TSTP Solution File: SEU327+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU327+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%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 : 600s
% DateTime : Tue Jul 19 08:48:53 EDT 2022
% Result : Theorem 4.09s 1.58s
% Output : Proof 6.86s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU327+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 10:43:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.50/0.60 ____ _
% 0.50/0.60 ___ / __ \_____(_)___ ________ __________
% 0.50/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.60
% 0.50/0.60 A Theorem Prover for First-Order Logic
% 0.50/0.60 (ePrincess v.1.0)
% 0.50/0.60
% 0.50/0.60 (c) Philipp Rümmer, 2009-2015
% 0.50/0.60 (c) Peter Backeman, 2014-2015
% 0.50/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.60 Bug reports to peter@backeman.se
% 0.50/0.60
% 0.50/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.60
% 0.50/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.81/0.98 Prover 0: Preprocessing ...
% 2.82/1.31 Prover 0: Warning: ignoring some quantifiers
% 3.05/1.34 Prover 0: Constructing countermodel ...
% 4.09/1.58 Prover 0: proved (929ms)
% 4.09/1.58
% 4.09/1.58 No countermodel exists, formula is valid
% 4.09/1.58 % SZS status Theorem for theBenchmark
% 4.09/1.58
% 4.09/1.58 Generating proof ... Warning: ignoring some quantifiers
% 6.51/2.10 found it (size 125)
% 6.51/2.10
% 6.51/2.10 % SZS output start Proof for theBenchmark
% 6.51/2.10 Assumed formulas after preprocessing and simplification:
% 6.51/2.10 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v7 = v5) & ~ (v1 = empty_set) & complements_of_subsets(v0, v1) = v4 & meet_of_subsets(v0, v4) = v5 & union_of_subsets(v0, v1) = v6 & subset_complement(v0, v6) = v7 & powerset(v2) = v3 & powerset(v0) = v2 & empty(empty_set) & v5_membered(v8) & v5_membered(empty_set) & v4_membered(v8) & v4_membered(empty_set) & v3_membered(v8) & v3_membered(empty_set) & v2_membered(v8) & v2_membered(empty_set) & element(v1, v3) & v1_membered(v8) & v1_membered(empty_set) & ~ empty(v8) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (subset_difference(v13, v12, v11) = v10) | ~ (subset_difference(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = empty_set | ~ (subset_difference(v9, v11, v12) = v13) | ~ (union_of_subsets(v9, v10) = v12) | ~ (cast_to_subset(v9) = v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (complements_of_subsets(v9, v10) = v16 & meet_of_subsets(v9, v16) = v17 & powerset(v14) = v15 & powerset(v9) = v14 & (v17 = v13 | ~ element(v10, v15)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v13) | ~ (powerset(v9) = v12) | ~ element(v11, v12) | ~ element(v10, v12) | subset_difference(v9, v10, v11) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (complements_of_subsets(v9, v11) = v12) | ~ (complements_of_subsets(v9, v10) = v11) | ? [v13] : ? [v14] : (powerset(v13) = v14 & powerset(v9) = v13 & ~ element(v10, v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (subset_complement(v9, v11) = v12) | ~ (subset_complement(v9, v10) = v11) | ? [v13] : (powerset(v9) = v13 & ~ element(v10, v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (complements_of_subsets(v12, v11) = v10) | ~ (complements_of_subsets(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (meet_of_subsets(v12, v11) = v10) | ~ (meet_of_subsets(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (union_of_subsets(v12, v11) = v10) | ~ (union_of_subsets(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subset_complement(v12, v11) = v10) | ~ (subset_complement(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (set_difference(v12, v11) = v10) | ~ (set_difference(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = empty_set | ~ (complements_of_subsets(v9, v10) = v11) | ~ (meet_of_subsets(v9, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (subset_difference(v9, v15, v16) = v17 & union_of_subsets(v9, v10) = v16 & cast_to_subset(v9) = v15 & powerset(v13) = v14 & powerset(v9) = v13 & (v17 = v12 | ~ element(v10, v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_meet(v10) = v12) | ~ (powerset(v9) = v11) | ? [v13] : ? [v14] : (meet_of_subsets(v9, v10) = v14 & powerset(v11) = v13 & (v14 = v12 | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v10) = v12) | ~ (powerset(v9) = v11) | ? [v13] : ? [v14] : (union_of_subsets(v9, v10) = v14 & powerset(v11) = v13 & (v14 = v12 | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v10, v11) = v12) | ? [v13] : ? [v14] : (set_difference(v10, v11) = v14 & powerset(v9) = v13 & (v14 = v12 | ~ element(v11, v13) | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (subset_difference(v9, v10, v11) = v12) | ? [v13] : (powerset(v9) = v13 & ( ~ element(v11, v13) | ~ element(v10, v13) | element(v12, v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v11) | ~ element(v10, v12) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ element(v10, v12) | ~ in(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (set_meet(v11) = v10) | ~ (set_meet(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (union(v11) = v10) | ~ (union(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (cast_to_subset(v11) = v10) | ~ (cast_to_subset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (powerset(v11) = v10) | ~ (powerset(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (complements_of_subsets(v9, v10) = v11) | ? [v12] : ? [v13] : (powerset(v12) = v13 & powerset(v9) = v12 & ( ~ element(v10, v13) | element(v11, v13)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (meet_of_subsets(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (set_meet(v10) = v14 & powerset(v12) = v13 & powerset(v9) = v12 & (v14 = v11 | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (meet_of_subsets(v9, v10) = v11) | ? [v12] : ? [v13] : (powerset(v12) = v13 & powerset(v9) = v12 & ( ~ element(v10, v13) | element(v11, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union_of_subsets(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (union(v10) = v14 & powerset(v12) = v13 & powerset(v9) = v12 & (v14 = v11 | ~ element(v10, v13)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union_of_subsets(v9, v10) = v11) | ? [v12] : ? [v13] : (powerset(v12) = v13 & powerset(v9) = v12 & ( ~ element(v10, v13) | element(v11, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : ? [v13] : (set_difference(v9, v10) = v13 & powerset(v9) = v12 & (v13 = v11 | ~ element(v10, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subset_complement(v9, v10) = v11) | ? [v12] : (powerset(v9) = v12 & ( ~ element(v10, v12) | element(v11, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v5_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v4_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v3_membered(v9) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v3_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v3_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v2_membered(v9) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v2_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v10) = v11) | ? [v12] : ? [v13] : (subset_complement(v9, v10) = v13 & powerset(v9) = v12 & (v13 = v11 | ~ element(v10, v12)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ subset(v9, v10) | element(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ~ element(v9, v11) | subset(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v5_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v5_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v4_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v4_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v3_membered(v9) | ~ element(v11, v10) | v3_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v3_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v3_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v2_membered(v9) | ~ element(v11, v10) | v2_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ v2_membered(v9) | ~ element(v11, v10) | v1_membered(v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (powerset(v9) = v10) | ~ element(v11, v10) | ~ v1_membered(v9) | v1_membered(v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (set_difference(v9, empty_set) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (cast_to_subset(v9) = v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ empty(v10) | ~ empty(v9)) & ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(empty_set, v9) = v10)) & ! [v9] : ! [v10] : ( ~ (cast_to_subset(v9) = v10) | ? [v11] : (powerset(v9) = v11 & element(v10, v11))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ~ empty(v10)) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | empty(v9) | ? [v11] : (element(v11, v10) & ~ empty(v11))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : (cast_to_subset(v9) = v11 & element(v11, v10))) & ! [v9] : ! [v10] : ( ~ (powerset(v9) = v10) | ? [v11] : (empty(v11) & element(v11, v10))) & ! [v9] : ! [v10] : ( ~ empty(v10) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | natural(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_int_1(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v5_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_int_1(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v4_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ v3_membered(v9) | ~ element(v10, v9) | v1_rat_1(v10)) & ! [v9] : ! [v10] : ( ~ v3_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v3_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ v2_membered(v9) | ~ element(v10, v9) | v1_xreal_0(v10)) & ! [v9] : ! [v10] : ( ~ v2_membered(v9) | ~ element(v10, v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v10, v9) | ~ v1_membered(v9) | v1_xcmplx_0(v10)) & ! [v9] : ! [v10] : ( ~ element(v9, v10) | empty(v10) | in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v10, v9) | ~ in(v9, v10)) & ! [v9] : ! [v10] : ( ~ in(v9, v10) | element(v9, v10)) & ! [v9] : (v9 = empty_set | ~ empty(v9)) & ! [v9] : ( ~ empty(v9) | v5_membered(v9)) & ! [v9] : ( ~ empty(v9) | v4_membered(v9)) & ! [v9] : ( ~ empty(v9) | v3_membered(v9)) & ! [v9] : ( ~ empty(v9) | v2_membered(v9)) & ! [v9] : ( ~ empty(v9) | v1_membered(v9)) & ! [v9] : ( ~ v5_membered(v9) | v4_membered(v9)) & ! [v9] : ( ~ v4_membered(v9) | v3_membered(v9)) & ! [v9] : ( ~ v3_membered(v9) | v2_membered(v9)) & ! [v9] : ( ~ v2_membered(v9) | v1_membered(v9)) & ? [v9] : ? [v10] : element(v10, v9) & ? [v9] : subset(v9, v9))
% 6.86/2.16 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 6.86/2.16 | (1) ~ (all_0_1_1 = all_0_3_3) & ~ (all_0_7_7 = empty_set) & complements_of_subsets(all_0_8_8, all_0_7_7) = all_0_4_4 & meet_of_subsets(all_0_8_8, all_0_4_4) = all_0_3_3 & union_of_subsets(all_0_8_8, all_0_7_7) = all_0_2_2 & subset_complement(all_0_8_8, all_0_2_2) = all_0_1_1 & powerset(all_0_6_6) = all_0_5_5 & powerset(all_0_8_8) = all_0_6_6 & empty(empty_set) & v5_membered(all_0_0_0) & v5_membered(empty_set) & v4_membered(all_0_0_0) & v4_membered(empty_set) & v3_membered(all_0_0_0) & v3_membered(empty_set) & v2_membered(all_0_0_0) & v2_membered(empty_set) & element(all_0_7_7, all_0_5_5) & v1_membered(all_0_0_0) & v1_membered(empty_set) & ~ empty(all_0_0_0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (complements_of_subsets(v0, v1) = v7 & meet_of_subsets(v0, v7) = v8 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ~ (meet_of_subsets(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_meet(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (set_meet(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1)) & ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ( ~ empty(v0) | v5_membered(v0)) & ! [v0] : ( ~ empty(v0) | v4_membered(v0)) & ! [v0] : ( ~ empty(v0) | v3_membered(v0)) & ! [v0] : ( ~ empty(v0) | v2_membered(v0)) & ! [v0] : ( ~ empty(v0) | v1_membered(v0)) & ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0)) & ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0)) & ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0)) & ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0)) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : subset(v0, v0)
