TSTP Solution File: SEU328+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU328+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 : n006.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 12.64s 2.46s
% Output : Proof 23.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU328+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 : n006.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 17:39:08 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.26/1.20 Prover 4: Preprocessing ...
% 3.26/1.20 Prover 1: Preprocessing ...
% 3.93/1.25 Prover 5: Preprocessing ...
% 3.93/1.25 Prover 3: Preprocessing ...
% 3.93/1.25 Prover 2: Preprocessing ...
% 3.93/1.25 Prover 0: Preprocessing ...
% 3.93/1.26 Prover 6: Preprocessing ...
% 8.27/1.89 Prover 1: Warning: ignoring some quantifiers
% 8.95/1.95 Prover 5: Proving ...
% 8.95/1.96 Prover 1: Constructing countermodel ...
% 8.95/1.97 Prover 3: Warning: ignoring some quantifiers
% 8.95/1.97 Prover 6: Proving ...
% 8.95/2.00 Prover 3: Constructing countermodel ...
% 8.95/2.04 Prover 2: Proving ...
% 10.32/2.14 Prover 4: Warning: ignoring some quantifiers
% 10.80/2.22 Prover 4: Constructing countermodel ...
% 11.11/2.30 Prover 0: Proving ...
% 12.64/2.46 Prover 5: proved (1823ms)
% 12.64/2.46
% 12.64/2.46 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.64/2.46
% 12.64/2.46 Prover 3: stopped
% 12.64/2.47 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.64/2.47 Prover 0: stopped
% 12.64/2.48 Prover 6: stopped
% 12.64/2.48 Prover 2: stopped
% 12.64/2.49 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.64/2.49 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.64/2.49 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.64/2.49 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 13.07/2.55 Prover 8: Preprocessing ...
% 13.41/2.55 Prover 7: Preprocessing ...
% 13.41/2.58 Prover 13: Preprocessing ...
% 13.41/2.58 Prover 11: Preprocessing ...
% 13.41/2.63 Prover 10: Preprocessing ...
% 13.41/2.69 Prover 7: Warning: ignoring some quantifiers
% 13.41/2.71 Prover 7: Constructing countermodel ...
% 14.50/2.75 Prover 10: Warning: ignoring some quantifiers
% 14.50/2.75 Prover 8: Warning: ignoring some quantifiers
% 14.50/2.76 Prover 13: Warning: ignoring some quantifiers
% 14.50/2.78 Prover 8: Constructing countermodel ...
% 14.50/2.78 Prover 10: Constructing countermodel ...
% 15.14/2.79 Prover 13: Constructing countermodel ...
% 16.37/2.96 Prover 11: Warning: ignoring some quantifiers
% 16.37/2.98 Prover 11: Constructing countermodel ...
% 18.35/3.31 Prover 10: gave up
% 18.35/3.33 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 18.35/3.35 Prover 13: gave up
% 18.35/3.36 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 19.03/3.38 Prover 16: Preprocessing ...
% 19.03/3.41 Prover 19: Preprocessing ...
% 20.18/3.48 Prover 16: Warning: ignoring some quantifiers
% 20.55/3.51 Prover 16: Constructing countermodel ...
% 20.84/3.62 Prover 19: Warning: ignoring some quantifiers
% 21.53/3.66 Prover 19: Constructing countermodel ...
% 23.10/3.88 Prover 7: Found proof (size 235)
% 23.10/3.88 Prover 7: proved (1416ms)
% 23.10/3.88 Prover 19: stopped
% 23.10/3.88 Prover 8: stopped
% 23.10/3.88 Prover 16: stopped
% 23.10/3.88 Prover 11: stopped
% 23.10/3.88 Prover 4: stopped
% 23.10/3.88 Prover 1: stopped
% 23.10/3.88
% 23.10/3.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.10/3.88
% 23.10/3.90 % SZS output start Proof for theBenchmark
% 23.10/3.90 Assumptions after simplification:
% 23.10/3.90 ---------------------------------
% 23.10/3.90
% 23.10/3.90 (d4_subset_1)
% 23.57/3.93 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (cast_to_subset(v0) = v1) | ~
% 23.57/3.93 $i(v0))
% 23.57/3.93
% 23.57/3.93 (d5_subset_1)
% 23.57/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) = v2) |
% 23.57/3.93 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v2 &
% 23.57/3.93 subset_complement(v0, v1) = v2 & $i(v2)) | (powerset(v0) = v3 & $i(v3) &
% 23.57/3.93 ~ element(v1, v3)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 23.57/3.93 (subset_complement(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ?
% 23.57/3.93 [v4: $i] : ((v4 = v2 & set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0)
% 23.57/3.93 = v3 & $i(v3) & ~ element(v1, v3))))
% 23.57/3.93
% 23.57/3.93 (dt_k2_subset_1)
% 23.57/3.93 ! [v0: $i] : ! [v1: $i] : ( ~ (cast_to_subset(v0) = v1) | ~ $i(v0) | ?
% 23.57/3.93 [v2: $i] : (powerset(v0) = v2 & $i(v2) & element(v1, v2))) & ! [v0: $i] :
% 23.57/3.93 ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ? [v2: $i] :
% 23.57/3.93 (cast_to_subset(v0) = v2 & $i(v2) & element(v2, v1)))
% 23.57/3.93
% 23.57/3.93 (dt_k3_subset_1)
% 23.57/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 23.57/3.93 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (powerset(v0) = v3 & $i(v3) & ( ~
% 23.57/3.93 element(v1, v3) | element(v2, v3))))
% 23.57/3.93
% 23.57/3.93 (dt_k5_setfam_1)
% 23.57/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union_of_subsets(v0, v1) = v2)
% 23.57/3.94 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v0) = v3 &
% 23.57/3.94 $i(v3) & (element(v2, v3) | (powerset(v3) = v4 & $i(v4) & ~ element(v1,
% 23.57/3.94 v4)))))
% 23.57/3.94
% 23.57/3.94 (dt_k6_setfam_1)
% 23.57/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (meet_of_subsets(v0, v1) = v2) |
% 23.57/3.94 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v0) = v3 &
% 23.57/3.94 $i(v3) & (element(v2, v3) | (powerset(v3) = v4 & $i(v4) & ~ element(v1,
% 23.57/3.94 v4)))))
% 23.57/3.94
% 23.57/3.94 (dt_k7_setfam_1)
% 23.57/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (complements_of_subsets(v0, v1)
% 23.57/3.94 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (powerset(v3)
% 23.57/3.94 = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ( ~ element(v1, v4) |
% 23.57/3.94 element(v2, v4))))
% 23.57/3.94
% 23.57/3.94 (involutiveness_k3_subset_1)
% 23.57/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0, v1) = v2)
% 23.57/3.94 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ((v4 = v1 &
% 23.57/3.94 subset_complement(v0, v2) = v1) | (powerset(v0) = v3 & $i(v3) & ~
% 23.57/3.94 element(v1, v3))))
% 23.57/3.94
% 23.57/3.94 (redefinition_k6_subset_1)
% 23.57/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.57/3.94 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 23.57/3.94 ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & set_difference(v1, v2) = v3 & $i(v3))
% 23.57/3.94 | (powerset(v0) = v4 & $i(v4) & ( ~ element(v2, v4) | ~ element(v1,
% 23.57/3.94 v4)))))
% 23.57/3.94
% 23.57/3.94 (t12_tops_2)
% 23.57/3.95 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ?
