TSTP Solution File: SEU182+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU182+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.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 08:47:24 EDT 2022
% Result : Theorem 41.35s 11.74s
% Output : Proof 104.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU182+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sun Jun 19 12:58:47 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.52/0.60 ____ _
% 0.52/0.60 ___ / __ \_____(_)___ ________ __________
% 0.52/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.52/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.52/0.60
% 0.52/0.60 A Theorem Prover for First-Order Logic
% 0.52/0.60 (ePrincess v.1.0)
% 0.52/0.60
% 0.52/0.60 (c) Philipp Rümmer, 2009-2015
% 0.52/0.60 (c) Peter Backeman, 2014-2015
% 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.60 Bug reports to peter@backeman.se
% 0.52/0.60
% 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.60
% 0.52/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.25/1.11 Prover 0: Preprocessing ...
% 5.32/1.79 Prover 0: Warning: ignoring some quantifiers
% 5.55/1.84 Prover 0: Constructing countermodel ...
% 22.74/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 23.40/6.07 Prover 1: Preprocessing ...
% 25.12/6.49 Prover 1: Warning: ignoring some quantifiers
% 25.12/6.51 Prover 1: Constructing countermodel ...
% 33.18/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 33.18/8.61 Prover 2: Preprocessing ...
% 34.82/8.94 Prover 2: Warning: ignoring some quantifiers
% 34.82/8.95 Prover 2: Constructing countermodel ...
% 41.27/11.60 Prover 0: stopped
% 41.35/11.74 Prover 1: proved (3132ms)
% 41.35/11.74 Prover 2: stopped
% 41.35/11.74
% 41.35/11.74 No countermodel exists, formula is valid
% 41.35/11.74 % SZS status Theorem for theBenchmark
% 41.35/11.74
% 41.35/11.74 Generating proof ... Warning: ignoring some quantifiers
% 103.43/53.75 found it (size 110)
% 103.43/53.75
% 103.43/53.75 % SZS output start Proof for theBenchmark
% 103.43/53.75 Assumed formulas after preprocessing and simplification:
% 103.43/53.75 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v8 = 0) & ~ (v6 = 0) & relation_composition(v1, v3) = v4 & relation_dom(v4) = v5 & relation_dom(v1) = v2 & empty(v10) = 0 & empty(v9) = 0 & empty(v7) = v8 & empty(empty_set) = 0 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation(v10) = 0 & relation(v3) = 0 & relation(v1) = 0 & subset(v5, v2) = v6 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = 0 | ~ (relation_composition(v11, v12) = v13) | ~ (relation(v13) = 0) | ~ (relation(v11) = 0) | ~ (ordered_pair(v14, v18) = v19) | ~ (ordered_pair(v14, v15) = v16) | ~ (in(v19, v11) = 0) | ~ (in(v16, v13) = v17) | ? [v20] : ? [v21] : (( ~ (v21 = 0) & ordered_pair(v18, v15) = v20 & in(v20, v12) = v21) | ( ~ (v20 = 0) & relation(v12) = v20))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_rng(v13) = v16) | ~ (relation_dom(v13) = v14) | ~ (in(v12, v16) = v17) | ~ (in(v11, v14) = v15) | ? [v18] : ? [v19] : ? [v20] : (relation(v13) = v18 & ordered_pair(v11, v12) = v19 & in(v19, v13) = v20 & ( ~ (v20 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ (in(v15, v16) = v17) | ? [v18] : ? [v19] : (in(v12, v14) = v19 & in(v11, v13) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (cartesian_product2(v12, v14) = v16) | ~ (cartesian_product2(v11, v13) = v15) | ~ (subset(v15, v16) = v17) | ? [v18] : ? [v19] : (subset(v13, v14) = v19 & subset(v11, v12) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (relation_rng(v13) = v16) | ~ (relation_dom(v13) = v14) | ~ (in(v12, v16) = v17) | ~ (in(v11, v14) = v15) | ? [v18] : ? [v19] : ? [v20] : (relation(v13) = v18 & ordered_pair(v11, v12) = v19 & in(v19, v13) = v20 & ( ~ (v20 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (cartesian_product2(v11, v12) = v13) | ~ (ordered_pair(v16, v17) = v14) | ~ (in(v14, v13) = v15) | ? [v18] : ? [v19] : (in(v17, v12) = v19 & in(v16, v11) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset_difference(v11, v12, v13) = v15) | ~ (element(v15, v14) = v16) | ~ (powerset(v11) = v14) | ? [v17] : ? [v18] : (element(v13, v14) = v18 & element(v12, v14) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (complements_of_subsets(v11, v12) = v15) | ~ (element(v15, v14) = v16) | ~ (powerset(v13) = v14) | ~ (powerset(v11) = v13) | ? [v17] : ( ~ (v17 = 0) & element(v12, v14) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relation_inverse(v11) = v12) | ~ (relation(v12) = 0) | ~ (ordered_pair(v13, v14) = v15) | ~ (in(v15, v12) = v16) | ? [v17] : ? [v18] : (( ~ (v18 = 0) & ordered_pair(v14, v13) = v17 & in(v17, v11) = v18) | ( ~ (v17 = 0) & relation(v11) = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relation_field(v13) = v14) | ~ (in(v12, v14) = v16) | ~ (in(v11, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : (relation(v13) = v17 & ordered_pair(v11, v12) = v18 & in(v18, v13) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (set_difference(v12, v14) = v15) | ~ (singleton(v13) = v14) | ~ (subset(v11, v15) = v16) | ? [v17] : ? [v18] : (subset(v11, v12) = v17 & in(v13, v11) = v18 & ( ~ (v17 = 0) | v18 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (set_difference(v12, v13) = v15) | ~ (set_difference(v11, v13) = v14) | ~ (subset(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & subset(v11, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v14, v15) = v16) | ~ (set_intersection2(v12, v13) = v15) | ~ (set_intersection2(v11, v13) = v14) | ? [v17] : ( ~ (v17 = 0) & subset(v11, v12) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (relation_field(v13) = v14) | ~ (in(v12, v14) = v16) | ~ (in(v11, v14) = v15) | ? [v17] : ? [v18] : ? [v19] : (relation(v13) = v17 & ordered_pair(v11, v12) = v18 & in(v18, v13) = v19 & ( ~ (v19 = 0) | ~ (v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = 0 | ~ (relation_rng(v11) = v12) | ~ (ordered_pair(v15, v13) = v16) | ~ (in(v16, v11) = 0) | ~ (in(v13, v12) = v14) | ? [v17] : ( ~ (v17 = 0) & relation(v11) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = 0 | ~ (relation_dom(v11) = v12) | ~ (ordered_pair(v13, v15) = v16) | ~ (in(v16, v11) = 0) | ~ (in(v13, v12) = v14) | ? [v17] : ( ~ (v17 = 0) & relation(v11) = v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v11, v12) = v13) | ~ (relation(v13) = 0) | ~ (relation(v11) = 0) | ~ (ordered_pair(v14, v15) = v16) | ~ (in(v16, v13) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v21 = 0 & v19 = 0 & ordered_pair(v17, v15) = v20 & ordered_pair(v14, v17) = v18 & in(v20, v12) = 0 & in(v18, v11) = 0) | ( ~ (v17 = 0) & relation(v12) = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (subset_complement(v11, v14) = v15) | ~ (element(v12, v13) = 0) | ~ (powerset(v11) = v13) | ~ (subset(v12, v15) = v16) | ? [v17] : ? [v18] : (disjoint(v12, v14) = v18 & element(v14, v13) = v17 & ( ~ (v17 = 0) | (( ~ (v18 = 0) | v16 = 0) & ( ~ (v16 = 0) | v18 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ (in(v15, v16) = 0) | (in(v12, v14) = 0 & in(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (cartesian_product2(v11, v13) = v14) | ~ (subset(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (cartesian_product2(v13, v12) = v19 & cartesian_product2(v13, v11) = v18 & subset(v18, v19) = v20 & subset(v11, v12) = v17 & ( ~ (v17 = 0) | (v20 = 0 & v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v11 = empty_set | ~ (set_meet(v11) = v12) | ~ (in(v13, v14) = v15) | ~ (in(v13, v12) = 0) | ? [v16] : ( ~ (v16 = 0) & in(v14, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (meet_of_subsets(v11, v12) = v14) | ~ (element(v14, v13) = v15) | ~ (powerset(v11) = v13) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & element(v12, v16) = v17 & powerset(v13) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (union_of_subsets(v11, v12) = v14) | ~ (element(v14, v13) = v15) | ~ (powerset(v11) = v13) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & element(v12, v16) = v17 & powerset(v13) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset_complement(v11, v12) = v14) | ~ (element(v14, v13) = v15) | ~ (powerset(v11) = v13) | ? [v16] : ( ~ (v16 = 0) & element(v12, v13) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (relation_rng(v11) = v13) | ~ (relation_dom(v11) = v12) | ~ (cartesian_product2(v12, v13) = v14) | ~ (subset(v11, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & relation(v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v12, v14) = 0) | ~ (element(v11, v13) = v15) | ~ (powerset(v13) = v14) | ? [v16] : ( ~ (v16 = 0) & in(v11, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v12, v13) = 0) | ~ (powerset(v11) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v14, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v13) = v15) | ~ (unordered_pair(v11, v12) = v14) | ? [v16] : ? [v17] : (in(v12, v13) = v17 & in(v11, v13) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v12) = v15) | ~ (set_union2(v11, v13) = v14) | ? [v16] : ? [v17] : (subset(v13, v12) = v17 & subset(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v11, v14) = v15) | ~ (set_intersection2(v12, v13) = v14) | ? [v16] : ? [v17] : (subset(v11, v13) = v17 & subset(v11, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v12 | ~ (ordered_pair(v13, v14) = v15) | ~ (ordered_pair(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v11 | v13 = v11 | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = 0 | ~ (union(v11) = v12) | ~ (in(v13, v15) = 0) | ~ (in(v13, v12) = v14) | ? [v16] : ( ~ (v16 = 0) & in(v15, v11) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v11 | ~ (ordered_pair(v13, v14) = v15) | ~ (ordered_pair(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (subset_difference(v15, v14, v13) = v12) | ~ (subset_difference(v15, v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = empty_set | ~ (subset_difference(v11, v13, v14) = v15) | ~ (meet_of_subsets(v11, v12) = v14) | ~ (cast_to_subset(v11) = v13) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (union_of_subsets(v11, v19) = v20 & complements_of_subsets(v11, v12) = v19 & element(v12, v17) = v18 & powerset(v16) = v17 & powerset(v11) = v16 & ( ~ (v18 = 0) | v20 = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = empty_set | ~ (subset_difference(v11, v13, v14) = v15) | ~ (union_of_subsets(v11, v12) = v14) | ~ (cast_to_subset(v11) = v13) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (meet_of_subsets(v11, v19) = v20 & complements_of_subsets(v11, v12) = v19 & element(v12, v17) = v18 & powerset(v16) = v17 & powerset(v11) = v16 & ( ~ (v18 = 0) | v20 = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse(v11) = v12) | ~ (relation(v12) = 0) | ~ (ordered_pair(v13, v14) = v15) | ~ (in(v15, v12) = 0) | ? [v16] : ? [v17] : ((v17 = 0 & ordered_pair(v14, v13) = v16 & in(v16, v11) = 0) | ( ~ (v16 = 0) & relation(v11) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | (v15 = 0 & ~ (v17 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (singleton(v11) = v14) | ~ (unordered_pair(v13, v14) = v15) | ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | (v17 = 0 & v15 = 0)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v11, v12) = v13) | ~ (in(v14, v11) = v15) | ? [v16] : ? [v17] : (in(v14, v13) = v17 & in(v14, v12) = v16 & (v17 = 0 | ( ~ (v16 = 0) & ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_composition(v11, v12) = v13) | ~ (relation(v14) = 0) | ~ (relation(v11) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (( ~ (v15 = 0) & relation(v12) = v15) | (ordered_pair(v15, v16) = v17 & in(v17, v14) = v18 & ( ~ (v18 = 0) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v15, v24) = v25) | ~ (in(v25, v11) = 0) | ? [v26] : ? [v27] : ( ~ (v27 = 0) & ordered_pair(v24, v16) = v26 & in(v26, v12) = v27))) & (v18 = 0 | (v23 = 0 & v21 = 0 & ordered_pair(v19, v16) = v22 & ordered_pair(v15, v19) = v20 & in(v22, v12) = 0 & in(v20, v11) = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | v14 = v11 | ~ (unordered_pair(v11, v12) = v13) | ~ (in(v14, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (subset_complement(v11, v13) = v14) | ~ (subset_complement(v11, v12) = v13) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & element(v12, v15) = v16 & powerset(v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v11) = v13) | ~ (set_union2(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_difference(v11, v13) = v14) | ~ (singleton(v12) = v13) | in(v12, v11) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v11 = empty_set | ~ (set_meet(v11) = v12) | ~ (in(v13, v12) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v11) = 0 & in(v13, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v13, v12) = v14) | ~ (singleton(v11) = v13) | in(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = 0) | ~ (disjoint(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (set_difference(v11, v12) = v13) | ~ (subset(v13, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (union(v12) = v13) | ~ (subset(v11, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (cast_to_subset(v11) = v12) | ~ (element(v12, v13) = v14) | ~ (powerset(v11) = v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v11, v13) = v14) | ~ (powerset(v12) = v13) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v12) = v16 & in(v15, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v11, v13) = v14) | ~ (powerset(v12) = v13) | ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (powerset(v11) = v12) | ~ (subset(v13, v11) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (singleton(v11) = v13) | ~ (subset(v13, v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v13, v11) = v14) | ~ (set_intersection2(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v13) = v14) | ~ (subset(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v11, v13) = v14) | ~ (set_union2(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v11, v12) = v13) | ~ (in(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (unordered_pair(v11, v12) = v13) | ~ (in(v11, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v11) = v14) | ~ (unordered_pair(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (are_equipotent(v14, v13) = v12) | ~ (are_equipotent(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (meet_of_subsets(v14, v13) = v12) | ~ (meet_of_subsets(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (union_of_subsets(v14, v13) = v12) | ~ (union_of_subsets(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (complements_of_subsets(v14, v13) = v12) | ~ (complements_of_subsets(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_composition(v14, v13) = v12) | ~ (relation_composition(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (disjoint(v14, v13) = v12) | ~ (disjoint(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset_complement(v14, v13) = v12) | ~ (subset_complement(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_difference(v14, v13) = v12) | ~ (set_difference(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (cartesian_product2(v14, v13) = v12) | ~ (cartesian_product2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (element(v14, v13) = v12) | ~ (element(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (singleton(v12) = v14) | ~ (singleton(v11) = v13) | ~ (subset(v13, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (singleton(v11) = v14) | ~ (unordered_pair(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (subset(v14, v13) = v12) | ~ (subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_intersection2(v14, v13) = v12) | ~ (set_intersection2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (set_union2(v14, v13) = v12) | ~ (set_union2(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (unordered_pair(v14, v13) = v12) | ~ (unordered_pair(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (proper_subset(v14, v13) = v12) | ~ (proper_subset(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (in(v14, v13) = v12) | ~ (in(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = empty_set | ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | ~ (powerset(v11) = v13) | ? [v15] : ( ~ (v15 = empty_set) & complements_of_subsets(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v11) = v13) | ~ (relation_dom(v11) = v12) | ~ (set_union2(v12, v13) = v14) | ? [v15] : ? [v16] : (relation_field(v11) = v16 & relation(v11) = v15 & ( ~ (v15 = 0) | v16 = v14))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v13, v12) = v14) | ~ (set_union2(v11, v12) = v13) | set_difference(v11, v12) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v11, v13) = v14) | set_union2(v11, v12) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v13) = v14) | ~ (set_difference(v11, v12) = v13) | set_intersection2(v11, v12) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v12) = v13) | ~ (in(v14, v11) = 0) | ? [v15] : ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & (v16 = 0 | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : (ordered_pair(v15, v16) = v14 & in(v16, v12) = 0 & in(v15, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v13, v14) = 0) | ~ (element(v12, v14) = 0) | ~ (powerset(v11) = v14) | ? [v15] : (subset_difference(v11, v12, v13) = v15 & set_difference(v12, v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v13, v14) = 0) | ~ (powerset(v11) = v14) | ~ (in(v12, v13) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & subset_complement(v11, v13) = v15 & in(v12, v15) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | ~ (powerset(v11) = v13) | ? [v15] : (meet_of_subsets(v11, v12) = v15 & set_meet(v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | ~ (powerset(v11) = v13) | ? [v15] : (union_of_subsets(v11, v12) = v15 & union(v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | ~ (powerset(v11) = v13) | ? [v15] : (complements_of_subsets(v11, v15) = v12 & complements_of_subsets(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | ~ (powerset(v11) = v13) | ? [v15] : (complements_of_subsets(v11, v12) = v15 & ! [v16] : (v16 = v15 | ~ (element(v16, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (subset_complement(v11, v17) = v19 & element(v17, v13) = 0 & in(v19, v12) = v20 & in(v17, v16) = v18 & ( ~ (v20 = 0) | ~ (v18 = 0)) & (v20 = 0 | v18 = 0))) & ! [v16] : ( ~ (element(v16, v13) = 0) | ~ (element(v15, v14) = 0) | ? [v17] : ? [v18] : ? [v19] : (subset_complement(v11, v16) = v18 & in(v18, v12) = v19 & in(v16, v15) = v17 & ( ~ (v19 = 0) | v17 = 0) & ( ~ (v17 = 0) | v19 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | ~ (in(v11, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & empty(v13) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v14, v13) = 0) | ~ (unordered_pair(v11, v12) = v14) | (in(v12, v13) = 0 & in(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ( ~ (v15 = 0) & disjoint(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ (in(v14, v11) = 0) | ? [v15] : ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_difference(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0) | v18 = 0) & (v16 = 0 | (v17 = 0 & ~ (v18 = 0))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (cartesian_product2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (in(v15, v11) = v16 & ( ~ (v16 = 0) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v23) = v15) | ? [v24] : ? [v25] : (in(v23, v13) = v25 & in(v22, v12) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0))))) & (v16 = 0 | (v21 = v15 & v20 = 0 & v19 = 0 & ordered_pair(v17, v18) = v15 & in(v18, v13) = 0 & in(v17, v12) = 0)))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_intersection2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v18 = 0) | ~ (v17 = 0) | ~ (v16 = 0)) & (v16 = 0 | (v18 = 0 & v17 = 0)))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_union2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v16 = 0) | ( ~ (v18 = 0) & ~ (v17 = 0))) & (v18 = 0 | v17 = 0 | v16 = 0))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (unordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (in(v15, v11) = v16 & ( ~ (v16 = 0) | ( ~ (v15 = v13) & ~ (v15 = v12))) & (v16 = 0 | v15 = v13 | v15 = v12))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_inverse(v11) = v12) | ~ (relation(v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ~ (v14 = 0) & relation(v11) = v14) | (ordered_pair(v15, v14) = v18 & ordered_pair(v14, v15) = v16 & in(v18, v11) = v19 & in(v16, v13) = v17 & ( ~ (v19 = 0) | ~ (v17 = 0)) & (v19 = 0 | v17 = 0)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v11 = empty_set | ~ (singleton(v12) = v13) | ~ (subset(v11, v13) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v11) = v12) | ~ (in(v13, v12) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_difference(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & disjoint(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = v11 | ~ (proper_subset(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = v13) | ? [v14] : ( ~ (v14 = v11) & set_difference(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (disjoint(v11, v12) = v13) | ? [v14] : (in(v14, v12) = 0 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (element(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v12) = v11) | ~ (subset(v11, v11) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v11) = v12) | ~ (subset(empty_set, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (singleton(v11) = v12) | ~ (in(v11, v12) = v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_inverse(v13) = v12) | ~ (relation_inverse(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_field(v13) = v12) | ~ (relation_field(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_rng(v13) = v12) | ~ (relation_rng(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (union(v13) = v12) | ~ (union(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cast_to_subset(v13) = v12) | ~ (cast_to_subset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation_dom(v13) = v12) | ~ (relation_dom(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (empty(v13) = v12) | ~ (empty(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (powerset(v13) = v12) | ~ (powerset(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singleton(v13) = v12) | ~ (singleton(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (set_meet(v13) = v12) | ~ (set_meet(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (relation(v13) = v12) | ~ (relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v11 = empty_set | ~ (element(v13, v12) = 0) | ~ (powerset(v11) = v12) | ? [v14] : (subset_complement(v11, v13) = v14 & ! [v15] : ! [v16] : (v16 = 0 | ~ (in(v15, v14) = v16) | ? [v17] : ? [v18] : (element(v15, v11) = v17 & in(v15, v13) = v18 & ( ~ (v17 = 0) | v18 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (relation(v13) = v16 & relation(v12) = v15 & relation(v11) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v16 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (disjoint(v13, v12) = 0) | ~ (singleton(v11) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (disjoint(v11, v12) = 0) | ~ (in(v13, v11) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & ordered_pair(v14, v13) = v15 & in(v15, v11) = 0) | ( ~ (v14 = 0) & relation(v11) = v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v13) = v11) | ~ (singleton(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & in(v12, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : (in(v14, v11) = 0 & in(v13, v14) = 0)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom(v11) = v12) | ~ (in(v13, v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & ordered_pair(v13, v14) = v15 & in(v15, v11) = 0) | ( ~ (v14 = 0) & relation(v11) = v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v16 & empty(v12) = v15 & empty(v11) = v14 & ( ~ (v16 = 0) | v15 = 0 | v14 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ~ (powerset(v11) = v13) | ? [v14] : (subset_complement(v11, v12) = v14 & set_difference(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v12, v11) = v13) | ? [v14] : ? [v15] : (empty(v11) = v14 & in(v12, v11) = v15 & (v14 = 0 | (( ~ (v15 = 0) | v13 = 0) & ( ~ (v13 = 0) | v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (element(v11, v13) = 0) | ~ (powerset(v12) = v13) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (empty(v12) = v13) | ~ (empty(v11) = 0) | ? [v14] : (element(v12, v11) = v14 & ( ~ (v14 = 0) | v13 = 0) & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v11) = v12) | ~ (subset(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v13) | ~ (subset(v13, v12) = 0) | in(v11, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset(v11, v12) = 0) | ~ (in(v13, v11) = 0) | in(v13, v12) = 0) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | set_intersection2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | ? [v14] : ? [v15] : ((v15 = 0 & in(v14, v13) = 0) | (v14 = 0 & disjoint(v11, v12) = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | ? [v14] : ? [v15] : (empty(v13) = v15 & empty(v11) = v14 & ( ~ (v15 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (relation(v13) = v16 & relation(v12) = v15 & relation(v11) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0) | v16 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ? [v14] : ? [v15] : (empty(v13) = v15 & empty(v11) = v14 & ( ~ (v15 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | v12 = empty_set | ~ (set_meet(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v14, v11) = v15 & ( ~ (v15 = 0) | (v17 = 0 & ~ (v18 = 0) & in(v16, v12) = 0 & in(v14, v16) = v18)) & (v15 = 0 | ! [v19] : ! [v20] : (v20 = 0 | ~ (in(v14, v19) = v20) | ? [v21] : ( ~ (v21 = 0) & in(v19, v12) = v21))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_rng(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (( ~ (v14 = 0) & relation(v12) = v14) | (in(v14, v11) = v15 & ( ~ (v15 = 0) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v14) = v20) | ~ (in(v20, v12) = 0))) & (v15 = 0 | (v18 = 0 & ordered_pair(v16, v14) = v17 & in(v17, v12) = 0))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (union(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (in(v14, v11) = v15 & ( ~ (v15 = 0) | ! [v19] : ( ~ (in(v14, v19) = 0) | ? [v20] : ( ~ (v20 = 0) & in(v19, v12) = v20))) & (v15 = 0 | (v18 = 0 & v17 = 0 & in(v16, v12) = 0 & in(v14, v16) = 0)))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (( ~ (v14 = 0) & relation(v12) = v14) | (in(v14, v11) = v15 & ( ~ (v15 = 0) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v14, v19) = v20) | ~ (in(v20, v12) = 0))) & (v15 = 0 | (v18 = 0 & ordered_pair(v14, v16) = v17 & in(v17, v12) = 0))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (powerset(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (subset(v14, v12) = v16 & in(v14, v11) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)) & (v16 = 0 | v15 = 0))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v12) = v13) | ? [v14] : ? [v15] : (in(v14, v11) = v15 & ( ~ (v15 = 0) | ~ (v14 = v12)) & (v15 = 0 | v14 = v12))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_difference(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (cast_to_subset(v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (empty(v12) = 0) | ~ (empty(v11) = 0)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (subset(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & subset(v12, v11) = v13)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_intersection2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_union2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(empty_set, v11) = v12)) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_intersection2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (empty(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & element(v14, v13) = 0 & empty(v14) = v15 & powerset(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (relation(v11) = v12) | ? [v13] : (in(v13, v11) = 0 & ! [v14] : ! [v15] : ~ (ordered_pair(v14, v15) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(v11, v11) = v12)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (subset(empty_set, v11) = v12)) & ! [v11] : ! [v12] : ( ~ (disjoint(v11, v12) = 0) | disjoint(v12, v11) = 0) & ! [v11] : ! [v12] : ( ~ (disjoint(v11, v12) = 0) | set_difference(v11, v12) = v11) & ! [v11] : ! [v12] : ( ~ (relation_inverse(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : (relation_rng(v12) = v17 & relation_rng(v11) = v14 & relation_dom(v12) = v15 & relation_dom(v11) = v16 & relation(v11) = v13 & ( ~ (v13 = 0) | (v17 = v16 & v15 = v14)))) & ! [v11] : ! [v12] : ( ~ (relation_inverse(v11) = v12) | ? [v13] : ? [v14] : (relation_inverse(v12) = v14 & relation(v11) = v13 & ( ~ (v13 = 0) | v14 = v11))) & ! [v11] : ! [v12] : ( ~ (relation_inverse(v11) = v12) | ? [v13] : ? [v14] : (relation(v12) = v14 & relation(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ? [v13] : ? [v14] : (relation_dom(v11) = v14 & relation(v11) = v13 & ( ~ (v13 = 0) | ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v15) = v16) | ~ (subset(v12, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_dom(v15) = v20 & relation(v15) = v18 & subset(v14, v20) = v21 & subset(v11, v15) = v19 & ( ~ (v19 = 0) | ~ (v18 = 0) | (v21 = 0 & v17 = 0))))))) & ! [v11] : ! [v12] : ( ~ (set_difference(v11, v12) = empty_set) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (element(v11, v12) = 0) | ? [v13] : ? [v14] : (empty(v12) = v13 & in(v11, v12) = v14 & (v14 = 0 | v13 = 0))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | union(v12) = v11) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (relation(v11) = 0) | ~ (in(v12, v11) = 0) | ? [v13] : ? [v14] : ordered_pair(v13, v14) = v12) & ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v12) = empty_set) | disjoint(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v11) = v12) | singleton(v11) = v12) & ! [v11] : ! [v12] : ( ~ (proper_subset(v12, v11) = 0) | ? [v13] : ( ~ (v13 = 0) & subset(v11, v12) = v13)) & ! [v11] : ! [v12] : ( ~ (proper_subset(v11, v12) = 0) | subset(v11, v12) = 0) & ! [v11] : ! [v12] : ( ~ (proper_subset(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & proper_subset(v12, v11) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (in(v11, v12) = 0) | ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) & ! [v11] : (v11 = empty_set | ~ (empty(v11) = 0)) & ! [v11] : (v11 = empty_set | ~ (set_meet(empty_set) = v11)) & ! [v11] : (v11 = empty_set | ~ (subset(v11, empty_set) = 0)) & ! [v11] : ~ (singleton(v11) = empty_set) & ! [v11] : ~ (proper_subset(v11, v11) = 0) & ! [v11] : ~ (in(v11, empty_set) = 0) & ? [v11] : ? [v12] : (v12 = v11 | ? [v13] : ? [v14] : ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)) & (v15 = 0 | v14 = 0))) & ? [v11] : ? [v12] : element(v12, v11) = 0 & ? [v11] : ? [v12] : (in(v11, v12) = 0 & ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v13) = v14) | ~ (in(v14, v12) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v13, v12) = v16)) & ! [v13] : ! [v14] : (v14 = 0 | ~ (are_equipotent(v13, v12) = v14) | ? [v15] : ? [v16] : (subset(v13, v12) = v15 & in(v13, v12) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v13] : ! [v14] : ( ~ (subset(v14, v13) = 0) | ? [v15] : ? [v16] : (in(v14, v12) = v16 & in(v13, v12) = v15 & ( ~ (v15 = 0) | v16 = 0)))) & ? [v11] : ? [v12] : (in(v11, v12) = 0 & ! [v13] : ! [v14] : (v14 = 0 | ~ (are_equipotent(v13, v12) = v14) | ? [v15] : ? [v16] : (subset(v13, v12) = v15 & in(v13, v12) = v16 & ( ~ (v15 = 0) | v16 = 0))) & ! [v13] : ! [v14] : ( ~ (subset(v14, v13) = 0) | ? [v15] : ? [v16] : (in(v14, v12) = v16 & in(v13, v12) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ! [v13] : ( ~ (in(v13, v12) = 0) | ? [v14] : (in(v14, v12) = 0 & ! [v15] : ( ~ (subset(v15, v13) = 0) | in(v15, v14) = 0)))) & ? [v11] : (v11 = empty_set | ? [v12] : in(v12, v11) = 0))
% 103.84/53.86 | 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, all_0_10_10 yields:
% 103.84/53.86 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6 & relation_dom(all_0_6_6) = all_0_5_5 & relation_dom(all_0_9_9) = all_0_8_8 & 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_10_10 & singleton(empty_set) = all_0_10_10 & relation(all_0_0_0) = 0 & relation(all_0_7_7) = 0 & relation(all_0_9_9) = 0 & subset(all_0_5_5, all_0_8_8) = all_0_4_4 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9))) & ! [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 | ~ (relation_inverse(v0) = v1) | ~ (relation(v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ordered_pair(v3, v2) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & relation(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v6 & ordered_pair(v0, v1) = v7 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [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] : (v4 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v6 & ordered_pair(v0, v1) = v7 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [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] : ( ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = 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 | ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v0) = 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] : ( ~ (relation_inverse(v0) = v1) | ~ (relation(v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | ( ~ (v5 = 0) & relation(v0) = v5))) & ! [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 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v3) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ordered_pair(v13, v5) = v15 & in(v15, v1) = v16))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 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 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(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] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [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 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0)))) & ! [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_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [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] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 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] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [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] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v1) = v6 & relation_rng(v0) = v3 & relation_dom(v1) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v3)))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v9 & relation(v4) = v7 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = 0))))))) & ! [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)
% 104.31/53.92 |
% 104.31/53.92 | Applying alpha-rule on (1) yields:
% 104.31/53.92 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 104.31/53.92 | (3) ! [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))))
% 104.31/53.92 | (4) relation(all_0_7_7) = 0
% 104.31/53.92 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v0) = v5))
% 104.31/53.92 | (6) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 104.31/53.92 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 104.31/53.92 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 104.31/53.92 | (9) ! [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)))