% 6.86/2.18 |
% 6.86/2.18 | Applying alpha-rule on (1) yields:
% 6.86/2.18 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ element(v2, v1) | ~ v1_membered(v0) | v1_membered(v2))
% 6.86/2.18 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v1_membered(v2))
% 6.86/2.18 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v2_membered(v2))
% 6.86/2.18 | (5) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ v1_membered(v0) | v1_xcmplx_0(v1))
% 6.86/2.18 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v3_membered(v2))
% 6.86/2.18 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 6.86/2.18 | (8) ! [v0] : ( ~ v5_membered(v0) | v4_membered(v0))
% 6.86/2.18 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v2_membered(v2))
% 6.86/2.18 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v4_membered(v2))
% 6.86/2.18 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v4_membered(v2))
% 6.86/2.18 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v1_membered(v2))
% 6.86/2.18 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 6.86/2.18 | (14) ? [v0] : ? [v1] : element(v1, v0)
% 6.86/2.18 | (15) v5_membered(all_0_0_0)
% 6.86/2.18 | (16) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 6.86/2.18 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v2_membered(v2))
% 6.86/2.18 | (18) complements_of_subsets(all_0_8_8, all_0_7_7) = all_0_4_4
% 6.86/2.18 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 6.86/2.18 | (20) v3_membered(empty_set)
% 6.86/2.18 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v5_membered(v2))
% 6.86/2.18 | (22) v1_membered(empty_set)
% 6.86/2.18 | (23) union_of_subsets(all_0_8_8, all_0_7_7) = all_0_2_2
% 6.86/2.18 | (24) v5_membered(empty_set)
% 6.86/2.18 | (25) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (empty(v2) & element(v2, v1)))
% 6.86/2.18 | (26) element(all_0_7_7, all_0_5_5)
% 6.86/2.18 | (27) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 6.86/2.18 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 6.86/2.18 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 6.86/2.18 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v1_membered(v2))
% 6.86/2.18 | (31) v1_membered(all_0_0_0)
% 6.86/2.18 | (32) ! [v0] : ( ~ empty(v0) | v3_membered(v0))
% 6.86/2.18 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4))))
% 6.86/2.19 | (34) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2)))
% 6.86/2.19 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v1_membered(v2))
% 6.86/2.19 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v2_membered(v0) | v2_membered(v2))
% 6.86/2.19 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v3_membered(v0) | ~ element(v2, v1) | v2_membered(v2))
% 6.86/2.19 | (38) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1))
% 6.86/2.19 | (39) ! [v0] : ( ~ empty(v0) | v2_membered(v0))
% 6.86/2.19 | (40) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1))
% 6.86/2.19 | (41) v2_membered(empty_set)
% 6.86/2.19 | (42) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1))
% 6.86/2.19 | (43) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 6.86/2.19 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (set_meet(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4))))
% 6.86/2.19 | (45) v4_membered(empty_set)
% 6.86/2.19 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = v2) | ~ (meet_of_subsets(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5))))
% 6.86/2.19 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_meet(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4))))
% 6.86/2.19 | (48) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1))
% 6.86/2.19 | (49) v3_membered(all_0_0_0)
% 6.86/2.19 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v2_membered(v2))
% 6.86/2.19 | (51) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1))
% 6.86/2.19 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v1_membered(v2))
% 6.86/2.19 | (53) ! [v0] : ! [v1] : ( ~ v2_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1))
% 6.86/2.19 | (54) ! [v0] : ! [v1] : ( ~ v3_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1))
% 6.86/2.19 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v4_membered(v2))
% 6.86/2.19 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 6.86/2.19 | (57) meet_of_subsets(all_0_8_8, all_0_4_4) = all_0_3_3
% 6.86/2.19 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 6.86/2.19 | (59) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | natural(v1))
% 6.86/2.19 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v2_membered(v2))
% 6.86/2.19 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 6.86/2.19 | (62) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 6.86/2.19 | (63) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1))
% 6.86/2.19 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v2_membered(v0) | ~ element(v2, v1) | v1_membered(v2))
% 6.86/2.19 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 6.86/2.19 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v4_membered(v2))