% 23.57/3.95 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v5) & ~ (v1 =
% 23.57/3.95 empty_set) & complements_of_subsets(v0, v1) = v4 & meet_of_subsets(v0, v1)
% 23.57/3.95 = v6 & union_of_subsets(v0, v4) = v5 & subset_complement(v0, v6) = v7 &
% 23.57/3.95 powerset(v2) = v3 & powerset(v0) = v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 23.57/3.95 $i(v3) & $i(v2) & $i(v1) & $i(v0) & element(v1, v3))
% 23.57/3.95
% 23.57/3.95 (t48_setfam_1)
% 23.57/3.95 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~
% 23.57/3.95 (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 23.57/3.95 : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ((v8
% 23.57/3.95 = v5 & subset_difference(v0, v6, v7) = v5 & meet_of_subsets(v0, v1) = v7
% 23.57/3.95 & union_of_subsets(v0, v2) = v5 & cast_to_subset(v0) = v6 & $i(v7) &
% 23.57/3.95 $i(v6) & $i(v5)) | (powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) &
% 23.57/3.95 $i(v3) & ~ element(v1, v4)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 23.57/3.95 : (v1 = empty_set | ~ (meet_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 23.57/3.95 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 23.57/3.95 [v8: $i] : ((v8 = v6 & complements_of_subsets(v0, v1) = v5 &
% 23.57/3.95 subset_difference(v0, v7, v2) = v6 & union_of_subsets(v0, v5) = v6 &
% 23.57/3.95 cast_to_subset(v0) = v7 & $i(v7) & $i(v6) & $i(v5)) | (powerset(v3) = v4
% 23.57/3.95 & powerset(v0) = v3 & $i(v4) & $i(v3) & ~ element(v1, v4))))
% 23.57/3.95
% 23.57/3.95 (function-axioms)
% 23.57/3.95 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 23.57/3.95 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3,
% 23.57/3.95 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 23.57/3.95 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~
% 23.57/3.95 (complements_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 23.57/3.95 $i] : ! [v3: $i] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~
% 23.57/3.95 (meet_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.57/3.95 ! [v3: $i] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~
% 23.57/3.95 (union_of_subsets(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.57/3.95 ! [v3: $i] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~
% 23.57/3.95 (set_difference(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.57/3.95 ! [v3: $i] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~
% 23.57/3.95 (subset_complement(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 23.57/3.95 : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0: $i] :
% 23.57/3.95 ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) =
% 23.57/3.95 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.57/3.95 (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0: $i] : !
% 23.57/3.95 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2)
% 23.57/3.95 = v0))
% 23.57/3.95
% 23.57/3.95 Further assumptions not needed in the proof:
% 23.57/3.95 --------------------------------------------
% 23.57/3.96 antisymmetry_r2_hidden, cc10_membered, cc11_membered, cc12_membered,
% 23.57/3.96 cc13_membered, cc14_membered, cc15_membered, cc16_membered, cc17_membered,
% 23.57/3.96 cc18_membered, cc19_membered, cc1_membered, cc20_membered, cc2_membered,
% 23.57/3.96 cc3_membered, cc4_membered, dt_k1_setfam_1, dt_k1_xboole_0, dt_k1_zfmisc_1,
% 23.57/3.96 dt_k3_tarski, dt_k4_xboole_0, dt_k6_subset_1, dt_m1_subset_1,
% 23.57/3.96 existence_m1_subset_1, fc1_subset_1, fc37_membered, fc38_membered,
% 23.57/3.96 fc39_membered, fc40_membered, fc41_membered, fc6_membered,
% 23.57/3.96 involutiveness_k7_setfam_1, rc1_membered, rc1_subset_1, rc2_subset_1,
% 23.57/3.96 redefinition_k5_setfam_1, redefinition_k6_setfam_1, reflexivity_r1_tarski,
% 23.57/3.96 t1_subset, t2_subset, t3_boole, t3_subset, t4_boole, t4_subset, t5_subset,
% 23.57/3.96 t6_boole, t7_boole, t8_boole
% 23.57/3.96
% 23.57/3.96 Those formulas are unsatisfiable:
% 23.57/3.96 ---------------------------------
% 23.57/3.96
% 23.57/3.96 Begin of proof
% 23.57/3.96 |
% 23.57/3.96 | ALPHA: (d5_subset_1) implies:
% 23.57/3.96 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset_complement(v0,
% 23.57/3.96 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] :
% 23.57/3.96 | ((v4 = v2 & set_difference(v0, v1) = v2 & $i(v2)) | (powerset(v0) =
% 23.57/3.96 | v3 & $i(v3) & ~ element(v1, v3))))
% 23.57/3.96 |
% 23.57/3.96 | ALPHA: (dt_k2_subset_1) implies:
% 23.57/3.96 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (powerset(v0) = v1) | ~ $i(v0) | ?
% 23.57/3.96 | [v2: $i] : (cast_to_subset(v0) = v2 & $i(v2) & element(v2, v1)))
% 23.57/3.96 |
% 23.57/3.96 | ALPHA: (t48_setfam_1) implies:
% 23.57/3.96 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~
% 23.57/3.96 | (meet_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i]
% 23.57/3.96 | : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i]
% 23.57/3.96 | : ((v8 = v6 & complements_of_subsets(v0, v1) = v5 &
% 23.57/3.96 | subset_difference(v0, v7, v2) = v6 & union_of_subsets(v0, v5) =
% 23.57/3.96 | v6 & cast_to_subset(v0) = v7 & $i(v7) & $i(v6) & $i(v5)) |
% 23.57/3.96 | (powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ~
% 23.57/3.96 | element(v1, v4))))
% 23.57/3.96 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = empty_set | ~
% 23.57/3.96 | (complements_of_subsets(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ?
% 23.57/3.96 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ?
% 23.57/3.96 | [v8: $i] : ((v8 = v5 & subset_difference(v0, v6, v7) = v5 &
% 23.57/3.96 | meet_of_subsets(v0, v1) = v7 & union_of_subsets(v0, v2) = v5 &
% 23.57/3.96 | cast_to_subset(v0) = v6 & $i(v7) & $i(v6) & $i(v5)) |
% 23.57/3.96 | (powerset(v3) = v4 & powerset(v0) = v3 & $i(v4) & $i(v3) & ~
% 23.57/3.96 | element(v1, v4))))
% 23.57/3.96 |
% 23.57/3.96 | ALPHA: (t12_tops_2) implies:
% 23.57/3.97 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 23.57/3.97 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v5) & ~ (v1 =
% 23.57/3.97 | empty_set) & complements_of_subsets(v0, v1) = v4 &
% 23.57/3.97 | meet_of_subsets(v0, v1) = v6 & union_of_subsets(v0, v4) = v5 &
% 23.57/3.97 | subset_complement(v0, v6) = v7 & powerset(v2) = v3 & powerset(v0) =
% 23.57/3.97 | v2 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) &
% 23.57/3.97 | $i(v0) & element(v1, v3))
% 23.57/3.97 |
% 23.57/3.97 | ALPHA: (function-axioms) implies:
% 23.57/3.97 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 23.57/3.97 | v1) | ~ (powerset(v2) = v0))
% 23.57/3.97 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 23.57/3.97 | (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 23.57/3.97 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.57/3.97 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 23.57/3.97 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.57/3.97 | (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 23.57/3.97 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.57/3.97 | (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 23.57/3.97 |
% 23.57/3.97 | DELTA: instantiating (5) with fresh symbols all_56_0, all_56_1, all_56_2,
% 23.57/3.97 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7 gives:
% 23.57/3.97 | (11) ~ (all_56_0 = all_56_2) & ~ (all_56_6 = empty_set) &
% 23.57/3.97 | complements_of_subsets(all_56_7, all_56_6) = all_56_3 &
% 23.57/3.97 | meet_of_subsets(all_56_7, all_56_6) = all_56_1 &
% 23.57/3.97 | union_of_subsets(all_56_7, all_56_3) = all_56_2 &
% 23.57/3.97 | subset_complement(all_56_7, all_56_1) = all_56_0 & powerset(all_56_5)
% 23.57/3.97 | = all_56_4 & powerset(all_56_7) = all_56_5 & $i(all_56_0) &
% 23.57/3.97 | $i(all_56_1) & $i(all_56_2) & $i(all_56_3) & $i(all_56_4) &
% 23.57/3.97 | $i(all_56_5) & $i(all_56_6) & $i(all_56_7) & element(all_56_6,
% 23.57/3.97 | all_56_4)
% 23.57/3.97 |
% 23.57/3.97 | ALPHA: (11) implies:
% 23.57/3.97 | (12) ~ (all_56_6 = empty_set)
% 23.57/3.97 | (13) ~ (all_56_0 = all_56_2)
% 23.57/3.97 | (14) element(all_56_6, all_56_4)
% 23.57/3.97 | (15) $i(all_56_7)
% 23.57/3.97 | (16) $i(all_56_6)
% 23.57/3.97 | (17) $i(all_56_3)
% 23.57/3.97 | (18) $i(all_56_1)
% 23.57/3.97 | (19) powerset(all_56_7) = all_56_5
% 23.57/3.97 | (20) powerset(all_56_5) = all_56_4
% 23.57/3.97 | (21) subset_complement(all_56_7, all_56_1) = all_56_0
% 23.57/3.97 | (22) union_of_subsets(all_56_7, all_56_3) = all_56_2
% 23.57/3.97 | (23) meet_of_subsets(all_56_7, all_56_6) = all_56_1
% 23.57/3.97 | (24) complements_of_subsets(all_56_7, all_56_6) = all_56_3
% 23.57/3.97 |
% 23.57/3.97 | GROUND_INST: instantiating (2) with all_56_7, all_56_5, simplifying with (15),
% 23.57/3.97 | (19) gives:
% 23.57/3.97 | (25) ? [v0: $i] : (cast_to_subset(all_56_7) = v0 & $i(v0) & element(v0,
% 23.57/3.97 | all_56_5))
% 23.57/3.97 |
% 23.57/3.99 | GROUND_INST: instantiating (1) with all_56_7, all_56_1, all_56_0, simplifying
% 23.57/3.99 | with (15), (18), (21) gives:
% 23.57/3.99 | (26) ? [v0: $i] : ? [v1: int] : ((v1 = all_56_0 &
% 23.57/3.99 | set_difference(all_56_7, all_56_1) = all_56_0 & $i(all_56_0)) |
% 23.57/3.99 | (powerset(all_56_7) = v0 & $i(v0) & ~ element(all_56_1, v0)))
% 23.57/3.99 |
% 23.57/3.99 | GROUND_INST: instantiating (involutiveness_k3_subset_1) with all_56_7,
% 23.57/3.99 | all_56_1, all_56_0, simplifying with (15), (18), (21) gives:
% 23.57/3.99 | (27) ? [v0: $i] : ? [v1: int] : ((v1 = all_56_1 &
% 23.57/3.99 | subset_complement(all_56_7, all_56_0) = all_56_1) |
% 23.57/3.99 | (powerset(all_56_7) = v0 & $i(v0) & ~ element(all_56_1, v0)))
% 23.57/3.99 |
% 23.57/3.99 | GROUND_INST: instantiating (dt_k3_subset_1) with all_56_7, all_56_1, all_56_0,
% 23.57/3.99 | simplifying with (15), (18), (21) gives:
% 23.57/3.99 | (28) ? [v0: $i] : (powerset(all_56_7) = v0 & $i(v0) & ( ~
% 23.57/3.99 | element(all_56_1, v0) | element(all_56_0, v0)))
% 23.57/3.99 |
% 23.57/4.00 | GROUND_INST: instantiating (dt_k5_setfam_1) with all_56_7, all_56_3, all_56_2,
% 23.57/4.00 | simplifying with (15), (17), (22) gives:
% 23.57/4.00 | (29) ? [v0: $i] : ? [v1: $i] : (powerset(all_56_7) = v0 & $i(v0) &
% 23.57/4.00 | (element(all_56_2, v0) | (powerset(v0) = v1 & $i(v1) & ~
% 23.57/4.00 | element(all_56_3, v1))))
% 23.57/4.00 |
% 23.57/4.00 | GROUND_INST: instantiating (3) with all_56_7, all_56_6, all_56_1, simplifying
% 23.57/4.00 | with (15), (16), (23) gives:
% 23.57/4.00 | (30) all_56_6 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 23.57/4.00 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v3 &
% 23.57/4.00 | complements_of_subsets(all_56_7, all_56_6) = v2 &
% 23.57/4.00 | subset_difference(all_56_7, v4, all_56_1) = v3 &
% 23.57/4.00 | union_of_subsets(all_56_7, v2) = v3 & cast_to_subset(all_56_7) =
% 23.57/4.00 | v4 & $i(v4) & $i(v3) & $i(v2)) | (powerset(v0) = v1 &
% 23.57/4.00 | powerset(all_56_7) = v0 & $i(v1) & $i(v0) & ~ element(all_56_6,
% 23.57/4.00 | v1)))
% 23.57/4.00 |
% 23.57/4.00 | GROUND_INST: instantiating (dt_k6_setfam_1) with all_56_7, all_56_6, all_56_1,
% 23.57/4.00 | simplifying with (15), (16), (23) gives:
% 23.57/4.00 | (31) ? [v0: $i] : ? [v1: $i] : (powerset(all_56_7) = v0 & $i(v0) &
% 23.57/4.00 | (element(all_56_1, v0) | (powerset(v0) = v1 & $i(v1) & ~
% 23.57/4.00 | element(all_56_6, v1))))
% 23.57/4.00 |
% 23.57/4.00 | GROUND_INST: instantiating (4) with all_56_7, all_56_6, all_56_3, simplifying
% 23.57/4.00 | with (15), (16), (24) gives:
% 23.57/4.00 | (32) all_56_6 = empty_set | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ?
% 23.57/4.00 | [v3: $i] : ? [v4: $i] : ? [v5: $i] : ((v5 = v2 &
% 23.57/4.00 | subset_difference(all_56_7, v3, v4) = v2 &
% 23.57/4.00 | meet_of_subsets(all_56_7, all_56_6) = v4 &
% 23.57/4.00 | union_of_subsets(all_56_7, all_56_3) = v2 &
% 23.57/4.00 | cast_to_subset(all_56_7) = v3 & $i(v4) & $i(v3) & $i(v2)) |
% 23.57/4.00 | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) & $i(v0) & ~
