TSTP Solution File: SEU178+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU178+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 08:47:21 EDT 2022
% Result : Theorem 31.01s 8.14s
% Output : Proof 102.88s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU178+2 : TPTP v8.1.0. Released v3.3.0.
% 0.05/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.31 % Computer : n022.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 600
% 0.10/0.31 % DateTime : Mon Jun 20 05:29:01 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.51/0.56 ____ _
% 0.51/0.56 ___ / __ \_____(_)___ ________ __________
% 0.51/0.56 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.56 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.56 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.56
% 0.51/0.56 A Theorem Prover for First-Order Logic
% 0.51/0.56 (ePrincess v.1.0)
% 0.51/0.56
% 0.51/0.56 (c) Philipp Rümmer, 2009-2015
% 0.51/0.56 (c) Peter Backeman, 2014-2015
% 0.51/0.56 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.56 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.56 Bug reports to peter@backeman.se
% 0.51/0.56
% 0.51/0.56 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.56
% 0.51/0.56 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.51/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.54/1.18 Prover 0: Preprocessing ...
% 6.25/2.14 Prover 0: Warning: ignoring some quantifiers
% 6.46/2.21 Prover 0: Constructing countermodel ...
% 21.89/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.11/5.99 Prover 1: Preprocessing ...
% 23.37/6.24 Prover 1: Warning: ignoring some quantifiers
% 23.37/6.26 Prover 1: Constructing countermodel ...
% 31.01/8.14 Prover 1: proved (2213ms)
% 31.01/8.14 Prover 0: stopped
% 31.01/8.14
% 31.01/8.14 No countermodel exists, formula is valid
% 31.01/8.14 % SZS status Theorem for theBenchmark
% 31.01/8.14
% 31.01/8.14 Generating proof ... Warning: ignoring some quantifiers
% 101.55/55.64 found it (size 39)
% 101.55/55.64
% 101.55/55.64 % SZS output start Proof for theBenchmark
% 101.55/55.64 Assumed formulas after preprocessing and simplification:
% 101.55/55.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v7 = 0) & ~ (v5 = 0) & relation_rng(v1) = v3 & relation_dom(v1) = v2 & cartesian_product2(v2, v3) = v4 & empty(v9) = 0 & empty(v8) = 0 & empty(v6) = v7 & empty(empty_set) = 0 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation(v9) = 0 & relation(v1) = 0 & subset(v1, v4) = v5 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relation_rng(v12) = v15) | ~ (relation_dom(v12) = v13) | ~ (in(v11, v15) = v16) | ~ (in(v10, v13) = v14) | ? [v17] : ? [v18] : ? [v19] : (relation(v12) = v17 & ordered_pair(v10, v11) = v18 & in(v18, v12) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = v16) | ? [v17] : ? [v18] : (in(v11, v13) = v18 & in(v10, v12) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (cartesian_product2(v11, v13) = v15) | ~ (cartesian_product2(v10, v12) = v14) | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : (subset(v12, v13) = v18 & subset(v10, v11) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = 0 | ~ (relation_rng(v12) = v15) | ~ (relation_dom(v12) = v13) | ~ (in(v11, v15) = v16) | ~ (in(v10, v13) = v14) | ? [v17] : ? [v18] : ? [v19] : (relation(v12) = v17 & ordered_pair(v10, v11) = v18 & in(v18, v12) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = 0 | ~ (cartesian_product2(v10, v11) = v12) | ~ (ordered_pair(v15, v16) = v13) | ~ (in(v13, v12) = v14) | ? [v17] : ? [v18] : (in(v16, v11) = v18 & in(v15, v10) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset_difference(v10, v11, v12) = v14) | ~ (element(v14, v13) = v15) | ~ (powerset(v10) = v13) | ? [v16] : ? [v17] : (element(v12, v13) = v17 & element(v11, v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (complements_of_subsets(v10, v11) = v14) | ~ (element(v14, v13) = v15) | ~ (powerset(v12) = v13) | ~ (powerset(v10) = v12) | ? [v16] : ( ~ (v16 = 0) & element(v11, v13) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_difference(v11, v13) = v14) | ~ (singleton(v12) = v13) | ~ (subset(v10, v14) = v15) | ? [v16] : ? [v17] : (subset(v10, v11) = v16 & in(v12, v10) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_difference(v11, v12) = v14) | ~ (set_difference(v10, v12) = v13) | ~ (subset(v13, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v13, v14) = v15) | ~ (set_intersection2(v11, v12) = v14) | ~ (set_intersection2(v10, v12) = v13) | ? [v16] : ( ~ (v16 = 0) & subset(v10, v11) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (relation_rng(v10) = v11) | ~ (ordered_pair(v14, v12) = v15) | ~ (in(v15, v10) = 0) | ~ (in(v12, v11) = v13) | ? [v16] : ( ~ (v16 = 0) & relation(v10) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = 0 | ~ (relation_dom(v10) = v11) | ~ (ordered_pair(v12, v14) = v15) | ~ (in(v15, v10) = 0) | ~ (in(v12, v11) = v13) | ? [v16] : ( ~ (v16 = 0) & relation(v10) = v16)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_complement(v10, v13) = v14) | ~ (element(v11, v12) = 0) | ~ (powerset(v10) = v12) | ~ (subset(v11, v14) = v15) | ? [v16] : ? [v17] : (disjoint(v11, v13) = v17 & element(v13, v12) = v16 & ( ~ (v16 = 0) | (( ~ (v17 = 0) | v15 = 0) & ( ~ (v15 = 0) | v17 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (ordered_pair(v10, v11) = v14) | ~ (in(v14, v15) = 0) | (in(v11, v13) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v11, v12) = v14) | ~ (cartesian_product2(v10, v12) = v13) | ~ (subset(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (cartesian_product2(v12, v11) = v18 & cartesian_product2(v12, v10) = v17 & subset(v17, v18) = v19 & subset(v10, v11) = v16 & ( ~ (v16 = 0) | (v19 = 0 & v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v10 = empty_set | ~ (set_meet(v10) = v11) | ~ (in(v12, v13) = v14) | ~ (in(v12, v11) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v13, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (meet_of_subsets(v10, v11) = v13) | ~ (element(v13, v12) = v14) | ~ (powerset(v10) = v12) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & element(v11, v15) = v16 & powerset(v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (union_of_subsets(v10, v11) = v13) | ~ (element(v13, v12) = v14) | ~ (powerset(v10) = v12) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & element(v11, v15) = v16 & powerset(v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset_complement(v10, v11) = v13) | ~ (element(v13, v12) = v14) | ~ (powerset(v10) = v12) | ? [v15] : ( ~ (v15 = 0) & element(v11, v12) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v11, v13) = 0) | ~ (element(v10, v12) = v14) | ~ (powerset(v12) = v13) | ? [v15] : ( ~ (v15 = 0) & in(v10, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v11, v12) = 0) | ~ (powerset(v10) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v11) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v12) = v14) | ~ (unordered_pair(v10, v11) = v13) | ? [v15] : ? [v16] : (in(v11, v12) = v16 & in(v10, v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v11) = v14) | ~ (set_union2(v10, v12) = v13) | ? [v15] : ? [v16] : (subset(v12, v11) = v16 & subset(v10, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v10, v13) = v14) | ~ (set_intersection2(v11, v12) = v13) | ? [v15] : ? [v16] : (subset(v10, v12) = v16 & subset(v10, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v15 & in(v13, v11) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v11 | ~ (ordered_pair(v12, v13) = v14) | ~ (ordered_pair(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v10 | v12 = v10 | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (union(v10) = v11) | ~ (in(v12, v14) = 0) | ~ (in(v12, v11) = v13) | ? [v15] : ( ~ (v15 = 0) & in(v14, v10) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v10 | ~ (ordered_pair(v12, v13) = v14) | ~ (ordered_pair(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (subset_difference(v14, v13, v12) = v11) | ~ (subset_difference(v14, v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = empty_set | ~ (subset_difference(v10, v12, v13) = v14) | ~ (meet_of_subsets(v10, v11) = v13) | ~ (cast_to_subset(v10) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (union_of_subsets(v10, v18) = v19 & complements_of_subsets(v10, v11) = v18 & element(v11, v16) = v17 & powerset(v15) = v16 & powerset(v10) = v15 & ( ~ (v17 = 0) | v19 = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = empty_set | ~ (subset_difference(v10, v12, v13) = v14) | ~ (union_of_subsets(v10, v11) = v13) | ~ (cast_to_subset(v10) = v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (meet_of_subsets(v10, v18) = v19 & complements_of_subsets(v10, v11) = v18 & element(v11, v16) = v17 & powerset(v15) = v16 & powerset(v10) = v15 & ( ~ (v17 = 0) | v19 = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v15 & in(v13, v11) = v16 & ( ~ (v15 = 0) | (v14 = 0 & ~ (v16 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v13) | ~ (unordered_pair(v12, v13) = v14) | ~ (unordered_pair(v10, v11) = v12) | ordered_pair(v10, v11) = v14) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v15 & in(v13, v11) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v14 = 0)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v10, v11) = v12) | ~ (in(v13, v10) = v14) | ? [v15] : ? [v16] : (in(v13, v12) = v16 & in(v13, v11) = v15 & (v16 = 0 | ( ~ (v15 = 0) & ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v13 = v10 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (subset_complement(v10, v12) = v13) | ~ (subset_complement(v10, v11) = v12) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & element(v11, v14) = v15 & powerset(v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v10) = v12) | ~ (set_union2(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_difference(v10, v12) = v13) | ~ (singleton(v11) = v12) | in(v11, v10) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v10 = empty_set | ~ (set_meet(v10) = v11) | ~ (in(v12, v11) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v10) = 0 & in(v12, v14) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v12, v11) = v13) | ~ (singleton(v10) = v12) | in(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = 0) | ~ (disjoint(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (set_difference(v10, v11) = v12) | ~ (subset(v12, v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (union(v11) = v12) | ~ (subset(v10, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (cast_to_subset(v10) = v11) | ~ (element(v11, v12) = v13) | ~ (powerset(v10) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v10, v12) = v13) | ~ (powerset(v11) = v12) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v11) = v15 & in(v14, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v10, v12) = v13) | ~ (powerset(v11) = v12) | ? [v14] : ( ~ (v14 = 0) & subset(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (powerset(v10) = v11) | ~ (subset(v12, v10) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v10) = v12) | ~ (subset(v12, v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v10) = v13) | ~ (set_intersection2(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v12) = v13) | ~ (subset(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v10, v12) = v13) | ~ (set_union2(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (unordered_pair(v10, v11) = v12) | ~ (in(v10, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v10) = v13) | ~ (unordered_pair(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (are_equipotent(v13, v12) = v11) | ~ (are_equipotent(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (meet_of_subsets(v13, v12) = v11) | ~ (meet_of_subsets(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (union_of_subsets(v13, v12) = v11) | ~ (union_of_subsets(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (complements_of_subsets(v13, v12) = v11) | ~ (complements_of_subsets(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (disjoint(v13, v12) = v11) | ~ (disjoint(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset_complement(v13, v12) = v11) | ~ (subset_complement(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_difference(v13, v12) = v11) | ~ (set_difference(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cartesian_product2(v13, v12) = v11) | ~ (cartesian_product2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (element(v13, v12) = v11) | ~ (element(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (singleton(v11) = v13) | ~ (singleton(v10) = v12) | ~ (subset(v12, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (singleton(v10) = v13) | ~ (unordered_pair(v11, v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (ordered_pair(v13, v12) = v11) | ~ (ordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (subset(v13, v12) = v11) | ~ (subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_intersection2(v13, v12) = v11) | ~ (set_intersection2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (set_union2(v13, v12) = v11) | ~ (set_union2(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (unordered_pair(v13, v12) = v11) | ~ (unordered_pair(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (proper_subset(v13, v12) = v11) | ~ (proper_subset(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (in(v13, v12) = v11) | ~ (in(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = empty_set | ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | ~ (powerset(v10) = v12) | ? [v14] : ( ~ (v14 = empty_set) & complements_of_subsets(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v10, v11) = v12) | set_difference(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v10) = v12) | ~ (set_union2(v10, v12) = v13) | set_union2(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v12) = v13) | ~ (set_difference(v10, v11) = v12) | set_intersection2(v10, v11) = v13) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v10, v11) = v12) | ~ (in(v13, v10) = 0) | ? [v14] : ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & (v15 = 0 | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v10, v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ? [v15] : (ordered_pair(v14, v15) = v13 & in(v15, v11) = 0 & in(v14, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ~ (element(v11, v13) = 0) | ~ (powerset(v10) = v13) | ? [v14] : (subset_difference(v10, v11, v12) = v14 & set_difference(v11, v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ~ (powerset(v10) = v13) | ~ (in(v11, v12) = 0) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & subset_complement(v10, v12) = v14 & in(v11, v14) = v15)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | ~ (powerset(v10) = v12) | ? [v14] : (meet_of_subsets(v10, v11) = v14 & set_meet(v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | ~ (powerset(v10) = v12) | ? [v14] : (union_of_subsets(v10, v11) = v14 & union(v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | ~ (powerset(v10) = v12) | ? [v14] : (complements_of_subsets(v10, v14) = v11 & complements_of_subsets(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | ~ (powerset(v10) = v12) | ? [v14] : (complements_of_subsets(v10, v11) = v14 & ! [v15] : (v15 = v14 | ~ (element(v15, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (subset_complement(v10, v16) = v18 & element(v16, v12) = 0 & in(v18, v11) = v19 & in(v16, v15) = v17 & ( ~ (v19 = 0) | ~ (v17 = 0)) & (v19 = 0 | v17 = 0))) & ! [v15] : ( ~ (element(v15, v12) = 0) | ~ (element(v14, v13) = 0) | ? [v16] : ? [v17] : ? [v18] : (subset_complement(v10, v15) = v17 & in(v17, v11) = v18 & in(v15, v14) = v16 & ( ~ (v18 = 0) | v16 = 0) & ( ~ (v16 = 0) | v18 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | ~ (in(v10, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v12) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v13, v12) = 0) | ~ (unordered_pair(v10, v11) = v13) | (in(v11, v12) = 0 & in(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & disjoint(v10, v11) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v10, v11) = v12) | ~ (in(v13, v10) = 0) | ? [v14] : ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_difference(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v14, v12) = v17 & in(v14, v11) = v16 & in(v14, v10) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0) & (v15 = 0 | (v16 = 0 & ~ (v17 = 0))))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (cartesian_product2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (in(v14, v10) = v15 & ( ~ (v15 = 0) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v22) = v14) | ? [v23] : ? [v24] : (in(v22, v12) = v24 & in(v21, v11) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0))))) & (v15 = 0 | (v20 = v14 & v19 = 0 & v18 = 0 & ordered_pair(v16, v17) = v14 & in(v17, v12) = 0 & in(v16, v11) = 0)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v14, v12) = v17 & in(v14, v11) = v16 & in(v14, v10) = v15 & ( ~ (v17 = 0) | ~ (v16 = 0) | ~ (v15 = 0)) & (v15 = 0 | (v17 = 0 & v16 = 0)))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v14, v12) = v17 & in(v14, v11) = v16 & in(v14, v10) = v15 & ( ~ (v15 = 0) | ( ~ (v17 = 0) & ~ (v16 = 0))) & (v17 = 0 | v16 = 0 | v15 = 0))) & ? [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (in(v14, v10) = v15 & ( ~ (v15 = 0) | ( ~ (v14 = v12) & ~ (v14 = v11))) & (v15 = 0 | v14 = v12 | v14 = v11))) & ! [v10] : ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | v10 = empty_set | ~ (singleton(v11) = v12) | ~ (subset(v10, v12) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v10) = v11) | ~ (in(v12, v11) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & disjoint(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = v10 | ~ (proper_subset(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & subset(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : ( ~ (v13 = v10) & set_difference(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (disjoint(v10, v11) = v12) | ? [v13] : (in(v13, v11) = 0 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (element(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (singleton(v11) = v10) | ~ (subset(v10, v10) = v12)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (singleton(v10) = v11) | ~ (subset(empty_set, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (singleton(v10) = v11) | ~ (in(v10, v11) = v12)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & in(v13, v11) = v14 & in(v13, v10) = 0)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_rng(v12) = v11) | ~ (relation_rng(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (union(v12) = v11) | ~ (union(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (cast_to_subset(v12) = v11) | ~ (cast_to_subset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation_dom(v12) = v11) | ~ (relation_dom(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (empty(v12) = v11) | ~ (empty(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (powerset(v12) = v11) | ~ (powerset(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singleton(v12) = v11) | ~ (singleton(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (set_meet(v12) = v11) | ~ (set_meet(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (relation(v12) = v11) | ~ (relation(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v10 = empty_set | ~ (element(v12, v11) = 0) | ~ (powerset(v10) = v11) | ? [v13] : (subset_complement(v10, v12) = v13 & ! [v14] : ! [v15] : (v15 = 0 | ~ (in(v14, v13) = v15) | ? [v16] : ? [v17] : (element(v14, v10) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | v17 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (disjoint(v12, v11) = 0) | ~ (singleton(v10) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (disjoint(v10, v11) = 0) | ~ (in(v12, v10) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_rng(v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & ordered_pair(v13, v12) = v14 & in(v14, v10) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_difference(v10, v12) = v10) | ~ (singleton(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & in(v11, v10) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : (in(v13, v10) = 0 & in(v12, v13) = 0)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (relation_dom(v10) = v11) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = 0 & ordered_pair(v12, v13) = v14 & in(v14, v10) = 0) | ( ~ (v13 = 0) & relation(v10) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (cartesian_product2(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (empty(v12) = v15 & empty(v11) = v14 & empty(v10) = v13 & ( ~ (v15 = 0) | v14 = 0 | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (element(v11, v12) = 0) | ~ (powerset(v10) = v12) | ? [v13] : (subset_complement(v10, v11) = v13 & set_difference(v10, v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (element(v11, v10) = v12) | ? [v13] : ? [v14] : (empty(v10) = v13 & in(v11, v10) = v14 & (v13 = 0 | (( ~ (v14 = 0) | v12 = 0) & ( ~ (v12 = 0) | v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (element(v10, v12) = 0) | ~ (powerset(v11) = v12) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (empty(v11) = v12) | ~ (empty(v10) = 0) | ? [v13] : (element(v11, v10) = v13 & ( ~ (v13 = 0) | v12 = 0) & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (powerset(v10) = v11) | ~ (subset(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v10) = v12) | ~ (subset(v12, v11) = 0) | in(v10, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v10] : ! [v11] : ! [v12] : ( ~ (subset(v10, v11) = 0) | ~ (in(v12, v10) = 0) | in(v12, v11) = 0) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | set_intersection2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_intersection2(v10, v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & in(v13, v12) = 0) | (v13 = 0 & disjoint(v10, v11) = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v11, v10) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | set_union2(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (set_union2(v10, v11) = v12) | ? [v13] : ? [v14] : (empty(v12) = v14 & empty(v10) = v13 & ( ~ (v14 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | unordered_pair(v11, v10) = v12) & ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | v11 = empty_set | ~ (set_meet(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v13, v10) = v14 & ( ~ (v14 = 0) | (v16 = 0 & ~ (v17 = 0) & in(v15, v11) = 0 & in(v13, v15) = v17)) & (v14 = 0 | ! [v18] : ! [v19] : (v19 = 0 | ~ (in(v13, v18) = v19) | ? [v20] : ( ~ (v20 = 0) & in(v18, v11) = v20))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v13 = 0) & relation(v11) = v13) | (in(v13, v10) = v14 & ( ~ (v14 = 0) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v13) = v19) | ~ (in(v19, v11) = 0))) & (v14 = 0 | (v17 = 0 & ordered_pair(v15, v13) = v16 & in(v16, v11) = 0))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (union(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (in(v13, v10) = v14 & ( ~ (v14 = 0) | ! [v18] : ( ~ (in(v13, v18) = 0) | ? [v19] : ( ~ (v19 = 0) & in(v18, v11) = v19))) & (v14 = 0 | (v17 = 0 & v16 = 0 & in(v15, v11) = 0 & in(v13, v15) = 0)))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (relation_dom(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v13 = 0) & relation(v11) = v13) | (in(v13, v10) = v14 & ( ~ (v14 = 0) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v13, v18) = v19) | ~ (in(v19, v11) = 0))) & (v14 = 0 | (v17 = 0 & ordered_pair(v13, v15) = v16 & in(v16, v11) = 0))))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (powerset(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (subset(v13, v11) = v15 & in(v13, v10) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)) & (v15 = 0 | v14 = 0))) & ? [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (singleton(v11) = v12) | ? [v13] : ? [v14] : (in(v13, v10) = v14 & ( ~ (v14 = 0) | ~ (v13 = v11)) & (v14 = 0 | v13 = v11))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_difference(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (cast_to_subset(v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (empty(v11) = 0) | ~ (empty(v10) = 0)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (subset(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v11, v10) = v12)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_intersection2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (set_union2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_difference(empty_set, v10) = v11)) & ! [v10] : ! [v11] : (v11 = empty_set | ~ (set_intersection2(v10, empty_set) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (empty(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ( ~ (v14 = 0) & element(v13, v12) = 0 & empty(v13) = v14 & powerset(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (relation(v10) = v11) | ? [v12] : (in(v12, v10) = 0 & ! [v13] : ! [v14] : ~ (ordered_pair(v13, v14) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(v10, v10) = v11)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (subset(empty_set, v10) = v11)) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | disjoint(v11, v10) = 0) & ! [v10] : ! [v11] : ( ~ (disjoint(v10, v11) = 0) | set_difference(v10, v11) = v10) & ! [v10] : ! [v11] : ( ~ (set_difference(v10, v11) = empty_set) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (element(v10, v11) = 0) | ? [v12] : ? [v13] : (empty(v11) = v12 & in(v10, v11) = v13 & (v13 = 0 | v12 = 0))) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | union(v11) = v10) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (powerset(v10) = v11) | ? [v12] : (element(v12, v11) = 0 & empty(v12) = 0)) & ! [v10] : ! [v11] : ( ~ (singleton(v10) = v11) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (relation(v10) = 0) | ~ (in(v11, v10) = 0) | ? [v12] : ? [v13] : ordered_pair(v12, v13) = v11) & ! [v10] : ! [v11] : ( ~ (set_intersection2(v10, v11) = empty_set) | disjoint(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v10) = v11) | singleton(v10) = v11) & ! [v10] : ! [v11] : ( ~ (proper_subset(v11, v10) = 0) | ? [v12] : ( ~ (v12 = 0) & subset(v10, v11) = v12)) & ! [v10] : ! [v11] : ( ~ (proper_subset(v10, v11) = 0) | subset(v10, v11) = 0) & ! [v10] : ! [v11] : ( ~ (proper_subset(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & proper_subset(v11, v10) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & empty(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (in(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v11, v10) = v12)) & ! [v10] : (v10 = empty_set | ~ (empty(v10) = 0)) & ! [v10] : (v10 = empty_set | ~ (set_meet(empty_set) = v10)) & ! [v10] : (v10 = empty_set | ~ (subset(v10, empty_set) = 0)) & ! [v10] : ~ (singleton(v10) = empty_set) & ! [v10] : ~ (proper_subset(v10, v10) = 0) & ! [v10] : ~ (in(v10, empty_set) = 0) & ? [v10] : ? [v11] : (v11 = v10 | ? [v12] : ? [v13] : ? [v14] : (in(v12, v11) = v14 & in(v12, v10) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)) & (v14 = 0 | v13 = 0))) & ? [v10] : ? [v11] : element(v11, v10) = 0 & ? [v10] : ? [v11] : (in(v10, v11) = 0 & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v12) = v13) | ~ (in(v13, v11) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v11) = v15)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (are_equipotent(v12, v11) = v13) | ? [v14] : ? [v15] : (subset(v12, v11) = v14 & in(v12, v11) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v12] : ! [v13] : ( ~ (subset(v13, v12) = 0) | ? [v14] : ? [v15] : (in(v13, v11) = v15 & in(v12, v11) = v14 & ( ~ (v14 = 0) | v15 = 0)))) & ? [v10] : ? [v11] : (in(v10, v11) = 0 & ! [v12] : ! [v13] : (v13 = 0 | ~ (are_equipotent(v12, v11) = v13) | ? [v14] : ? [v15] : (subset(v12, v11) = v14 & in(v12, v11) = v15 & ( ~ (v14 = 0) | v15 = 0))) & ! [v12] : ! [v13] : ( ~ (subset(v13, v12) = 0) | ? [v14] : ? [v15] : (in(v13, v11) = v15 & in(v12, v11) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v12] : ( ~ (in(v12, v11) = 0) | ? [v13] : (in(v13, v11) = 0 & ! [v14] : ( ~ (subset(v14, v12) = 0) | in(v14, v13) = 0)))) & ? [v10] : (v10 = empty_set | ? [v11] : in(v11, v10) = 0))
% 102.09/55.80 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 102.09/55.80 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & relation_rng(all_0_8_8) = all_0_6_6 & relation_dom(all_0_8_8) = all_0_7_7 & cartesian_product2(all_0_7_7, all_0_6_6) = all_0_5_5 & empty(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(empty_set) = 0 & powerset(empty_set) = all_0_9_9 & singleton(empty_set) = all_0_9_9 & relation(all_0_0_0) = 0 & relation(all_0_8_8) = 0 & subset(all_0_8_8, all_0_5_5) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (relation(v2) = v7 & ordered_pair(v0, v1) = v8 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [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 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (relation(v2) = v7 & ordered_pair(v0, v1) = v8 & in(v8, v2) = v9 & ( ~ (v9 = 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 | ~ (subset_difference(v0, v1, v2) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v0) = v3) | ? [v6] : ? [v7] : (element(v2, v3) = v7 & element(v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 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] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (subset(v1, v4) = v5) | ? [v6] : ? [v7] : (disjoint(v1, v3) = v7 & element(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [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 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (meet_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5)) & ! [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] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (union_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = 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 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5)) & ! [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 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2)) & ! [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 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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 | ~ (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 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [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] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4)) & ! [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(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (powerset(v0) = v3) | ? [v4] : (subset_difference(v0, v1, v2) = v4 & set_difference(v1, v2) = v4)) & ! [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] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4)) & ! [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 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(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] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(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] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = 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] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0))) & ! [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] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [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] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | (v6 = 0 & ~ (v7 = 0) & in(v5, v1) = 0 & in(v3, v5) = v7)) & (v4 = 0 | ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v1) = v10))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0))))) & ? [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 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 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 | ~ (cast_to_subset(v0) = 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 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = 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] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [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 | ~ (set_meet(empty_set) = v0)) & ! [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)
