TSTP Solution File: SEU174+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 08:47:19 EDT 2022
% Result : Theorem 24.86s 6.67s
% Output : Proof 32.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 20 01:09:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.63/0.62 ____ _
% 0.63/0.62 ___ / __ \_____(_)___ ________ __________
% 0.63/0.62 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.63/0.62 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.63/0.62
% 0.63/0.62 A Theorem Prover for First-Order Logic
% 0.63/0.62 (ePrincess v.1.0)
% 0.63/0.62
% 0.63/0.62 (c) Philipp Rümmer, 2009-2015
% 0.63/0.62 (c) Peter Backeman, 2014-2015
% 0.63/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62 Bug reports to peter@backeman.se
% 0.63/0.62
% 0.63/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62
% 0.63/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.71 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.61/1.19 Prover 0: Preprocessing ...
% 5.36/1.92 Prover 0: Warning: ignoring some quantifiers
% 5.36/1.96 Prover 0: Constructing countermodel ...
% 22.16/5.99 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.25/6.10 Prover 1: Preprocessing ...
% 23.60/6.32 Prover 1: Warning: ignoring some quantifiers
% 23.60/6.33 Prover 1: Constructing countermodel ...
% 24.86/6.67 Prover 1: proved (673ms)
% 24.86/6.67 Prover 0: stopped
% 24.86/6.67
% 24.86/6.67 No countermodel exists, formula is valid
% 24.86/6.67 % SZS status Theorem for theBenchmark
% 24.86/6.67
% 24.86/6.67 Generating proof ... Warning: ignoring some quantifiers
% 31.21/8.13 found it (size 112)
% 31.21/8.13
% 31.21/8.13 % SZS output start Proof for theBenchmark
% 31.21/8.13 Assumed formulas after preprocessing and simplification:
% 31.21/8.13 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v6 = 0) & ~ (v2 = empty_set) & complements_of_subsets(v1, v2) = empty_set & element(v2, v4) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & powerset(v3) = v4 & powerset(v1) = v3 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (in(v12, v13) = v14) | ? [v15] : ? [v16] : (in(v9, v11) = v16 & in(v8, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (cartesian_product2(v9, v11) = v13) | ~ (cartesian_product2(v8, v10) = v12) | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : (subset(v10, v11) = v16 & subset(v8, v9) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = 0 | ~ (cartesian_product2(v8, v9) = v10) | ~ (ordered_pair(v13, v14) = v11) | ~ (in(v11, v10) = v12) | ? [v15] : ? [v16] : (in(v14, v9) = v16 & in(v13, v8) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (complements_of_subsets(v8, v9) = v12) | ~ (element(v12, v11) = v13) | ~ (powerset(v10) = v11) | ~ (powerset(v8) = v10) | ? [v14] : ( ~ (v14 = 0) & element(v9, v11) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v11) = v12) | ~ (singleton(v10) = v11) | ~ (subset(v8, v12) = v13) | ? [v14] : ? [v15] : (subset(v8, v9) = v14 & in(v10, v8) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v9, v10) = v12) | ~ (set_difference(v8, v10) = v11) | ~ (subset(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ~ (set_intersection2(v9, v10) = v12) | ~ (set_intersection2(v8, v10) = v11) | ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (in(v12, v13) = 0) | (in(v9, v11) = 0 & in(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v9, v10) = v12) | ~ (cartesian_product2(v8, v10) = v11) | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (cartesian_product2(v10, v9) = v16 & cartesian_product2(v10, v8) = v15 & subset(v15, v16) = v17 & subset(v8, v9) = v14 & ( ~ (v14 = 0) | (v17 = 0 & v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset_complement(v8, v9) = v11) | ~ (element(v11, v10) = v12) | ~ (powerset(v8) = v10) | ? [v13] : ( ~ (v13 = 0) & element(v9, v10) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v9, v11) = 0) | ~ (element(v8, v10) = v12) | ~ (powerset(v10) = v11) | ? [v13] : ( ~ (v13 = 0) & in(v8, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v9, v10) = 0) | ~ (powerset(v8) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v11, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v10) = v12) | ~ (unordered_pair(v8, v9) = v11) | ? [v13] : ? [v14] : (in(v9, v10) = v14 & in(v8, v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v9) = v12) | ~ (set_union2(v8, v10) = v11) | ? [v13] : ? [v14] : (subset(v10, v9) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v8, v11) = v12) | ~ (set_intersection2(v9, v10) = v11) | ? [v13] : ? [v14] : (subset(v8, v10) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v8 | v10 = v8 | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (union(v8) = v9) | ~ (in(v10, v12) = 0) | ~ (in(v10, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & in(v12, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v8 | ~ (ordered_pair(v10, v11) = v12) | ~ (ordered_pair(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v12 = 0 & ~ (v14 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v11) | ~ (unordered_pair(v10, v11) = v12) | ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v8, v9) = v10) | ~ (in(v11, v8) = v12) | ? [v13] : ? [v14] : (in(v11, v10) = v14 & in(v11, v9) = v13 & (v14 = 0 | ( ~ (v13 = 0) & ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | v11 = v8 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v11, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (subset_complement(v8, v10) = v11) | ~ (subset_complement(v8, v9) = v10) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & element(v9, v12) = v13 & powerset(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (singleton(v8) = v10) | ~ (set_union2(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_difference(v8, v10) = v11) | ~ (singleton(v9) = v10) | in(v9, v8) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v10, v9) = v11) | ~ (singleton(v8) = v10) | in(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = 0) | ~ (disjoint(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (set_difference(v8, v9) = v10) | ~ (subset(v10, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v9) = v10) | ~ (subset(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (element(v8, v10) = v11) | ~ (powerset(v9) = v10) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & in(v12, v9) = v13 & in(v12, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (element(v8, v10) = v11) | ~ (powerset(v9) = v10) | ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (powerset(v8) = v9) | ~ (subset(v10, v8) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v10, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (singleton(v8) = v10) | ~ (subset(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v8) = v11) | ~ (set_intersection2(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (subset(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v8, v10) = v11) | ~ (set_union2(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (in(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v8) = v11) | ~ (unordered_pair(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (are_equipotent(v11, v10) = v9) | ~ (are_equipotent(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (complements_of_subsets(v11, v10) = v9) | ~ (complements_of_subsets(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset_complement(v11, v10) = v9) | ~ (subset_complement(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_difference(v11, v10) = v9) | ~ (set_difference(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cartesian_product2(v11, v10) = v9) | ~ (cartesian_product2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (element(v11, v10) = v9) | ~ (element(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (singleton(v9) = v11) | ~ (singleton(v8) = v10) | ~ (subset(v10, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (singleton(v8) = v11) | ~ (unordered_pair(v9, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subset(v11, v10) = v9) | ~ (subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_intersection2(v11, v10) = v9) | ~ (set_intersection2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (set_union2(v11, v10) = v9) | ~ (set_union2(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (proper_subset(v11, v10) = v9) | ~ (proper_subset(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (in(v11, v10) = v9) | ~ (in(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v10, v9) = v11) | ~ (set_union2(v8, v9) = v10) | set_difference(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v9, v8) = v10) | ~ (set_union2(v8, v10) = v11) | set_union2(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v10) = v11) | ~ (set_difference(v8, v9) = v10) | set_intersection2(v8, v9) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_difference(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & (v13 = 0 | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cartesian_product2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ? [v13] : (ordered_pair(v12, v13) = v11 & in(v13, v9) = 0 & in(v12, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v11, v10) = 0) | ~ (element(v9, v10) = 0) | ~ (powerset(v8) = v10) | ? [v12] : ? [v13] : ? [v14] : (disjoint(v9, v11) = v12 & subset_complement(v8, v11) = v13 & subset(v9, v13) = v14 & ( ~ (v14 = 0) | v12 = 0) & ( ~ (v12 = 0) | v14 = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ~ (powerset(v8) = v11) | ~ (in(v9, v10) = 0) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & subset_complement(v8, v10) = v12 & in(v9, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v9, v11) = 0) | ~ (powerset(v10) = v11) | ~ (powerset(v8) = v10) | ? [v12] : (complements_of_subsets(v8, v12) = v9 & complements_of_subsets(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v9, v11) = 0) | ~ (powerset(v10) = v11) | ~ (powerset(v8) = v10) | ? [v12] : (complements_of_subsets(v8, v9) = v12 & ! [v13] : (v13 = v12 | ~ (element(v13, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (subset_complement(v8, v14) = v16 & element(v14, v10) = 0 & in(v16, v9) = v17 & in(v14, v13) = v15 & ( ~ (v17 = 0) | ~ (v15 = 0)) & (v17 = 0 | v15 = 0))) & ! [v13] : ( ~ (element(v13, v10) = 0) | ~ (element(v12, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : (subset_complement(v8, v13) = v15 & in(v15, v9) = v16 & in(v13, v12) = v14 & ( ~ (v16 = 0) | v14 = 0) & ( ~ (v14 = 0) | v16 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (element(v9, v11) = 0) | ~ (powerset(v10) = v11) | ~ (in(v8, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (subset(v11, v10) = 0) | ~ (unordered_pair(v8, v9) = v11) | (in(v9, v10) = 0 & in(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & disjoint(v8, v9) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) | ~ (in(v11, v8) = 0) | ? [v12] : ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_difference(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0) | v15 = 0) & (v13 = 0 | (v14 = 0 & ~ (v15 = 0))))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (cartesian_product2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v12, v8) = v13 & ( ~ (v13 = 0) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v20) = v12) | ? [v21] : ? [v22] : (in(v20, v10) = v22 & in(v19, v9) = v21 & ( ~ (v22 = 0) | ~ (v21 = 0))))) & (v13 = 0 | (v18 = v12 & v17 = 0 & v16 = 0 & ordered_pair(v14, v15) = v12 & in(v15, v10) = 0 & in(v14, v9) = 0)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_intersection2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v15 = 0) | ~ (v14 = 0) | ~ (v13 = 0)) & (v13 = 0 | (v15 = 0 & v14 = 0)))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (set_union2(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) & ~ (v14 = 0))) & (v15 = 0 | v14 = 0 | v13 = 0))) & ? [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (unordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : (in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v12 = v10) & ~ (v12 = v9))) & (v13 = 0 | v12 = v10 | v12 = v9))) & ! [v8] : ! [v9] : ! [v10] : (v10 = v9 | ~ (set_union2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | v8 = empty_set | ~ (singleton(v9) = v10) | ~ (subset(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v8) = v9) | ~ (in(v10, v9) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_difference(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = empty_set | ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (proper_subset(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : ( ~ (v11 = v8) & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : (in(v11, v9) = 0 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (element(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v9) = v8) | ~ (subset(v8, v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (subset(empty_set, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (singleton(v8) = v9) | ~ (in(v8, v9) = v10)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subset(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (union(v10) = v9) | ~ (union(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (empty(v10) = v9) | ~ (empty(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (powerset(v10) = v9) | ~ (powerset(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v8 = empty_set | ~ (element(v10, v9) = 0) | ~ (powerset(v8) = v9) | ? [v11] : (subset_complement(v8, v10) = v11 & ! [v12] : ! [v13] : (v13 = 0 | ~ (in(v12, v11) = v13) | ? [v14] : ? [v15] : (element(v12, v8) = v14 & in(v12, v10) = v15 & ( ~ (v14 = 0) | v15 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v10, v9) = 0) | ~ (singleton(v8) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (in(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_difference(v8, v10) = v8) | ~ (singleton(v9) = v10) | ? [v11] : ( ~ (v11 = 0) & in(v9, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8) = v9) | ~ (in(v10, v9) = 0) | ? [v11] : (in(v11, v8) = 0 & in(v10, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (element(v9, v10) = 0) | ~ (powerset(v8) = v10) | ? [v11] : (subset_complement(v8, v9) = v11 & set_difference(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (element(v9, v8) = v10) | ? [v11] : ? [v12] : (empty(v8) = v11 & in(v9, v8) = v12 & (v11 = 0 | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (element(v8, v10) = 0) | ~ (powerset(v9) = v10) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (empty(v9) = v10) | ~ (empty(v8) = 0) | ? [v11] : (element(v9, v8) = v11 & ( ~ (v11 = 0) | v10 = 0) & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (powerset(v8) = v9) | ~ (subset(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v10) | ~ (subset(v10, v9) = 0) | in(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subset(v8, v9) = 0) | ~ (in(v10, v8) = 0) | in(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | (v11 = 0 & disjoint(v8, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v9, v8) = v10) | ? [v11] : ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (set_union2(v8, v9) = v10) | ? [v11] : ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (union(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (in(v11, v8) = v12 & ( ~ (v12 = 0) | ! [v16] : ( ~ (in(v11, v16) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v16, v9) = v17))) & (v12 = 0 | (v15 = 0 & v14 = 0 & in(v13, v9) = 0 & in(v11, v13) = 0)))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (powerset(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (subset(v11, v9) = v13 & in(v11, v8) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)) & (v13 = 0 | v12 = 0))) & ? [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (singleton(v9) = v10) | ? [v11] : ? [v12] : (in(v11, v8) = v12 & ( ~ (v12 = 0) | ~ (v11 = v9)) & (v12 = 0 | v11 = v9))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_difference(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (empty(v9) = 0) | ~ (empty(v8) = 0)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v9, v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_intersection2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (set_union2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_difference(empty_set, v8) = v9)) & ! [v8] : ! [v9] : (v9 = empty_set | ~ (set_intersection2(v8, empty_set) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (empty(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ( ~ (v12 = 0) & element(v11, v10) = 0 & empty(v11) = v12 & powerset(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subset(empty_set, v8) = v9)) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) & ! [v8] : ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_difference(v8, v9) = v8) & ! [v8] : ! [v9] : ( ~ (set_difference(v8, v9) = empty_set) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (element(v8, v9) = 0) | ? [v10] : ? [v11] : (empty(v9) = v10 & in(v8, v9) = v11 & (v11 = 0 | v10 = 0))) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | union(v9) = v8) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (powerset(v8) = v9) | ? [v10] : (element(v10, v9) = 0 & empty(v10) = 0)) & ! [v8] : ! [v9] : ( ~ (set_intersection2(v8, v9) = empty_set) | disjoint(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) & ! [v8] : ! [v9] : ( ~ (proper_subset(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & subset(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | subset(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & proper_subset(v9, v8) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (in(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) & ! [v8] : (v8 = empty_set | ~ (empty(v8) = 0)) & ! [v8] : (v8 = empty_set | ~ (subset(v8, empty_set) = 0)) & ! [v8] : ~ (singleton(v8) = empty_set) & ! [v8] : ~ (proper_subset(v8, v8) = 0) & ! [v8] : ~ (in(v8, empty_set) = 0) & ? [v8] : ? [v9] : (v9 = v8 | ? [v10] : ? [v11] : ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)) & (v12 = 0 | v11 = 0))) & ? [v8] : ? [v9] : element(v9, v8) = 0 & ? [v8] : ? [v9] : (in(v8, v9) = 0 & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (powerset(v10) = v11) | ~ (in(v11, v9) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v9) = v13)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (are_equipotent(v10, v9) = v11) | ? [v12] : ? [v13] : (subset(v10, v9) = v12 & in(v10, v9) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (subset(v11, v10) = 0) | ? [v12] : ? [v13] : (in(v11, v9) = v13 & in(v10, v9) = v12 & ( ~ (v12 = 0) | v13 = 0)))) & ? [v8] : ? [v9] : (in(v8, v9) = 0 & ! [v10] : ! [v11] : (v11 = 0 | ~ (are_equipotent(v10, v9) = v11) | ? [v12] : ? [v13] : (subset(v10, v9) = v12 & in(v10, v9) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (subset(v11, v10) = 0) | ? [v12] : ? [v13] : (in(v11, v9) = v13 & in(v10, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ( ~ (in(v10, v9) = 0) | ? [v11] : (in(v11, v9) = 0 & ! [v12] : ( ~ (subset(v12, v10) = 0) | in(v12, v11) = 0)))) & ? [v8] : (v8 = empty_set | ? [v9] : in(v9, v8) = 0))
% 31.54/8.20 | 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 yields:
% 31.54/8.20 | (1) ~ (all_0_1_1 = 0) & ~ (all_0_5_5 = empty_set) & complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set & element(all_0_5_5, all_0_3_3) = 0 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & powerset(all_0_4_4) = all_0_3_3 & powerset(all_0_6_6) = all_0_4_4 & powerset(empty_set) = all_0_7_7 & singleton(empty_set) = all_0_7_7 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (complements_of_subsets(v0, v1) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset_complement(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ~ (powerset(v2) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(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 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v3, v2) = 0) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (powerset(v0) = v3) | ~ (in(v1, v2) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (element(v2, v1) = 0) | ~ (powerset(v0) = v1) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & powerset(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0)))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 31.54/8.23 |
% 31.54/8.23 | Applying alpha-rule on (1) yields:
% 31.54/8.23 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v3, v2) = 0) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : ? [v6] : (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))
% 31.54/8.23 | (3) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 31.54/8.23 | (4) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 31.54/8.23 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 31.54/8.23 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 31.54/8.23 | (7) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 31.54/8.23 | (8) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 31.54/8.23 | (9) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 31.54/8.23 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.54/8.23 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 31.54/8.23 | (12) singleton(empty_set) = all_0_7_7
% 31.54/8.23 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 31.54/8.23 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 31.54/8.23 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0)))))
% 31.54/8.23 | (16) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 31.54/8.23 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 31.54/8.23 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 31.54/8.23 | (19) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 31.54/8.23 | (20) powerset(all_0_6_6) = all_0_4_4
% 31.54/8.23 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0)
% 31.54/8.23 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 31.54/8.23 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4))
% 31.54/8.23 | (24) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & powerset(v0) = v2))
% 31.54/8.23 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 31.54/8.23 | (26) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 31.54/8.23 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 31.54/8.23 | (28) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0)))))
% 31.54/8.23 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 31.54/8.24 | (30) ! [v0] : ~ (in(v0, empty_set) = 0)
% 31.54/8.24 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 31.54/8.24 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 31.54/8.24 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 31.54/8.24 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 31.54/8.24 | (35) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 31.54/8.24 | (36) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 31.54/8.24 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 31.54/8.24 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 31.54/8.24 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 31.54/8.24 | (40) empty(empty_set) = 0
