
% 201.79/35.96 | all_91_2 gives:
% 201.79/35.96 | (12) ~ (all_91_0 = 0) & powerset(all_91_2) = all_91_1 &
% 201.79/35.96 | preboolean(all_91_1) = all_91_0 & $i(all_91_1) & $i(all_91_2)
% 201.79/35.96 |
% 201.79/35.96 | ALPHA: (12) implies:
% 201.79/35.96 | (13) ~ (all_91_0 = 0)
% 201.79/35.96 | (14) $i(all_91_2)
% 201.79/35.96 | (15) $i(all_91_1)
% 201.79/35.96 | (16) preboolean(all_91_1) = all_91_0
% 201.79/35.96 | (17) powerset(all_91_2) = all_91_1
% 201.79/35.96 |
% 201.79/35.96 | DELTA: instantiating (rc1_finsub_1) with fresh symbols all_93_0, all_93_1
% 201.79/35.96 | gives:
% 201.79/35.96 | (18) ~ (all_93_0 = 0) & cap_closed(all_93_1) = 0 & diff_closed(all_93_1) =
% 201.79/35.96 | 0 & preboolean(all_93_1) = 0 & cup_closed(all_93_1) = 0 &
% 201.79/35.96 | empty(all_93_1) = all_93_0 & $i(all_93_1)
% 201.79/35.96 |
% 201.79/35.96 | ALPHA: (18) implies:
% 201.79/35.96 | (19) ~ (all_93_0 = 0)
% 201.79/35.96 | (20) $i(all_93_1)
% 201.79/35.96 | (21) empty(all_93_1) = all_93_0
% 201.79/35.96 |
% 201.79/35.96 | GROUND_INST: instantiating (rc4_finset_1) with all_83_1, all_83_0, simplifying
% 201.79/35.96 | with (10), (11) gives:
% 201.79/35.97 | (22) all_83_0 = 0 | ? [v0: $i] : (powerset(all_83_1) = v0 & $i(v0) & ?
% 201.79/35.97 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 &
% 201.79/35.97 | finite(v1) = 0 & empty(v1) = v2 & $i(v1)))
% 201.79/35.97 |
% 201.79/35.97 | GROUND_INST: instantiating (rc1_subset_1) with all_83_1, all_83_0, simplifying
% 201.79/35.97 | with (10), (11) gives:
% 201.79/35.97 | (23) all_83_0 = 0 | ? [v0: $i] : (powerset(all_83_1) = v0 & $i(v0) & ?
% 201.79/35.97 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 &
% 201.79/35.97 | empty(v1) = v2 & $i(v1)))
% 201.79/35.97 |
% 201.79/35.97 | GROUND_INST: instantiating (rc1_subset_1) with all_93_1, all_93_0, simplifying
% 201.79/35.97 | with (20), (21) gives:
% 201.79/35.97 | (24) all_93_0 = 0 | ? [v0: $i] : (powerset(all_93_1) = v0 & $i(v0) & ?
% 201.79/35.97 | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 &
% 201.79/35.97 | empty(v1) = v2 & $i(v1)))
% 201.79/35.97 |
% 201.79/35.97 | GROUND_INST: instantiating (1) with all_91_1, all_91_0, simplifying with (15),
% 201.79/35.97 | (16) gives:
% 201.79/35.97 | (25) all_91_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any]
% 201.79/35.97 | : ? [v4: $i] : ? [v5: any] : (set_difference(v0, v1) = v4 &
% 201.79/35.97 | set_union2(v0, v1) = v2 & in(v4, all_91_1) = v5 & in(v2, all_91_1) =
% 201.79/35.97 | v3 & in(v1, all_91_1) = 0 & in(v0, all_91_1) = 0 & $i(v4) & $i(v2) &
% 201.79/35.97 | $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~ (v3 = 0)))
% 201.79/35.97 |
% 201.79/35.97 | GROUND_INST: instantiating (fc1_subset_1) with all_91_2, all_91_1, simplifying
% 201.79/35.97 | with (14), (17) gives:
% 201.79/35.97 | (26) ? [v0: int] : ( ~ (v0 = 0) & empty(all_91_1) = v0)
% 201.79/35.97 |
% 201.79/35.97 | GROUND_INST: instantiating (rc2_finset_1) with all_91_2, all_91_1, simplifying
% 201.79/35.97 | with (14), (17) gives:
% 201.79/35.97 | (27) ? [v0: $i] : (relation(v0) = 0 & function(v0) = 0 & one_to_one(v0) =
% 201.79/35.97 | 0 & epsilon_transitive(v0) = 0 & epsilon_connected(v0) = 0 &
% 201.79/35.97 | ordinal(v0) = 0 & natural(v0) = 0 & element(v0, all_91_1) = 0 &
% 201.79/35.97 | finite(v0) = 0 & empty(v0) = 0 & $i(v0))
% 201.79/35.97 |
% 201.79/35.97 | GROUND_INST: instantiating (rc2_subset_1) with all_91_2, all_91_1, simplifying
% 201.79/35.97 | with (14), (17) gives:
% 201.79/35.97 | (28) ? [v0: $i] : (element(v0, all_91_1) = 0 & empty(v0) = 0 & $i(v0))
% 201.79/35.97 |
% 201.79/35.97 | DELTA: instantiating (26) with fresh symbol all_102_0 gives:
% 201.79/35.97 | (29) ~ (all_102_0 = 0) & empty(all_91_1) = all_102_0
% 201.79/35.97 |
% 201.79/35.97 | ALPHA: (29) implies:
% 201.79/35.97 | (30) ~ (all_102_0 = 0)
% 201.79/35.97 | (31) empty(all_91_1) = all_102_0
% 201.79/35.97 |
% 201.79/35.97 | DELTA: instantiating (28) with fresh symbol all_104_0 gives:
% 201.79/35.97 | (32) element(all_104_0, all_91_1) = 0 & empty(all_104_0) = 0 &
% 201.79/35.97 | $i(all_104_0)
% 201.79/35.97 |
% 201.79/35.97 | ALPHA: (32) implies:
% 201.79/35.97 | (33) $i(all_104_0)
% 201.79/35.97 | (34) empty(all_104_0) = 0
% 201.79/35.97 | (35) element(all_104_0, all_91_1) = 0
% 201.79/35.97 |
% 201.79/35.97 | DELTA: instantiating (27) with fresh symbol all_109_0 gives:
% 201.79/35.98 | (36) relation(all_109_0) = 0 & function(all_109_0) = 0 &
% 201.79/35.98 | one_to_one(all_109_0) = 0 & epsilon_transitive(all_109_0) = 0 &
% 201.79/35.98 | epsilon_connected(all_109_0) = 0 & ordinal(all_109_0) = 0 &
% 201.79/35.98 | natural(all_109_0) = 0 & element(all_109_0, all_91_1) = 0 &
% 201.79/35.98 | finite(all_109_0) = 0 & empty(all_109_0) = 0 & $i(all_109_0)
% 201.79/35.98 |
% 201.79/35.98 | ALPHA: (36) implies:
% 201.79/35.98 | (37) $i(all_109_0)
% 201.79/35.98 | (38) empty(all_109_0) = 0
% 201.79/35.98 | (39) element(all_109_0, all_91_1) = 0
% 201.79/35.98 |
% 201.79/35.98 | BETA: splitting (24) gives:
% 201.79/35.98 |
% 201.79/35.98 | Case 1:
% 201.79/35.98 | |
% 201.79/35.98 | | (40) all_93_0 = 0
% 201.79/35.98 | |
% 201.79/35.98 | | REDUCE: (19), (40) imply:
% 201.79/35.98 | | (41) $false
% 201.87/35.98 | |
% 201.87/35.98 | | CLOSE: (41) is inconsistent.
% 201.87/35.98 | |
% 201.87/35.98 | Case 2:
% 201.87/35.98 | |
% 201.87/35.98 | | (42) ? [v0: $i] : (powerset(all_93_1) = v0 & $i(v0) & ? [v1: $i] : ?
% 201.87/35.98 | | [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & empty(v1) = v2 &
% 201.87/35.98 | | $i(v1)))
% 201.87/35.98 | |
% 201.87/35.98 | | DELTA: instantiating (42) with fresh symbol all_136_0 gives:
% 201.87/35.98 | | (43) powerset(all_93_1) = all_136_0 & $i(all_136_0) & ? [v0: $i] : ?
