TSTP Solution File: SEU327+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:44:07 EDT 2023
% Result : Theorem 13.46s 2.56s
% Output : Proof 25.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU327+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n014.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Aug 23 16:01:49 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.60 Running up to 7 provers in parallel.
% 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.47/1.17 Prover 1: Preprocessing ...
% 3.47/1.17 Prover 4: Preprocessing ...
% 3.64/1.20 Prover 0: Preprocessing ...
% 3.64/1.20 Prover 5: Preprocessing ...
% 3.64/1.21 Prover 2: Preprocessing ...
% 3.64/1.21 Prover 3: Preprocessing ...
% 3.64/1.21 Prover 6: Preprocessing ...
% 8.48/1.88 Prover 1: Warning: ignoring some quantifiers
% 8.91/1.94 Prover 3: Warning: ignoring some quantifiers
% 8.91/1.96 Prover 1: Constructing countermodel ...
% 8.91/1.96 Prover 5: Proving ...
% 8.91/1.97 Prover 3: Constructing countermodel ...
% 8.91/1.97 Prover 6: Proving ...
% 9.54/2.08 Prover 2: Proving ...
% 10.03/2.16 Prover 4: Warning: ignoring some quantifiers
% 10.03/2.21 Prover 4: Constructing countermodel ...
% 11.88/2.40 Prover 0: Proving ...
% 13.35/2.55 Prover 5: proved (1939ms)
% 13.35/2.56
% 13.46/2.56 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.46/2.56
% 13.46/2.56 Prover 3: stopped
% 13.46/2.56 Prover 0: stopped
% 13.46/2.57 Prover 6: stopped
% 13.46/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.46/2.58 Prover 2: stopped
% 13.46/2.58 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.46/2.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.46/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.46/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.14/2.69 Prover 11: Preprocessing ...
% 14.14/2.70 Prover 10: Preprocessing ...
% 14.14/2.70 Prover 8: Preprocessing ...
% 14.14/2.71 Prover 13: Preprocessing ...
% 14.14/2.72 Prover 7: Preprocessing ...
% 15.12/2.93 Prover 13: Warning: ignoring some quantifiers
% 15.12/2.93 Prover 7: Warning: ignoring some quantifiers
% 15.12/2.94 Prover 10: Warning: ignoring some quantifiers
% 15.12/2.96 Prover 7: Constructing countermodel ...
% 15.12/2.97 Prover 10: Constructing countermodel ...
% 15.12/2.99 Prover 13: Constructing countermodel ...
% 16.75/3.03 Prover 8: Warning: ignoring some quantifiers
% 16.75/3.05 Prover 8: Constructing countermodel ...
% 18.55/3.26 Prover 11: Warning: ignoring some quantifiers
% 18.55/3.28 Prover 11: Constructing countermodel ...
% 20.12/3.46 Prover 10: gave up
% 20.12/3.47 Prover 13: gave up
% 20.12/3.48 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 20.12/3.48 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 20.46/3.53 Prover 19: Preprocessing ...
% 20.46/3.54 Prover 16: Preprocessing ...
% 21.75/3.69 Prover 16: Warning: ignoring some quantifiers
% 21.75/3.72 Prover 16: Constructing countermodel ...
% 22.19/3.74 Prover 19: Warning: ignoring some quantifiers
% 22.19/3.75 Prover 19: Constructing countermodel ...
% 24.72/4.11 Prover 7: Found proof (size 160)
% 24.72/4.11 Prover 7: proved (1545ms)
% 24.72/4.11 Prover 16: stopped
% 24.72/4.11 Prover 19: stopped
% 24.72/4.11 Prover 4: stopped
% 24.72/4.11 Prover 8: stopped
% 24.72/4.11 Prover 1: stopped
% 24.72/4.11 Prover 11: stopped
% 24.72/4.11
% 24.72/4.11 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.72/4.11
% 25.20/4.12 % SZS output start Proof for theBenchmark
% 25.20/4.13 Assumptions after simplification:
% 25.20/4.13 ---------------------------------
% 25.20/4.13
% 25.20/4.13 (d4_subset_1)
% 25.20/4.15 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (cast_to_subset(v0) = v1) | ~
% 25.20/4.15 $i(v0))
% 25.20/4.15
% 25.20/4.15 (d5_subset_1)
% 25.20/4.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 25.20/4.15 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v2 &
% 25.20/4.15 subset_complement(v0, v1) = v2 & $i(v2)) | (powerset(v0) = v3 & $i(v3) &
% 25.20/4.15 ~ element(v1, v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 25.20/4.15 (subset_complement(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 25.20/4.15 [v4: $i] : ((v4 = v2 & set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0)
% 25.20/4.15 = v3 & $i(v3) & ~ element(v1, v3))))
% 25.20/4.15
% 25.20/4.15 (dt_k2_subset_1)
% 25.20/4.15 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_to_subset(v0) = v1) | ~ $i(v0) | ?