% 31.54/8.24 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 31.54/8.24 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 31.54/8.24 | (43) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 31.54/8.24 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 31.54/8.24 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 31.54/8.24 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 31.54/8.24 | (47) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 31.54/8.24 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 31.54/8.24 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 31.54/8.24 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 31.54/8.24 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 31.54/8.24 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 31.54/8.24 | (53) element(all_0_5_5, all_0_3_3) = 0
% 31.54/8.24 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 31.54/8.24 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 31.54/8.24 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 31.54/8.24 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 31.54/8.24 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))
% 31.54/8.24 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0))
% 31.54/8.24 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ~ (powerset(v2) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 31.54/8.24 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 31.54/8.24 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 31.54/8.24 | (63) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 31.54/8.24 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 31.54/8.24 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 31.54/8.24 | (66) powerset(all_0_4_4) = all_0_3_3
% 31.54/8.24 | (67) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.54/8.24 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 31.54/8.25 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (powerset(v0) = v3) | ~ (in(v1, v2) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5))
% 31.54/8.25 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 31.54/8.25 | (71) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 31.54/8.25 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 31.54/8.25 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 31.54/8.25 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 31.54/8.25 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0))
% 31.54/8.25 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 31.54/8.25 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 31.54/8.25 | (78) ! [v0] : ~ (singleton(v0) = empty_set)
% 31.54/8.25 | (79) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 31.54/8.25 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 31.54/8.25 | (81) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 31.54/8.25 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 31.54/8.25 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 31.54/8.25 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 31.54/8.25 | (85) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 31.54/8.25 | (86) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 31.54/8.25 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5))
% 31.54/8.25 | (88) empty(all_0_0_0) = 0
% 31.54/8.25 | (89) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 31.54/8.25 | (90) ~ (all_0_5_5 = empty_set)
% 31.54/8.25 | (91) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 31.54/8.25 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 31.54/8.25 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 31.54/8.25 | (94) ? [v0] : ? [v1] : element(v1, v0) = 0
% 31.54/8.25 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 31.54/8.25 | (96) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 31.54/8.25 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset_complement(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5))
% 31.54/8.25 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 31.54/8.25 | (99) ~ (all_0_1_1 = 0)
% 31.54/8.25 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 31.54/8.25 | (101) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 31.54/8.25 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 31.54/8.25 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 31.54/8.25 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 31.54/8.25 | (105) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 31.54/8.25 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 31.54/8.25 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 31.54/8.26 | (108) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 31.54/8.26 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 31.54/8.26 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v0) = v4))
% 31.54/8.26 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 31.54/8.26 | (112) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 31.54/8.26 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 31.54/8.26 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 31.54/8.26 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (complements_of_subsets(v0, v1) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6))
% 31.54/8.26 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 31.54/8.26 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 31.54/8.26 | (118) complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set
% 31.54/8.26 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 31.54/8.26 | (120) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 31.54/8.26 | (121) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 31.54/8.26 | (122) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.54/8.26 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 31.54/8.26 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 31.54/8.26 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 31.54/8.26 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 31.54/8.26 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 31.54/8.26 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 31.54/8.26 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 31.54/8.26 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 31.54/8.26 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 31.54/8.26 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 31.54/8.26 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 31.54/8.26 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 31.54/8.26 | (135) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 31.54/8.26 | (136) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 31.54/8.26 | (137) empty(all_0_2_2) = all_0_1_1
% 31.54/8.26 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 31.97/8.27 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 31.97/8.27 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 31.97/8.27 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 31.97/8.27 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 31.97/8.27 | (143) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0))))
% 31.97/8.27 | (144) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 31.97/8.27 | (145) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.97/8.27 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 31.97/8.27 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 31.97/8.27 | (148) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 31.97/8.27 | (149) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 31.97/8.27 | (150) ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (element(v2, v1) = 0) | ~ (powerset(v0) = v1) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0)))))
% 31.97/8.27 | (151) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 31.97/8.27 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 31.97/8.27 | (153) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))