% 201.87/35.98 | | [v1: int] : ( ~ (v1 = 0) & element(v0, all_136_0) = 0 & empty(v0) =
% 201.87/35.98 | | v1 & $i(v0))
% 201.87/35.98 | |
% 201.87/35.98 | | ALPHA: (43) implies:
% 201.87/35.98 | | (44) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_136_0) =
% 201.87/35.98 | | 0 & empty(v0) = v1 & $i(v0))
% 201.87/35.98 | |
% 201.87/35.98 | | DELTA: instantiating (44) with fresh symbols all_138_0, all_138_1 gives:
% 201.87/35.98 | | (45) ~ (all_138_0 = 0) & element(all_138_1, all_136_0) = 0 &
% 201.87/35.98 | | empty(all_138_1) = all_138_0 & $i(all_138_1)
% 201.87/35.98 | |
% 201.87/35.98 | | ALPHA: (45) implies:
% 201.87/35.98 | | (46) ~ (all_138_0 = 0)
% 201.87/35.98 | | (47) $i(all_138_1)
% 201.87/35.98 | | (48) empty(all_138_1) = all_138_0
% 201.87/35.98 | |
% 201.87/35.98 | | BETA: splitting (23) gives:
% 201.87/35.98 | |
% 201.87/35.98 | | Case 1:
% 201.87/35.98 | | |
% 201.87/35.98 | | | (49) all_83_0 = 0
% 201.87/35.98 | | |
% 201.87/35.98 | | | REDUCE: (9), (49) imply:
% 201.87/35.98 | | | (50) $false
% 201.87/35.98 | | |
% 201.87/35.98 | | | CLOSE: (50) is inconsistent.
% 201.87/35.98 | | |
% 201.87/35.98 | | Case 2:
% 201.87/35.98 | | |
% 201.87/35.98 | | | (51) ? [v0: $i] : (powerset(all_83_1) = v0 & $i(v0) & ? [v1: $i] : ?
% 201.87/35.98 | | | [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & empty(v1) = v2
% 201.87/35.98 | | | & $i(v1)))
% 201.87/35.98 | | |
% 201.87/35.98 | | | DELTA: instantiating (51) with fresh symbol all_143_0 gives:
% 201.87/35.98 | | | (52) powerset(all_83_1) = all_143_0 & $i(all_143_0) & ? [v0: $i] : ?
% 201.87/35.98 | | | [v1: int] : ( ~ (v1 = 0) & element(v0, all_143_0) = 0 & empty(v0)
% 201.87/35.98 | | | = v1 & $i(v0))
% 201.87/35.98 | | |
% 201.87/35.98 | | | ALPHA: (52) implies:
% 201.87/35.98 | | | (53) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_143_0)
% 201.87/35.98 | | | = 0 & empty(v0) = v1 & $i(v0))
% 201.87/35.98 | | |
% 201.87/35.98 | | | DELTA: instantiating (53) with fresh symbols all_145_0, all_145_1 gives:
% 201.87/35.99 | | | (54) ~ (all_145_0 = 0) & element(all_145_1, all_143_0) = 0 &
% 201.87/35.99 | | | empty(all_145_1) = all_145_0 & $i(all_145_1)
% 201.87/35.99 | | |
% 201.87/35.99 | | | ALPHA: (54) implies:
% 201.87/35.99 | | | (55) ~ (all_145_0 = 0)
% 201.87/35.99 | | | (56) $i(all_145_1)
% 201.87/35.99 | | | (57) empty(all_145_1) = all_145_0
% 201.87/35.99 | | |
% 201.87/35.99 | | | BETA: splitting (22) gives:
% 201.87/35.99 | | |
% 201.87/35.99 | | | Case 1:
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | (58) all_83_0 = 0
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | REDUCE: (9), (58) imply:
% 201.87/35.99 | | | | (59) $false
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | CLOSE: (59) is inconsistent.
% 201.87/35.99 | | | |
% 201.87/35.99 | | | Case 2:
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | (60) ? [v0: $i] : (powerset(all_83_1) = v0 & $i(v0) & ? [v1: $i] :
% 201.87/35.99 | | | | ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0 & finite(v1)
% 201.87/35.99 | | | | = 0 & empty(v1) = v2 & $i(v1)))
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | DELTA: instantiating (60) with fresh symbol all_150_0 gives:
% 201.87/35.99 | | | | (61) powerset(all_83_1) = all_150_0 & $i(all_150_0) & ? [v0: $i] :
% 201.87/35.99 | | | | ? [v1: int] : ( ~ (v1 = 0) & element(v0, all_150_0) = 0 &
% 201.87/35.99 | | | | finite(v0) = 0 & empty(v0) = v1 & $i(v0))
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | ALPHA: (61) implies:
% 201.87/35.99 | | | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 201.87/35.99 | | | | all_150_0) = 0 & finite(v0) = 0 & empty(v0) = v1 & $i(v0))
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | DELTA: instantiating (62) with fresh symbols all_152_0, all_152_1 gives:
% 201.87/35.99 | | | | (63) ~ (all_152_0 = 0) & element(all_152_1, all_150_0) = 0 &
% 201.87/35.99 | | | | finite(all_152_1) = 0 & empty(all_152_1) = all_152_0 &
% 201.87/35.99 | | | | $i(all_152_1)
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | ALPHA: (63) implies:
% 201.87/35.99 | | | | (64) ~ (all_152_0 = 0)
% 201.87/35.99 | | | | (65) $i(all_152_1)
% 201.87/35.99 | | | | (66) empty(all_152_1) = all_152_0
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | BETA: splitting (25) gives:
% 201.87/35.99 | | | |
% 201.87/35.99 | | | | Case 1:
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | | (67) all_91_0 = 0
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | | REDUCE: (13), (67) imply:
% 201.87/35.99 | | | | | (68) $false
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | | CLOSE: (68) is inconsistent.
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | Case 2:
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | | (69) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ?
% 201.87/35.99 | | | | | [v4: $i] : ? [v5: any] : (set_difference(v0, v1) = v4 &
% 201.87/35.99 | | | | | set_union2(v0, v1) = v2 & in(v4, all_91_1) = v5 & in(v2,
% 201.87/35.99 | | | | | all_91_1) = v3 & in(v1, all_91_1) = 0 & in(v0, all_91_1) =
% 201.87/35.99 | | | | | 0 & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v5 = 0) | ~
% 201.87/35.99 | | | | | (v3 = 0)))
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | | DELTA: instantiating (69) with fresh symbols all_157_0, all_157_1,
% 201.87/35.99 | | | | | all_157_2, all_157_3, all_157_4, all_157_5 gives:
% 201.87/35.99 | | | | | (70) set_difference(all_157_5, all_157_4) = all_157_1 &
% 201.87/35.99 | | | | | set_union2(all_157_5, all_157_4) = all_157_3 & in(all_157_1,
% 201.87/35.99 | | | | | all_91_1) = all_157_0 & in(all_157_3, all_91_1) = all_157_2
% 201.87/35.99 | | | | | & in(all_157_4, all_91_1) = 0 & in(all_157_5, all_91_1) = 0 &
% 201.87/35.99 | | | | | $i(all_157_1) & $i(all_157_3) & $i(all_157_4) & $i(all_157_5)
% 201.87/35.99 | | | | | & ( ~ (all_157_0 = 0) | ~ (all_157_2 = 0))
% 201.87/35.99 | | | | |
% 201.87/35.99 | | | | | ALPHA: (70) implies:
% 201.87/35.99 | | | | | (71) $i(all_157_5)
% 201.87/35.99 | | | | | (72) $i(all_157_4)
% 201.87/35.99 | | | | | (73) $i(all_157_3)
% 201.87/35.99 | | | | | (74) $i(all_157_1)
% 201.87/35.99 | | | | | (75) in(all_157_5, all_91_1) = 0
% 201.87/35.99 | | | | | (76) in(all_157_4, all_91_1) = 0
% 201.87/35.99 | | | | | (77) in(all_157_3, all_91_1) = all_157_2
% 201.87/35.99 | | | | | (78) in(all_157_1, all_91_1) = all_157_0
% 201.87/35.99 | | | | | (79) set_union2(all_157_5, all_157_4) = all_157_3
% 201.87/35.99 | | | | | (80) set_difference(all_157_5, all_157_4) = all_157_1
% 201.87/36.00 | | | | | (81) ~ (all_157_0 = 0) | ~ (all_157_2 = 0)
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (t1_subset) with all_157_5, all_91_1,
% 201.87/36.00 | | | | | simplifying with (15), (71), (75) gives:
% 201.87/36.00 | | | | | (82) element(all_157_5, all_91_1) = 0
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with all_157_5,
% 201.87/36.00 | | | | | all_91_1, simplifying with (15), (71), (75) gives:
% 201.87/36.00 | | | | | (83) ? [v0: int] : ( ~ (v0 = 0) & in(all_91_1, all_157_5) = v0)
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (t1_subset) with all_157_4, all_91_1,
% 201.87/36.00 | | | | | simplifying with (15), (72), (76) gives:
% 201.87/36.00 | | | | | (84) element(all_157_4, all_91_1) = 0
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (t2_subset) with all_157_3, all_91_1,
% 201.87/36.00 | | | | | all_157_2, simplifying with (15), (73), (77) gives:
% 201.87/36.00 | | | | | (85) all_157_2 = 0 | ? [v0: any] : ? [v1: any] :
% 201.87/36.00 | | | | | (element(all_157_3, all_91_1) = v0 & empty(all_91_1) = v1 & (
% 201.87/36.00 | | | | | ~ (v0 = 0) | v1 = 0))
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (t2_subset) with all_157_1, all_91_1,
% 201.87/36.00 | | | | | all_157_0, simplifying with (15), (74), (78) gives:
% 201.87/36.00 | | | | | (86) all_157_0 = 0 | ? [v0: any] : ? [v1: any] :
% 201.87/36.00 | | | | | (element(all_157_1, all_91_1) = v0 & empty(all_91_1) = v1 & (
% 201.87/36.00 | | | | | ~ (v0 = 0) | v1 = 0))
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (t8_boole) with all_104_0, all_109_0,
% 201.87/36.00 | | | | | simplifying with (33), (34), (37), (38) gives:
% 201.87/36.00 | | | | | (87) all_109_0 = all_104_0
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (2) with all_109_0, simplifying with (37),
% 201.87/36.00 | | | | | (38) gives:
% 201.87/36.00 | | | | | (88) all_109_0 = empty_set
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_138_1, all_138_0,
% 201.87/36.00 | | | | | simplifying with (47), (48) gives:
% 201.87/36.00 | | | | | (89) all_138_0 = 0 | ? [v0: $i] : (powerset(all_138_1) = v0 &
% 201.87/36.00 | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 201.87/36.00 | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1)))
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (rc4_finset_1) with all_145_1, all_145_0,
% 201.87/36.00 | | | | | simplifying with (56), (57) gives:
% 201.87/36.00 | | | | | (90) all_145_0 = 0 | ? [v0: $i] : (powerset(all_145_1) = v0 &