% 6.86/2.19 | (67) powerset(all_0_8_8) = all_0_6_6
% 6.86/2.19 | (68) ~ empty(all_0_0_0)
% 6.86/2.19 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4))))
% 6.86/2.19 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 6.86/2.19 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 6.86/2.19 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 6.86/2.19 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v1_membered(v2))
% 6.86/2.19 | (74) empty(empty_set)
% 6.86/2.19 | (75) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 6.86/2.19 | (76) v2_membered(all_0_0_0)
% 6.86/2.19 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v4_membered(v0) | ~ element(v2, v1) | v3_membered(v2))
% 6.86/2.19 | (78) ! [v0] : ( ~ empty(v0) | v1_membered(v0))
% 6.86/2.19 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 6.86/2.20 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v5_membered(v2))
% 6.86/2.20 | (81) ! [v0] : ( ~ v3_membered(v0) | v2_membered(v0))
% 6.86/2.20 | (82) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 6.86/2.20 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v2_membered(v2))
% 6.86/2.20 | (84) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_int_1(v1))
% 6.86/2.20 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ empty(v2) | ~ element(v1, v3) | ~ in(v0, v1))
% 6.86/2.20 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4)))
% 6.86/2.20 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4))))
% 6.86/2.20 | (88) ? [v0] : subset(v0, v0)
% 6.86/2.20 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 6.86/2.20 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v5_membered(v0) | v3_membered(v2))
% 6.86/2.20 | (91) ! [v0] : ( ~ v4_membered(v0) | v3_membered(v0))
% 6.86/2.20 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 6.86/2.20 | (93) subset_complement(all_0_8_8, all_0_2_2) = all_0_1_1
% 6.86/2.20 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 6.86/2.20 | (95) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1)))
% 6.86/2.20 | (96) ! [v0] : ( ~ empty(v0) | v4_membered(v0))
% 6.86/2.20 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ v5_membered(v0) | ~ element(v2, v1) | v3_membered(v2))
% 6.86/2.20 | (98) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_rat_1(v1))
% 6.86/2.20 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5)))
% 6.86/2.20 | (100) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 6.86/2.20 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 6.86/2.20 | (102) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 6.86/2.20 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v3_membered(v0) | v3_membered(v2))
% 6.86/2.20 | (104) ~ (all_0_7_7 = empty_set)
% 6.86/2.20 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4)
% 6.86/2.20 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 6.86/2.20 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 6.86/2.20 | (108) ! [v0] : ( ~ empty(v0) | v5_membered(v0))
% 6.86/2.20 | (109) v4_membered(all_0_0_0)
% 6.86/2.20 | (110) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_int_1(v1))
% 6.86/2.20 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 6.86/2.20 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v1_membered(v2))
% 6.86/2.20 | (113) ! [v0] : ( ~ v2_membered(v0) | v1_membered(v0))
% 6.86/2.20 | (114) powerset(all_0_6_6) = all_0_5_5
% 6.86/2.20 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 6.86/2.20 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v4_membered(v0) | v3_membered(v2))
% 6.86/2.20 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ~ v1_membered(v0) | v1_membered(v2))
% 6.86/2.20 | (118) ! [v0] : ! [v1] : ( ~ v5_membered(v0) | ~ element(v1, v0) | v1_xreal_0(v1))
% 6.86/2.20 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3))))
% 6.86/2.20 | (120) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 6.86/2.20 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (complements_of_subsets(v0, v1) = v7 & meet_of_subsets(v0, v7) = v8 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6))))
% 6.86/2.20 | (122) ~ (all_0_1_1 = all_0_3_3)
% 6.86/2.20 | (123) ! [v0] : ! [v1] : ( ~ v4_membered(v0) | ~ element(v1, v0) | v1_xcmplx_0(v1))
% 6.86/2.20 |
% 6.86/2.20 | Instantiating formula (87) with all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms complements_of_subsets(all_0_8_8, all_0_7_7) = all_0_4_4, yields:
% 6.86/2.20 | (124) ? [v0] : ? [v1] : (powerset(v0) = v1 & powerset(all_0_8_8) = v0 & ( ~ element(all_0_7_7, v1) | element(all_0_4_4, v1)))
% 6.86/2.20 |
% 6.86/2.20 | Instantiating formula (46) with all_0_3_3, all_0_4_4, all_0_7_7, all_0_8_8 and discharging atoms complements_of_subsets(all_0_8_8, all_0_7_7) = all_0_4_4, meet_of_subsets(all_0_8_8, all_0_4_4) = all_0_3_3, yields:
% 6.86/2.21 | (125) all_0_7_7 = empty_set | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset_difference(all_0_8_8, v2, v3) = v4 & union_of_subsets(all_0_8_8, all_0_7_7) = v3 & cast_to_subset(all_0_8_8) = v2 & powerset(v0) = v1 & powerset(all_0_8_8) = v0 & (v4 = all_0_3_3 | ~ element(all_0_7_7, v1)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (44) with all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms meet_of_subsets(all_0_8_8, all_0_4_4) = all_0_3_3, yields:
% 6.86/2.21 | (126) ? [v0] : ? [v1] : ? [v2] : (set_meet(all_0_4_4) = v2 & powerset(v0) = v1 & powerset(all_0_8_8) = v0 & (v2 = all_0_3_3 | ~ element(all_0_4_4, v1)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (71) with all_0_3_3, all_0_4_4, all_0_8_8 and discharging atoms meet_of_subsets(all_0_8_8, all_0_4_4) = all_0_3_3, yields:
% 6.86/2.21 | (127) ? [v0] : ? [v1] : (powerset(v0) = v1 & powerset(all_0_8_8) = v0 & ( ~ element(all_0_4_4, v1) | element(all_0_3_3, v0)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (33) with all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms union_of_subsets(all_0_8_8, all_0_7_7) = all_0_2_2, yields:
% 6.86/2.21 | (128) ? [v0] : ? [v1] : ? [v2] : (union(all_0_7_7) = v2 & powerset(v0) = v1 & powerset(all_0_8_8) = v0 & (v2 = all_0_2_2 | ~ element(all_0_7_7, v1)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (79) with all_0_2_2, all_0_7_7, all_0_8_8 and discharging atoms union_of_subsets(all_0_8_8, all_0_7_7) = all_0_2_2, yields:
% 6.86/2.21 | (129) ? [v0] : ? [v1] : (powerset(v0) = v1 & powerset(all_0_8_8) = v0 & ( ~ element(all_0_7_7, v1) | element(all_0_2_2, v0)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (19) with all_0_1_1, all_0_2_2, all_0_8_8 and discharging atoms subset_complement(all_0_8_8, all_0_2_2) = all_0_1_1, yields:
% 6.86/2.21 | (130) ? [v0] : ? [v1] : (set_difference(all_0_8_8, all_0_2_2) = v1 & powerset(all_0_8_8) = v0 & (v1 = all_0_1_1 | ~ element(all_0_2_2, v0)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (119) with all_0_1_1, all_0_2_2, all_0_8_8 and discharging atoms subset_complement(all_0_8_8, all_0_2_2) = all_0_1_1, yields:
% 6.86/2.21 | (131) ? [v0] : (powerset(all_0_8_8) = v0 & ( ~ element(all_0_2_2, v0) | element(all_0_1_1, v0)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (95) with all_0_6_6, all_0_8_8 and discharging atoms powerset(all_0_8_8) = all_0_6_6, yields:
% 6.86/2.21 | (132) ? [v0] : (cast_to_subset(all_0_8_8) = v0 & element(v0, all_0_6_6))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (131) with all_19_0_15 yields:
% 6.86/2.21 | (133) powerset(all_0_8_8) = all_19_0_15 & ( ~ element(all_0_2_2, all_19_0_15) | element(all_0_1_1, all_19_0_15))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (133) yields:
% 6.86/2.21 | (134) powerset(all_0_8_8) = all_19_0_15
% 6.86/2.21 | (135) ~ element(all_0_2_2, all_19_0_15) | element(all_0_1_1, all_19_0_15)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (130) with all_21_0_16, all_21_1_17 yields:
% 6.86/2.21 | (136) set_difference(all_0_8_8, all_0_2_2) = all_21_0_16 & powerset(all_0_8_8) = all_21_1_17 & (all_21_0_16 = all_0_1_1 | ~ element(all_0_2_2, all_21_1_17))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (136) yields:
% 6.86/2.21 | (137) set_difference(all_0_8_8, all_0_2_2) = all_21_0_16
% 6.86/2.21 | (138) powerset(all_0_8_8) = all_21_1_17
% 6.86/2.21 | (139) all_21_0_16 = all_0_1_1 | ~ element(all_0_2_2, all_21_1_17)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (132) with all_23_0_18 yields:
% 6.86/2.21 | (140) cast_to_subset(all_0_8_8) = all_23_0_18 & element(all_23_0_18, all_0_6_6)
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (140) yields:
% 6.86/2.21 | (141) cast_to_subset(all_0_8_8) = all_23_0_18
% 6.86/2.21 | (142) element(all_23_0_18, all_0_6_6)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (127) with all_25_0_19, all_25_1_20 yields:
% 6.86/2.21 | (143) powerset(all_25_1_20) = all_25_0_19 & powerset(all_0_8_8) = all_25_1_20 & ( ~ element(all_0_4_4, all_25_0_19) | element(all_0_3_3, all_25_1_20))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (143) yields:
% 6.86/2.21 | (144) powerset(all_25_1_20) = all_25_0_19
% 6.86/2.21 | (145) powerset(all_0_8_8) = all_25_1_20
% 6.86/2.21 | (146) ~ element(all_0_4_4, all_25_0_19) | element(all_0_3_3, all_25_1_20)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (126) with all_27_0_21, all_27_1_22, all_27_2_23 yields:
% 6.86/2.21 | (147) set_meet(all_0_4_4) = all_27_0_21 & powerset(all_27_2_23) = all_27_1_22 & powerset(all_0_8_8) = all_27_2_23 & (all_27_0_21 = all_0_3_3 | ~ element(all_0_4_4, all_27_1_22))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (147) yields:
% 6.86/2.21 | (148) set_meet(all_0_4_4) = all_27_0_21
% 6.86/2.21 | (149) powerset(all_27_2_23) = all_27_1_22
% 6.86/2.21 | (150) powerset(all_0_8_8) = all_27_2_23
% 6.86/2.21 | (151) all_27_0_21 = all_0_3_3 | ~ element(all_0_4_4, all_27_1_22)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (129) with all_29_0_24, all_29_1_25 yields:
% 6.86/2.21 | (152) powerset(all_29_1_25) = all_29_0_24 & powerset(all_0_8_8) = all_29_1_25 & ( ~ element(all_0_7_7, all_29_0_24) | element(all_0_2_2, all_29_1_25))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (152) yields:
% 6.86/2.21 | (153) powerset(all_29_1_25) = all_29_0_24
% 6.86/2.21 | (154) powerset(all_0_8_8) = all_29_1_25
% 6.86/2.21 | (155) ~ element(all_0_7_7, all_29_0_24) | element(all_0_2_2, all_29_1_25)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (128) with all_31_0_26, all_31_1_27, all_31_2_28 yields:
% 6.86/2.21 | (156) union(all_0_7_7) = all_31_0_26 & powerset(all_31_2_28) = all_31_1_27 & powerset(all_0_8_8) = all_31_2_28 & (all_31_0_26 = all_0_2_2 | ~ element(all_0_7_7, all_31_1_27))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (156) yields:
% 6.86/2.21 | (157) union(all_0_7_7) = all_31_0_26
% 6.86/2.21 | (158) powerset(all_31_2_28) = all_31_1_27
% 6.86/2.21 | (159) powerset(all_0_8_8) = all_31_2_28
% 6.86/2.21 | (160) all_31_0_26 = all_0_2_2 | ~ element(all_0_7_7, all_31_1_27)
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (124) with all_33_0_29, all_33_1_30 yields:
% 6.86/2.21 | (161) powerset(all_33_1_30) = all_33_0_29 & powerset(all_0_8_8) = all_33_1_30 & ( ~ element(all_0_7_7, all_33_0_29) | element(all_0_4_4, all_33_0_29))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (161) yields:
% 6.86/2.21 | (162) powerset(all_33_1_30) = all_33_0_29
% 6.86/2.21 | (163) powerset(all_0_8_8) = all_33_1_30
% 6.86/2.21 | (164) ~ element(all_0_7_7, all_33_0_29) | element(all_0_4_4, all_33_0_29)
% 6.86/2.21 |
% 6.86/2.21 +-Applying beta-rule and splitting (125), into two cases.