% 31.97/8.27 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 31.97/8.27 | (155) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1)))
% 31.97/8.27 | (156) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 31.97/8.27 | (157) powerset(empty_set) = all_0_7_7
% 31.97/8.27 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 31.97/8.27 | (159) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 31.97/8.27 | (160) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 31.97/8.27 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 31.97/8.27 | (162) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 31.97/8.27 | (163) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 31.97/8.27 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (136) with all_0_3_3, all_0_4_4 and discharging atoms powerset(all_0_4_4) = all_0_3_3, yields:
% 31.97/8.28 | (165) ? [v0] : (element(v0, all_0_3_3) = 0 & empty(v0) = 0)
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (23) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms element(all_0_5_5, all_0_3_3) = 0, powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, yields:
% 31.97/8.28 | (166) ? [v0] : (complements_of_subsets(all_0_6_6, v0) = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_5_5) = v0)
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (141) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms element(all_0_5_5, all_0_3_3) = 0, powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, yields:
% 31.97/8.28 | (167) ? [v0] : (complements_of_subsets(all_0_6_6, all_0_5_5) = v0 & ! [v1] : (v1 = v0 | ~ (element(v1, all_0_3_3) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (subset_complement(all_0_6_6, v2) = v4 & element(v2, all_0_4_4) = 0 & in(v4, all_0_5_5) = v5 & in(v2, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0)) & (v5 = 0 | v3 = 0))) & ! [v1] : ( ~ (element(v1, all_0_4_4) = 0) | ~ (element(v0, all_0_3_3) = 0) | ? [v2] : ? [v3] : ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & in(v3, all_0_5_5) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (136) with all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, yields:
% 31.97/8.28 | (168) ? [v0] : (element(v0, all_0_4_4) = 0 & empty(v0) = 0)
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (136) with all_0_7_7, empty_set and discharging atoms powerset(empty_set) = all_0_7_7, yields:
% 31.97/8.28 | (169) ? [v0] : (element(v0, all_0_7_7) = 0 & empty(v0) = 0)
% 31.97/8.28 |
% 31.97/8.28 | Instantiating (167) with all_45_0_26 yields:
% 31.97/8.28 | (170) complements_of_subsets(all_0_6_6, all_0_5_5) = all_45_0_26 & ! [v0] : (v0 = all_45_0_26 | ~ (element(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, all_0_5_5) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) & ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) | ~ (element(all_45_0_26, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, all_0_5_5) = v3 & in(v0, all_45_0_26) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 31.97/8.28 |
% 31.97/8.28 | Applying alpha-rule on (170) yields:
% 31.97/8.28 | (171) complements_of_subsets(all_0_6_6, all_0_5_5) = all_45_0_26
% 31.97/8.28 | (172) ! [v0] : (v0 = all_45_0_26 | ~ (element(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, all_0_5_5) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0)))
% 31.97/8.28 | (173) ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) | ~ (element(all_45_0_26, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, all_0_5_5) = v3 & in(v0, all_45_0_26) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (172) with all_0_5_5 and discharging atoms element(all_0_5_5, all_0_3_3) = 0, yields:
% 31.97/8.28 | (174) all_45_0_26 = all_0_5_5 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & element(v0, all_0_4_4) = 0 & in(v2, all_0_5_5) = v3 & in(v0, all_0_5_5) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))
% 31.97/8.28 |
% 31.97/8.28 | Instantiating (166) with all_48_0_27 yields:
% 31.97/8.28 | (175) complements_of_subsets(all_0_6_6, all_48_0_27) = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27
% 31.97/8.28 |
% 31.97/8.28 | Applying alpha-rule on (175) yields:
% 31.97/8.28 | (176) complements_of_subsets(all_0_6_6, all_48_0_27) = all_0_5_5
% 31.97/8.28 | (177) complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27
% 31.97/8.28 |
% 31.97/8.28 | Instantiating (169) with all_54_0_32 yields:
% 31.97/8.28 | (178) element(all_54_0_32, all_0_7_7) = 0 & empty(all_54_0_32) = 0
% 31.97/8.28 |
% 31.97/8.28 | Applying alpha-rule on (178) yields:
% 31.97/8.28 | (179) element(all_54_0_32, all_0_7_7) = 0
% 31.97/8.28 | (180) empty(all_54_0_32) = 0
% 31.97/8.28 |
% 31.97/8.28 | Instantiating (168) with all_71_0_41 yields:
% 31.97/8.28 | (181) element(all_71_0_41, all_0_4_4) = 0 & empty(all_71_0_41) = 0
% 31.97/8.28 |
% 31.97/8.28 | Applying alpha-rule on (181) yields:
% 31.97/8.28 | (182) element(all_71_0_41, all_0_4_4) = 0
% 31.97/8.28 | (183) empty(all_71_0_41) = 0
% 31.97/8.28 |
% 31.97/8.28 | Instantiating (165) with all_77_0_45 yields:
% 31.97/8.28 | (184) element(all_77_0_45, all_0_3_3) = 0 & empty(all_77_0_45) = 0
% 31.97/8.28 |
% 31.97/8.28 | Applying alpha-rule on (184) yields:
% 31.97/8.28 | (185) element(all_77_0_45, all_0_3_3) = 0
% 31.97/8.28 | (186) empty(all_77_0_45) = 0
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (164) with all_0_6_6, all_0_5_5, all_48_0_27, empty_set and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27, complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set, yields:
% 31.97/8.28 | (187) all_48_0_27 = empty_set
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (164) with all_0_6_6, all_0_5_5, all_45_0_26, all_48_0_27 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27, complements_of_subsets(all_0_6_6, all_0_5_5) = all_45_0_26, yields:
% 31.97/8.28 | (188) all_48_0_27 = all_45_0_26
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (4) with all_77_0_45 and discharging atoms empty(all_77_0_45) = 0, yields:
% 31.97/8.28 | (189) all_77_0_45 = empty_set
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (19) with all_71_0_41, all_77_0_45 and discharging atoms empty(all_77_0_45) = 0, empty(all_71_0_41) = 0, yields:
% 31.97/8.28 | (190) all_77_0_45 = all_71_0_41
% 31.97/8.28 |
% 31.97/8.28 | Instantiating formula (19) with all_54_0_32, all_77_0_45 and discharging atoms empty(all_77_0_45) = 0, empty(all_54_0_32) = 0, yields:
% 31.97/8.28 | (191) all_77_0_45 = all_54_0_32
% 31.97/8.28 |
% 31.97/8.28 | Combining equations (191,190) yields a new equation:
% 31.97/8.28 | (192) all_71_0_41 = all_54_0_32
% 31.97/8.28 |
% 31.97/8.28 | Combining equations (189,190) yields a new equation:
% 31.97/8.28 | (193) all_71_0_41 = empty_set
% 31.97/8.28 |
% 32.07/8.28 | Combining equations (193,192) yields a new equation:
% 32.07/8.28 | (194) all_54_0_32 = empty_set
% 32.07/8.28 |
% 32.07/8.28 | Combining equations (187,188) yields a new equation:
% 32.07/8.28 | (195) all_45_0_26 = empty_set
% 32.07/8.28 |
% 32.07/8.28 | Combining equations (195,188) yields a new equation:
% 32.07/8.28 | (187) all_48_0_27 = empty_set
% 32.07/8.28 |
% 32.07/8.28 | Combining equations (194,192) yields a new equation:
% 32.07/8.28 | (193) all_71_0_41 = empty_set
% 32.07/8.28 |
% 32.07/8.28 | Combining equations (193,190) yields a new equation:
% 32.07/8.28 | (189) all_77_0_45 = empty_set
% 32.07/8.28 |
% 32.07/8.28 | From (187) and (176) follows:
% 32.07/8.28 | (199) complements_of_subsets(all_0_6_6, empty_set) = all_0_5_5
% 32.07/8.28 |
% 32.07/8.28 | From (189) and (185) follows:
% 32.07/8.29 | (200) element(empty_set, all_0_3_3) = 0
% 32.07/8.29 |
% 32.07/8.29 | From (193) and (182) follows:
% 32.07/8.29 | (201) element(empty_set, all_0_4_4) = 0
% 32.07/8.29 |
% 32.07/8.29 +-Applying beta-rule and splitting (174), into two cases.
% 32.07/8.29 |-Branch one:
% 32.07/8.29 | (202) all_45_0_26 = all_0_5_5
% 32.07/8.29 |
% 32.07/8.29 | Combining equations (202,195) yields a new equation:
% 32.07/8.29 | (203) all_0_5_5 = empty_set
% 32.07/8.29 |
% 32.07/8.29 | Simplifying 203 yields:
% 32.07/8.29 | (204) all_0_5_5 = empty_set
% 32.07/8.29 |
% 32.07/8.29 | Equations (204) can reduce 90 to:
% 32.07/8.29 | (205) $false
% 32.07/8.29 |
% 32.07/8.29 |-The branch is then unsatisfiable
% 32.07/8.29 |-Branch two:
% 32.07/8.29 | (206) ~ (all_45_0_26 = all_0_5_5)
% 32.07/8.29 | (207) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & element(v0, all_0_4_4) = 0 & in(v2, all_0_5_5) = v3 & in(v0, all_0_5_5) = v1 & ( ~ (v3 = 0) | ~ (v1 = 0)) & (v3 = 0 | v1 = 0))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating (207) with all_102_0_50, all_102_1_51, all_102_2_52, all_102_3_53 yields:
% 32.07/8.29 | (208) subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51 & element(all_102_3_53, all_0_4_4) = 0 & in(all_102_1_51, all_0_5_5) = all_102_0_50 & in(all_102_3_53, all_0_5_5) = all_102_2_52 & ( ~ (all_102_0_50 = 0) | ~ (all_102_2_52 = 0)) & (all_102_0_50 = 0 | all_102_2_52 = 0)
% 32.07/8.29 |
% 32.07/8.29 | Applying alpha-rule on (208) yields:
% 32.07/8.29 | (209) in(all_102_3_53, all_0_5_5) = all_102_2_52
% 32.07/8.29 | (210) subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51
% 32.07/8.29 | (211) in(all_102_1_51, all_0_5_5) = all_102_0_50
% 32.07/8.29 | (212) element(all_102_3_53, all_0_4_4) = 0
% 32.07/8.29 | (213) ~ (all_102_0_50 = 0) | ~ (all_102_2_52 = 0)
% 32.07/8.29 | (214) all_102_0_50 = 0 | all_102_2_52 = 0
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (2) with all_102_3_53, all_0_4_4, all_102_3_53, all_0_6_6 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29 | (215) ? [v0] : ? [v1] : ? [v2] : (disjoint(all_102_3_53, all_102_3_53) = v0 & subset_complement(all_0_6_6, all_102_3_53) = v1 & subset(all_102_3_53, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (127) with all_0_4_4, all_102_3_53, all_0_6_6 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29 | (216) ? [v0] : (subset_complement(all_0_6_6, all_102_3_53) = v0 & set_difference(all_0_6_6, all_102_3_53) = v0)
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (141) with all_0_3_3, all_0_4_4, empty_set, all_0_6_6 and discharging atoms element(empty_set, all_0_3_3) = 0, powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29 | (217) ? [v0] : (complements_of_subsets(all_0_6_6, empty_set) = v0 & ! [v1] : (v1 = v0 | ~ (element(v1, all_0_3_3) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (subset_complement(all_0_6_6, v2) = v4 & element(v2, all_0_4_4) = 0 & in(v4, empty_set) = v5 & in(v2, v1) = v3 & ( ~ (v5 = 0) | ~ (v3 = 0)) & (v5 = 0 | v3 = 0))) & ! [v1] : ( ~ (element(v1, all_0_4_4) = 0) | ~ (element(v0, all_0_3_3) = 0) | ? [v2] : ? [v3] : ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & in(v3, empty_set) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (173) with all_102_3_53 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, yields:
% 32.07/8.29 | (218) ~ (element(all_45_0_26, all_0_3_3) = 0) | ? [v0] : ? [v1] : ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, all_0_5_5) = v2 & in(all_102_3_53, all_45_0_26) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (2) with all_102_3_53, all_0_4_4, empty_set, all_0_6_6 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, element(empty_set, all_0_4_4) = 0, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29 | (219) ? [v0] : ? [v1] : ? [v2] : (disjoint(empty_set, all_102_3_53) = v0 & subset_complement(all_0_6_6, all_102_3_53) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating (217) with all_138_0_56 yields:
% 32.07/8.29 | (220) complements_of_subsets(all_0_6_6, empty_set) = all_138_0_56 & ! [v0] : (v0 = all_138_0_56 | ~ (element(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, empty_set) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) & ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) | ~ (element(all_138_0_56, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, empty_set) = v3 & in(v0, all_138_0_56) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 32.07/8.29 |
% 32.07/8.29 | Applying alpha-rule on (220) yields:
% 32.07/8.29 | (221) complements_of_subsets(all_0_6_6, empty_set) = all_138_0_56
% 32.07/8.29 | (222) ! [v0] : (v0 = all_138_0_56 | ~ (element(v0, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, empty_set) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | ~ (v2 = 0)) & (v4 = 0 | v2 = 0)))
% 32.07/8.29 | (223) ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) | ~ (element(all_138_0_56, all_0_3_3) = 0) | ? [v1] : ? [v2] : ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, empty_set) = v3 & in(v0, all_138_0_56) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (223) with all_102_3_53 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, yields:
% 32.07/8.29 | (224) ~ (element(all_138_0_56, all_0_3_3) = 0) | ? [v0] : ? [v1] : ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, empty_set) = v2 & in(all_102_3_53, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating formula (223) with empty_set and discharging atoms element(empty_set, all_0_4_4) = 0, yields:
% 32.07/8.29 | (225) ~ (element(all_138_0_56, all_0_3_3) = 0) | ? [v0] : ? [v1] : ? [v2] : (subset_complement(all_0_6_6, empty_set) = v1 & in(v1, empty_set) = v2 & in(empty_set, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29 |
% 32.07/8.29 | Instantiating (215) with all_152_0_64, all_152_1_65, all_152_2_66 yields:
% 32.07/8.29 | (226) disjoint(all_102_3_53, all_102_3_53) = all_152_2_66 & subset_complement(all_0_6_6, all_102_3_53) = all_152_1_65 & subset(all_102_3_53, all_152_1_65) = all_152_0_64 & ( ~ (all_152_0_64 = 0) | all_152_2_66 = 0) & ( ~ (all_152_2_66 = 0) | all_152_0_64 = 0)
% 32.07/8.29 |
% 32.07/8.29 | Applying alpha-rule on (226) yields:
% 32.07/8.29 | (227) disjoint(all_102_3_53, all_102_3_53) = all_152_2_66
% 32.07/8.29 | (228) subset_complement(all_0_6_6, all_102_3_53) = all_152_1_65
% 32.07/8.29 | (229) subset(all_102_3_53, all_152_1_65) = all_152_0_64
% 32.07/8.29 | (230) ~ (all_152_0_64 = 0) | all_152_2_66 = 0
% 32.07/8.29 | (231) ~ (all_152_2_66 = 0) | all_152_0_64 = 0
% 32.07/8.29 |
% 32.07/8.29 | Instantiating (219) with all_162_0_73, all_162_1_74, all_162_2_75 yields:
% 32.07/8.29 | (232) disjoint(empty_set, all_102_3_53) = all_162_2_75 & subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74 & subset(empty_set, all_162_1_74) = all_162_0_73 & ( ~ (all_162_0_73 = 0) | all_162_2_75 = 0) & ( ~ (all_162_2_75 = 0) | all_162_0_73 = 0)
% 32.07/8.29 |
% 32.07/8.29 | Applying alpha-rule on (232) yields:
% 32.07/8.29 | (233) ~ (all_162_0_73 = 0) | all_162_2_75 = 0
% 32.07/8.29 | (234) subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74
% 32.07/8.29 | (235) disjoint(empty_set, all_102_3_53) = all_162_2_75
% 32.07/8.29 | (236) ~ (all_162_2_75 = 0) | all_162_0_73 = 0
% 32.07/8.29 | (237) subset(empty_set, all_162_1_74) = all_162_0_73
% 32.07/8.30 |
% 32.07/8.30 | Instantiating (216) with all_176_0_85 yields:
% 32.07/8.30 | (238) subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85 & set_difference(all_0_6_6, all_102_3_53) = all_176_0_85
% 32.07/8.30 |
% 32.07/8.30 | Applying alpha-rule on (238) yields:
% 32.07/8.30 | (239) subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85
% 32.07/8.30 | (240) set_difference(all_0_6_6, all_102_3_53) = all_176_0_85
% 32.07/8.30 |
% 32.07/8.30 +-Applying beta-rule and splitting (218), into two cases.