% 201.87/36.00 | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 201.87/36.00 | | | | | element(v1, v0) = 0 & finite(v1) = 0 & empty(v1) = v2 &
% 201.87/36.00 | | | | | $i(v1)))
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (rc4_finset_1) with all_152_1, all_152_0,
% 201.87/36.00 | | | | | simplifying with (65), (66) gives:
% 201.87/36.00 | | | | | (91) all_152_0 = 0 | ? [v0: $i] : (powerset(all_152_1) = v0 &
% 201.87/36.00 | | | | | $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 201.87/36.00 | | | | | element(v1, v0) = 0 & finite(v1) = 0 & empty(v1) = v2 &
% 201.87/36.00 | | | | | $i(v1)))
% 201.87/36.00 | | | | |
% 201.87/36.00 | | | | | GROUND_INST: instantiating (commutativity_k4_subset_1) with all_91_2,
% 201.87/36.00 | | | | | all_104_0, all_104_0, all_91_1, simplifying with (14),
% 201.87/36.00 | | | | | (17), (33), (35) gives:
% 201.87/36.01 | | | | | (92) ? [v0: $i] : (subset_union2(all_91_2, all_104_0, all_104_0) =
% 201.87/36.01 | | | | | v0 & $i(v0))
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_104_0, all_104_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (33), (35) gives:
% 201.87/36.01 | | | | | (93) ? [v0: $i] : (subset_union2(all_91_2, all_104_0, all_104_0) =
% 201.87/36.01 | | | | | v0 & set_union2(all_104_0, all_104_0) = v0 & $i(v0))
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (commutativity_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_109_0, all_109_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (37), (39) gives:
% 201.87/36.01 | | | | | (94) ? [v0: $i] : (subset_union2(all_91_2, all_109_0, all_109_0) =
% 201.87/36.01 | | | | | v0 & $i(v0))
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_109_0, all_109_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (37), (39) gives:
% 201.87/36.01 | | | | | (95) ? [v0: $i] : (subset_union2(all_91_2, all_109_0, all_109_0) =
% 201.87/36.01 | | | | | v0 & set_union2(all_109_0, all_109_0) = v0 & $i(v0))
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (idempotence_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_104_0, all_109_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (33), (35), (37), (39) gives:
% 201.87/36.01 | | | | | (96) subset_union2(all_91_2, all_104_0, all_104_0) = all_104_0
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (commutativity_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_104_0, all_109_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (33), (35), (37), (39) gives:
% 201.87/36.01 | | | | | (97) ? [v0: $i] : (subset_union2(all_91_2, all_109_0, all_104_0) =
% 201.87/36.01 | | | | | v0 & subset_union2(all_91_2, all_104_0, all_109_0) = v0 &
% 201.87/36.01 | | | | | $i(v0))
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_104_0, all_109_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (33), (35), (37), (39) gives:
% 201.87/36.01 | | | | | (98) ? [v0: $i] : (subset_union2(all_91_2, all_104_0, all_109_0) =
% 201.87/36.01 | | | | | v0 & set_union2(all_104_0, all_109_0) = v0 & $i(v0))
% 201.87/36.01 | | | | |
% 201.87/36.01 | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with all_91_2,
% 201.87/36.01 | | | | | all_109_0, all_104_0, all_91_1, simplifying with (14),
% 201.87/36.01 | | | | | (17), (33), (35), (37), (39) gives:
% 202.05/36.01 | | | | | (99) ? [v0: $i] : (subset_union2(all_91_2, all_109_0, all_104_0) =
% 202.05/36.01 | | | | | v0 & set_union2(all_109_0, all_104_0) = v0 & $i(v0))
% 202.05/36.01 | | | | |
% 202.05/36.01 | | | | | COMBINE_EQS: (87), (88) imply:
% 202.05/36.01 | | | | | (100) all_104_0 = empty_set
% 202.05/36.01 | | | | |
% 202.05/36.01 | | | | | DELTA: instantiating (94) with fresh symbol all_179_0 gives:
% 202.05/36.01 | | | | | (101) subset_union2(all_91_2, all_109_0, all_109_0) = all_179_0 &
% 202.05/36.01 | | | | | $i(all_179_0)
% 202.05/36.01 | | | | |
% 202.05/36.01 | | | | | ALPHA: (101) implies:
% 202.05/36.01 | | | | | (102) $i(all_179_0)
% 202.05/36.01 | | | | | (103) subset_union2(all_91_2, all_109_0, all_109_0) = all_179_0
% 202.05/36.01 | | | | |
% 202.05/36.01 | | | | | DELTA: instantiating (92) with fresh symbol all_189_0 gives:
% 202.05/36.01 | | | | | (104) subset_union2(all_91_2, all_104_0, all_104_0) = all_189_0 &
% 202.05/36.01 | | | | | $i(all_189_0)
% 202.05/36.01 | | | | |
% 202.05/36.01 | | | | | ALPHA: (104) implies:
% 202.05/36.01 | | | | | (105) subset_union2(all_91_2, all_104_0, all_104_0) = all_189_0
% 202.05/36.01 | | | | |
% 202.05/36.01 | | | | | DELTA: instantiating (83) with fresh symbol all_191_0 gives:
% 202.05/36.02 | | | | | (106) ~ (all_191_0 = 0) & in(all_91_1, all_157_5) = all_191_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | ALPHA: (106) implies:
% 202.05/36.02 | | | | | (107) ~ (all_191_0 = 0)
% 202.05/36.02 | | | | | (108) in(all_91_1, all_157_5) = all_191_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | DELTA: instantiating (99) with fresh symbol all_199_0 gives:
% 202.05/36.02 | | | | | (109) subset_union2(all_91_2, all_109_0, all_104_0) = all_199_0 &
% 202.05/36.02 | | | | | set_union2(all_109_0, all_104_0) = all_199_0 & $i(all_199_0)
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | ALPHA: (109) implies:
% 202.05/36.02 | | | | | (110) subset_union2(all_91_2, all_109_0, all_104_0) = all_199_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | DELTA: instantiating (95) with fresh symbol all_201_0 gives:
% 202.05/36.02 | | | | | (111) subset_union2(all_91_2, all_109_0, all_109_0) = all_201_0 &
% 202.05/36.02 | | | | | set_union2(all_109_0, all_109_0) = all_201_0 & $i(all_201_0)
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | ALPHA: (111) implies:
% 202.05/36.02 | | | | | (112) subset_union2(all_91_2, all_109_0, all_109_0) = all_201_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | DELTA: instantiating (93) with fresh symbol all_253_0 gives:
% 202.05/36.02 | | | | | (113) subset_union2(all_91_2, all_104_0, all_104_0) = all_253_0 &
% 202.05/36.02 | | | | | set_union2(all_104_0, all_104_0) = all_253_0 & $i(all_253_0)
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | ALPHA: (113) implies:
% 202.05/36.02 | | | | | (114) subset_union2(all_91_2, all_104_0, all_104_0) = all_253_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | DELTA: instantiating (98) with fresh symbol all_261_0 gives:
% 202.05/36.02 | | | | | (115) subset_union2(all_91_2, all_104_0, all_109_0) = all_261_0 &
% 202.05/36.02 | | | | | set_union2(all_104_0, all_109_0) = all_261_0 & $i(all_261_0)
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | ALPHA: (115) implies:
% 202.05/36.02 | | | | | (116) subset_union2(all_91_2, all_104_0, all_109_0) = all_261_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | DELTA: instantiating (97) with fresh symbol all_263_0 gives:
% 202.05/36.02 | | | | | (117) subset_union2(all_91_2, all_109_0, all_104_0) = all_263_0 &
% 202.05/36.02 | | | | | subset_union2(all_91_2, all_104_0, all_109_0) = all_263_0 &
% 202.05/36.02 | | | | | $i(all_263_0)
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | ALPHA: (117) implies:
% 202.05/36.02 | | | | | (118) subset_union2(all_91_2, all_104_0, all_109_0) = all_263_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (88), (112) imply:
% 202.05/36.02 | | | | | (119) subset_union2(all_91_2, empty_set, empty_set) = all_201_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (88), (103) imply:
% 202.05/36.02 | | | | | (120) subset_union2(all_91_2, empty_set, empty_set) = all_179_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (88), (100), (110) imply:
% 202.05/36.02 | | | | | (121) subset_union2(all_91_2, empty_set, empty_set) = all_199_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (88), (100), (118) imply:
% 202.05/36.02 | | | | | (122) subset_union2(all_91_2, empty_set, empty_set) = all_263_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (88), (100), (116) imply:
% 202.05/36.02 | | | | | (123) subset_union2(all_91_2, empty_set, empty_set) = all_261_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (100), (114) imply:
% 202.05/36.02 | | | | | (124) subset_union2(all_91_2, empty_set, empty_set) = all_253_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (100), (105) imply:
% 202.05/36.02 | | | | | (125) subset_union2(all_91_2, empty_set, empty_set) = all_189_0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (96), (100) imply:
% 202.05/36.02 | | | | | (126) subset_union2(all_91_2, empty_set, empty_set) = empty_set
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | REDUCE: (35), (100) imply:
% 202.05/36.02 | | | | | (127) element(empty_set, all_91_1) = 0
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | BETA: splitting (91) gives:
% 202.05/36.02 | | | | |
% 202.05/36.02 | | | | | Case 1:
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | (128) all_152_0 = 0
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | REDUCE: (64), (128) imply:
% 202.05/36.02 | | | | | | (129) $false
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | CLOSE: (129) is inconsistent.