% 25.20/4.15 [v2: $i] : (powerset(v0) = v2 & $i(v2) & element(v1, v2))) & ! [v0: $i] :
% 25.20/4.15 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 25.20/4.15 (cast_to_subset(v0) = v2 & $i(v2) & element(v2, v1)))
% 25.20/4.15
% 25.20/4.15 (dt_k3_subset_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 25.20/4.16 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~
% 25.20/4.16 element(v1, v3) | element(v2, v3))))
% 25.20/4.16
% 25.20/4.16 (dt_k5_setfam_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union_of_subsets(v0, v1) = v2)
% 25.20/4.16 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v0) = v3 &
% 25.20/4.16 $i(v3) & (element(v2, v3) | (powerset(v3) = v4 & $i(v4) & ~ element(v1,
% 25.20/4.16 v4)))))
% 25.20/4.16
% 25.20/4.16 (dt_k6_setfam_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (meet_of_subsets(v0, v1) = v2) |
% 25.20/4.16 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v0) = v3 &
% 25.20/4.16 $i(v3) & (element(v2, v3) | (powerset(v3) = v4 & $i(v4) & ~ element(v1,
% 25.20/4.16 v4)))))
% 25.20/4.16
% 25.20/4.16 (dt_k7_setfam_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (complements_of_subsets(v0, v1)
% 25.20/4.16 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v3)
% 25.20/4.16 = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ element(v1, v4) |
% 25.20/4.16 element(v2, v4))))
% 25.20/4.16
% 25.20/4.16 (fc1_subset_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ~
% 25.20/4.16 empty(v1))
% 25.20/4.16
% 25.20/4.16 (rc2_subset_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i]
% 25.20/4.16 : ($i(v2) & empty(v2) & element(v2, v1)))
% 25.20/4.16
% 25.20/4.16 (redefinition_k6_subset_1)
% 25.20/4.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 25.20/4.16 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 25.20/4.16 ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & set_difference(v1, v2) = v3 & $i(v3))
% 25.20/4.16 | (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ element(v1,
% 25.20/4.16 v4)))))
% 25.20/4.16
% 25.20/4.16 (t11_tops_2)
% 25.20/4.16 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 25.20/4.16 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v5) & ~ (v1 =
% 25.20/4.17 empty_set) & complements_of_subsets(v0, v1) = v4 & meet_of_subsets(v0, v4)
% 25.20/4.17 = v5 & union_of_subsets(v0, v1) = v6 & subset_complement(v0, v6) = v7 &
% 25.20/4.17 powerset(v2) = v3 & powerset(v0) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 25.20/4.17 $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v1, v3))
% 25.20/4.17
% 25.20/4.17 (t2_subset)
% 25.20/4.17 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) |
% 25.20/4.17 empty(v1) | in(v0, v1))
% 25.20/4.17
% 25.20/4.17 (t47_setfam_1)
% 25.20/4.17 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~
% 25.20/4.17 (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 25.20/4.17 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ((v8
% 25.20/4.17 = v7 & subset_difference(v0, v5, v6) = v7 & meet_of_subsets(v0, v2) = v7
% 25.20/4.17 & union_of_subsets(v0, v1) = v6 & cast_to_subset(v0) = v5 & $i(v7) &
% 25.20/4.17 $i(v6) & $i(v5)) | (powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) &
% 25.20/4.17 $i(v3) & ~ element(v1, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 25.20/4.17 : (v1 = empty_set | ~ (union_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 25.20/4.17 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 25.20/4.17 [v8: $i] : ((v8 = v6 & complements_of_subsets(v0, v1) = v7 &
% 25.20/4.17 subset_difference(v0, v5, v2) = v6 & meet_of_subsets(v0, v7) = v6 &
% 25.20/4.17 cast_to_subset(v0) = v5 & $i(v7) & $i(v6) & $i(v5)) | (powerset(v3) = v4
% 25.20/4.17 & powerset(v0) = v3 & $i(v4) & $i(v3) & ~ element(v1, v4))))
% 25.20/4.17
% 25.20/4.17 (function-axioms)
% 25.20/4.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 25.20/4.17 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 25.20/4.17 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 25.20/4.17 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 25.20/4.17 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 25.20/4.17 $i] : ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 25.20/4.17 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 25.20/4.17 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 25.20/4.17 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 25.20/4.17 ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 25.20/4.17 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 25.20/4.17 ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 25.20/4.17 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 25.20/4.17 : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] :
% 25.20/4.17 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) =
% 25.20/4.17 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 25.20/4.17 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 25.20/4.17 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 25.20/4.17 = v0))
% 25.20/4.17
% 25.20/4.17 Further assumptions not needed in the proof:
% 25.20/4.17 --------------------------------------------
% 25.20/4.17 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered,
% 25.20/4.17 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 25.20/4.17 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered,
% 25.20/4.17 cc3_membered, cc4_membered, dt_k1_setfam_1, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 25.20/4.17 dt_k3_tarski, dt_k4_xboole_0, dt_k6_subset_1, dt_m1_subset_1,
% 25.20/4.17 existence_m1_subset_1, fc37_membered, fc38_membered, fc39_membered,
% 25.20/4.17 fc40_membered, fc41_membered, fc6_membered, involutiveness_k3_subset_1,
% 25.20/4.17 involutiveness_k7_setfam_1, rc1_membered, rc1_subset_1,