% 23.57/4.00 | element(all_56_6, v1)))
% 23.57/4.00 |
% 23.57/4.00 | GROUND_INST: instantiating (dt_k7_setfam_1) with all_56_7, all_56_6, all_56_3,
% 23.57/4.00 | simplifying with (15), (16), (24) gives:
% 23.57/4.00 | (33) ? [v0: $i] : ? [v1: $i] : (powerset(v0) = v1 & powerset(all_56_7) =
% 23.57/4.00 | v0 & $i(v1) & $i(v0) & ( ~ element(all_56_6, v1) | element(all_56_3,
% 23.57/4.00 | v1)))
% 23.57/4.00 |
% 23.57/4.00 | DELTA: instantiating (25) with fresh symbol all_70_0 gives:
% 23.57/4.00 | (34) cast_to_subset(all_56_7) = all_70_0 & $i(all_70_0) & element(all_70_0,
% 23.57/4.00 | all_56_5)
% 23.57/4.00 |
% 23.57/4.00 | ALPHA: (34) implies:
% 23.57/4.00 | (35) element(all_70_0, all_56_5)
% 23.57/4.00 | (36) cast_to_subset(all_56_7) = all_70_0
% 23.57/4.00 |
% 23.57/4.00 | DELTA: instantiating (28) with fresh symbol all_76_0 gives:
% 23.57/4.00 | (37) powerset(all_56_7) = all_76_0 & $i(all_76_0) & ( ~ element(all_56_1,
% 23.57/4.00 | all_76_0) | element(all_56_0, all_76_0))
% 23.57/4.00 |
% 23.57/4.00 | ALPHA: (37) implies:
% 23.57/4.00 | (38) powerset(all_56_7) = all_76_0
% 23.57/4.00 |
% 23.57/4.00 | DELTA: instantiating (27) with fresh symbols all_78_0, all_78_1 gives:
% 23.57/4.00 | (39) (all_78_0 = all_56_1 & subset_complement(all_56_7, all_56_0) =
% 23.57/4.00 | all_56_1) | (powerset(all_56_7) = all_78_1 & $i(all_78_1) & ~
% 23.57/4.00 | element(all_56_1, all_78_1))
% 23.57/4.00 |
% 23.57/4.00 | DELTA: instantiating (33) with fresh symbols all_79_0, all_79_1 gives:
% 23.57/4.00 | (40) powerset(all_79_1) = all_79_0 & powerset(all_56_7) = all_79_1 &
% 23.57/4.00 | $i(all_79_0) & $i(all_79_1) & ( ~ element(all_56_6, all_79_0) |
% 23.57/4.00 | element(all_56_3, all_79_0))
% 23.57/4.00 |
% 23.57/4.00 | ALPHA: (40) implies:
% 23.57/4.01 | (41) powerset(all_56_7) = all_79_1
% 23.57/4.01 | (42) powerset(all_79_1) = all_79_0
% 23.57/4.01 |
% 23.57/4.01 | DELTA: instantiating (31) with fresh symbols all_81_0, all_81_1 gives:
% 23.57/4.01 | (43) powerset(all_56_7) = all_81_1 & $i(all_81_1) & (element(all_56_1,
% 23.57/4.01 | all_81_1) | (powerset(all_81_1) = all_81_0 & $i(all_81_0) & ~
% 23.57/4.01 | element(all_56_6, all_81_0)))
% 23.57/4.01 |
% 23.57/4.01 | ALPHA: (43) implies:
% 23.57/4.01 | (44) powerset(all_56_7) = all_81_1
% 23.57/4.01 | (45) element(all_56_1, all_81_1) | (powerset(all_81_1) = all_81_0 &
% 23.57/4.01 | $i(all_81_0) & ~ element(all_56_6, all_81_0))
% 23.57/4.01 |
% 23.57/4.01 | DELTA: instantiating (29) with fresh symbols all_83_0, all_83_1 gives:
% 23.57/4.01 | (46) powerset(all_56_7) = all_83_1 & $i(all_83_1) & (element(all_56_2,
% 23.57/4.01 | all_83_1) | (powerset(all_83_1) = all_83_0 & $i(all_83_0) & ~
% 23.57/4.01 | element(all_56_3, all_83_0)))
% 23.57/4.01 |
% 23.57/4.01 | ALPHA: (46) implies:
% 23.57/4.01 | (47) powerset(all_56_7) = all_83_1
% 23.57/4.01 |
% 23.57/4.01 | DELTA: instantiating (26) with fresh symbols all_85_0, all_85_1 gives:
% 23.57/4.01 | (48) (all_85_0 = all_56_0 & set_difference(all_56_7, all_56_1) = all_56_0 &
% 23.57/4.01 | $i(all_56_0)) | (powerset(all_56_7) = all_85_1 & $i(all_85_1) & ~
% 23.57/4.01 | element(all_56_1, all_85_1))
% 23.57/4.01 |
% 23.57/4.01 | BETA: splitting (32) gives:
% 23.57/4.01 |
% 23.57/4.01 | Case 1:
% 23.57/4.01 | |
% 23.57/4.01 | | (49) all_56_6 = empty_set
% 23.57/4.01 | |
% 23.57/4.01 | | REDUCE: (12), (49) imply:
% 23.57/4.01 | | (50) $false
% 23.57/4.01 | |
% 23.57/4.01 | | CLOSE: (50) is inconsistent.
% 23.57/4.01 | |
% 23.57/4.01 | Case 2:
% 23.57/4.01 | |
% 23.57/4.01 | | (51) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i]
% 23.57/4.01 | | : ? [v5: $i] : ((v5 = v2 & subset_difference(all_56_7, v3, v4) = v2
% 23.57/4.01 | | & meet_of_subsets(all_56_7, all_56_6) = v4 &
% 23.57/4.01 | | union_of_subsets(all_56_7, all_56_3) = v2 &
% 23.57/4.01 | | cast_to_subset(all_56_7) = v3 & $i(v4) & $i(v3) & $i(v2)) |
% 23.57/4.01 | | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) & $i(v0) &
% 23.57/4.01 | | ~ element(all_56_6, v1)))
% 23.57/4.01 | |
% 23.57/4.01 | | DELTA: instantiating (51) with fresh symbols all_96_0, all_96_1, all_96_2,
% 23.57/4.01 | | all_96_3, all_96_4, all_96_5 gives:
% 23.57/4.01 | | (52) (all_96_0 = all_96_3 & subset_difference(all_56_7, all_96_2,
% 23.57/4.01 | | all_96_1) = all_96_3 & meet_of_subsets(all_56_7, all_56_6) =
% 23.57/4.01 | | all_96_1 & union_of_subsets(all_56_7, all_56_3) = all_96_3 &
% 23.57/4.01 | | cast_to_subset(all_56_7) = all_96_2 & $i(all_96_1) & $i(all_96_2)
% 23.57/4.01 | | & $i(all_96_3)) | (powerset(all_96_5) = all_96_4 &
% 23.57/4.01 | | powerset(all_56_7) = all_96_5 & $i(all_96_4) & $i(all_96_5) & ~
% 23.57/4.01 | | element(all_56_6, all_96_4))
% 23.57/4.01 | |
% 23.57/4.01 | | BETA: splitting (52) gives:
% 23.57/4.01 | |
% 23.57/4.01 | | Case 1:
% 23.57/4.01 | | |
% 23.57/4.01 | | | (53) all_96_0 = all_96_3 & subset_difference(all_56_7, all_96_2,
% 23.57/4.01 | | | all_96_1) = all_96_3 & meet_of_subsets(all_56_7, all_56_6) =
% 23.57/4.01 | | | all_96_1 & union_of_subsets(all_56_7, all_56_3) = all_96_3 &
% 23.57/4.01 | | | cast_to_subset(all_56_7) = all_96_2 & $i(all_96_1) & $i(all_96_2)
% 23.57/4.01 | | | & $i(all_96_3)
% 23.57/4.01 | | |
% 23.57/4.01 | | | ALPHA: (53) implies:
% 23.57/4.01 | | | (54) $i(all_96_2)
% 23.57/4.01 | | | (55) $i(all_96_1)
% 23.57/4.01 | | | (56) cast_to_subset(all_56_7) = all_96_2
% 23.57/4.01 | | | (57) union_of_subsets(all_56_7, all_56_3) = all_96_3
% 23.57/4.01 | | | (58) meet_of_subsets(all_56_7, all_56_6) = all_96_1
% 23.57/4.01 | | | (59) subset_difference(all_56_7, all_96_2, all_96_1) = all_96_3
% 23.57/4.01 | | |
% 23.57/4.01 | | | BETA: splitting (30) gives:
% 23.57/4.01 | | |
% 23.57/4.01 | | | Case 1:
% 23.57/4.01 | | | |
% 23.57/4.01 | | | | (60) all_56_6 = empty_set
% 23.57/4.01 | | | |
% 23.57/4.01 | | | | REDUCE: (12), (60) imply:
% 23.57/4.01 | | | | (61) $false
% 23.57/4.01 | | | |
% 23.57/4.01 | | | | CLOSE: (61) is inconsistent.