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | Case 2:
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | (130) ? [v0: $i] : (powerset(all_152_1) = v0 & $i(v0) & ? [v1:
% 202.05/36.02 | | | | | | $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0) = 0
% 202.05/36.02 | | | | | | & finite(v1) = 0 & empty(v1) = v2 & $i(v1)))
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | DELTA: instantiating (130) with fresh symbol all_331_0 gives:
% 202.05/36.02 | | | | | | (131) powerset(all_152_1) = all_331_0 & $i(all_331_0) & ? [v0:
% 202.05/36.02 | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 202.05/36.02 | | | | | | all_331_0) = 0 & finite(v0) = 0 & empty(v0) = v1 &
% 202.05/36.02 | | | | | | $i(v0))
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | ALPHA: (131) implies:
% 202.05/36.02 | | | | | | (132) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 202.05/36.02 | | | | | | all_331_0) = 0 & finite(v0) = 0 & empty(v0) = v1 &
% 202.05/36.02 | | | | | | $i(v0))
% 202.05/36.02 | | | | | |
% 202.05/36.02 | | | | | | DELTA: instantiating (132) with fresh symbols all_333_0, all_333_1
% 202.05/36.02 | | | | | | gives:
% 202.05/36.03 | | | | | | (133) ~ (all_333_0 = 0) & element(all_333_1, all_331_0) = 0 &
% 202.05/36.03 | | | | | | finite(all_333_1) = 0 & empty(all_333_1) = all_333_0 &
% 202.05/36.03 | | | | | | $i(all_333_1)
% 202.05/36.03 | | | | | |
% 202.05/36.03 | | | | | | ALPHA: (133) implies:
% 202.05/36.03 | | | | | | (134) ~ (all_333_0 = 0)
% 202.05/36.03 | | | | | | (135) $i(all_333_1)
% 202.05/36.03 | | | | | | (136) empty(all_333_1) = all_333_0
% 202.05/36.03 | | | | | |
% 202.05/36.03 | | | | | | BETA: splitting (89) gives:
% 202.05/36.03 | | | | | |
% 202.05/36.03 | | | | | | Case 1:
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | (137) all_138_0 = 0
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | REDUCE: (46), (137) imply:
% 202.05/36.03 | | | | | | | (138) $false
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | CLOSE: (138) is inconsistent.
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | Case 2:
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | (139) ? [v0: $i] : (powerset(all_138_1) = v0 & $i(v0) & ?
% 202.05/36.03 | | | | | | | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & element(v1,
% 202.05/36.03 | | | | | | | v0) = 0 & empty(v1) = v2 & $i(v1)))
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | DELTA: instantiating (139) with fresh symbol all_380_0 gives:
% 202.05/36.03 | | | | | | | (140) powerset(all_138_1) = all_380_0 & $i(all_380_0) & ? [v0:
% 202.05/36.03 | | | | | | | $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 202.05/36.03 | | | | | | | all_380_0) = 0 & empty(v0) = v1 & $i(v0))
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | ALPHA: (140) implies:
% 202.05/36.03 | | | | | | | (141) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 202.05/36.03 | | | | | | | all_380_0) = 0 & empty(v0) = v1 & $i(v0))
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | DELTA: instantiating (141) with fresh symbols all_382_0, all_382_1
% 202.05/36.03 | | | | | | | gives:
% 202.05/36.03 | | | | | | | (142) ~ (all_382_0 = 0) & element(all_382_1, all_380_0) = 0 &
% 202.05/36.03 | | | | | | | empty(all_382_1) = all_382_0 & $i(all_382_1)
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | ALPHA: (142) implies:
% 202.05/36.03 | | | | | | | (143) ~ (all_382_0 = 0)
% 202.05/36.03 | | | | | | | (144) $i(all_382_1)
% 202.05/36.03 | | | | | | | (145) empty(all_382_1) = all_382_0
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | BETA: splitting (90) gives:
% 202.05/36.03 | | | | | | |
% 202.05/36.03 | | | | | | | Case 1:
% 202.05/36.03 | | | | | | | |
% 202.05/36.03 | | | | | | | | (146) all_145_0 = 0
% 202.05/36.03 | | | | | | | |
% 202.05/36.03 | | | | | | | | REDUCE: (55), (146) imply:
% 202.05/36.03 | | | | | | | | (147) $false
% 202.05/36.03 | | | | | | | |
% 202.05/36.03 | | | | | | | | CLOSE: (147) is inconsistent.