% 25.20/4.17 redefinition_k5_setfam_1, redefinition_k6_setfam_1, reflexivity_r1_tarski,
% 25.20/4.17 t1_subset, t3_boole, t3_subset, t4_boole, t4_subset, t5_subset, t6_boole,
% 25.20/4.17 t7_boole, t8_boole
% 25.20/4.17
% 25.20/4.17 Those formulas are unsatisfiable:
% 25.20/4.17 ---------------------------------
% 25.20/4.17
% 25.20/4.17 Begin of proof
% 25.20/4.17 |
% 25.20/4.18 | ALPHA: (d5_subset_1) implies:
% 25.20/4.18 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0,
% 25.20/4.18 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 25.20/4.18 | ((v4 = v2 & set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0) =
% 25.20/4.18 | v3 & $i(v3) & ~ element(v1, v3))))
% 25.20/4.18 |
% 25.20/4.18 | ALPHA: (dt_k2_subset_1) implies:
% 25.20/4.18 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ?
% 25.20/4.18 | [v2: $i] : (cast_to_subset(v0) = v2 & $i(v2) & element(v2, v1)))
% 25.20/4.18 |
% 25.20/4.18 | ALPHA: (t47_setfam_1) implies:
% 25.20/4.18 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~
% 25.20/4.18 | (union_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 25.20/4.18 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 25.20/4.18 | : ((v8 = v6 & complements_of_subsets(v0, v1) = v7 &
% 25.20/4.18 | subset_difference(v0, v5, v2) = v6 & meet_of_subsets(v0, v7) = v6
% 25.20/4.18 | & cast_to_subset(v0) = v5 & $i(v7) & $i(v6) & $i(v5)) |
% 25.20/4.18 | (powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ~
% 25.20/4.18 | element(v1, v4))))
% 25.20/4.18 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~
% 25.20/4.18 | (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 25.20/4.18 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 25.20/4.18 | [v8: $i] : ((v8 = v7 & subset_difference(v0, v5, v6) = v7 &
% 25.20/4.18 | meet_of_subsets(v0, v2) = v7 & union_of_subsets(v0, v1) = v6 &
% 25.20/4.18 | cast_to_subset(v0) = v5 & $i(v7) & $i(v6) & $i(v5)) |
% 25.20/4.18 | (powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ~
% 25.20/4.18 | element(v1, v4))))
% 25.20/4.18 |
% 25.20/4.18 | ALPHA: (t11_tops_2) implies:
% 25.20/4.18 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 25.20/4.18 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v5) & ~ (v1 =
% 25.20/4.18 | empty_set) & complements_of_subsets(v0, v1) = v4 &
% 25.20/4.18 | meet_of_subsets(v0, v4) = v5 & union_of_subsets(v0, v1) = v6 &
% 25.20/4.18 | subset_complement(v0, v6) = v7 & powerset(v2) = v3 & powerset(v0) =
% 25.20/4.18 | v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 25.20/4.18 | $i(v0) & element(v1, v3))
% 25.20/4.18 |
% 25.20/4.18 | ALPHA: (function-axioms) implies:
% 25.20/4.18 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 25.20/4.18 | v1) | ~ (powerset(v2) = v0))
% 25.20/4.19 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 25.20/4.19 | (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 25.20/4.19 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.20/4.19 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 25.20/4.19 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.20/4.19 | (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 25.20/4.19 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 25.20/4.19 | (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 25.20/4.19 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 25.20/4.19 | (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~
% 25.20/4.19 | (subset_difference(v4, v3, v2) = v0))
% 25.20/4.19 |
% 25.20/4.19 | DELTA: instantiating (5) with fresh symbols all_56_0, all_56_1, all_56_2,
% 25.20/4.19 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7 gives:
% 25.20/4.19 | (12) ~ (all_56_0 = all_56_2) & ~ (all_56_6 = empty_set) &
% 25.20/4.19 | complements_of_subsets(all_56_7, all_56_6) = all_56_3 &
% 25.20/4.19 | meet_of_subsets(all_56_7, all_56_3) = all_56_2 &
% 25.20/4.19 | union_of_subsets(all_56_7, all_56_6) = all_56_1 &
% 25.20/4.19 | subset_complement(all_56_7, all_56_1) = all_56_0 & powerset(all_56_5)
% 25.20/4.19 | = all_56_4 & powerset(all_56_7) = all_56_5 & $i(all_56_0) &
% 25.20/4.19 | $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) &
% 25.20/4.19 | $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & element(all_56_6,
% 25.20/4.19 | all_56_4)
% 25.20/4.19 |
% 25.20/4.19 | ALPHA: (12) implies:
% 25.20/4.19 | (13) ~ (all_56_6 = empty_set)
% 25.20/4.19 | (14) ~ (all_56_0 = all_56_2)
% 25.20/4.19 | (15) element(all_56_6, all_56_4)
% 25.20/4.19 | (16) $i(all_56_7)
% 25.20/4.19 | (17) $i(all_56_6)
% 25.20/4.19 | (18) $i(all_56_3)
% 25.20/4.19 | (19) $i(all_56_1)
% 25.20/4.19 | (20) powerset(all_56_7) = all_56_5
% 25.20/4.19 | (21) powerset(all_56_5) = all_56_4
% 25.20/4.19 | (22) subset_complement(all_56_7, all_56_1) = all_56_0
% 25.20/4.19 | (23) union_of_subsets(all_56_7, all_56_6) = all_56_1
% 25.20/4.19 | (24) meet_of_subsets(all_56_7, all_56_3) = all_56_2
% 25.20/4.19 | (25) complements_of_subsets(all_56_7, all_56_6) = all_56_3
% 25.20/4.19 |
% 25.20/4.19 | GROUND_INST: instantiating (2) with all_56_7, all_56_5, simplifying with (16),
% 25.20/4.19 | (20) gives:
% 25.20/4.19 | (26) ? [v0: $i] : (cast_to_subset(all_56_7) = v0 & $i(v0) & element(v0,
% 25.20/4.19 | all_56_5))
% 25.20/4.19 |
% 25.20/4.19 | GROUND_INST: instantiating (rc2_subset_1) with all_56_7, all_56_5, simplifying
% 25.20/4.19 | with (16), (20) gives:
% 25.20/4.19 | (27) ? [v0: $i] : ($i(v0) & empty(v0) & element(v0, all_56_5))
% 25.20/4.19 |
% 25.20/4.19 | GROUND_INST: instantiating (1) with all_56_7, all_56_1, all_56_0, simplifying
% 25.20/4.19 | with (16), (19), (22) gives:
% 25.20/4.19 | (28) ? [v0: $i] : ? [v1: int] : ((v1 = all_56_0 &
% 25.20/4.19 | set_difference(all_56_7, all_56_1) = all_56_0 & $i(all_56_0)) |
% 25.20/4.19 | (powerset(all_56_7) = v0 & $i(v0) & ~ element(all_56_1, v0)))
% 25.20/4.19 |