% 32.07/8.30 |-Branch one:
% 32.07/8.30 | (241) ~ (element(all_45_0_26, all_0_3_3) = 0)
% 32.07/8.30 |
% 32.07/8.30 | From (195) and (241) follows:
% 32.07/8.30 | (242) ~ (element(empty_set, all_0_3_3) = 0)
% 32.07/8.30 |
% 32.07/8.30 | Using (200) and (242) yields:
% 32.07/8.30 | (243) $false
% 32.07/8.30 |
% 32.07/8.30 |-The branch is then unsatisfiable
% 32.07/8.30 |-Branch two:
% 32.07/8.30 | (244) element(all_45_0_26, all_0_3_3) = 0
% 32.07/8.30 | (245) ? [v0] : ? [v1] : ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, all_0_5_5) = v2 & in(all_102_3_53, all_45_0_26) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.30 |
% 32.07/8.30 | Instantiating (245) with all_276_0_126, all_276_1_127, all_276_2_128 yields:
% 32.07/8.30 | (246) subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127 & in(all_276_1_127, all_0_5_5) = all_276_0_126 & in(all_102_3_53, all_45_0_26) = all_276_2_128 & ( ~ (all_276_0_126 = 0) | all_276_2_128 = 0) & ( ~ (all_276_2_128 = 0) | all_276_0_126 = 0)
% 32.07/8.30 |
% 32.07/8.30 | Applying alpha-rule on (246) yields:
% 32.07/8.30 | (247) in(all_102_3_53, all_45_0_26) = all_276_2_128
% 32.07/8.30 | (248) subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127
% 32.07/8.30 | (249) in(all_276_1_127, all_0_5_5) = all_276_0_126
% 32.07/8.30 | (250) ~ (all_276_2_128 = 0) | all_276_0_126 = 0
% 32.07/8.30 | (251) ~ (all_276_0_126 = 0) | all_276_2_128 = 0
% 32.07/8.30 |
% 32.07/8.30 | From (195) and (247) follows:
% 32.07/8.30 | (252) in(all_102_3_53, empty_set) = all_276_2_128
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (164) with all_0_6_6, empty_set, all_138_0_56, all_0_5_5 and discharging atoms complements_of_subsets(all_0_6_6, empty_set) = all_138_0_56, complements_of_subsets(all_0_6_6, empty_set) = all_0_5_5, yields:
% 32.07/8.30 | (253) all_138_0_56 = all_0_5_5
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (152) with all_0_6_6, all_102_3_53, all_176_0_85, all_276_1_127 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127, subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85, yields:
% 32.07/8.30 | (254) all_276_1_127 = all_176_0_85
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (152) with all_0_6_6, all_102_3_53, all_162_1_74, all_102_1_51 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74, subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51, yields:
% 32.07/8.30 | (255) all_162_1_74 = all_102_1_51
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (152) with all_0_6_6, all_102_3_53, all_162_1_74, all_176_0_85 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85, subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74, yields:
% 32.07/8.30 | (256) all_176_0_85 = all_162_1_74
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (152) with all_0_6_6, all_102_3_53, all_152_1_65, all_276_1_127 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127, subset_complement(all_0_6_6, all_102_3_53) = all_152_1_65, yields:
% 32.07/8.30 | (257) all_276_1_127 = all_152_1_65
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (134) with all_102_1_51, all_0_5_5, all_276_0_126, all_102_0_50 and discharging atoms in(all_102_1_51, all_0_5_5) = all_102_0_50, yields:
% 32.07/8.30 | (258) all_276_0_126 = all_102_0_50 | ~ (in(all_102_1_51, all_0_5_5) = all_276_0_126)
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (30) with all_102_3_53 yields:
% 32.07/8.30 | (259) ~ (in(all_102_3_53, empty_set) = 0)
% 32.07/8.30 |
% 32.07/8.30 | Combining equations (254,257) yields a new equation:
% 32.07/8.30 | (260) all_176_0_85 = all_152_1_65
% 32.07/8.30 |
% 32.07/8.30 | Simplifying 260 yields:
% 32.07/8.30 | (261) all_176_0_85 = all_152_1_65
% 32.07/8.30 |
% 32.07/8.30 | Combining equations (256,261) yields a new equation:
% 32.07/8.30 | (262) all_162_1_74 = all_152_1_65
% 32.07/8.30 |
% 32.07/8.30 | Simplifying 262 yields:
% 32.07/8.30 | (263) all_162_1_74 = all_152_1_65
% 32.07/8.30 |
% 32.07/8.30 | Combining equations (255,263) yields a new equation:
% 32.07/8.30 | (264) all_152_1_65 = all_102_1_51
% 32.07/8.30 |
% 32.07/8.30 | Combining equations (264,257) yields a new equation:
% 32.07/8.30 | (265) all_276_1_127 = all_102_1_51
% 32.07/8.30 |
% 32.07/8.30 | From (264) and (228) follows:
% 32.07/8.30 | (210) subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51
% 32.07/8.30 |
% 32.07/8.30 | From (265) and (249) follows:
% 32.07/8.30 | (267) in(all_102_1_51, all_0_5_5) = all_276_0_126
% 32.07/8.30 |
% 32.07/8.30 +-Applying beta-rule and splitting (225), into two cases.
% 32.07/8.30 |-Branch one:
% 32.07/8.30 | (268) ~ (element(all_138_0_56, all_0_3_3) = 0)
% 32.07/8.30 |
% 32.07/8.30 | From (253) and (268) follows:
% 32.07/8.30 | (269) ~ (element(all_0_5_5, all_0_3_3) = 0)
% 32.07/8.30 |
% 32.07/8.30 | Using (53) and (269) yields:
% 32.07/8.30 | (243) $false
% 32.07/8.30 |
% 32.07/8.30 |-The branch is then unsatisfiable
% 32.07/8.30 |-Branch two:
% 32.07/8.30 | (271) element(all_138_0_56, all_0_3_3) = 0
% 32.07/8.30 | (272) ? [v0] : ? [v1] : ? [v2] : (subset_complement(all_0_6_6, empty_set) = v1 & in(v1, empty_set) = v2 & in(empty_set, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.30 |
% 32.07/8.30 | From (253) and (271) follows:
% 32.07/8.30 | (53) element(all_0_5_5, all_0_3_3) = 0
% 32.07/8.30 |
% 32.07/8.30 +-Applying beta-rule and splitting (258), into two cases.
% 32.07/8.30 |-Branch one:
% 32.07/8.30 | (274) ~ (in(all_102_1_51, all_0_5_5) = all_276_0_126)
% 32.07/8.30 |
% 32.07/8.30 | Using (267) and (274) yields:
% 32.07/8.30 | (243) $false
% 32.07/8.30 |
% 32.07/8.30 |-The branch is then unsatisfiable
% 32.07/8.30 |-Branch two:
% 32.07/8.30 | (267) in(all_102_1_51, all_0_5_5) = all_276_0_126
% 32.07/8.30 | (277) all_276_0_126 = all_102_0_50
% 32.07/8.30 |
% 32.07/8.30 +-Applying beta-rule and splitting (224), into two cases.