% 202.05/36.03 | | | | | | | |
% 202.05/36.03 | | | | | | | Case 2:
% 202.05/36.03 | | | | | | | |
% 202.05/36.03 | | | | | | | |
% 202.05/36.03 | | | | | | | | GROUND_INST: instantiating (7) with empty_set, all_199_0,
% 202.05/36.03 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.05/36.03 | | | | | | | | (121), (126) gives:
% 202.05/36.03 | | | | | | | | (148) all_199_0 = empty_set
% 202.05/36.03 | | | | | | | |
% 202.15/36.03 | | | | | | | | GROUND_INST: instantiating (7) with all_201_0, all_253_0,
% 202.15/36.03 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.15/36.03 | | | | | | | | (119), (124) gives:
% 202.15/36.03 | | | | | | | | (149) all_253_0 = all_201_0
% 202.15/36.03 | | | | | | | |
% 202.15/36.03 | | | | | | | | GROUND_INST: instantiating (7) with all_199_0, all_253_0,
% 202.15/36.03 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.15/36.03 | | | | | | | | (121), (124) gives:
% 202.15/36.03 | | | | | | | | (150) all_253_0 = all_199_0
% 202.15/36.03 | | | | | | | |
% 202.15/36.03 | | | | | | | | GROUND_INST: instantiating (7) with all_199_0, all_261_0,
% 202.15/36.03 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.15/36.03 | | | | | | | | (121), (123) gives:
% 202.15/36.03 | | | | | | | | (151) all_261_0 = all_199_0
% 202.15/36.03 | | | | | | | |
% 202.15/36.03 | | | | | | | | GROUND_INST: instantiating (7) with all_179_0, all_261_0,
% 202.15/36.03 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.15/36.03 | | | | | | | | (120), (123) gives:
% 202.15/36.03 | | | | | | | | (152) all_261_0 = all_179_0
% 202.15/36.03 | | | | | | | |
% 202.15/36.03 | | | | | | | | GROUND_INST: instantiating (7) with all_253_0, all_263_0,
% 202.15/36.03 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.15/36.03 | | | | | | | | (122), (124) gives:
% 202.15/36.03 | | | | | | | | (153) all_263_0 = all_253_0
% 202.15/36.03 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (7) with all_189_0, all_263_0,
% 202.15/36.04 | | | | | | | | empty_set, empty_set, all_91_2, simplifying with
% 202.15/36.04 | | | | | | | | (122), (125) gives:
% 202.15/36.04 | | | | | | | | (154) all_263_0 = all_189_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (153), (154) imply:
% 202.15/36.04 | | | | | | | | (155) all_253_0 = all_189_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | SIMP: (155) implies:
% 202.15/36.04 | | | | | | | | (156) all_253_0 = all_189_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (151), (152) imply:
% 202.15/36.04 | | | | | | | | (157) all_199_0 = all_179_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | SIMP: (157) implies:
% 202.15/36.04 | | | | | | | | (158) all_199_0 = all_179_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (149), (150) imply:
% 202.15/36.04 | | | | | | | | (159) all_201_0 = all_199_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (149), (156) imply:
% 202.15/36.04 | | | | | | | | (160) all_201_0 = all_189_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (159), (160) imply:
% 202.15/36.04 | | | | | | | | (161) all_199_0 = all_189_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | SIMP: (161) implies:
% 202.15/36.04 | | | | | | | | (162) all_199_0 = all_189_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (148), (162) imply:
% 202.15/36.04 | | | | | | | | (163) all_189_0 = empty_set
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (158), (162) imply:
% 202.15/36.04 | | | | | | | | (164) all_189_0 = all_179_0
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | COMBINE_EQS: (163), (164) imply:
% 202.15/36.04 | | | | | | | | (165) all_179_0 = empty_set
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | SIMP: (165) implies:
% 202.15/36.04 | | | | | | | | (166) all_179_0 = empty_set
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | REDUCE: (102), (166) imply:
% 202.15/36.04 | | | | | | | | (167) $i(empty_set)
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (t2_subset) with all_91_1, all_157_5,
% 202.15/36.04 | | | | | | | | all_191_0, simplifying with (15), (71), (108)
% 202.15/36.04 | | | | | | | | gives:
% 202.15/36.04 | | | | | | | | (168) all_191_0 = 0 | ? [v0: any] : ? [v1: any] :
% 202.15/36.04 | | | | | | | | (element(all_91_1, all_157_5) = v0 & empty(all_157_5) =
% 202.15/36.04 | | | | | | | | v1 & ( ~ (v0 = 0) | v1 = 0))
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_333_1,
% 202.15/36.04 | | | | | | | | all_333_0, simplifying with (135), (136) gives:
% 202.15/36.04 | | | | | | | | (169) all_333_0 = 0 | ? [v0: $i] : (powerset(all_333_1) = v0
% 202.15/36.04 | | | | | | | | & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 202.15/36.04 | | | | | | | | & element(v1, v0) = 0 & empty(v1) = v2 & $i(v1)))
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (rc1_subset_1) with all_382_1,
% 202.15/36.04 | | | | | | | | all_382_0, simplifying with (144), (145) gives:
% 202.15/36.04 | | | | | | | | (170) all_382_0 = 0 | ? [v0: $i] : (powerset(all_382_1) = v0
% 202.15/36.04 | | | | | | | | & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0)
% 202.15/36.04 | | | | | | | | & element(v1, v0) = 0 & empty(v1) = v2 & $i(v1)))
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (commutativity_k4_subset_1) with
% 202.15/36.04 | | | | | | | | all_91_2, all_157_5, all_157_5, all_91_1,
% 202.15/36.04 | | | | | | | | simplifying with (14), (17), (71), (82) gives:
% 202.15/36.04 | | | | | | | | (171) ? [v0: $i] : (subset_union2(all_91_2, all_157_5,
% 202.15/36.04 | | | | | | | | all_157_5) = v0 & $i(v0))
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with
% 202.15/36.04 | | | | | | | | all_91_2, all_157_5, all_157_5, all_91_1,
% 202.15/36.04 | | | | | | | | simplifying with (14), (17), (71), (82) gives:
% 202.15/36.04 | | | | | | | | (172) ? [v0: $i] : (subset_union2(all_91_2, all_157_5,
% 202.15/36.04 | | | | | | | | all_157_5) = v0 & set_union2(all_157_5, all_157_5)
% 202.15/36.04 | | | | | | | | = v0 & $i(v0))
% 202.15/36.04 | | | | | | | |
% 202.15/36.04 | | | | | | | | GROUND_INST: instantiating (commutativity_k4_subset_1) with
% 202.15/36.04 | | | | | | | | all_91_2, all_157_4, all_157_4, all_91_1,
% 202.15/36.04 | | | | | | | | simplifying with (14), (17), (72), (84) gives:
% 202.15/36.04 | | | | | | | | (173) ? [v0: $i] : (subset_union2(all_91_2, all_157_4,
% 202.15/36.04 | | | | | | | | all_157_4) = v0 & $i(v0))
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_4, all_157_4, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (72), (84) gives:
% 202.15/36.05 | | | | | | | | (174) ? [v0: $i] : (subset_union2(all_91_2, all_157_4,
% 202.15/36.05 | | | | | | | | all_157_4) = v0 & set_union2(all_157_4, all_157_4)
% 202.15/36.05 | | | | | | | | = v0 & $i(v0))
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (idempotence_k4_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_5, all_157_4, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (71), (72), (82), (84)
% 202.15/36.05 | | | | | | | | gives:
% 202.15/36.05 | | | | | | | | (175) subset_union2(all_91_2, all_157_5, all_157_5) =
% 202.15/36.05 | | | | | | | | all_157_5
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (redefinition_k6_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_5, all_157_4, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (71), (72), (82), (84)
% 202.15/36.05 | | | | | | | | gives:
% 202.15/36.05 | | | | | | | | (176) ? [v0: $i] : (set_difference(all_157_5, all_157_4) =
% 202.15/36.05 | | | | | | | | v0 & subset_difference(all_91_2, all_157_5,
% 202.15/36.05 | | | | | | | | all_157_4) = v0 & $i(v0))
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (commutativity_k4_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_5, all_157_4, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (71), (72), (82), (84)
% 202.15/36.05 | | | | | | | | gives:
% 202.15/36.05 | | | | | | | | (177) ? [v0: $i] : (subset_union2(all_91_2, all_157_4,
% 202.15/36.05 | | | | | | | | all_157_5) = v0 & subset_union2(all_91_2,
% 202.15/36.05 | | | | | | | | all_157_5, all_157_4) = v0 & $i(v0))
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_5, all_157_4, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (71), (72), (82), (84)
% 202.15/36.05 | | | | | | | | gives:
% 202.15/36.05 | | | | | | | | (178) ? [v0: $i] : (subset_union2(all_91_2, all_157_5,
% 202.15/36.05 | | | | | | | | all_157_4) = v0 & set_union2(all_157_5, all_157_4)
% 202.15/36.05 | | | | | | | | = v0 & $i(v0))
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (redefinition_k4_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_4, all_157_5, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (71), (72), (82), (84)
% 202.15/36.05 | | | | | | | | gives:
% 202.15/36.05 | | | | | | | | (179) ? [v0: $i] : (subset_union2(all_91_2, all_157_4,
% 202.15/36.05 | | | | | | | | all_157_5) = v0 & set_union2(all_157_4, all_157_5)
% 202.15/36.05 | | | | | | | | = v0 & $i(v0))
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | GROUND_INST: instantiating (idempotence_k4_subset_1) with
% 202.15/36.05 | | | | | | | | all_91_2, all_157_4, empty_set, all_91_1,
% 202.15/36.05 | | | | | | | | simplifying with (14), (17), (72), (84), (127),
% 202.15/36.05 | | | | | | | | (167) gives:
% 202.15/36.05 | | | | | | | | (180) subset_union2(all_91_2, all_157_4, all_157_4) =
% 202.15/36.05 | | | | | | | | all_157_4