% 102.58/55.84 |
% 102.58/55.84 | Applying alpha-rule on (1) yields:
% 102.58/55.84 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 102.58/55.85 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 102.58/55.85 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 102.58/55.85 | (5) ! [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))))
% 102.58/55.85 | (6) ? [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)))
% 102.58/55.85 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 102.58/55.85 | (8) relation_rng(all_0_8_8) = all_0_6_6
% 102.58/55.85 | (9) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 102.58/55.85 | (10) empty(all_0_0_0) = 0
% 102.58/55.85 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (subset(v1, v4) = v5) | ? [v6] : ? [v7] : (disjoint(v1, v3) = v7 & element(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0)))))
% 102.58/55.85 | (12) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 102.58/55.85 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 102.58/55.85 | (14) ! [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))
% 102.58/55.85 | (15) ! [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)))))
% 102.58/55.85 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (meet_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5))
% 102.58/55.85 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5))
% 102.58/55.85 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 102.58/55.85 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 102.58/55.85 | (20) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 102.58/55.85 | (21) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 102.58/55.85 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 102.58/55.85 | (23) ! [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)))))
% 102.58/55.85 | (24) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0)))))
% 102.58/55.85 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 102.58/55.85 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (relation(v2) = v7 & ordered_pair(v0, v1) = v8 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0))))
% 102.58/55.86 | (27) relation_dom(all_0_8_8) = all_0_7_7
% 102.58/55.86 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 102.58/55.86 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 102.58/55.86 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 102.58/55.86 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset_difference(v0, v1, v2) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v0) = v3) | ? [v6] : ? [v7] : (element(v2, v3) = v7 & element(v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 102.58/55.86 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 102.58/55.86 | (33) ~ (all_0_2_2 = 0)
% 102.58/55.86 | (34) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 102.58/55.86 | (35) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 102.58/55.86 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 102.58/55.86 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 102.58/55.86 | (38) empty(all_0_3_3) = all_0_2_2
% 102.58/55.86 | (39) singleton(empty_set) = all_0_9_9
% 102.58/55.86 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 102.58/55.86 | (41) ! [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)))))
% 102.58/55.86 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 102.58/55.86 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 102.58/55.86 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 102.58/55.86 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4))
% 102.58/55.86 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0)
% 102.58/55.86 | (47) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 102.58/55.86 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 102.58/55.86 | (49) ? [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))))
% 102.58/55.86 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 102.58/55.86 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 102.58/55.86 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 102.58/55.86 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 102.58/55.86 | (54) ! [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))
% 102.58/55.86 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 102.58/55.86 | (56) ! [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))))
% 102.58/55.86 | (57) ! [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))
% 102.58/55.86 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 102.58/55.87 | (59) relation(all_0_8_8) = 0
% 102.58/55.87 | (60) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 102.58/55.87 | (61) ! [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)))))
% 102.58/55.87 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 102.58/55.87 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 102.58/55.87 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 102.58/55.87 | (65) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 102.58/55.87 | (66) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 102.58/55.87 | (67) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 102.58/55.87 | (68) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 102.58/55.87 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 102.58/55.87 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 102.58/55.87 | (71) ! [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)))
% 102.58/55.87 | (72) ! [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))
% 102.58/55.87 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 102.58/55.87 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 102.58/55.87 | (75) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 102.58/55.87 | (76) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 102.58/55.87 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 102.58/55.87 | (78) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 102.58/55.87 | (79) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 102.58/55.87 | (80) ! [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))))
% 102.58/55.87 | (81) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 102.58/55.87 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 102.58/55.87 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (relation(v2) = v7 & ordered_pair(v0, v1) = v8 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0))))
% 102.58/55.87 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 102.58/55.87 | (85) empty(all_0_1_1) = 0
% 102.58/55.87 | (86) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 102.58/55.87 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 102.58/55.87 | (88) ! [v0] : ~ (in(v0, empty_set) = 0)
% 102.58/55.87 | (89) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 102.58/55.88 | (90) ! [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))))
% 102.58/55.88 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4))
% 102.58/55.88 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0))
% 102.58/55.88 | (93) ! [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))
% 102.58/55.88 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 102.58/55.88 | (95) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 102.58/55.88 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (union_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4)))
% 102.58/55.88 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4)))
% 102.58/55.88 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0)))
% 102.58/55.88 | (99) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 102.58/55.88 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 102.58/55.88 | (101) ! [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))