% 23.57/4.01 | | | |
% 23.57/4.01 | | | Case 2:
% 23.57/4.01 | | | |
% 23.57/4.01 | | | | (62) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 23.57/4.01 | | | | $i] : ? [v5: $i] : ((v5 = v3 &
% 23.57/4.02 | | | | complements_of_subsets(all_56_7, all_56_6) = v2 &
% 23.57/4.02 | | | | subset_difference(all_56_7, v4, all_56_1) = v3 &
% 23.57/4.02 | | | | union_of_subsets(all_56_7, v2) = v3 &
% 23.57/4.02 | | | | cast_to_subset(all_56_7) = v4 & $i(v4) & $i(v3) & $i(v2)) |
% 23.57/4.02 | | | | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) & $i(v0)
% 23.57/4.02 | | | | & ~ element(all_56_6, v1)))
% 23.57/4.02 | | | |
% 23.57/4.02 | | | | DELTA: instantiating (62) with fresh symbols all_104_0, all_104_1,
% 23.57/4.02 | | | | all_104_2, all_104_3, all_104_4, all_104_5 gives:
% 23.57/4.02 | | | | (63) (all_104_0 = all_104_2 & complements_of_subsets(all_56_7,
% 23.57/4.02 | | | | all_56_6) = all_104_3 & subset_difference(all_56_7,
% 23.57/4.02 | | | | all_104_1, all_56_1) = all_104_2 &
% 23.57/4.02 | | | | union_of_subsets(all_56_7, all_104_3) = all_104_2 &
% 23.57/4.02 | | | | cast_to_subset(all_56_7) = all_104_1 & $i(all_104_1) &
% 23.57/4.02 | | | | $i(all_104_2) & $i(all_104_3)) | (powerset(all_104_5) =
% 23.57/4.02 | | | | all_104_4 & powerset(all_56_7) = all_104_5 & $i(all_104_4) &
% 23.57/4.02 | | | | $i(all_104_5) & ~ element(all_56_6, all_104_4))
% 23.57/4.02 | | | |
% 23.57/4.02 | | | | BETA: splitting (63) gives:
% 23.57/4.02 | | | |
% 23.57/4.02 | | | | Case 1:
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | (64) all_104_0 = all_104_2 & complements_of_subsets(all_56_7,
% 23.57/4.02 | | | | | all_56_6) = all_104_3 & subset_difference(all_56_7,
% 23.57/4.02 | | | | | all_104_1, all_56_1) = all_104_2 &
% 23.57/4.02 | | | | | union_of_subsets(all_56_7, all_104_3) = all_104_2 &
% 23.57/4.02 | | | | | cast_to_subset(all_56_7) = all_104_1 & $i(all_104_1) &
% 23.57/4.02 | | | | | $i(all_104_2) & $i(all_104_3)
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | ALPHA: (64) implies:
% 23.57/4.02 | | | | | (65) cast_to_subset(all_56_7) = all_104_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_56_5, all_81_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (19), (44) gives:
% 23.57/4.02 | | | | | (66) all_81_1 = all_56_5
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_81_1, all_83_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (44), (47) gives:
% 23.57/4.02 | | | | | (67) all_83_1 = all_81_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_79_1, all_83_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (41), (47) gives:
% 23.57/4.02 | | | | | (68) all_83_1 = all_79_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_76_0, all_83_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (38), (47) gives:
% 23.57/4.02 | | | | | (69) all_83_1 = all_76_0
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (7) with all_96_2, all_104_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (56), (65) gives:
% 23.57/4.02 | | | | | (70) all_104_1 = all_96_2
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (7) with all_70_0, all_104_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (36), (65) gives:
% 23.57/4.02 | | | | | (71) all_104_1 = all_70_0
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (9) with all_56_2, all_96_3, all_56_3,
% 23.57/4.02 | | | | | all_56_7, simplifying with (22), (57) gives:
% 23.57/4.02 | | | | | (72) all_96_3 = all_56_2
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (10) with all_56_1, all_96_1, all_56_6,
% 23.57/4.02 | | | | | all_56_7, simplifying with (23), (58) gives:
% 23.57/4.02 | | | | | (73) all_96_1 = all_56_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | COMBINE_EQS: (70), (71) imply:
% 23.57/4.02 | | | | | (74) all_96_2 = all_70_0
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | SIMP: (74) implies:
% 23.57/4.02 | | | | | (75) all_96_2 = all_70_0
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | COMBINE_EQS: (68), (69) imply:
% 23.57/4.02 | | | | | (76) all_79_1 = all_76_0
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | COMBINE_EQS: (67), (68) imply:
% 23.57/4.02 | | | | | (77) all_81_1 = all_79_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | SIMP: (77) implies:
% 23.57/4.02 | | | | | (78) all_81_1 = all_79_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | COMBINE_EQS: (66), (78) imply:
% 23.57/4.02 | | | | | (79) all_79_1 = all_56_5
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | SIMP: (79) implies:
% 23.57/4.02 | | | | | (80) all_79_1 = all_56_5
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | COMBINE_EQS: (76), (80) imply:
% 23.57/4.02 | | | | | (81) all_76_0 = all_56_5
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | REF_CLOSE: (6), (8), (13), (14), (15), (20), (35), (38), (39), (45),
% 23.57/4.02 | | | | | (48), (54), (55), (56), (59), (66), (72), (73), (75), (81),
% 23.57/4.02 | | | | | (d4_subset_1), (redefinition_k6_subset_1) are inconsistent
% 23.57/4.02 | | | | | by sub-proof #1.
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | Case 2:
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | (82) powerset(all_104_5) = all_104_4 & powerset(all_56_7) =
% 23.57/4.02 | | | | | all_104_5 & $i(all_104_4) & $i(all_104_5) & ~
% 23.57/4.02 | | | | | element(all_56_6, all_104_4)
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | ALPHA: (82) implies:
% 23.57/4.02 | | | | | (83) powerset(all_56_7) = all_104_5
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_79_1, all_81_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (41), (44) gives:
% 23.57/4.02 | | | | | (84) all_81_1 = all_79_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_56_5, all_83_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (19), (47) gives:
% 23.57/4.02 | | | | | (85) all_83_1 = all_56_5
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_79_1, all_83_1, all_56_7,
% 23.57/4.02 | | | | | simplifying with (41), (47) gives:
% 23.57/4.02 | | | | | (86) all_83_1 = all_79_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_81_1, all_104_5, all_56_7,
% 23.57/4.02 | | | | | simplifying with (44), (83) gives:
% 23.57/4.02 | | | | | (87) all_104_5 = all_81_1
% 23.57/4.02 | | | | |
% 23.57/4.02 | | | | | GROUND_INST: instantiating (6) with all_76_0, all_104_5, all_56_7,
% 23.57/4.02 | | | | | simplifying with (38), (83) gives:
% 23.57/4.03 | | | | | (88) all_104_5 = all_76_0
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (7) with all_70_0, all_96_2, all_56_7,
% 23.57/4.03 | | | | | simplifying with (36), (56) gives:
% 23.57/4.03 | | | | | (89) all_96_2 = all_70_0
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (9) with all_56_2, all_96_3, all_56_3,
% 23.57/4.03 | | | | | all_56_7, simplifying with (22), (57) gives:
% 23.57/4.03 | | | | | (90) all_96_3 = all_56_2
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (10) with all_56_1, all_96_1, all_56_6,
% 23.57/4.03 | | | | | all_56_7, simplifying with (23), (58) gives:
% 23.57/4.03 | | | | | (91) all_96_1 = all_56_1
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (87), (88) imply:
% 23.57/4.03 | | | | | (92) all_81_1 = all_76_0
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | SIMP: (92) implies:
% 23.57/4.03 | | | | | (93) all_81_1 = all_76_0
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (85), (86) imply:
% 23.57/4.03 | | | | | (94) all_79_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | SIMP: (94) implies:
% 23.57/4.03 | | | | | (95) all_79_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (84), (93) imply:
% 23.57/4.03 | | | | | (96) all_79_1 = all_76_0
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | SIMP: (96) implies:
% 23.57/4.03 | | | | | (97) all_79_1 = all_76_0
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (95), (97) imply:
% 23.57/4.03 | | | | | (98) all_76_0 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (93), (98) imply:
% 23.57/4.03 | | | | | (99) all_81_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | REF_CLOSE: (6), (8), (13), (14), (15), (20), (35), (38), (39), (45),
% 23.57/4.03 | | | | | (48), (54), (55), (56), (59), (89), (90), (91), (98), (99),
% 23.57/4.03 | | | | | (d4_subset_1), (redefinition_k6_subset_1) are inconsistent
% 23.57/4.03 | | | | | by sub-proof #1.
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | End of split
% 23.57/4.03 | | | |
% 23.57/4.03 | | | End of split
% 23.57/4.03 | | |
% 23.57/4.03 | | Case 2:
% 23.57/4.03 | | |
% 23.57/4.03 | | | (100) powerset(all_96_5) = all_96_4 & powerset(all_56_7) = all_96_5 &
% 23.57/4.03 | | | $i(all_96_4) & $i(all_96_5) & ~ element(all_56_6, all_96_4)
% 23.57/4.03 | | |
% 23.57/4.03 | | | ALPHA: (100) implies:
% 23.57/4.03 | | | (101) ~ element(all_56_6, all_96_4)
% 23.57/4.03 | | | (102) powerset(all_56_7) = all_96_5
% 23.57/4.03 | | | (103) powerset(all_96_5) = all_96_4
% 23.57/4.03 | | |
% 23.57/4.03 | | | BETA: splitting (30) gives:
% 23.57/4.03 | | |
% 23.57/4.03 | | | Case 1:
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | (104) all_56_6 = empty_set
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | REDUCE: (12), (104) imply:
% 23.57/4.03 | | | | (105) $false
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | CLOSE: (105) is inconsistent.