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | DELTA: instantiating (173) with fresh symbol all_426_0 gives:
% 202.15/36.05 | | | | | | | | (181) subset_union2(all_91_2, all_157_4, all_157_4) =
% 202.15/36.05 | | | | | | | | all_426_0 & $i(all_426_0)
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | ALPHA: (181) implies:
% 202.15/36.05 | | | | | | | | (182) $i(all_426_0)
% 202.15/36.05 | | | | | | | | (183) subset_union2(all_91_2, all_157_4, all_157_4) =
% 202.15/36.05 | | | | | | | | all_426_0
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | DELTA: instantiating (171) with fresh symbol all_428_0 gives:
% 202.15/36.05 | | | | | | | | (184) subset_union2(all_91_2, all_157_5, all_157_5) =
% 202.15/36.05 | | | | | | | | all_428_0 & $i(all_428_0)
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | ALPHA: (184) implies:
% 202.15/36.05 | | | | | | | | (185) $i(all_428_0)
% 202.15/36.05 | | | | | | | | (186) subset_union2(all_91_2, all_157_5, all_157_5) =
% 202.15/36.05 | | | | | | | | all_428_0
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | DELTA: instantiating (179) with fresh symbol all_604_0 gives:
% 202.15/36.05 | | | | | | | | (187) subset_union2(all_91_2, all_157_4, all_157_5) =
% 202.15/36.05 | | | | | | | | all_604_0 & set_union2(all_157_4, all_157_5) =
% 202.15/36.05 | | | | | | | | all_604_0 & $i(all_604_0)
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | ALPHA: (187) implies:
% 202.15/36.05 | | | | | | | | (188) subset_union2(all_91_2, all_157_4, all_157_5) =
% 202.15/36.05 | | | | | | | | all_604_0
% 202.15/36.05 | | | | | | | |
% 202.15/36.05 | | | | | | | | DELTA: instantiating (178) with fresh symbol all_606_0 gives:
% 202.15/36.06 | | | | | | | | (189) subset_union2(all_91_2, all_157_5, all_157_4) =
% 202.15/36.06 | | | | | | | | all_606_0 & set_union2(all_157_5, all_157_4) =
% 202.15/36.06 | | | | | | | | all_606_0 & $i(all_606_0)
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | ALPHA: (189) implies:
% 202.15/36.06 | | | | | | | | (190) set_union2(all_157_5, all_157_4) = all_606_0
% 202.15/36.06 | | | | | | | | (191) subset_union2(all_91_2, all_157_5, all_157_4) =
% 202.15/36.06 | | | | | | | | all_606_0
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | DELTA: instantiating (177) with fresh symbol all_644_0 gives:
% 202.15/36.06 | | | | | | | | (192) subset_union2(all_91_2, all_157_4, all_157_5) =
% 202.15/36.06 | | | | | | | | all_644_0 & subset_union2(all_91_2, all_157_5,
% 202.15/36.06 | | | | | | | | all_157_4) = all_644_0 & $i(all_644_0)
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | ALPHA: (192) implies:
% 202.15/36.06 | | | | | | | | (193) subset_union2(all_91_2, all_157_5, all_157_4) =
% 202.15/36.06 | | | | | | | | all_644_0
% 202.15/36.06 | | | | | | | | (194) subset_union2(all_91_2, all_157_4, all_157_5) =
% 202.15/36.06 | | | | | | | | all_644_0
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | DELTA: instantiating (172) with fresh symbol all_668_0 gives:
% 202.15/36.06 | | | | | | | | (195) subset_union2(all_91_2, all_157_5, all_157_5) =
% 202.15/36.06 | | | | | | | | all_668_0 & set_union2(all_157_5, all_157_5) =
% 202.15/36.06 | | | | | | | | all_668_0 & $i(all_668_0)
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | ALPHA: (195) implies:
% 202.15/36.06 | | | | | | | | (196) subset_union2(all_91_2, all_157_5, all_157_5) =
% 202.15/36.06 | | | | | | | | all_668_0
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | DELTA: instantiating (176) with fresh symbol all_674_0 gives:
% 202.15/36.06 | | | | | | | | (197) set_difference(all_157_5, all_157_4) = all_674_0 &
% 202.15/36.06 | | | | | | | | subset_difference(all_91_2, all_157_5, all_157_4) =
% 202.15/36.06 | | | | | | | | all_674_0 & $i(all_674_0)
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | ALPHA: (197) implies:
% 202.15/36.06 | | | | | | | | (198) subset_difference(all_91_2, all_157_5, all_157_4) =
% 202.15/36.06 | | | | | | | | all_674_0
% 202.15/36.06 | | | | | | | | (199) set_difference(all_157_5, all_157_4) = all_674_0
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | DELTA: instantiating (174) with fresh symbol all_676_0 gives:
% 202.15/36.06 | | | | | | | | (200) subset_union2(all_91_2, all_157_4, all_157_4) =
% 202.15/36.06 | | | | | | | | all_676_0 & set_union2(all_157_4, all_157_4) =
% 202.15/36.06 | | | | | | | | all_676_0 & $i(all_676_0)
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | ALPHA: (200) implies:
% 202.15/36.06 | | | | | | | | (201) subset_union2(all_91_2, all_157_4, all_157_4) =
% 202.15/36.06 | | | | | | | | all_676_0
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | BETA: splitting (169) gives:
% 202.15/36.06 | | | | | | | |
% 202.15/36.06 | | | | | | | | Case 1:
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | (202) all_333_0 = 0
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | REDUCE: (134), (202) imply:
% 202.15/36.06 | | | | | | | | | (203) $false
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | CLOSE: (203) is inconsistent.
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | Case 2:
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | (204) ? [v0: $i] : (powerset(all_333_1) = v0 & $i(v0) & ?
% 202.15/36.06 | | | | | | | | | [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 202.15/36.06 | | | | | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1)))
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | DELTA: instantiating (204) with fresh symbol all_952_0 gives:
% 202.15/36.06 | | | | | | | | | (205) powerset(all_333_1) = all_952_0 & $i(all_952_0) & ?
% 202.15/36.06 | | | | | | | | | [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & element(v0,
% 202.15/36.06 | | | | | | | | | all_952_0) = 0 & empty(v0) = v1 & $i(v0))
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | ALPHA: (205) implies:
% 202.15/36.06 | | | | | | | | | (206) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 202.15/36.06 | | | | | | | | | element(v0, all_952_0) = 0 & empty(v0) = v1 &
% 202.15/36.06 | | | | | | | | | $i(v0))
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | DELTA: instantiating (206) with fresh symbols all_954_0,
% 202.15/36.06 | | | | | | | | | all_954_1 gives:
% 202.15/36.06 | | | | | | | | | (207) ~ (all_954_0 = 0) & element(all_954_1, all_952_0) =
% 202.15/36.06 | | | | | | | | | 0 & empty(all_954_1) = all_954_0 & $i(all_954_1)
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | ALPHA: (207) implies:
% 202.15/36.06 | | | | | | | | | (208) ~ (all_954_0 = 0)
% 202.15/36.06 | | | | | | | | | (209) $i(all_954_1)
% 202.15/36.06 | | | | | | | | | (210) empty(all_954_1) = all_954_0
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | BETA: splitting (170) gives:
% 202.15/36.06 | | | | | | | | |
% 202.15/36.06 | | | | | | | | | Case 1:
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | (211) all_382_0 = 0
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | REDUCE: (143), (211) imply:
% 202.15/36.06 | | | | | | | | | | (212) $false
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | CLOSE: (212) is inconsistent.
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | Case 2:
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | (213) ? [v0: $i] : (powerset(all_382_1) = v0 & $i(v0) &
% 202.15/36.06 | | | | | | | | | | ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) &
% 202.15/36.06 | | | | | | | | | | element(v1, v0) = 0 & empty(v1) = v2 & $i(v1)))
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | DELTA: instantiating (213) with fresh symbol all_1148_0
% 202.15/36.06 | | | | | | | | | | gives:
% 202.15/36.06 | | | | | | | | | | (214) powerset(all_382_1) = all_1148_0 & $i(all_1148_0) &
% 202.15/36.06 | | | | | | | | | | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 202.15/36.06 | | | | | | | | | | element(v0, all_1148_0) = 0 & empty(v0) = v1 &
% 202.15/36.06 | | | | | | | | | | $i(v0))
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | ALPHA: (214) implies:
% 202.15/36.06 | | | | | | | | | | (215) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 202.15/36.06 | | | | | | | | | | element(v0, all_1148_0) = 0 & empty(v0) = v1 &
% 202.15/36.06 | | | | | | | | | | $i(v0))
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | DELTA: instantiating (215) with fresh symbols all_1150_0,
% 202.15/36.06 | | | | | | | | | | all_1150_1 gives:
% 202.15/36.06 | | | | | | | | | | (216) ~ (all_1150_0 = 0) & element(all_1150_1,
% 202.15/36.06 | | | | | | | | | | all_1148_0) = 0 & empty(all_1150_1) = all_1150_0
% 202.15/36.06 | | | | | | | | | | & $i(all_1150_1)
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | ALPHA: (216) implies:
% 202.15/36.06 | | | | | | | | | | (217) ~ (all_1150_0 = 0)
% 202.15/36.06 | | | | | | | | | | (218) $i(all_1150_1)
% 202.15/36.06 | | | | | | | | | | (219) empty(all_1150_1) = all_1150_0
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | BETA: splitting (168) gives:
% 202.15/36.06 | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | Case 1:
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | | (220) all_191_0 = 0
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | | REDUCE: (107), (220) imply:
% 202.15/36.06 | | | | | | | | | | | (221) $false
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | | CLOSE: (221) is inconsistent.