% 25.20/4.19 | GROUND_INST: instantiating (dt_k3_subset_1) with all_56_7, all_56_1, all_56_0,
% 25.20/4.19 | simplifying with (16), (19), (22) gives:
% 25.20/4.19 | (29) ? [v0: $i] : (powerset(all_56_7) = v0 & $i(v0) & ( ~
% 25.20/4.19 | element(all_56_1, v0) | element(all_56_0, v0)))
% 25.20/4.19 |
% 25.20/4.20 | GROUND_INST: instantiating (3) with all_56_7, all_56_6, all_56_1, simplifying
% 25.20/4.20 | with (16), (17), (23) gives:
% 25.20/4.20 | (30) all_56_6 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 25.20/4.20 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 &
% 25.20/4.20 | complements_of_subsets(all_56_7, all_56_6) = v4 &
% 25.20/4.20 | subset_difference(all_56_7, v2, all_56_1) = v3 &
% 25.20/4.20 | meet_of_subsets(all_56_7, v4) = v3 & cast_to_subset(all_56_7) = v2
% 25.20/4.20 | & $i(v4) & $i(v3) & $i(v2)) | (powerset(v0) = v1 &
% 25.20/4.20 | powerset(all_56_7) = v0 & $i(v1) & $i(v0) & ~ element(all_56_6,
% 25.20/4.20 | v1)))
% 25.20/4.20 |
% 25.20/4.20 | GROUND_INST: instantiating (dt_k5_setfam_1) with all_56_7, all_56_6, all_56_1,
% 25.20/4.20 | simplifying with (16), (17), (23) gives:
% 25.20/4.20 | (31) ? [v0: $i] : ? [v1: $i] : (powerset(all_56_7) = v0 & $i(v0) &
% 25.20/4.20 | (element(all_56_1, v0) | (powerset(v0) = v1 & $i(v1) & ~
% 25.20/4.20 | element(all_56_6, v1))))
% 25.20/4.20 |
% 25.20/4.20 | GROUND_INST: instantiating (dt_k6_setfam_1) with all_56_7, all_56_3, all_56_2,
% 25.20/4.20 | simplifying with (16), (18), (24) gives:
% 25.20/4.20 | (32) ? [v0: $i] : ? [v1: $i] : (powerset(all_56_7) = v0 & $i(v0) &
% 25.20/4.20 | (element(all_56_2, v0) | (powerset(v0) = v1 & $i(v1) & ~
% 25.20/4.20 | element(all_56_3, v1))))
% 25.20/4.20 |
% 25.20/4.20 | GROUND_INST: instantiating (4) with all_56_7, all_56_6, all_56_3, simplifying
% 25.20/4.20 | with (16), (17), (25) gives:
% 25.20/4.20 | (33) all_56_6 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 25.20/4.20 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v4 &
% 25.20/4.20 | subset_difference(all_56_7, v2, v3) = v4 &
% 25.20/4.20 | meet_of_subsets(all_56_7, all_56_3) = v4 &
% 25.20/4.20 | union_of_subsets(all_56_7, all_56_6) = v3 &
% 25.20/4.20 | cast_to_subset(all_56_7) = v2 & $i(v4) & $i(v3) & $i(v2)) |
% 25.20/4.20 | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) & $i(v0) & ~
% 25.20/4.20 | element(all_56_6, v1)))
% 25.20/4.20 |
% 25.20/4.20 | GROUND_INST: instantiating (dt_k7_setfam_1) with all_56_7, all_56_6, all_56_3,
% 25.20/4.20 | simplifying with (16), (17), (25) gives:
% 25.20/4.20 | (34) ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & powerset(all_56_7) =
% 25.20/4.20 | v0 & $i(v1) & $i(v0) & ( ~ element(all_56_6, v1) | element(all_56_3,
% 25.20/4.20 | v1)))
% 25.20/4.20 |
% 25.20/4.20 | DELTA: instantiating (27) with fresh symbol all_68_0 gives:
% 25.20/4.20 | (35) $i(all_68_0) & empty(all_68_0) & element(all_68_0, all_56_5)
% 25.20/4.20 |
% 25.20/4.20 | ALPHA: (35) implies:
% 25.20/4.20 | (36) element(all_68_0, all_56_5)
% 25.20/4.20 | (37) $i(all_68_0)
% 25.20/4.20 |
% 25.20/4.20 | DELTA: instantiating (26) with fresh symbol all_70_0 gives:
% 25.20/4.20 | (38) cast_to_subset(all_56_7) = all_70_0 & $i(all_70_0) & element(all_70_0,
% 25.20/4.20 | all_56_5)
% 25.20/4.20 |
% 25.20/4.20 | ALPHA: (38) implies:
% 25.20/4.20 | (39) element(all_70_0, all_56_5)
% 25.20/4.20 | (40) cast_to_subset(all_56_7) = all_70_0
% 25.20/4.20 |
% 25.20/4.20 | DELTA: instantiating (29) with fresh symbol all_76_0 gives:
% 25.20/4.20 | (41) powerset(all_56_7) = all_76_0 & $i(all_76_0) & ( ~ element(all_56_1,
% 25.20/4.20 | all_76_0) | element(all_56_0, all_76_0))
% 25.20/4.20 |
% 25.20/4.20 | ALPHA: (41) implies:
% 25.20/4.20 | (42) $i(all_76_0)
% 25.20/4.20 | (43) powerset(all_56_7) = all_76_0
% 25.20/4.20 |
% 25.20/4.20 | DELTA: instantiating (28) with fresh symbols all_79_0, all_79_1 gives:
% 25.20/4.20 | (44) (all_79_0 = all_56_0 & set_difference(all_56_7, all_56_1) = all_56_0 &
% 25.20/4.20 | $i(all_56_0)) | (powerset(all_56_7) = all_79_1 & $i(all_79_1) & ~
% 25.20/4.20 | element(all_56_1, all_79_1))
% 25.20/4.20 |
% 25.20/4.20 | DELTA: instantiating (34) with fresh symbols all_80_0, all_80_1 gives:
% 25.20/4.20 | (45) powerset(all_80_1) = all_80_0 & powerset(all_56_7) = all_80_1 &
% 25.20/4.20 | $i(all_80_0) & $i(all_80_1) & ( ~ element(all_56_6, all_80_0) |
% 25.20/4.20 | element(all_56_3, all_80_0))
% 25.20/4.20 |
% 25.20/4.20 | ALPHA: (45) implies:
% 25.20/4.20 | (46) powerset(all_56_7) = all_80_1
% 25.20/4.21 | (47) powerset(all_80_1) = all_80_0
% 25.20/4.21 |
% 25.20/4.21 | DELTA: instantiating (32) with fresh symbols all_82_0, all_82_1 gives:
% 25.20/4.21 | (48) powerset(all_56_7) = all_82_1 & $i(all_82_1) & (element(all_56_2,
% 25.20/4.21 | all_82_1) | (powerset(all_82_1) = all_82_0 & $i(all_82_0) & ~
% 25.20/4.21 | element(all_56_3, all_82_0)))
% 25.20/4.21 |
% 25.20/4.21 | ALPHA: (48) implies:
% 25.20/4.21 | (49) powerset(all_56_7) = all_82_1
% 25.20/4.21 |
% 25.20/4.21 | DELTA: instantiating (31) with fresh symbols all_84_0, all_84_1 gives:
% 25.20/4.21 | (50) powerset(all_56_7) = all_84_1 & $i(all_84_1) & (element(all_56_1,
% 25.20/4.21 | all_84_1) | (powerset(all_84_1) = all_84_0 & $i(all_84_0) & ~
% 25.20/4.21 | element(all_56_6, all_84_0)))
% 25.20/4.21 |
% 25.20/4.21 | ALPHA: (50) implies:
% 25.20/4.21 | (51) powerset(all_56_7) = all_84_1
% 25.20/4.21 | (52) element(all_56_1, all_84_1) | (powerset(all_84_1) = all_84_0 &
% 25.20/4.21 | $i(all_84_0) & ~ element(all_56_6, all_84_0))
% 25.20/4.21 |
% 25.20/4.21 | BETA: splitting (30) gives:
% 25.20/4.21 |
% 25.20/4.21 | Case 1:
% 25.20/4.21 | |
% 25.20/4.21 | | (53) all_56_6 = empty_set
% 25.20/4.21 | |
% 25.20/4.21 | | REDUCE: (13), (53) imply:
% 25.20/4.21 | | (54) $false
% 25.20/4.21 | |
% 25.20/4.21 | | CLOSE: (54) is inconsistent.