% 102.58/55.88 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 102.58/55.88 | (103) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 102.58/55.88 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 102.58/55.88 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 102.58/55.88 | (106) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 102.58/55.88 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5))
% 102.58/55.88 | (108) ! [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))
% 102.58/55.88 | (109) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 102.58/55.88 | (110) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 102.58/55.88 | (111) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 102.58/55.88 | (112) ! [v0] : ~ (singleton(v0) = empty_set)
% 102.58/55.88 | (113) ? [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))))
% 102.58/55.89 | (114) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 102.58/55.89 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 102.58/55.89 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 102.58/55.89 | (117) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2)))
% 102.58/55.89 | (118) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 102.58/55.89 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 102.58/55.89 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 102.58/55.89 | (121) ! [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))
% 102.58/55.89 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 102.58/55.89 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4))
% 102.58/55.89 | (124) ! [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)))
% 102.58/55.89 | (125) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 102.58/55.89 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 102.58/55.89 | (127) ? [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)))
% 102.58/55.89 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 102.58/55.89 | (129) ! [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)))
% 102.58/55.89 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 102.58/55.89 | (131) ! [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))))
% 102.58/55.89 | (132) ? [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))))
% 102.58/55.89 | (133) ! [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))
% 102.58/55.89 | (134) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 102.58/55.89 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 102.58/55.89 | (136) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 102.58/55.89 | (137) ~ (all_0_4_4 = 0)
% 102.58/55.89 | (138) subset(all_0_8_8, all_0_5_5) = all_0_4_4
% 102.58/55.89 | (139) ? [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))))
% 102.58/55.89 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2))
% 102.58/55.90 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 102.58/55.90 | (142) ? [v0] : ? [v1] : element(v1, v0) = 0
% 102.58/55.90 | (143) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 102.58/55.90 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 102.58/55.90 | (145) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 102.58/55.90 | (146) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 102.58/55.90 | (147) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0)))))
% 102.58/55.90 | (148) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 102.58/55.90 | (149) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 102.58/55.90 | (150) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 102.58/55.90 | (151) ? [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)))))
% 102.58/55.90 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 102.58/55.90 | (153) cartesian_product2(all_0_7_7, all_0_6_6) = all_0_5_5
% 102.58/55.90 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 102.58/55.90 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 102.58/55.90 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 102.58/55.90 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 102.58/55.90 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (powerset(v0) = v3) | ? [v4] : (subset_difference(v0, v1, v2) = v4 & set_difference(v1, v2) = v4))
% 102.58/55.90 | (159) powerset(empty_set) = all_0_9_9
% 102.58/55.90 | (160) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 102.58/55.90 | (161) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 102.58/55.90 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 102.58/55.90 | (163) ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 102.58/55.90 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 102.58/55.90 | (165) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 102.58/55.90 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 102.58/55.90 | (167) relation(all_0_0_0) = 0
% 102.58/55.90 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 102.58/55.90 | (169) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 102.58/55.90 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 102.58/55.90 | (171) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 102.58/55.91 | (172) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 102.58/55.91 | (173) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | (v6 = 0 & ~ (v7 = 0) & in(v5, v1) = 0 & in(v3, v5) = v7)) & (v4 = 0 | ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v1) = v10)))))
% 102.58/55.91 | (174) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 102.58/55.91 | (175) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 102.58/55.91 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 102.58/55.91 | (177) ! [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))
% 102.58/55.91 | (178) ! [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))
% 102.58/55.91 | (179) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & powerset(v0) = v2))
% 102.58/55.91 | (180) ! [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))
% 102.58/55.91 | (181) ? [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))))
% 102.58/55.91 | (182) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 102.58/55.91 | (183) ! [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)))
% 102.58/55.91 | (184) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 102.58/55.91 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 102.58/55.91 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 102.58/55.91 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 102.58/55.91 | (188) ? [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)))
% 102.58/55.91 | (189) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5))
% 102.88/55.91 | (190) ! [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))))
% 102.88/55.91 | (191) empty(empty_set) = 0
% 102.88/55.91 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 102.88/55.91 | (193) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 102.88/55.91 | (194) ! [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))))
% 102.88/55.91 | (195) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 102.88/55.91 | (196) ! [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))
% 102.88/55.92 | (197) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 102.88/55.92 | (198) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 102.88/55.92 | (199) ! [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))))
% 102.88/55.92 | (200) ! [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)))))
% 102.88/55.92 | (201) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 102.88/55.92 | (202) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 102.88/55.92 | (203) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 102.88/55.92 |
% 102.88/55.92 | Instantiating formula (175) with all_0_4_4, all_0_5_5, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_5_5) = all_0_4_4, yields:
% 102.88/55.92 | (204) all_0_4_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_8_8) = 0)
% 102.88/55.92 |
% 102.88/55.92 +-Applying beta-rule and splitting (204), into two cases.