% 6.86/2.21 |-Branch one:
% 6.86/2.21 | (165) all_0_7_7 = empty_set
% 6.86/2.21 |
% 6.86/2.21 | Equations (165) can reduce 104 to:
% 6.86/2.21 | (166) $false
% 6.86/2.21 |
% 6.86/2.21 |-The branch is then unsatisfiable
% 6.86/2.21 |-Branch two:
% 6.86/2.21 | (104) ~ (all_0_7_7 = empty_set)
% 6.86/2.21 | (168) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset_difference(all_0_8_8, v2, v3) = v4 & union_of_subsets(all_0_8_8, all_0_7_7) = v3 & cast_to_subset(all_0_8_8) = v2 & powerset(v0) = v1 & powerset(all_0_8_8) = v0 & (v4 = all_0_3_3 | ~ element(all_0_7_7, v1)))
% 6.86/2.21 |
% 6.86/2.21 | Instantiating (168) with all_39_0_31, all_39_1_32, all_39_2_33, all_39_3_34, all_39_4_35 yields:
% 6.86/2.21 | (169) subset_difference(all_0_8_8, all_39_2_33, all_39_1_32) = all_39_0_31 & union_of_subsets(all_0_8_8, all_0_7_7) = all_39_1_32 & cast_to_subset(all_0_8_8) = all_39_2_33 & powerset(all_39_4_35) = all_39_3_34 & powerset(all_0_8_8) = all_39_4_35 & (all_39_0_31 = all_0_3_3 | ~ element(all_0_7_7, all_39_3_34))
% 6.86/2.21 |
% 6.86/2.21 | Applying alpha-rule on (169) yields:
% 6.86/2.21 | (170) all_39_0_31 = all_0_3_3 | ~ element(all_0_7_7, all_39_3_34)
% 6.86/2.21 | (171) powerset(all_0_8_8) = all_39_4_35
% 6.86/2.21 | (172) cast_to_subset(all_0_8_8) = all_39_2_33
% 6.86/2.21 | (173) union_of_subsets(all_0_8_8, all_0_7_7) = all_39_1_32
% 6.86/2.21 | (174) powerset(all_39_4_35) = all_39_3_34
% 6.86/2.21 | (175) subset_difference(all_0_8_8, all_39_2_33, all_39_1_32) = all_39_0_31
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (89) with all_0_8_8, all_0_7_7, all_39_1_32, all_0_2_2 and discharging atoms union_of_subsets(all_0_8_8, all_0_7_7) = all_39_1_32, union_of_subsets(all_0_8_8, all_0_7_7) = all_0_2_2, yields:
% 6.86/2.21 | (176) all_39_1_32 = all_0_2_2
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (82) with all_39_2_33, all_0_8_8 and discharging atoms cast_to_subset(all_0_8_8) = all_39_2_33, yields:
% 6.86/2.21 | (177) all_39_2_33 = all_0_8_8
% 6.86/2.21 |
% 6.86/2.21 | Instantiating formula (58) with all_0_8_8, all_23_0_18, all_39_2_33 and discharging atoms cast_to_subset(all_0_8_8) = all_39_2_33, cast_to_subset(all_0_8_8) = all_23_0_18, yields:
% 6.86/2.22 | (178) all_39_2_33 = all_23_0_18
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_39_4_35, all_0_6_6 and discharging atoms powerset(all_0_8_8) = all_39_4_35, powerset(all_0_8_8) = all_0_6_6, yields:
% 6.86/2.22 | (179) all_39_4_35 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_33_1_30, all_39_4_35 and discharging atoms powerset(all_0_8_8) = all_39_4_35, powerset(all_0_8_8) = all_33_1_30, yields:
% 6.86/2.22 | (180) all_39_4_35 = all_33_1_30
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_31_2_28, all_33_1_30 and discharging atoms powerset(all_0_8_8) = all_33_1_30, powerset(all_0_8_8) = all_31_2_28, yields:
% 6.86/2.22 | (181) all_33_1_30 = all_31_2_28
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_29_1_25, all_33_1_30 and discharging atoms powerset(all_0_8_8) = all_33_1_30, powerset(all_0_8_8) = all_29_1_25, yields:
% 6.86/2.22 | (182) all_33_1_30 = all_29_1_25
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_27_2_23, all_33_1_30 and discharging atoms powerset(all_0_8_8) = all_33_1_30, powerset(all_0_8_8) = all_27_2_23, yields:
% 6.86/2.22 | (183) all_33_1_30 = all_27_2_23
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_25_1_20, all_31_2_28 and discharging atoms powerset(all_0_8_8) = all_31_2_28, powerset(all_0_8_8) = all_25_1_20, yields:
% 6.86/2.22 | (184) all_31_2_28 = all_25_1_20
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_21_1_17, all_33_1_30 and discharging atoms powerset(all_0_8_8) = all_33_1_30, powerset(all_0_8_8) = all_21_1_17, yields:
% 6.86/2.22 | (185) all_33_1_30 = all_21_1_17
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_8_8, all_19_0_15, all_21_1_17 and discharging atoms powerset(all_0_8_8) = all_21_1_17, powerset(all_0_8_8) = all_19_0_15, yields:
% 6.86/2.22 | (186) all_21_1_17 = all_19_0_15
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (178,177) yields a new equation:
% 6.86/2.22 | (187) all_23_0_18 = all_0_8_8
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 187 yields:
% 6.86/2.22 | (188) all_23_0_18 = all_0_8_8
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (180,179) yields a new equation:
% 6.86/2.22 | (189) all_33_1_30 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 189 yields:
% 6.86/2.22 | (190) all_33_1_30 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (185,182) yields a new equation:
% 6.86/2.22 | (191) all_29_1_25 = all_21_1_17
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (181,182) yields a new equation:
% 6.86/2.22 | (192) all_31_2_28 = all_29_1_25
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 192 yields:
% 6.86/2.22 | (193) all_31_2_28 = all_29_1_25
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (190,182) yields a new equation:
% 6.86/2.22 | (194) all_29_1_25 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (183,182) yields a new equation:
% 6.86/2.22 | (195) all_29_1_25 = all_27_2_23
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (193,184) yields a new equation:
% 6.86/2.22 | (196) all_29_1_25 = all_25_1_20
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 196 yields:
% 6.86/2.22 | (197) all_29_1_25 = all_25_1_20
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (197,195) yields a new equation:
% 6.86/2.22 | (198) all_27_2_23 = all_25_1_20
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (194,195) yields a new equation:
% 6.86/2.22 | (199) all_27_2_23 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (191,195) yields a new equation:
% 6.86/2.22 | (200) all_27_2_23 = all_21_1_17
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (199,198) yields a new equation:
% 6.86/2.22 | (201) all_25_1_20 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (200,198) yields a new equation:
% 6.86/2.22 | (202) all_25_1_20 = all_21_1_17
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (202,201) yields a new equation:
% 6.86/2.22 | (203) all_21_1_17 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 203 yields:
% 6.86/2.22 | (204) all_21_1_17 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (186,204) yields a new equation:
% 6.86/2.22 | (205) all_19_0_15 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 205 yields:
% 6.86/2.22 | (206) all_19_0_15 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (201,198) yields a new equation:
% 6.86/2.22 | (199) all_27_2_23 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (199,195) yields a new equation:
% 6.86/2.22 | (194) all_29_1_25 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (201,184) yields a new equation:
% 6.86/2.22 | (209) all_31_2_28 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (194,182) yields a new equation:
% 6.86/2.22 | (190) all_33_1_30 = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | From (177)(176) and (175) follows:
% 6.86/2.22 | (211) subset_difference(all_0_8_8, all_0_8_8, all_0_2_2) = all_39_0_31
% 6.86/2.22 |
% 6.86/2.22 | From (179) and (174) follows:
% 6.86/2.22 | (212) powerset(all_0_6_6) = all_39_3_34
% 6.86/2.22 |
% 6.86/2.22 | From (190) and (162) follows:
% 6.86/2.22 | (213) powerset(all_0_6_6) = all_33_0_29
% 6.86/2.22 |
% 6.86/2.22 | From (209) and (158) follows:
% 6.86/2.22 | (214) powerset(all_0_6_6) = all_31_1_27
% 6.86/2.22 |
% 6.86/2.22 | From (194) and (153) follows:
% 6.86/2.22 | (215) powerset(all_0_6_6) = all_29_0_24
% 6.86/2.22 |
% 6.86/2.22 | From (199) and (149) follows:
% 6.86/2.22 | (216) powerset(all_0_6_6) = all_27_1_22
% 6.86/2.22 |
% 6.86/2.22 | From (206) and (134) follows:
% 6.86/2.22 | (67) powerset(all_0_8_8) = all_0_6_6
% 6.86/2.22 |
% 6.86/2.22 | From (188) and (142) follows:
% 6.86/2.22 | (218) element(all_0_8_8, all_0_6_6)
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_6_6, all_33_0_29, all_0_5_5 and discharging atoms powerset(all_0_6_6) = all_33_0_29, powerset(all_0_6_6) = all_0_5_5, yields:
% 6.86/2.22 | (219) all_33_0_29 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_6_6, all_31_1_27, all_33_0_29 and discharging atoms powerset(all_0_6_6) = all_33_0_29, powerset(all_0_6_6) = all_31_1_27, yields:
% 6.86/2.22 | (220) all_33_0_29 = all_31_1_27
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_6_6, all_29_0_24, all_39_3_34 and discharging atoms powerset(all_0_6_6) = all_39_3_34, powerset(all_0_6_6) = all_29_0_24, yields:
% 6.86/2.22 | (221) all_39_3_34 = all_29_0_24
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_6_6, all_29_0_24, all_31_1_27 and discharging atoms powerset(all_0_6_6) = all_31_1_27, powerset(all_0_6_6) = all_29_0_24, yields:
% 6.86/2.22 | (222) all_31_1_27 = all_29_0_24
% 6.86/2.22 |
% 6.86/2.22 | Instantiating formula (115) with all_0_6_6, all_27_1_22, all_39_3_34 and discharging atoms powerset(all_0_6_6) = all_39_3_34, powerset(all_0_6_6) = all_27_1_22, yields:
% 6.86/2.22 | (223) all_39_3_34 = all_27_1_22
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (221,223) yields a new equation:
% 6.86/2.22 | (224) all_29_0_24 = all_27_1_22
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 224 yields:
% 6.86/2.22 | (225) all_29_0_24 = all_27_1_22
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (220,219) yields a new equation:
% 6.86/2.22 | (226) all_31_1_27 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 226 yields:
% 6.86/2.22 | (227) all_31_1_27 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (222,227) yields a new equation:
% 6.86/2.22 | (228) all_29_0_24 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Simplifying 228 yields:
% 6.86/2.22 | (229) all_29_0_24 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (229,225) yields a new equation:
% 6.86/2.22 | (230) all_27_1_22 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (230,225) yields a new equation:
% 6.86/2.22 | (229) all_29_0_24 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 | Combining equations (230,223) yields a new equation:
% 6.86/2.22 | (232) all_39_3_34 = all_0_5_5
% 6.86/2.22 |
% 6.86/2.22 +-Applying beta-rule and splitting (160), into two cases.
% 6.86/2.22 |-Branch one:
% 6.86/2.22 | (233) ~ element(all_0_7_7, all_31_1_27)
% 6.86/2.22 |
% 6.86/2.22 | From (227) and (233) follows:
% 6.86/2.22 | (234) ~ element(all_0_7_7, all_0_5_5)
% 6.86/2.22 |
% 6.86/2.22 | Using (26) and (234) yields:
% 6.86/2.22 | (235) $false
% 6.86/2.22 |
% 6.86/2.22 |-The branch is then unsatisfiable
% 6.86/2.22 |-Branch two:
% 6.86/2.22 | (236) element(all_0_7_7, all_31_1_27)
% 6.86/2.22 | (237) all_31_0_26 = all_0_2_2
% 6.86/2.22 |
% 6.86/2.22 | From (227) and (236) follows:
% 6.86/2.22 | (26) element(all_0_7_7, all_0_5_5)
% 6.86/2.22 |
% 6.86/2.22 +-Applying beta-rule and splitting (155), into two cases.
% 6.86/2.22 |-Branch one:
% 6.86/2.22 | (239) ~ element(all_0_7_7, all_29_0_24)
% 6.86/2.22 |
% 6.86/2.22 | From (229) and (239) follows:
% 6.86/2.23 | (234) ~ element(all_0_7_7, all_0_5_5)
% 6.86/2.23 |
% 6.86/2.23 | Using (26) and (234) yields:
% 6.86/2.23 | (235) $false
% 6.86/2.23 |
% 6.86/2.23 |-The branch is then unsatisfiable
% 6.86/2.23 |-Branch two:
% 6.86/2.23 | (242) element(all_0_7_7, all_29_0_24)
% 6.86/2.23 | (243) element(all_0_2_2, all_29_1_25)
% 6.86/2.23 |
% 6.86/2.23 | From (194) and (243) follows:
% 6.86/2.23 | (244) element(all_0_2_2, all_0_6_6)
% 6.86/2.23 |
% 6.86/2.23 | From (229) and (242) follows:
% 6.86/2.23 | (26) element(all_0_7_7, all_0_5_5)
% 6.86/2.23 |
% 6.86/2.23 +-Applying beta-rule and splitting (135), into two cases.