% 23.57/4.03 | | | |
% 23.57/4.03 | | | Case 2:
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | (106) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4:
% 23.57/4.03 | | | | $i] : ? [v5: $i] : ((v5 = v3 &
% 23.57/4.03 | | | | complements_of_subsets(all_56_7, all_56_6) = v2 &
% 23.57/4.03 | | | | subset_difference(all_56_7, v4, all_56_1) = v3 &
% 23.57/4.03 | | | | union_of_subsets(all_56_7, v2) = v3 &
% 23.57/4.03 | | | | cast_to_subset(all_56_7) = v4 & $i(v4) & $i(v3) & $i(v2)) |
% 23.57/4.03 | | | | (powerset(v0) = v1 & powerset(all_56_7) = v0 & $i(v1) &
% 23.57/4.03 | | | | $i(v0) & ~ element(all_56_6, v1)))
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | DELTA: instantiating (106) with fresh symbols all_104_0, all_104_1,
% 23.57/4.03 | | | | all_104_2, all_104_3, all_104_4, all_104_5 gives:
% 23.57/4.03 | | | | (107) (all_104_0 = all_104_2 & complements_of_subsets(all_56_7,
% 23.57/4.03 | | | | all_56_6) = all_104_3 & subset_difference(all_56_7,
% 23.57/4.03 | | | | all_104_1, all_56_1) = all_104_2 &
% 23.57/4.03 | | | | union_of_subsets(all_56_7, all_104_3) = all_104_2 &
% 23.57/4.03 | | | | cast_to_subset(all_56_7) = all_104_1 & $i(all_104_1) &
% 23.57/4.03 | | | | $i(all_104_2) & $i(all_104_3)) | (powerset(all_104_5) =
% 23.57/4.03 | | | | all_104_4 & powerset(all_56_7) = all_104_5 & $i(all_104_4) &
% 23.57/4.03 | | | | $i(all_104_5) & ~ element(all_56_6, all_104_4))
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | BETA: splitting (107) gives:
% 23.57/4.03 | | | |
% 23.57/4.03 | | | | Case 1:
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (6) with all_56_5, all_83_1, all_56_7,
% 23.57/4.03 | | | | | simplifying with (19), (47) gives:
% 23.57/4.03 | | | | | (108) all_83_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (6) with all_81_1, all_83_1, all_56_7,
% 23.57/4.03 | | | | | simplifying with (44), (47) gives:
% 23.57/4.03 | | | | | (109) all_83_1 = all_81_1
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (6) with all_81_1, all_96_5, all_56_7,
% 23.57/4.03 | | | | | simplifying with (44), (102) gives:
% 23.57/4.03 | | | | | (110) all_96_5 = all_81_1
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (6) with all_79_1, all_96_5, all_56_7,
% 23.57/4.03 | | | | | simplifying with (41), (102) gives:
% 23.57/4.03 | | | | | (111) all_96_5 = all_79_1
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (6) with all_56_4, all_96_4, all_56_5,
% 23.57/4.03 | | | | | simplifying with (20) gives:
% 23.57/4.03 | | | | | (112) all_96_4 = all_56_4 | ~ (powerset(all_56_5) = all_96_4)
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | GROUND_INST: instantiating (6) with all_79_0, all_96_4, all_79_1,
% 23.57/4.03 | | | | | simplifying with (42) gives:
% 23.57/4.03 | | | | | (113) all_96_4 = all_79_0 | ~ (powerset(all_79_1) = all_96_4)
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | PRED_UNIFY: (14), (101) imply:
% 23.57/4.03 | | | | | (114) ~ (all_96_4 = all_56_4)
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (110), (111) imply:
% 23.57/4.03 | | | | | (115) all_81_1 = all_79_1
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | SIMP: (115) implies:
% 23.57/4.03 | | | | | (116) all_81_1 = all_79_1
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (108), (109) imply:
% 23.57/4.03 | | | | | (117) all_81_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | SIMP: (117) implies:
% 23.57/4.03 | | | | | (118) all_81_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (116), (118) imply:
% 23.57/4.03 | | | | | (119) all_79_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | SIMP: (119) implies:
% 23.57/4.03 | | | | | (120) all_79_1 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | COMBINE_EQS: (111), (120) imply:
% 23.57/4.03 | | | | | (121) all_96_5 = all_56_5
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | REDUCE: (103), (121) imply:
% 23.57/4.03 | | | | | (122) powerset(all_56_5) = all_96_4
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | BETA: splitting (113) gives:
% 23.57/4.03 | | | | |
% 23.57/4.03 | | | | | Case 1:
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | | (123) ~ (powerset(all_79_1) = all_96_4)
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | | REDUCE: (120), (123) imply:
% 23.57/4.03 | | | | | | (124) ~ (powerset(all_56_5) = all_96_4)
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | | PRED_UNIFY: (122), (124) imply:
% 23.57/4.03 | | | | | | (125) $false
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | | CLOSE: (125) is inconsistent.
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | Case 2:
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | | (126) all_96_4 = all_79_0
% 23.57/4.03 | | | | | |
% 23.57/4.03 | | | | | | REDUCE: (114), (126) imply:
% 23.57/4.03 | | | | | | (127) ~ (all_79_0 = all_56_4)
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | BETA: splitting (112) gives:
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | Case 1:
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | (128) ~ (powerset(all_56_5) = all_96_4)
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | PRED_UNIFY: (122), (128) imply:
% 23.57/4.04 | | | | | | | (129) $false
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | CLOSE: (129) is inconsistent.
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | Case 2:
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | (130) all_96_4 = all_56_4
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | COMBINE_EQS: (126), (130) imply:
% 23.57/4.04 | | | | | | | (131) all_79_0 = all_56_4
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | REDUCE: (127), (131) imply:
% 23.57/4.04 | | | | | | | (132) $false
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | | CLOSE: (132) is inconsistent.