% 102.88/55.92 |-Branch one:
% 102.88/55.92 | (205) all_0_4_4 = 0
% 102.88/55.92 |
% 102.88/55.92 | Equations (205) can reduce 137 to:
% 102.88/55.92 | (206) $false
% 102.88/55.92 |
% 102.88/55.92 |-The branch is then unsatisfiable
% 102.88/55.92 |-Branch two:
% 102.88/55.92 | (137) ~ (all_0_4_4 = 0)
% 102.88/55.92 | (208) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = v1 & in(v0, all_0_8_8) = 0)
% 102.88/55.92 |
% 102.88/55.92 | Instantiating (208) with all_85_0_43, all_85_1_44 yields:
% 102.88/55.92 | (209) ~ (all_85_0_43 = 0) & in(all_85_1_44, all_0_5_5) = all_85_0_43 & in(all_85_1_44, all_0_8_8) = 0
% 102.88/55.92 |
% 102.88/55.92 | Applying alpha-rule on (209) yields:
% 102.88/55.92 | (210) ~ (all_85_0_43 = 0)
% 102.88/55.92 | (211) in(all_85_1_44, all_0_5_5) = all_85_0_43
% 102.88/55.92 | (212) in(all_85_1_44, all_0_8_8) = 0
% 102.88/55.92 |
% 102.88/55.92 | Instantiating formula (163) with all_85_1_44, all_0_8_8 and discharging atoms relation(all_0_8_8) = 0, in(all_85_1_44, all_0_8_8) = 0, yields:
% 102.88/55.92 | (213) ? [v0] : ? [v1] : ordered_pair(v0, v1) = all_85_1_44
% 102.88/55.92 |
% 102.88/55.92 | Instantiating (213) with all_137_0_67, all_137_1_68 yields:
% 102.88/55.92 | (214) ordered_pair(all_137_1_68, all_137_0_67) = all_85_1_44
% 102.88/55.92 |
% 102.88/55.92 | Instantiating formula (131) with all_85_0_43, all_0_5_5, all_85_1_44, all_0_6_6, all_0_7_7, all_137_0_67, all_137_1_68 and discharging atoms cartesian_product2(all_0_7_7, all_0_6_6) = all_0_5_5, ordered_pair(all_137_1_68, all_137_0_67) = all_85_1_44, in(all_85_1_44, all_0_5_5) = all_85_0_43, yields:
% 102.88/55.92 | (215) all_85_0_43 = 0 | ? [v0] : ? [v1] : (in(all_137_0_67, all_0_6_6) = v1 & in(all_137_1_68, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 102.88/55.92 |
% 102.88/55.92 +-Applying beta-rule and splitting (215), into two cases.
% 102.88/55.92 |-Branch one:
% 102.88/55.92 | (216) all_85_0_43 = 0
% 102.88/55.92 |
% 102.88/55.92 | Equations (216) can reduce 210 to:
% 102.88/55.92 | (206) $false
% 102.88/55.92 |
% 102.88/55.92 |-The branch is then unsatisfiable
% 102.88/55.92 |-Branch two:
% 102.88/55.93 | (210) ~ (all_85_0_43 = 0)
% 102.88/55.93 | (219) ? [v0] : ? [v1] : (in(all_137_0_67, all_0_6_6) = v1 & in(all_137_1_68, all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 102.88/55.93 |
% 102.88/55.93 | Instantiating (219) with all_480_0_188, all_480_1_189 yields:
% 102.88/55.93 | (220) in(all_137_0_67, all_0_6_6) = all_480_0_188 & in(all_137_1_68, all_0_7_7) = all_480_1_189 & ( ~ (all_480_0_188 = 0) | ~ (all_480_1_189 = 0))
% 102.88/55.93 |
% 102.88/55.93 | Applying alpha-rule on (220) yields:
% 102.88/55.93 | (221) in(all_137_0_67, all_0_6_6) = all_480_0_188
% 102.88/55.93 | (222) in(all_137_1_68, all_0_7_7) = all_480_1_189
% 102.88/55.93 | (223) ~ (all_480_0_188 = 0) | ~ (all_480_1_189 = 0)
% 102.88/55.93 |
% 102.88/55.93 | Instantiating formula (202) with all_85_1_44, all_137_1_68, all_480_0_188, all_137_0_67, all_0_6_6, all_0_8_8 and discharging atoms relation_rng(all_0_8_8) = all_0_6_6, ordered_pair(all_137_1_68, all_137_0_67) = all_85_1_44, in(all_137_0_67, all_0_6_6) = all_480_0_188, in(all_85_1_44, all_0_8_8) = 0, yields:
% 102.88/55.93 | (224) all_480_0_188 = 0 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_8_8) = v0)
% 102.88/55.93 |
% 102.88/55.93 | Instantiating formula (26) with all_480_0_188, all_0_6_6, all_480_1_189, all_0_7_7, all_0_8_8, all_137_0_67, all_137_1_68 and discharging atoms relation_rng(all_0_8_8) = all_0_6_6, relation_dom(all_0_8_8) = all_0_7_7, in(all_137_0_67, all_0_6_6) = all_480_0_188, in(all_137_1_68, all_0_7_7) = all_480_1_189, yields:
% 102.88/55.93 | (225) all_480_1_189 = 0 | ? [v0] : ? [v1] : ? [v2] : (relation(all_0_8_8) = v0 & ordered_pair(all_137_1_68, all_137_0_67) = v1 & in(v1, all_0_8_8) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 102.88/55.93 |
% 102.88/55.93 | Instantiating formula (120) with all_85_1_44, all_137_0_67, all_480_1_189, all_137_1_68, all_0_7_7, all_0_8_8 and discharging atoms relation_dom(all_0_8_8) = all_0_7_7, ordered_pair(all_137_1_68, all_137_0_67) = all_85_1_44, in(all_137_1_68, all_0_7_7) = all_480_1_189, in(all_85_1_44, all_0_8_8) = 0, yields:
% 102.88/55.93 | (226) all_480_1_189 = 0 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_8_8) = v0)
% 102.88/55.93 |
% 102.88/55.93 +-Applying beta-rule and splitting (225), into two cases.