% 6.86/2.23 |-Branch one:
% 6.86/2.23 | (246) ~ element(all_0_2_2, all_19_0_15)
% 6.86/2.23 |
% 6.86/2.23 | From (206) and (246) follows:
% 6.86/2.23 | (247) ~ element(all_0_2_2, all_0_6_6)
% 6.86/2.23 |
% 6.86/2.23 | Using (244) and (247) yields:
% 6.86/2.23 | (235) $false
% 6.86/2.23 |
% 6.86/2.23 |-The branch is then unsatisfiable
% 6.86/2.23 |-Branch two:
% 6.86/2.23 | (249) element(all_0_2_2, all_19_0_15)
% 6.86/2.23 | (250) element(all_0_1_1, all_19_0_15)
% 6.86/2.23 |
% 6.86/2.23 | From (206) and (249) follows:
% 6.86/2.23 | (244) element(all_0_2_2, all_0_6_6)
% 6.86/2.23 |
% 6.86/2.23 +-Applying beta-rule and splitting (139), into two cases.
% 6.86/2.23 |-Branch one:
% 6.86/2.23 | (252) ~ element(all_0_2_2, all_21_1_17)
% 6.86/2.23 |
% 6.86/2.23 | From (204) and (252) follows:
% 6.86/2.23 | (247) ~ element(all_0_2_2, all_0_6_6)
% 6.86/2.23 |
% 6.86/2.23 | Using (244) and (247) yields:
% 6.86/2.23 | (235) $false
% 6.86/2.23 |
% 6.86/2.23 |-The branch is then unsatisfiable
% 6.86/2.23 |-Branch two:
% 6.86/2.23 | (255) element(all_0_2_2, all_21_1_17)
% 6.86/2.23 | (256) all_21_0_16 = all_0_1_1
% 6.86/2.23 |
% 6.86/2.23 | From (256) and (137) follows:
% 6.86/2.23 | (257) set_difference(all_0_8_8, all_0_2_2) = all_0_1_1
% 6.86/2.23 |
% 6.86/2.23 | From (204) and (255) follows:
% 6.86/2.23 | (244) element(all_0_2_2, all_0_6_6)
% 6.86/2.23 |
% 6.86/2.23 +-Applying beta-rule and splitting (164), into two cases.
% 6.86/2.23 |-Branch one:
% 6.86/2.23 | (259) ~ element(all_0_7_7, all_33_0_29)
% 6.86/2.23 |
% 6.86/2.23 | From (219) and (259) follows:
% 6.86/2.23 | (234) ~ element(all_0_7_7, all_0_5_5)
% 6.86/2.23 |
% 6.86/2.23 | Using (26) and (234) yields:
% 6.86/2.23 | (235) $false
% 6.86/2.23 |
% 6.86/2.23 |-The branch is then unsatisfiable
% 6.86/2.23 |-Branch two:
% 6.86/2.23 | (262) element(all_0_7_7, all_33_0_29)
% 6.86/2.23 | (263) element(all_0_4_4, all_33_0_29)
% 6.86/2.23 |
% 6.86/2.23 | From (219) and (262) follows:
% 6.86/2.23 | (26) element(all_0_7_7, all_0_5_5)
% 6.86/2.23 |
% 6.86/2.23 +-Applying beta-rule and splitting (170), into two cases.
% 6.86/2.23 |-Branch one:
% 6.86/2.23 | (265) ~ element(all_0_7_7, all_39_3_34)
% 6.86/2.23 |
% 6.86/2.23 | From (232) and (265) follows:
% 6.86/2.23 | (234) ~ element(all_0_7_7, all_0_5_5)
% 6.86/2.23 |
% 6.86/2.23 | Using (26) and (234) yields:
% 6.86/2.23 | (235) $false
% 6.86/2.23 |
% 6.86/2.23 |-The branch is then unsatisfiable
% 6.86/2.23 |-Branch two:
% 6.86/2.23 | (268) element(all_0_7_7, all_39_3_34)
% 6.86/2.23 | (269) all_39_0_31 = all_0_3_3
% 6.86/2.23 |
% 6.86/2.23 | From (269) and (211) follows:
% 6.86/2.23 | (270) subset_difference(all_0_8_8, all_0_8_8, all_0_2_2) = all_0_3_3
% 6.86/2.23 |
% 6.86/2.23 | Instantiating formula (105) with all_0_1_1, all_0_6_6, all_0_2_2, all_0_8_8, all_0_8_8 and discharging atoms set_difference(all_0_8_8, all_0_2_2) = all_0_1_1, powerset(all_0_8_8) = all_0_6_6, element(all_0_2_2, all_0_6_6), element(all_0_8_8, all_0_6_6), yields:
% 6.86/2.23 | (271) subset_difference(all_0_8_8, all_0_8_8, all_0_2_2) = all_0_1_1
% 6.86/2.23 |
% 6.86/2.23 | Instantiating formula (111) with all_0_8_8, all_0_8_8, all_0_2_2, all_0_1_1, all_0_3_3 and discharging atoms subset_difference(all_0_8_8, all_0_8_8, all_0_2_2) = all_0_1_1, subset_difference(all_0_8_8, all_0_8_8, all_0_2_2) = all_0_3_3, yields:
% 6.86/2.23 | (272) all_0_1_1 = all_0_3_3
% 6.86/2.23 |
% 6.86/2.23 | Equations (272) can reduce 122 to:
% 6.86/2.23 | (166) $false
% 6.86/2.23 |
% 6.86/2.23 |-The branch is then unsatisfiable
% 6.86/2.23 % SZS output end Proof for theBenchmark
% 6.86/2.23
% 6.86/2.23 1618ms
%------------------------------------------------------------------------------