% 32.07/8.30 |-Branch one:
% 32.07/8.30 | (268) ~ (element(all_138_0_56, all_0_3_3) = 0)
% 32.07/8.30 |
% 32.07/8.30 | From (253) and (268) follows:
% 32.07/8.30 | (269) ~ (element(all_0_5_5, all_0_3_3) = 0)
% 32.07/8.30 |
% 32.07/8.30 | Using (53) and (269) yields:
% 32.07/8.30 | (243) $false
% 32.07/8.30 |
% 32.07/8.30 |-The branch is then unsatisfiable
% 32.07/8.30 |-Branch two:
% 32.07/8.30 | (271) element(all_138_0_56, all_0_3_3) = 0
% 32.07/8.30 | (282) ? [v0] : ? [v1] : ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, empty_set) = v2 & in(all_102_3_53, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.30 |
% 32.07/8.30 | Instantiating (282) with all_359_0_147, all_359_1_148, all_359_2_149 yields:
% 32.07/8.30 | (283) subset_complement(all_0_6_6, all_102_3_53) = all_359_1_148 & in(all_359_1_148, empty_set) = all_359_0_147 & in(all_102_3_53, all_138_0_56) = all_359_2_149 & ( ~ (all_359_0_147 = 0) | all_359_2_149 = 0) & ( ~ (all_359_2_149 = 0) | all_359_0_147 = 0)
% 32.07/8.30 |
% 32.07/8.30 | Applying alpha-rule on (283) yields:
% 32.07/8.30 | (284) in(all_102_3_53, all_138_0_56) = all_359_2_149
% 32.07/8.30 | (285) in(all_359_1_148, empty_set) = all_359_0_147
% 32.07/8.30 | (286) ~ (all_359_0_147 = 0) | all_359_2_149 = 0
% 32.07/8.30 | (287) ~ (all_359_2_149 = 0) | all_359_0_147 = 0
% 32.07/8.30 | (288) subset_complement(all_0_6_6, all_102_3_53) = all_359_1_148
% 32.07/8.30 |
% 32.07/8.30 | From (253) and (284) follows:
% 32.07/8.30 | (289) in(all_102_3_53, all_0_5_5) = all_359_2_149
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (152) with all_0_6_6, all_102_3_53, all_359_1_148, all_102_1_51 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_359_1_148, subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51, yields:
% 32.07/8.30 | (290) all_359_1_148 = all_102_1_51
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (30) with all_359_1_148 yields:
% 32.07/8.30 | (291) ~ (in(all_359_1_148, empty_set) = 0)
% 32.07/8.30 |
% 32.07/8.30 | Instantiating formula (134) with all_102_3_53, all_0_5_5, all_359_2_149, all_102_2_52 and discharging atoms in(all_102_3_53, all_0_5_5) = all_359_2_149, in(all_102_3_53, all_0_5_5) = all_102_2_52, yields:
% 32.07/8.30 | (292) all_359_2_149 = all_102_2_52
% 32.07/8.30 |
% 32.07/8.30 | Using (252) and (259) yields:
% 32.07/8.30 | (293) ~ (all_276_2_128 = 0)
% 32.07/8.30 |
% 32.07/8.30 | From (290) and (285) follows:
% 32.07/8.30 | (294) in(all_102_1_51, empty_set) = all_359_0_147
% 32.07/8.30 |
% 32.07/8.30 | From (290) and (291) follows:
% 32.07/8.30 | (295) ~ (in(all_102_1_51, empty_set) = 0)
% 32.07/8.30 |
% 32.07/8.30 +-Applying beta-rule and splitting (251), into two cases.
% 32.07/8.30 |-Branch one:
% 32.07/8.30 | (296) ~ (all_276_0_126 = 0)
% 32.07/8.30 |
% 32.07/8.30 | Equations (277) can reduce 296 to:
% 32.07/8.30 | (297) ~ (all_102_0_50 = 0)
% 32.07/8.30 |
% 32.07/8.30 +-Applying beta-rule and splitting (214), into two cases.
% 32.07/8.30 |-Branch one:
% 32.07/8.30 | (298) all_102_0_50 = 0
% 32.07/8.30 |
% 32.07/8.30 | Equations (298) can reduce 297 to:
% 32.07/8.30 | (205) $false
% 32.07/8.30 |
% 32.07/8.30 |-The branch is then unsatisfiable
% 32.07/8.30 |-Branch two:
% 32.07/8.30 | (297) ~ (all_102_0_50 = 0)
% 32.07/8.30 | (301) all_102_2_52 = 0
% 32.07/8.30 |
% 32.07/8.30 | Combining equations (301,292) yields a new equation:
% 32.07/8.30 | (302) all_359_2_149 = 0
% 32.07/8.30 |
% 32.07/8.31 +-Applying beta-rule and splitting (287), into two cases.
% 32.07/8.31 |-Branch one:
% 32.07/8.31 | (303) ~ (all_359_2_149 = 0)
% 32.07/8.31 |
% 32.07/8.31 | Equations (302) can reduce 303 to:
% 32.07/8.31 | (205) $false
% 32.07/8.31 |
% 32.07/8.31 |-The branch is then unsatisfiable
% 32.07/8.31 |-Branch two:
% 32.07/8.31 | (302) all_359_2_149 = 0
% 32.07/8.31 | (306) all_359_0_147 = 0
% 32.07/8.31 |
% 32.07/8.31 | From (306) and (294) follows:
% 32.07/8.31 | (307) in(all_102_1_51, empty_set) = 0
% 32.07/8.31 |
% 32.07/8.31 | Using (307) and (295) yields:
% 32.07/8.31 | (243) $false
% 32.07/8.31 |
% 32.07/8.31 |-The branch is then unsatisfiable
% 32.07/8.31 |-Branch two:
% 32.07/8.31 | (309) all_276_0_126 = 0
% 32.07/8.31 | (310) all_276_2_128 = 0
% 32.07/8.31 |
% 32.07/8.31 | Equations (310) can reduce 293 to:
% 32.07/8.31 | (205) $false
% 32.07/8.31 |
% 32.07/8.31 |-The branch is then unsatisfiable
% 32.07/8.31 % SZS output end Proof for theBenchmark
% 32.07/8.31
% 32.07/8.31 7664ms
%------------------------------------------------------------------------------