% 102.88/55.93 |-Branch one:
% 102.88/55.93 | (227) all_480_1_189 = 0
% 102.88/55.93 |
% 102.88/55.93 +-Applying beta-rule and splitting (223), into two cases.
% 102.88/55.93 |-Branch one:
% 102.88/55.93 | (228) ~ (all_480_0_188 = 0)
% 102.88/55.93 |
% 102.88/55.93 +-Applying beta-rule and splitting (224), into two cases.
% 102.88/55.93 |-Branch one:
% 102.88/55.93 | (229) all_480_0_188 = 0
% 102.88/55.93 |
% 102.88/55.93 | Equations (229) can reduce 228 to:
% 102.88/55.93 | (206) $false
% 102.88/55.93 |
% 102.88/55.93 |-The branch is then unsatisfiable
% 102.88/55.93 |-Branch two:
% 102.88/55.93 | (228) ~ (all_480_0_188 = 0)
% 102.88/55.93 | (232) ? [v0] : ( ~ (v0 = 0) & relation(all_0_8_8) = v0)
% 102.88/55.93 |
% 102.88/55.93 | Instantiating (232) with all_2593_0_611 yields:
% 102.88/55.93 | (233) ~ (all_2593_0_611 = 0) & relation(all_0_8_8) = all_2593_0_611
% 102.88/55.93 |
% 102.88/55.93 | Applying alpha-rule on (233) yields:
% 102.88/55.93 | (234) ~ (all_2593_0_611 = 0)
% 102.88/55.93 | (235) relation(all_0_8_8) = all_2593_0_611
% 102.88/55.93 |
% 102.88/55.93 | Instantiating formula (86) with all_0_8_8, all_2593_0_611, 0 and discharging atoms relation(all_0_8_8) = all_2593_0_611, relation(all_0_8_8) = 0, yields:
% 102.88/55.93 | (236) all_2593_0_611 = 0
% 102.88/55.93 |
% 102.88/55.93 | Equations (236) can reduce 234 to:
% 102.88/55.93 | (206) $false
% 102.88/55.93 |
% 102.88/55.93 |-The branch is then unsatisfiable
% 102.88/55.93 |-Branch two:
% 102.88/55.93 | (229) all_480_0_188 = 0
% 102.88/55.93 | (239) ~ (all_480_1_189 = 0)
% 102.88/55.93 |
% 102.88/55.93 | Equations (227) can reduce 239 to:
% 102.88/55.93 | (206) $false
% 102.88/55.93 |
% 102.88/55.93 |-The branch is then unsatisfiable
% 102.88/55.93 |-Branch two:
% 102.88/55.93 | (239) ~ (all_480_1_189 = 0)
% 102.88/55.93 | (242) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_8_8) = v0 & ordered_pair(all_137_1_68, all_137_0_67) = v1 & in(v1, all_0_8_8) = v2 & ( ~ (v2 = 0) | ~ (v0 = 0)))
% 102.88/55.93 |
% 102.88/55.93 +-Applying beta-rule and splitting (226), into two cases.
% 102.88/55.93 |-Branch one:
% 102.88/55.93 | (227) all_480_1_189 = 0
% 102.88/55.93 |
% 102.88/55.93 | Equations (227) can reduce 239 to:
% 102.88/55.93 | (206) $false
% 102.88/55.93 |
% 102.88/55.93 |-The branch is then unsatisfiable
% 102.88/55.93 |-Branch two:
% 102.88/55.93 | (239) ~ (all_480_1_189 = 0)
% 102.88/55.93 | (232) ? [v0] : ( ~ (v0 = 0) & relation(all_0_8_8) = v0)
% 102.88/55.93 |
% 102.88/55.93 | Instantiating (232) with all_2537_0_653 yields:
% 102.88/55.93 | (247) ~ (all_2537_0_653 = 0) & relation(all_0_8_8) = all_2537_0_653
% 102.88/55.93 |
% 102.88/55.93 | Applying alpha-rule on (247) yields:
% 102.88/55.93 | (248) ~ (all_2537_0_653 = 0)
% 102.88/55.93 | (249) relation(all_0_8_8) = all_2537_0_653
% 102.88/55.93 |
% 102.88/55.93 | Instantiating formula (86) with all_0_8_8, all_2537_0_653, 0 and discharging atoms relation(all_0_8_8) = all_2537_0_653, relation(all_0_8_8) = 0, yields:
% 102.88/55.93 | (250) all_2537_0_653 = 0
% 102.88/55.93 |
% 102.88/55.93 | Equations (250) can reduce 248 to:
% 102.88/55.93 | (206) $false
% 102.88/55.93 |
% 102.88/55.93 |-The branch is then unsatisfiable
% 102.88/55.93 % SZS output end Proof for theBenchmark
% 102.88/55.93
% 102.88/55.93 55361ms
%------------------------------------------------------------------------------