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | Case 2:
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | | GROUND_INST: instantiating (5) with all_157_3, all_606_0,
% 202.15/36.06 | | | | | | | | | | | all_157_4, all_157_5, simplifying with (79), (190)
% 202.15/36.06 | | | | | | | | | | | gives:
% 202.15/36.06 | | | | | | | | | | | (222) all_606_0 = all_157_3
% 202.15/36.06 | | | | | | | | | | |
% 202.15/36.06 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_428_0, all_668_0,
% 202.15/36.06 | | | | | | | | | | | all_157_5, all_157_5, all_91_2, simplifying with
% 202.15/36.06 | | | | | | | | | | | (186), (196) gives:
% 202.15/36.06 | | | | | | | | | | | (223) all_668_0 = all_428_0
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_157_5, all_668_0,
% 202.15/36.07 | | | | | | | | | | | all_157_5, all_157_5, all_91_2, simplifying with
% 202.15/36.07 | | | | | | | | | | | (175), (196) gives:
% 202.15/36.07 | | | | | | | | | | | (224) all_668_0 = all_157_5
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_606_0, all_644_0,
% 202.15/36.07 | | | | | | | | | | | all_157_4, all_157_5, all_91_2, simplifying with
% 202.15/36.07 | | | | | | | | | | | (191), (193) gives:
% 202.15/36.07 | | | | | | | | | | | (225) all_644_0 = all_606_0
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_604_0, all_644_0,
% 202.15/36.07 | | | | | | | | | | | all_157_5, all_157_4, all_91_2, simplifying with
% 202.15/36.07 | | | | | | | | | | | (188), (194) gives:
% 202.15/36.07 | | | | | | | | | | | (226) all_644_0 = all_604_0
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_426_0, all_676_0,
% 202.15/36.07 | | | | | | | | | | | all_157_4, all_157_4, all_91_2, simplifying with
% 202.15/36.07 | | | | | | | | | | | (183), (201) gives:
% 202.15/36.07 | | | | | | | | | | | (227) all_676_0 = all_426_0
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | GROUND_INST: instantiating (7) with all_157_4, all_676_0,
% 202.15/36.07 | | | | | | | | | | | all_157_4, all_157_4, all_91_2, simplifying with
% 202.15/36.07 | | | | | | | | | | | (180), (201) gives:
% 202.15/36.07 | | | | | | | | | | | (228) all_676_0 = all_157_4
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_157_1, all_674_0,
% 202.15/36.07 | | | | | | | | | | | all_157_4, all_157_5, simplifying with (80), (199)
% 202.15/36.07 | | | | | | | | | | | gives:
% 202.15/36.07 | | | | | | | | | | | (229) all_674_0 = all_157_1
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | COMBINE_EQS: (227), (228) imply:
% 202.15/36.07 | | | | | | | | | | | (230) all_426_0 = all_157_4
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | SIMP: (230) implies:
% 202.15/36.07 | | | | | | | | | | | (231) all_426_0 = all_157_4
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | COMBINE_EQS: (223), (224) imply:
% 202.15/36.07 | | | | | | | | | | | (232) all_428_0 = all_157_5
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | COMBINE_EQS: (225), (226) imply:
% 202.15/36.07 | | | | | | | | | | | (233) all_606_0 = all_604_0
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | SIMP: (233) implies:
% 202.15/36.07 | | | | | | | | | | | (234) all_606_0 = all_604_0
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | COMBINE_EQS: (222), (234) imply:
% 202.15/36.07 | | | | | | | | | | | (235) all_604_0 = all_157_3
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | REDUCE: (198), (229) imply:
% 202.15/36.07 | | | | | | | | | | | (236) subset_difference(all_91_2, all_157_5, all_157_4)
% 202.15/36.07 | | | | | | | | | | | = all_157_1
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | REDUCE: (191), (222) imply:
% 202.15/36.07 | | | | | | | | | | | (237) subset_union2(all_91_2, all_157_5, all_157_4) =
% 202.15/36.07 | | | | | | | | | | | all_157_3
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | BETA: splitting (81) gives:
% 202.15/36.07 | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | Case 1:
% 202.15/36.07 | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | (238) ~ (all_157_0 = 0)
% 202.15/36.07 | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | BETA: splitting (86) gives:
% 202.15/36.07 | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | Case 1:
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | (239) all_157_0 = 0
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | REDUCE: (238), (239) imply:
% 202.15/36.07 | | | | | | | | | | | | | (240) $false
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | Case 2:
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | (241) ? [v0: any] : ? [v1: any] : (element(all_157_1,
% 202.15/36.07 | | | | | | | | | | | | | all_91_1) = v0 & empty(all_91_1) = v1 & ( ~
% 202.15/36.07 | | | | | | | | | | | | | (v0 = 0) | v1 = 0))
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | DELTA: instantiating (241) with fresh symbols all_1273_0,
% 202.15/36.07 | | | | | | | | | | | | | all_1273_1 gives:
% 202.15/36.07 | | | | | | | | | | | | | (242) element(all_157_1, all_91_1) = all_1273_1 &
% 202.15/36.07 | | | | | | | | | | | | | empty(all_91_1) = all_1273_0 & ( ~ (all_1273_1 =
% 202.15/36.07 | | | | | | | | | | | | | 0) | all_1273_0 = 0)
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | ALPHA: (242) implies:
% 202.15/36.07 | | | | | | | | | | | | | (243) empty(all_91_1) = all_1273_0
% 202.15/36.07 | | | | | | | | | | | | | (244) element(all_157_1, all_91_1) = all_1273_1
% 202.15/36.07 | | | | | | | | | | | | | (245) ~ (all_1273_1 = 0) | all_1273_0 = 0
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_102_0, all_1273_0,
% 202.15/36.07 | | | | | | | | | | | | | all_91_1, simplifying with (31), (243) gives:
% 202.15/36.07 | | | | | | | | | | | | | (246) all_1273_0 = all_102_0
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | BETA: splitting (245) gives:
% 202.15/36.07 | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | Case 1:
% 202.15/36.07 | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | (247) ~ (all_1273_1 = 0)
% 202.15/36.07 | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | GROUND_INST: instantiating (rc4_finset_1) with all_954_1,
% 202.15/36.07 | | | | | | | | | | | | | | all_954_0, simplifying with (209), (210) gives:
% 202.15/36.07 | | | | | | | | | | | | | | (248) all_954_0 = 0 | ? [v0: $i] : (powerset(all_954_1)
% 202.15/36.07 | | | | | | | | | | | | | | = v0 & $i(v0) & ? [v1: $i] : ? [v2: int] : ( ~
% 202.15/36.07 | | | | | | | | | | | | | | (v2 = 0) & element(v1, v0) = 0 & finite(v1) =
% 202.15/36.07 | | | | | | | | | | | | | | 0 & empty(v1) = v2 & $i(v1)))
% 202.15/36.07 | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | GROUND_INST: instantiating (dt_k6_subset_1) with all_91_2,
% 202.15/36.07 | | | | | | | | | | | | | | all_157_5, all_157_4, all_91_1, all_157_1,
% 202.15/36.07 | | | | | | | | | | | | | | all_1273_1, simplifying with (14), (17), (71),
% 202.15/36.07 | | | | | | | | | | | | | | (72), (236), (244) gives:
% 202.15/36.07 | | | | | | | | | | | | | | (249) all_1273_1 = 0 | ? [v0: any] : ? [v1: any] :
% 202.15/36.07 | | | | | | | | | | | | | | (element(all_157_4, all_91_1) = v1 &
% 202.15/36.07 | | | | | | | | | | | | | | element(all_157_5, all_91_1) = v0 & ( ~ (v1 = 0)
% 202.15/36.07 | | | | | | | | | | | | | | | ~ (v0 = 0)))
% 202.15/36.07 | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 202.15/36.07 | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | Case 1:
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | (250) all_1273_1 = 0
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | REDUCE: (247), (250) imply:
% 202.15/36.07 | | | | | | | | | | | | | | | (251) $false
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | CLOSE: (251) is inconsistent.
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | Case 2:
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | (252) ? [v0: any] : ? [v1: any] : (element(all_157_4,
% 202.15/36.07 | | | | | | | | | | | | | | | all_91_1) = v1 & element(all_157_5, all_91_1)
% 202.15/36.07 | | | | | | | | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | DELTA: instantiating (252) with fresh symbols all_2703_0,
% 202.15/36.07 | | | | | | | | | | | | | | | all_2703_1 gives:
% 202.15/36.07 | | | | | | | | | | | | | | | (253) element(all_157_4, all_91_1) = all_2703_0 &
% 202.15/36.07 | | | | | | | | | | | | | | | element(all_157_5, all_91_1) = all_2703_1 & ( ~
% 202.15/36.07 | | | | | | | | | | | | | | | (all_2703_0 = 0) | ~ (all_2703_1 = 0))
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 202.15/36.07 | | | | | | | | | | | | | | | (254) element(all_157_5, all_91_1) = all_2703_1
% 202.15/36.07 | | | | | | | | | | | | | | | (255) element(all_157_4, all_91_1) = all_2703_0
% 202.15/36.07 | | | | | | | | | | | | | | | (256) ~ (all_2703_0 = 0) | ~ (all_2703_1 = 0)
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 202.15/36.07 | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | Case 1:
% 202.15/36.07 | | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | | (257) all_954_0 = 0
% 202.15/36.07 | | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | | REDUCE: (208), (257) imply:
% 202.15/36.07 | | | | | | | | | | | | | | | | (258) $false
% 202.15/36.07 | | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | | CLOSE: (258) is inconsistent.