% 25.20/4.21 | |
% 25.20/4.21 | Case 2:
% 25.20/4.21 | |
% 25.20/4.21 | | (55) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 25.20/4.21 | | : ? [v5: $i] : ((v5 = v3 & complements_of_subsets(all_56_7,
% 25.20/4.21 | | all_56_6) = v4 & subset_difference(all_56_7, v2, all_56_1) =
% 25.20/4.21 | | v3 & meet_of_subsets(all_56_7, v4) = v3 &
% 25.20/4.21 | | cast_to_subset(all_56_7) = v2 & $i(v4) & $i(v3) & $i(v2)) |
% 25.20/4.21 | | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) & $i(v0) &
% 25.20/4.21 | | ~ element(all_56_6, v1)))
% 25.20/4.21 | |
% 25.20/4.21 | | DELTA: instantiating (55) with fresh symbols all_96_0, all_96_1, all_96_2,
% 25.20/4.21 | | all_96_3, all_96_4, all_96_5 gives:
% 25.20/4.21 | | (56) (all_96_0 = all_96_2 & complements_of_subsets(all_56_7, all_56_6) =
% 25.20/4.21 | | all_96_1 & subset_difference(all_56_7, all_96_3, all_56_1) =
% 25.20/4.21 | | all_96_2 & meet_of_subsets(all_56_7, all_96_1) = all_96_2 &
% 25.20/4.21 | | cast_to_subset(all_56_7) = all_96_3 & $i(all_96_1) & $i(all_96_2)
% 25.20/4.21 | | & $i(all_96_3)) | (powerset(all_96_5) = all_96_4 &
% 25.20/4.21 | | powerset(all_56_7) = all_96_5 & $i(all_96_4) & $i(all_96_5) & ~
% 25.20/4.21 | | element(all_56_6, all_96_4))
% 25.20/4.21 | |
% 25.20/4.21 | | BETA: splitting (33) gives:
% 25.20/4.21 | |
% 25.20/4.21 | | Case 1:
% 25.20/4.21 | | |
% 25.20/4.21 | | | (57) all_56_6 = empty_set
% 25.20/4.21 | | |
% 25.20/4.21 | | | REDUCE: (13), (57) imply:
% 25.20/4.21 | | | (58) $false
% 25.20/4.21 | | |
% 25.20/4.21 | | | CLOSE: (58) is inconsistent.
% 25.20/4.21 | | |
% 25.20/4.21 | | Case 2:
% 25.20/4.21 | | |
% 25.20/4.21 | | | (59) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 25.20/4.21 | | | $i] : ? [v5: $i] : ((v5 = v4 & subset_difference(all_56_7, v2,
% 25.20/4.21 | | | v3) = v4 & meet_of_subsets(all_56_7, all_56_3) = v4 &
% 25.20/4.21 | | | union_of_subsets(all_56_7, all_56_6) = v3 &
% 25.20/4.21 | | | cast_to_subset(all_56_7) = v2 & $i(v4) & $i(v3) & $i(v2)) |
% 25.20/4.21 | | | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) & $i(v0) &
% 25.20/4.21 | | | ~ element(all_56_6, v1)))
% 25.20/4.21 | | |
% 25.20/4.21 | | | DELTA: instantiating (59) with fresh symbols all_100_0, all_100_1,
% 25.20/4.21 | | | all_100_2, all_100_3, all_100_4, all_100_5 gives:
% 25.20/4.22 | | | (60) (all_100_0 = all_100_1 & subset_difference(all_56_7, all_100_3,
% 25.20/4.22 | | | all_100_2) = all_100_1 & meet_of_subsets(all_56_7, all_56_3) =
% 25.20/4.22 | | | all_100_1 & union_of_subsets(all_56_7, all_56_6) = all_100_2 &
% 25.20/4.22 | | | cast_to_subset(all_56_7) = all_100_3 & $i(all_100_1) &
% 25.20/4.22 | | | $i(all_100_2) & $i(all_100_3)) | (powerset(all_100_5) =
% 25.20/4.22 | | | all_100_4 & powerset(all_56_7) = all_100_5 & $i(all_100_4) &
% 25.20/4.22 | | | $i(all_100_5) & ~ element(all_56_6, all_100_4))
% 25.20/4.22 | | |
% 25.20/4.22 | | | BETA: splitting (60) gives:
% 25.20/4.22 | | |
% 25.20/4.22 | | | Case 1:
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | (61) all_100_0 = all_100_1 & subset_difference(all_56_7, all_100_3,
% 25.20/4.22 | | | | all_100_2) = all_100_1 & meet_of_subsets(all_56_7, all_56_3) =
% 25.20/4.22 | | | | all_100_1 & union_of_subsets(all_56_7, all_56_6) = all_100_2 &
% 25.20/4.22 | | | | cast_to_subset(all_56_7) = all_100_3 & $i(all_100_1) &
% 25.20/4.22 | | | | $i(all_100_2) & $i(all_100_3)
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | ALPHA: (61) implies:
% 25.20/4.22 | | | | (62) $i(all_100_2)
% 25.20/4.22 | | | | (63) cast_to_subset(all_56_7) = all_100_3
% 25.20/4.22 | | | | (64) union_of_subsets(all_56_7, all_56_6) = all_100_2
% 25.20/4.22 | | | | (65) meet_of_subsets(all_56_7, all_56_3) = all_100_1
% 25.20/4.22 | | | | (66) subset_difference(all_56_7, all_100_3, all_100_2) = all_100_1
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (6) with all_76_0, all_80_1, all_56_7,
% 25.20/4.22 | | | | simplifying with (43), (46) gives:
% 25.20/4.22 | | | | (67) all_80_1 = all_76_0
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (6) with all_80_1, all_82_1, all_56_7,
% 25.20/4.22 | | | | simplifying with (46), (49) gives:
% 25.20/4.22 | | | | (68) all_82_1 = all_80_1
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (6) with all_56_5, all_84_1, all_56_7,
% 25.20/4.22 | | | | simplifying with (20), (51) gives:
% 25.20/4.22 | | | | (69) all_84_1 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (6) with all_82_1, all_84_1, all_56_7,
% 25.20/4.22 | | | | simplifying with (49), (51) gives:
% 25.20/4.22 | | | | (70) all_84_1 = all_82_1
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (7) with all_70_0, all_100_3, all_56_7,
% 25.20/4.22 | | | | simplifying with (40), (63) gives:
% 25.20/4.22 | | | | (71) all_100_3 = all_70_0
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (9) with all_56_1, all_100_2, all_56_6,
% 25.20/4.22 | | | | all_56_7, simplifying with (23), (64) gives:
% 25.20/4.22 | | | | (72) all_100_2 = all_56_1
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | GROUND_INST: instantiating (10) with all_56_2, all_100_1, all_56_3,
% 25.20/4.22 | | | | all_56_7, simplifying with (24), (65) gives:
% 25.20/4.22 | | | | (73) all_100_1 = all_56_2
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | COMBINE_EQS: (69), (70) imply:
% 25.20/4.22 | | | | (74) all_82_1 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | SIMP: (74) implies:
% 25.20/4.22 | | | | (75) all_82_1 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | COMBINE_EQS: (68), (75) imply:
% 25.20/4.22 | | | | (76) all_80_1 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | SIMP: (76) implies:
% 25.20/4.22 | | | | (77) all_80_1 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | COMBINE_EQS: (67), (77) imply:
% 25.20/4.22 | | | | (78) all_76_0 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | SIMP: (78) implies:
% 25.20/4.22 | | | | (79) all_76_0 = all_56_5
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | REDUCE: (66), (71), (72), (73) imply:
% 25.20/4.22 | | | | (80) subset_difference(all_56_7, all_70_0, all_56_1) = all_56_2
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | REDUCE: (42), (79) imply:
% 25.20/4.22 | | | | (81) $i(all_56_5)
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | BETA: splitting (52) gives:
% 25.20/4.22 | | | |
% 25.20/4.22 | | | | Case 1:
% 25.20/4.22 | | | | |
% 25.20/4.22 | | | | | (82) element(all_56_1, all_84_1)
% 25.20/4.22 | | | | |
% 25.20/4.22 | | | | | REDUCE: (69), (82) imply:
% 25.20/4.22 | | | | | (83) element(all_56_1, all_56_5)
% 25.20/4.22 | | | | |
% 25.20/4.22 | | | | | BETA: splitting (44) gives:
% 25.20/4.22 | | | | |
% 25.20/4.22 | | | | | Case 1:
% 25.20/4.22 | | | | | |
% 25.20/4.22 | | | | | | (84) all_79_0 = all_56_0 & set_difference(all_56_7, all_56_1) =
% 25.20/4.22 | | | | | | all_56_0 & $i(all_56_0)
% 25.20/4.22 | | | | | |
% 25.20/4.22 | | | | | | ALPHA: (84) implies:
% 25.20/4.22 | | | | | | (85) set_difference(all_56_7, all_56_1) = all_56_0
% 25.20/4.22 | | | | | |
% 25.20/4.22 | | | | | | BETA: splitting (56) gives:
% 25.20/4.22 | | | | | |
% 25.20/4.22 | | | | | | Case 1:
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | (86) all_96_0 = all_96_2 & complements_of_subsets(all_56_7,
% 25.20/4.22 | | | | | | | all_56_6) = all_96_1 & subset_difference(all_56_7,
% 25.20/4.22 | | | | | | | all_96_3, all_56_1) = all_96_2 &
% 25.20/4.22 | | | | | | | meet_of_subsets(all_56_7, all_96_1) = all_96_2 &
% 25.20/4.22 | | | | | | | cast_to_subset(all_56_7) = all_96_3 & $i(all_96_1) &
% 25.20/4.22 | | | | | | | $i(all_96_2) & $i(all_96_3)
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | ALPHA: (86) implies:
% 25.20/4.22 | | | | | | | (87) $i(all_96_3)
% 25.20/4.22 | | | | | | | (88) cast_to_subset(all_56_7) = all_96_3
% 25.20/4.22 | | | | | | | (89) subset_difference(all_56_7, all_96_3, all_56_1) = all_96_2
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | GROUND_INST: instantiating (7) with all_70_0, all_96_3, all_56_7,
% 25.20/4.22 | | | | | | | simplifying with (40), (88) gives:
% 25.20/4.22 | | | | | | | (90) all_96_3 = all_70_0
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | GROUND_INST: instantiating (11) with all_56_2, all_96_2, all_56_1,
% 25.20/4.22 | | | | | | | all_70_0, all_56_7, simplifying with (80) gives:
% 25.20/4.22 | | | | | | | (91) all_96_2 = all_56_2 | ~ (subset_difference(all_56_7,
% 25.20/4.22 | | | | | | | all_70_0, all_56_1) = all_96_2)
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | REDUCE: (89), (90) imply:
% 25.20/4.22 | | | | | | | (92) subset_difference(all_56_7, all_70_0, all_56_1) = all_96_2
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | REDUCE: (87), (90) imply:
% 25.20/4.22 | | | | | | | (93) $i(all_70_0)
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | BETA: splitting (91) gives:
% 25.20/4.22 | | | | | | |
% 25.20/4.22 | | | | | | | Case 1:
% 25.20/4.22 | | | | | | | |
% 25.20/4.22 | | | | | | | | (94) ~ (subset_difference(all_56_7, all_70_0, all_56_1) =
% 25.20/4.22 | | | | | | | | all_96_2)
% 25.20/4.22 | | | | | | | |
% 25.20/4.23 | | | | | | | | PRED_UNIFY: (92), (94) imply:
% 25.20/4.23 | | | | | | | | (95) $false
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | CLOSE: (95) is inconsistent.
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | Case 2:
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | (96) all_96_2 = all_56_2
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | GROUND_INST: instantiating (t2_subset) with all_68_0, all_56_5,
% 25.20/4.23 | | | | | | | | simplifying with (36), (37), (81) gives:
% 25.20/4.23 | | | | | | | | (97) empty(all_56_5) | in(all_68_0, all_56_5)
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | GROUND_INST: instantiating (fc1_subset_1) with all_56_7,
% 25.20/4.23 | | | | | | | | all_56_5, simplifying with (16), (20) gives:
% 25.20/4.23 | | | | | | | | (98) ~ empty(all_56_5)
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | GROUND_INST: instantiating (d4_subset_1) with all_56_7,
% 25.20/4.23 | | | | | | | | all_70_0, simplifying with (16), (40) gives:
% 25.20/4.23 | | | | | | | | (99) all_70_0 = all_56_7
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | GROUND_INST: instantiating (redefinition_k6_subset_1) with
% 25.20/4.23 | | | | | | | | all_56_7, all_70_0, all_56_1, all_56_2, simplifying
% 25.20/4.23 | | | | | | | | with (16), (19), (80), (93) gives:
% 25.20/4.23 | | | | | | | | (100) ? [v0: $i] : ? [v1: int] : ((v1 = all_56_2 &
% 25.20/4.23 | | | | | | | | set_difference(all_70_0, all_56_1) = all_56_2 &
% 25.20/4.23 | | | | | | | | $i(all_56_2)) | (powerset(all_56_7) = v0 & $i(v0) &
% 25.20/4.23 | | | | | | | | ( ~ element(all_70_0, v0) | ~ element(all_56_1,
% 25.20/4.23 | | | | | | | | v0))))
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | DELTA: instantiating (100) with fresh symbols all_164_0,
% 25.20/4.23 | | | | | | | | all_164_1 gives:
% 25.20/4.23 | | | | | | | | (101) (all_164_0 = all_56_2 & set_difference(all_70_0,
% 25.20/4.23 | | | | | | | | all_56_1) = all_56_2 & $i(all_56_2)) |
% 25.20/4.23 | | | | | | | | (powerset(all_56_7) = all_164_1 & $i(all_164_1) & ( ~
% 25.20/4.23 | | | | | | | | element(all_70_0, all_164_1) | ~ element(all_56_1,
% 25.20/4.23 | | | | | | | | all_164_1)))
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | REDUCE: (39), (99) imply:
% 25.20/4.23 | | | | | | | | (102) element(all_56_7, all_56_5)
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | BETA: splitting (101) gives:
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | Case 1:
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | (103) all_164_0 = all_56_2 & set_difference(all_70_0,
% 25.20/4.23 | | | | | | | | | all_56_1) = all_56_2 & $i(all_56_2)
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | ALPHA: (103) implies:
% 25.20/4.23 | | | | | | | | | (104) set_difference(all_70_0, all_56_1) = all_56_2
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | REDUCE: (99), (104) imply:
% 25.20/4.23 | | | | | | | | | (105) set_difference(all_56_7, all_56_1) = all_56_2
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | GROUND_INST: instantiating (8) with all_56_0, all_56_2,
% 25.20/4.23 | | | | | | | | | all_56_1, all_56_7, simplifying with (85), (105)
% 25.20/4.23 | | | | | | | | | gives:
% 25.20/4.23 | | | | | | | | | (106) all_56_0 = all_56_2
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | REDUCE: (14), (106) imply:
% 25.20/4.23 | | | | | | | | | (107) $false
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | CLOSE: (107) is inconsistent.