% 23.57/4.04 | | | | | | |
% 23.57/4.04 | | | | | | End of split
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | End of split
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | Case 2:
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | (133) powerset(all_104_5) = all_104_4 & powerset(all_56_7) =
% 23.57/4.04 | | | | | all_104_5 & $i(all_104_4) & $i(all_104_5) & ~
% 23.57/4.04 | | | | | element(all_56_6, all_104_4)
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | ALPHA: (133) implies:
% 23.57/4.04 | | | | | (134) ~ element(all_56_6, all_104_4)
% 23.57/4.04 | | | | | (135) powerset(all_56_7) = all_104_5
% 23.57/4.04 | | | | | (136) powerset(all_104_5) = all_104_4
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_56_5, all_79_1, all_56_7,
% 23.57/4.04 | | | | | simplifying with (19), (41) gives:
% 23.57/4.04 | | | | | (137) all_79_1 = all_56_5
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_81_1, all_83_1, all_56_7,
% 23.57/4.04 | | | | | simplifying with (44), (47) gives:
% 23.57/4.04 | | | | | (138) all_83_1 = all_81_1
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_79_1, all_83_1, all_56_7,
% 23.57/4.04 | | | | | simplifying with (41), (47) gives:
% 23.57/4.04 | | | | | (139) all_83_1 = all_79_1
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_83_1, all_96_5, all_56_7,
% 23.57/4.04 | | | | | simplifying with (47), (102) gives:
% 23.57/4.04 | | | | | (140) all_96_5 = all_83_1
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_96_5, all_104_5, all_56_7,
% 23.57/4.04 | | | | | simplifying with (102), (135) gives:
% 23.57/4.04 | | | | | (141) all_104_5 = all_96_5
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_76_0, all_104_5, all_56_7,
% 23.57/4.04 | | | | | simplifying with (38), (135) gives:
% 23.57/4.04 | | | | | (142) all_104_5 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | GROUND_INST: instantiating (6) with all_56_4, all_104_4, all_56_5,
% 23.57/4.04 | | | | | simplifying with (20) gives:
% 23.57/4.04 | | | | | (143) all_104_4 = all_56_4 | ~ (powerset(all_56_5) = all_104_4)
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | PRED_UNIFY: (14), (134) imply:
% 23.57/4.04 | | | | | (144) ~ (all_104_4 = all_56_4)
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (141), (142) imply:
% 23.57/4.04 | | | | | (145) all_96_5 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | SIMP: (145) implies:
% 23.57/4.04 | | | | | (146) all_96_5 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (140), (146) imply:
% 23.57/4.04 | | | | | (147) all_83_1 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | SIMP: (147) implies:
% 23.57/4.04 | | | | | (148) all_83_1 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (138), (148) imply:
% 23.57/4.04 | | | | | (149) all_81_1 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (138), (139) imply:
% 23.57/4.04 | | | | | (150) all_81_1 = all_79_1
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (149), (150) imply:
% 23.57/4.04 | | | | | (151) all_79_1 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | SIMP: (151) implies:
% 23.57/4.04 | | | | | (152) all_79_1 = all_76_0
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (137), (152) imply:
% 23.57/4.04 | | | | | (153) all_76_0 = all_56_5
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | COMBINE_EQS: (142), (153) imply:
% 23.57/4.04 | | | | | (154) all_104_5 = all_56_5
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | REDUCE: (136), (154) imply:
% 23.57/4.04 | | | | | (155) powerset(all_56_5) = all_104_4
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | BETA: splitting (143) gives:
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | | Case 1:
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | (156) ~ (powerset(all_56_5) = all_104_4)
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | PRED_UNIFY: (155), (156) imply:
% 23.57/4.04 | | | | | | (157) $false
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | CLOSE: (157) is inconsistent.
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | Case 2:
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | (158) all_104_4 = all_56_4
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | REDUCE: (144), (158) imply:
% 23.57/4.04 | | | | | | (159) $false
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | | CLOSE: (159) is inconsistent.
% 23.57/4.04 | | | | | |
% 23.57/4.04 | | | | | End of split
% 23.57/4.04 | | | | |
% 23.57/4.04 | | | | End of split
% 23.57/4.04 | | | |
% 23.57/4.04 | | | End of split
% 23.57/4.04 | | |
% 23.57/4.04 | | End of split
% 23.57/4.04 | |
% 23.57/4.04 | End of split
% 23.57/4.04 |
% 23.57/4.04 End of proof
% 23.57/4.04
% 23.57/4.04 Sub-proof #1 shows that the following formulas are inconsistent:
% 23.57/4.04 ----------------------------------------------------------------
% 23.57/4.04 (1) $i(all_96_1)
% 23.57/4.04 (2) powerset(all_56_5) = all_56_4
% 23.57/4.04 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 23.57/4.04 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 23.57/4.04 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) =
% 23.57/4.04 v1) | ~ (powerset(v2) = v0))
% 23.57/4.04 (5) all_81_1 = all_56_5
% 23.57/4.04 (6) powerset(all_56_7) = all_76_0
% 23.57/4.04 (7) $i(all_56_7)
% 23.57/4.04 (8) all_96_2 = all_70_0
% 23.57/4.04 (9) (all_78_0 = all_56_1 & subset_complement(all_56_7, all_56_0) = all_56_1)
% 23.57/4.04 | (powerset(all_56_7) = all_78_1 & $i(all_78_1) & ~ element(all_56_1,
% 23.57/4.04 all_78_1))
% 23.57/4.04 (10) all_96_1 = all_56_1
% 23.57/4.04 (11) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (cast_to_subset(v0) = v1) | ~
% 23.57/4.04 $i(v0))
% 23.57/4.04 (12) all_76_0 = all_56_5
% 23.57/4.04 (13) cast_to_subset(all_56_7) = all_96_2
% 23.57/4.04 (14) ~ (all_56_0 = all_56_2)
% 23.57/4.04 (15) $i(all_96_2)
% 23.57/4.04 (16) element(all_56_6, all_56_4)
% 23.57/4.04 (17) all_96_3 = all_56_2
% 23.57/4.04 (18) element(all_70_0, all_56_5)
% 23.57/4.04 (19) element(all_56_1, all_81_1) | (powerset(all_81_1) = all_81_0 &
% 23.57/4.04 $i(all_81_0) & ~ element(all_56_6, all_81_0))
% 23.57/4.05 (20) (all_85_0 = all_56_0 & set_difference(all_56_7, all_56_1) = all_56_0 &
% 23.57/4.05 $i(all_56_0)) | (powerset(all_56_7) = all_85_1 & $i(all_85_1) & ~
% 23.57/4.05 element(all_56_1, all_85_1))
% 23.57/4.05 (21) subset_difference(all_56_7, all_96_2, all_96_1) = all_96_3
% 23.57/4.05 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 23.57/4.05 (subset_difference(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.57/4.05 $i(v0) | ? [v4: $i] : ? [v5: $i] : ((v5 = v3 & set_difference(v1,
% 23.57/4.05 v2) = v3 & $i(v3)) | (powerset(v0) = v4 & $i(v4) & ( ~
% 23.57/4.05 element(v2, v4) | ~ element(v1, v4)))))
% 23.57/4.05
% 23.57/4.05 Begin of proof
% 23.57/4.05 |
% 23.57/4.05 | REDUCE: (8), (10), (17), (21) imply:
% 23.57/4.05 | (23) subset_difference(all_56_7, all_70_0, all_56_1) = all_56_2
% 23.57/4.05 |
% 23.57/4.05 | REDUCE: (8), (13) imply:
% 23.57/4.05 | (24) cast_to_subset(all_56_7) = all_70_0
% 23.57/4.05 |
% 23.57/4.05 | REDUCE: (6), (12) imply:
% 23.57/4.05 | (25) powerset(all_56_7) = all_56_5
% 23.57/4.05 |
% 23.57/4.05 | REDUCE: (1), (10) imply:
% 23.57/4.05 | (26) $i(all_56_1)
% 23.57/4.05 |
% 23.57/4.05 | REDUCE: (8), (15) imply:
% 23.57/4.05 | (27) $i(all_70_0)
% 23.57/4.05 |
% 23.57/4.05 | BETA: splitting (19) gives:
% 23.57/4.05 |
% 23.57/4.05 | Case 1:
% 23.57/4.05 | |
% 23.57/4.05 | | (28) element(all_56_1, all_81_1)
% 23.57/4.05 | |
% 23.57/4.05 | | REDUCE: (5), (28) imply:
% 23.57/4.05 | | (29) element(all_56_1, all_56_5)
% 23.57/4.05 | |
% 23.57/4.05 | | BETA: splitting (20) gives:
% 23.57/4.05 | |
% 23.57/4.05 | | Case 1:
% 23.57/4.05 | | |
% 23.57/4.05 | | | (30) all_85_0 = all_56_0 & set_difference(all_56_7, all_56_1) =
% 23.57/4.05 | | | all_56_0 & $i(all_56_0)
% 23.57/4.05 | | |
% 23.57/4.05 | | | ALPHA: (30) implies:
% 23.57/4.05 | | | (31) set_difference(all_56_7, all_56_1) = all_56_0
% 23.57/4.05 | | |
% 23.57/4.05 | | | BETA: splitting (9) gives:
% 23.57/4.05 | | |
% 23.57/4.05 | | | Case 1:
% 23.57/4.05 | | | |
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | GROUND_INST: instantiating (11) with all_56_7, all_70_0, simplifying
% 23.57/4.05 | | | | with (7), (24) gives:
% 23.57/4.05 | | | | (32) all_70_0 = all_56_7
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | GROUND_INST: instantiating (22) with all_56_7, all_70_0, all_56_1,
% 23.57/4.05 | | | | all_56_2, simplifying with (7), (23), (26), (27) gives:
% 23.57/4.05 | | | | (33) ? [v0: $i] : ? [v1: int] : ((v1 = all_56_2 &
% 23.57/4.05 | | | | set_difference(all_70_0, all_56_1) = all_56_2 &
% 23.57/4.05 | | | | $i(all_56_2)) | (powerset(all_56_7) = v0 & $i(v0) & ( ~
% 23.57/4.05 | | | | element(all_70_0, v0) | ~ element(all_56_1, v0))))
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | DELTA: instantiating (33) with fresh symbols all_160_0, all_160_1 gives:
% 23.57/4.05 | | | | (34) (all_160_0 = all_56_2 & set_difference(all_70_0, all_56_1) =
% 23.57/4.05 | | | | all_56_2 & $i(all_56_2)) | (powerset(all_56_7) = all_160_1 &
% 23.57/4.05 | | | | $i(all_160_1) & ( ~ element(all_70_0, all_160_1) | ~
% 23.57/4.05 | | | | element(all_56_1, all_160_1)))
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | REDUCE: (18), (32) imply:
% 23.57/4.05 | | | | (35) element(all_56_7, all_56_5)
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | BETA: splitting (34) gives:
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | Case 1:
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | (36) all_160_0 = all_56_2 & set_difference(all_70_0, all_56_1) =
% 23.57/4.05 | | | | | all_56_2 & $i(all_56_2)
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | ALPHA: (36) implies:
% 23.57/4.05 | | | | | (37) set_difference(all_70_0, all_56_1) = all_56_2
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | REDUCE: (32), (37) imply:
% 23.57/4.05 | | | | | (38) set_difference(all_56_7, all_56_1) = all_56_2
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | GROUND_INST: instantiating (3) with all_56_0, all_56_2, all_56_1,
% 23.57/4.05 | | | | | all_56_7, simplifying with (31), (38) gives:
% 23.57/4.05 | | | | | (39) all_56_0 = all_56_2
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | REDUCE: (14), (39) imply:
% 23.57/4.05 | | | | | (40) $false
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | CLOSE: (40) is inconsistent.