% 202.15/36.07 | | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | Case 2:
% 202.15/36.07 | | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | |
% 202.15/36.07 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_2703_1, all_91_1,
% 202.15/36.07 | | | | | | | | | | | | | | | | all_157_5, simplifying with (82), (254) gives:
% 202.15/36.08 | | | | | | | | | | | | | | | | (259) all_2703_1 = 0
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_2703_0, all_91_1,
% 202.15/36.08 | | | | | | | | | | | | | | | | all_157_4, simplifying with (84), (255) gives:
% 202.15/36.08 | | | | | | | | | | | | | | | | (260) all_2703_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | BETA: splitting (256) gives:
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | Case 1:
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | (261) ~ (all_2703_0 = 0)
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | REDUCE: (260), (261) imply:
% 202.15/36.08 | | | | | | | | | | | | | | | | | (262) $false
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | CLOSE: (262) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | (263) ~ (all_2703_1 = 0)
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | REDUCE: (259), (263) imply:
% 202.15/36.08 | | | | | | | | | | | | | | | | | (264) $false
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | (265) all_1273_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | COMBINE_EQS: (246), (265) imply:
% 202.15/36.08 | | | | | | | | | | | | | | (266) all_102_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | REDUCE: (30), (266) imply:
% 202.15/36.08 | | | | | | | | | | | | | | (267) $false
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | (268) ~ (all_157_2 = 0)
% 202.15/36.08 | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | BETA: splitting (85) gives:
% 202.15/36.08 | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | Case 1:
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | (269) all_157_2 = 0
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | REDUCE: (268), (269) imply:
% 202.15/36.08 | | | | | | | | | | | | | (270) $false
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | CLOSE: (270) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | (271) ? [v0: any] : ? [v1: any] : (element(all_157_3,
% 202.15/36.08 | | | | | | | | | | | | | all_91_1) = v0 & empty(all_91_1) = v1 & ( ~
% 202.15/36.08 | | | | | | | | | | | | | (v0 = 0) | v1 = 0))
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | DELTA: instantiating (271) with fresh symbols all_1273_0,
% 202.15/36.08 | | | | | | | | | | | | | all_1273_1 gives:
% 202.15/36.08 | | | | | | | | | | | | | (272) element(all_157_3, all_91_1) = all_1273_1 &
% 202.15/36.08 | | | | | | | | | | | | | empty(all_91_1) = all_1273_0 & ( ~ (all_1273_1 =
% 202.15/36.08 | | | | | | | | | | | | | 0) | all_1273_0 = 0)
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | ALPHA: (272) implies:
% 202.15/36.08 | | | | | | | | | | | | | (273) empty(all_91_1) = all_1273_0
% 202.15/36.08 | | | | | | | | | | | | | (274) element(all_157_3, all_91_1) = all_1273_1
% 202.15/36.08 | | | | | | | | | | | | | (275) ~ (all_1273_1 = 0) | all_1273_0 = 0
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_102_0, all_1273_0,
% 202.15/36.08 | | | | | | | | | | | | | all_91_1, simplifying with (31), (273) gives:
% 202.15/36.08 | | | | | | | | | | | | | (276) all_1273_0 = all_102_0
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | BETA: splitting (275) gives:
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | Case 1:
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | (277) ~ (all_1273_1 = 0)
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (rc4_finset_1) with all_1150_1,
% 202.15/36.08 | | | | | | | | | | | | | | all_1150_0, simplifying with (218), (219) gives:
% 202.15/36.08 | | | | | | | | | | | | | | (278) all_1150_0 = 0 | ? [v0: $i] :
% 202.15/36.08 | | | | | | | | | | | | | | (powerset(all_1150_1) = v0 & $i(v0) & ? [v1: $i]
% 202.15/36.08 | | | | | | | | | | | | | | : ? [v2: int] : ( ~ (v2 = 0) & element(v1, v0)
% 202.15/36.08 | | | | | | | | | | | | | | = 0 & finite(v1) = 0 & empty(v1) = v2 &
% 202.15/36.08 | | | | | | | | | | | | | | $i(v1)))
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | GROUND_INST: instantiating (dt_k4_subset_1) with all_91_2,
% 202.15/36.08 | | | | | | | | | | | | | | all_157_5, all_157_4, all_91_1, all_157_3,
% 202.15/36.08 | | | | | | | | | | | | | | all_1273_1, simplifying with (14), (17), (71),
% 202.15/36.08 | | | | | | | | | | | | | | (72), (237), (274) gives:
% 202.15/36.08 | | | | | | | | | | | | | | (279) all_1273_1 = 0 | ? [v0: any] : ? [v1: any] :
% 202.15/36.08 | | | | | | | | | | | | | | (element(all_157_4, all_91_1) = v1 &
% 202.15/36.08 | | | | | | | | | | | | | | element(all_157_5, all_91_1) = v0 & ( ~ (v1 = 0)
% 202.15/36.08 | | | | | | | | | | | | | | | ~ (v0 = 0)))
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | BETA: splitting (279) gives:
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | Case 1:
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | (280) all_1273_1 = 0
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | REDUCE: (277), (280) imply:
% 202.15/36.08 | | | | | | | | | | | | | | | (281) $false
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | CLOSE: (281) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | (282) ? [v0: any] : ? [v1: any] : (element(all_157_4,
% 202.15/36.08 | | | | | | | | | | | | | | | all_91_1) = v1 & element(all_157_5, all_91_1)
% 202.15/36.08 | | | | | | | | | | | | | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | DELTA: instantiating (282) with fresh symbols all_2685_0,
% 202.15/36.08 | | | | | | | | | | | | | | | all_2685_1 gives:
% 202.15/36.08 | | | | | | | | | | | | | | | (283) element(all_157_4, all_91_1) = all_2685_0 &
% 202.15/36.08 | | | | | | | | | | | | | | | element(all_157_5, all_91_1) = all_2685_1 & ( ~
% 202.15/36.08 | | | | | | | | | | | | | | | (all_2685_0 = 0) | ~ (all_2685_1 = 0))
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | ALPHA: (283) implies:
% 202.15/36.08 | | | | | | | | | | | | | | | (284) element(all_157_5, all_91_1) = all_2685_1
% 202.15/36.08 | | | | | | | | | | | | | | | (285) element(all_157_4, all_91_1) = all_2685_0
% 202.15/36.08 | | | | | | | | | | | | | | | (286) ~ (all_2685_0 = 0) | ~ (all_2685_1 = 0)
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | Case 1:
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | (287) all_1150_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | REDUCE: (217), (287) imply:
% 202.15/36.08 | | | | | | | | | | | | | | | | (288) $false
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | CLOSE: (288) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_2685_1, all_91_1,
% 202.15/36.08 | | | | | | | | | | | | | | | | all_157_5, simplifying with (82), (284) gives:
% 202.15/36.08 | | | | | | | | | | | | | | | | (289) all_2685_1 = 0
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (4) with 0, all_2685_0, all_91_1,
% 202.15/36.08 | | | | | | | | | | | | | | | | all_157_4, simplifying with (84), (285) gives:
% 202.15/36.08 | | | | | | | | | | | | | | | | (290) all_2685_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | Case 1:
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | (291) ~ (all_2685_0 = 0)
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | REDUCE: (290), (291) imply:
% 202.15/36.08 | | | | | | | | | | | | | | | | | (292) $false
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | CLOSE: (292) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | (293) ~ (all_2685_1 = 0)
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | REDUCE: (289), (293) imply:
% 202.15/36.08 | | | | | | | | | | | | | | | | | (294) $false
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | | CLOSE: (294) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | Case 2:
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | (295) all_1273_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | COMBINE_EQS: (276), (295) imply:
% 202.15/36.08 | | | | | | | | | | | | | | (296) all_102_0 = 0
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | REDUCE: (30), (296) imply:
% 202.15/36.08 | | | | | | | | | | | | | | (297) $false
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | | CLOSE: (297) is inconsistent.
% 202.15/36.08 | | | | | | | | | | | | | |
% 202.15/36.08 | | | | | | | | | | | | | End of split
% 202.15/36.08 | | | | | | | | | | | | |
% 202.15/36.09 | | | | | | | | | | | | End of split
% 202.15/36.09 | | | | | | | | | | | |
% 202.15/36.09 | | | | | | | | | | | End of split
% 202.15/36.09 | | | | | | | | | | |
% 202.15/36.09 | | | | | | | | | | End of split
% 202.15/36.09 | | | | | | | | | |
% 202.15/36.09 | | | | | | | | | End of split
% 202.15/36.09 | | | | | | | | |
% 202.15/36.09 | | | | | | | | End of split
% 202.15/36.09 | | | | | | | |
% 202.15/36.09 | | | | | | | End of split
% 202.15/36.09 | | | | | | |
% 202.15/36.09 | | | | | | End of split
% 202.15/36.09 | | | | | |
% 202.15/36.09 | | | | | End of split
% 202.15/36.09 | | | | |
% 202.15/36.09 | | | | End of split
% 202.15/36.09 | | | |
% 202.15/36.09 | | | End of split
% 202.15/36.09 | | |
% 202.15/36.09 | | End of split
% 202.15/36.09 | |
% 202.15/36.09 | End of split
% 202.15/36.09 |
% 202.15/36.09 End of proof
% 202.15/36.09 % SZS output end Proof for theBenchmark
% 202.15/36.09
% 202.15/36.09 35472ms
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