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | Case 2:
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | (108) powerset(all_56_7) = all_164_1 & $i(all_164_1) & ( ~
% 25.20/4.23 | | | | | | | | | element(all_70_0, all_164_1) | ~ element(all_56_1,
% 25.20/4.23 | | | | | | | | | all_164_1))
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | ALPHA: (108) implies:
% 25.20/4.23 | | | | | | | | | (109) powerset(all_56_7) = all_164_1
% 25.20/4.23 | | | | | | | | | (110) ~ element(all_70_0, all_164_1) | ~
% 25.20/4.23 | | | | | | | | | element(all_56_1, all_164_1)
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | BETA: splitting (97) gives:
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | | Case 1:
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | (111) empty(all_56_5)
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | PRED_UNIFY: (98), (111) imply:
% 25.20/4.23 | | | | | | | | | | (112) $false
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | CLOSE: (112) is inconsistent.
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | Case 2:
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | GROUND_INST: instantiating (6) with all_56_5, all_164_1,
% 25.20/4.23 | | | | | | | | | | all_56_7, simplifying with (20), (109) gives:
% 25.20/4.23 | | | | | | | | | | (113) all_164_1 = all_56_5
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | BETA: splitting (110) gives:
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | Case 1:
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | (114) ~ element(all_70_0, all_164_1)
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | REDUCE: (99), (113), (114) imply:
% 25.20/4.23 | | | | | | | | | | | (115) ~ element(all_56_7, all_56_5)
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | PRED_UNIFY: (102), (115) imply:
% 25.20/4.23 | | | | | | | | | | | (116) $false
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | CLOSE: (116) is inconsistent.
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | Case 2:
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | (117) ~ element(all_56_1, all_164_1)
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | REDUCE: (113), (117) imply:
% 25.20/4.23 | | | | | | | | | | | (118) ~ element(all_56_1, all_56_5)
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | PRED_UNIFY: (83), (118) imply:
% 25.20/4.23 | | | | | | | | | | | (119) $false
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | | CLOSE: (119) is inconsistent.
% 25.20/4.23 | | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | | End of split
% 25.20/4.23 | | | | | | | | | |
% 25.20/4.23 | | | | | | | | | End of split
% 25.20/4.23 | | | | | | | | |
% 25.20/4.23 | | | | | | | | End of split
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | End of split
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | Case 2:
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | (120) powerset(all_96_5) = all_96_4 & powerset(all_56_7) =
% 25.20/4.23 | | | | | | | all_96_5 & $i(all_96_4) & $i(all_96_5) & ~
% 25.20/4.23 | | | | | | | element(all_56_6, all_96_4)
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | ALPHA: (120) implies:
% 25.20/4.23 | | | | | | | (121) ~ element(all_56_6, all_96_4)
% 25.20/4.23 | | | | | | | (122) powerset(all_56_7) = all_96_5
% 25.20/4.23 | | | | | | | (123) powerset(all_96_5) = all_96_4
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | GROUND_INST: instantiating (6) with all_56_5, all_96_5, all_56_7,
% 25.20/4.23 | | | | | | | simplifying with (20), (122) gives:
% 25.20/4.23 | | | | | | | (124) all_96_5 = all_56_5
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | GROUND_INST: instantiating (6) with all_56_4, all_96_4, all_56_5,
% 25.20/4.23 | | | | | | | simplifying with (21) gives:
% 25.20/4.23 | | | | | | | (125) all_96_4 = all_56_4 | ~ (powerset(all_56_5) = all_96_4)
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | PRED_UNIFY: (15), (121) imply:
% 25.20/4.23 | | | | | | | (126) ~ (all_96_4 = all_56_4)
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | REDUCE: (123), (124) imply:
% 25.20/4.23 | | | | | | | (127) powerset(all_56_5) = all_96_4
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | BETA: splitting (125) gives:
% 25.20/4.23 | | | | | | |
% 25.20/4.23 | | | | | | | Case 1:
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | (128) ~ (powerset(all_56_5) = all_96_4)
% 25.20/4.23 | | | | | | | |
% 25.20/4.23 | | | | | | | | PRED_UNIFY: (127), (128) imply:
% 25.20/4.24 | | | | | | | | (129) $false
% 25.20/4.24 | | | | | | | |
% 25.20/4.24 | | | | | | | | CLOSE: (129) is inconsistent.
% 25.20/4.24 | | | | | | | |
% 25.20/4.24 | | | | | | | Case 2:
% 25.20/4.24 | | | | | | | |
% 25.20/4.24 | | | | | | | | (130) all_96_4 = all_56_4
% 25.20/4.24 | | | | | | | |
% 25.20/4.24 | | | | | | | | REDUCE: (126), (130) imply:
% 25.20/4.24 | | | | | | | | (131) $false
% 25.20/4.24 | | | | | | | |
% 25.20/4.24 | | | | | | | | CLOSE: (131) is inconsistent.
% 25.20/4.24 | | | | | | | |
% 25.20/4.24 | | | | | | | End of split
% 25.20/4.24 | | | | | | |
% 25.20/4.24 | | | | | | End of split
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | Case 2:
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | (132) powerset(all_56_7) = all_79_1 & $i(all_79_1) & ~
% 25.20/4.24 | | | | | | element(all_56_1, all_79_1)
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | ALPHA: (132) implies:
% 25.20/4.24 | | | | | | (133) ~ element(all_56_1, all_79_1)
% 25.20/4.24 | | | | | | (134) powerset(all_56_7) = all_79_1
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | GROUND_INST: instantiating (6) with all_56_5, all_79_1, all_56_7,
% 25.20/4.24 | | | | | | simplifying with (20), (134) gives:
% 25.20/4.24 | | | | | | (135) all_79_1 = all_56_5
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | PRED_UNIFY: (83), (133) imply:
% 25.20/4.24 | | | | | | (136) ~ (all_79_1 = all_56_5)
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | REDUCE: (135), (136) imply:
% 25.20/4.24 | | | | | | (137) $false
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | CLOSE: (137) is inconsistent.