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | Case 2:
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | (41) powerset(all_56_7) = all_160_1 & $i(all_160_1) & ( ~
% 23.57/4.05 | | | | | element(all_70_0, all_160_1) | ~ element(all_56_1,
% 23.57/4.05 | | | | | all_160_1))
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | ALPHA: (41) implies:
% 23.57/4.05 | | | | | (42) powerset(all_56_7) = all_160_1
% 23.57/4.05 | | | | | (43) ~ element(all_70_0, all_160_1) | ~ element(all_56_1,
% 23.57/4.05 | | | | | all_160_1)
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | GROUND_INST: instantiating (4) with all_56_5, all_160_1, all_56_7,
% 23.57/4.05 | | | | | simplifying with (25), (42) gives:
% 23.57/4.05 | | | | | (44) all_160_1 = all_56_5
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | BETA: splitting (43) gives:
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | | Case 1:
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | (45) ~ element(all_70_0, all_160_1)
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | REDUCE: (32), (44), (45) imply:
% 23.57/4.05 | | | | | | (46) ~ element(all_56_7, all_56_5)
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | PRED_UNIFY: (35), (46) imply:
% 23.57/4.05 | | | | | | (47) $false
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | CLOSE: (47) is inconsistent.
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | Case 2:
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | (48) ~ element(all_56_1, all_160_1)
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | REDUCE: (44), (48) imply:
% 23.57/4.05 | | | | | | (49) ~ element(all_56_1, all_56_5)
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | PRED_UNIFY: (29), (49) imply:
% 23.57/4.05 | | | | | | (50) $false
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | | CLOSE: (50) is inconsistent.
% 23.57/4.05 | | | | | |
% 23.57/4.05 | | | | | End of split
% 23.57/4.05 | | | | |
% 23.57/4.05 | | | | End of split
% 23.57/4.05 | | | |
% 23.57/4.05 | | | Case 2:
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | (51) powerset(all_56_7) = all_78_1 & $i(all_78_1) & ~
% 23.57/4.05 | | | | element(all_56_1, all_78_1)
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | ALPHA: (51) implies:
% 23.57/4.05 | | | | (52) ~ element(all_56_1, all_78_1)
% 23.57/4.05 | | | | (53) powerset(all_56_7) = all_78_1
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | GROUND_INST: instantiating (4) with all_56_5, all_78_1, all_56_7,
% 23.57/4.05 | | | | simplifying with (25), (53) gives:
% 23.57/4.05 | | | | (54) all_78_1 = all_56_5
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | PRED_UNIFY: (29), (52) imply:
% 23.57/4.05 | | | | (55) ~ (all_78_1 = all_56_5)
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | REDUCE: (54), (55) imply:
% 23.57/4.05 | | | | (56) $false
% 23.57/4.05 | | | |
% 23.57/4.05 | | | | CLOSE: (56) is inconsistent.
% 23.57/4.05 | | | |
% 23.57/4.05 | | | End of split
% 23.57/4.05 | | |
% 23.57/4.05 | | Case 2:
% 23.57/4.05 | | |
% 23.57/4.05 | | | (57) powerset(all_56_7) = all_85_1 & $i(all_85_1) & ~
% 23.57/4.05 | | | element(all_56_1, all_85_1)
% 23.57/4.05 | | |
% 23.57/4.06 | | | ALPHA: (57) implies:
% 23.57/4.06 | | | (58) ~ element(all_56_1, all_85_1)
% 23.57/4.06 | | | (59) powerset(all_56_7) = all_85_1
% 23.57/4.06 | | |
% 23.57/4.06 | | | GROUND_INST: instantiating (4) with all_56_5, all_85_1, all_56_7,
% 23.57/4.06 | | | simplifying with (25), (59) gives:
% 23.57/4.06 | | | (60) all_85_1 = all_56_5
% 23.57/4.06 | | |
% 23.57/4.06 | | | PRED_UNIFY: (29), (58) imply:
% 23.57/4.06 | | | (61) ~ (all_85_1 = all_56_5)
% 23.57/4.06 | | |
% 23.57/4.06 | | | REDUCE: (60), (61) imply:
% 23.57/4.06 | | | (62) $false
% 23.57/4.06 | | |
% 23.57/4.06 | | | CLOSE: (62) is inconsistent.
% 23.57/4.06 | | |
% 23.57/4.06 | | End of split
% 23.57/4.06 | |
% 23.57/4.06 | Case 2:
% 23.57/4.06 | |
% 23.57/4.06 | | (63) powerset(all_81_1) = all_81_0 & $i(all_81_0) & ~ element(all_56_6,
% 23.57/4.06 | | all_81_0)
% 23.57/4.06 | |
% 23.57/4.06 | | ALPHA: (63) implies:
% 23.57/4.06 | | (64) ~ element(all_56_6, all_81_0)
% 23.57/4.06 | | (65) powerset(all_81_1) = all_81_0
% 23.57/4.06 | |
% 23.57/4.06 | | REDUCE: (5), (65) imply:
% 23.57/4.06 | | (66) powerset(all_56_5) = all_81_0
% 23.57/4.06 | |
% 23.57/4.06 | | GROUND_INST: instantiating (4) with all_56_4, all_81_0, all_56_5,
% 23.57/4.06 | | simplifying with (2), (66) gives:
% 23.57/4.06 | | (67) all_81_0 = all_56_4
% 23.57/4.06 | |
% 23.57/4.06 | | PRED_UNIFY: (16), (64) imply:
% 23.57/4.06 | | (68) ~ (all_81_0 = all_56_4)
% 23.57/4.06 | |
% 23.57/4.06 | | REDUCE: (67), (68) imply:
% 23.57/4.06 | | (69) $false
% 23.57/4.06 | |
% 23.57/4.06 | | CLOSE: (69) is inconsistent.
% 23.57/4.06 | |
% 23.57/4.06 | End of split
% 23.57/4.06 |
% 23.57/4.06 End of proof
% 23.57/4.06 % SZS output end Proof for theBenchmark
% 23.57/4.06
% 23.57/4.06 3452ms
%------------------------------------------------------------------------------