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | End of split
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | Case 2:
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | (138) powerset(all_84_1) = all_84_0 & $i(all_84_0) & ~
% 25.20/4.24 | | | | | element(all_56_6, all_84_0)
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | ALPHA: (138) implies:
% 25.20/4.24 | | | | | (139) ~ element(all_56_6, all_84_0)
% 25.20/4.24 | | | | | (140) powerset(all_84_1) = all_84_0
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | REDUCE: (69), (140) imply:
% 25.20/4.24 | | | | | (141) powerset(all_56_5) = all_84_0
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | GROUND_INST: instantiating (6) with all_56_4, all_84_0, all_56_5,
% 25.20/4.24 | | | | | simplifying with (21), (141) gives:
% 25.20/4.24 | | | | | (142) all_84_0 = all_56_4
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | PRED_UNIFY: (15), (139) imply:
% 25.20/4.24 | | | | | (143) ~ (all_84_0 = all_56_4)
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | REDUCE: (142), (143) imply:
% 25.20/4.24 | | | | | (144) $false
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | CLOSE: (144) is inconsistent.
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | End of split
% 25.20/4.24 | | | |
% 25.20/4.24 | | | Case 2:
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | (145) powerset(all_100_5) = all_100_4 & powerset(all_56_7) =
% 25.20/4.24 | | | | all_100_5 & $i(all_100_4) & $i(all_100_5) & ~
% 25.20/4.24 | | | | element(all_56_6, all_100_4)
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | ALPHA: (145) implies:
% 25.20/4.24 | | | | (146) ~ element(all_56_6, all_100_4)
% 25.20/4.24 | | | | (147) powerset(all_56_7) = all_100_5
% 25.20/4.24 | | | | (148) powerset(all_100_5) = all_100_4
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_56_5, all_82_1, all_56_7,
% 25.20/4.24 | | | | simplifying with (20), (49) gives:
% 25.20/4.24 | | | | (149) all_82_1 = all_56_5
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_80_1, all_82_1, all_56_7,
% 25.20/4.24 | | | | simplifying with (46), (49) gives:
% 25.20/4.24 | | | | (150) all_82_1 = all_80_1
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_80_1, all_84_1, all_56_7,
% 25.20/4.24 | | | | simplifying with (46), (51) gives:
% 25.20/4.24 | | | | (151) all_84_1 = all_80_1
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_84_1, all_100_5, all_56_7,
% 25.20/4.24 | | | | simplifying with (51), (147) gives:
% 25.20/4.24 | | | | (152) all_100_5 = all_84_1
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_76_0, all_100_5, all_56_7,
% 25.20/4.24 | | | | simplifying with (43), (147) gives:
% 25.20/4.24 | | | | (153) all_100_5 = all_76_0
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_56_4, all_100_4, all_56_5,
% 25.20/4.24 | | | | simplifying with (21) gives:
% 25.20/4.24 | | | | (154) all_100_4 = all_56_4 | ~ (powerset(all_56_5) = all_100_4)
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | GROUND_INST: instantiating (6) with all_80_0, all_100_4, all_80_1,
% 25.20/4.24 | | | | simplifying with (47) gives:
% 25.20/4.24 | | | | (155) all_100_4 = all_80_0 | ~ (powerset(all_80_1) = all_100_4)
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | PRED_UNIFY: (15), (146) imply:
% 25.20/4.24 | | | | (156) ~ (all_100_4 = all_56_4)
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | COMBINE_EQS: (152), (153) imply:
% 25.20/4.24 | | | | (157) all_84_1 = all_76_0
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | SIMP: (157) implies:
% 25.20/4.24 | | | | (158) all_84_1 = all_76_0
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | COMBINE_EQS: (151), (158) imply:
% 25.20/4.24 | | | | (159) all_80_1 = all_76_0
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | SIMP: (159) implies:
% 25.20/4.24 | | | | (160) all_80_1 = all_76_0
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | COMBINE_EQS: (149), (150) imply:
% 25.20/4.24 | | | | (161) all_80_1 = all_56_5
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | SIMP: (161) implies:
% 25.20/4.24 | | | | (162) all_80_1 = all_56_5
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | COMBINE_EQS: (160), (162) imply:
% 25.20/4.24 | | | | (163) all_76_0 = all_56_5
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | COMBINE_EQS: (153), (163) imply:
% 25.20/4.24 | | | | (164) all_100_5 = all_56_5
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | REDUCE: (148), (164) imply:
% 25.20/4.24 | | | | (165) powerset(all_56_5) = all_100_4
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | BETA: splitting (155) gives:
% 25.20/4.24 | | | |
% 25.20/4.24 | | | | Case 1:
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | (166) ~ (powerset(all_80_1) = all_100_4)
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | REDUCE: (162), (166) imply:
% 25.20/4.24 | | | | | (167) ~ (powerset(all_56_5) = all_100_4)
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | PRED_UNIFY: (165), (167) imply:
% 25.20/4.24 | | | | | (168) $false
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | CLOSE: (168) is inconsistent.
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | Case 2:
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | (169) all_100_4 = all_80_0
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | REDUCE: (156), (169) imply:
% 25.20/4.24 | | | | | (170) ~ (all_80_0 = all_56_4)
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | REDUCE: (165), (169) imply:
% 25.20/4.24 | | | | | (171) powerset(all_56_5) = all_80_0
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | BETA: splitting (154) gives:
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | | Case 1:
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | (172) ~ (powerset(all_56_5) = all_100_4)
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | REDUCE: (169), (172) imply:
% 25.20/4.24 | | | | | | (173) ~ (powerset(all_56_5) = all_80_0)
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | PRED_UNIFY: (171), (173) imply:
% 25.20/4.24 | | | | | | (174) $false
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | CLOSE: (174) is inconsistent.
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | Case 2:
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | (175) all_100_4 = all_56_4
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | COMBINE_EQS: (169), (175) imply:
% 25.20/4.24 | | | | | | (176) all_80_0 = all_56_4
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | REDUCE: (170), (176) imply:
% 25.20/4.24 | | | | | | (177) $false
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | | CLOSE: (177) is inconsistent.
% 25.20/4.24 | | | | | |
% 25.20/4.24 | | | | | End of split
% 25.20/4.24 | | | | |
% 25.20/4.24 | | | | End of split
% 25.20/4.24 | | | |
% 25.20/4.24 | | | End of split
% 25.20/4.24 | | |
% 25.20/4.24 | | End of split
% 25.20/4.24 | |
% 25.20/4.24 | End of split
% 25.20/4.24 |
% 25.20/4.24 End of proof
% 25.20/4.25 % SZS output end Proof for theBenchmark
% 25.20/4.25
% 25.20/4.25 3654ms
%------------------------------------------------------------------------------