% 104.31/53.92 | (10) ! [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))
% 104.31/53.92 | (11) ! [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))
% 104.31/53.92 | (12) powerset(empty_set) = all_0_10_10
% 104.31/53.92 | (13) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 104.31/53.92 | (14) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 104.31/53.92 | (15) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 104.31/53.92 | (16) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 104.31/53.92 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 104.31/53.92 | (18) ! [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)))))
% 104.31/53.92 | (19) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 104.31/53.92 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 104.31/53.92 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 104.31/53.92 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 104.31/53.92 | (23) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 104.31/53.92 | (24) ! [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)))
% 104.31/53.92 | (25) ! [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)))))
% 104.31/53.92 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 104.31/53.92 | (27) ! [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))
% 104.31/53.92 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 104.31/53.92 | (29) relation_dom(all_0_6_6) = all_0_5_5
% 104.31/53.92 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 104.31/53.92 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 104.31/53.92 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 104.31/53.92 | (33) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 104.31/53.92 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 104.31/53.92 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 104.31/53.92 | (36) ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 104.31/53.92 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 104.31/53.92 | (38) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & powerset(v0) = v2))
% 104.31/53.92 | (39) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 104.31/53.92 | (40) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 104.31/53.92 | (41) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0)))
% 104.31/53.93 | (42) ? [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)))))
% 104.31/53.93 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9)))
% 104.31/53.93 | (44) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 104.31/53.93 | (45) ! [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)))
% 104.31/53.93 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2)))
% 104.31/53.93 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 104.31/53.93 | (48) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 104.31/53.93 | (49) relation_dom(all_0_9_9) = all_0_8_8
% 104.31/53.93 | (50) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 104.31/53.93 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 104.31/53.93 | (52) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 104.31/53.93 | (53) ? [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))))
% 104.31/53.93 | (54) relation(all_0_9_9) = 0
% 104.31/53.93 | (55) ! [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))))
% 104.31/53.93 | (56) ! [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))
% 104.31/53.93 | (57) ! [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))))
% 104.31/53.93 | (58) relation(all_0_0_0) = 0
% 104.31/53.93 | (59) relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6
% 104.31/53.93 | (60) ! [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))))
% 104.31/53.93 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 104.31/53.93 | (62) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 104.31/53.93 | (63) ! [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))))
% 104.31/53.93 | (64) singleton(empty_set) = all_0_10_10
% 104.31/53.93 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 104.31/53.93 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 104.31/53.93 | (67) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v9 & relation(v4) = v7 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = 0)))))))
% 104.31/53.93 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 104.31/53.93 | (69) ! [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)))))
% 104.31/53.93 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 104.31/53.93 | (71) subset(all_0_5_5, all_0_8_8) = all_0_4_4
% 104.31/53.93 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 104.31/53.93 | (73) ! [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)))))
% 104.31/53.93 | (74) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 104.31/53.93 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 104.31/53.93 | (76) ! [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)))
% 104.31/53.93 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v6 & ordered_pair(v0, v1) = v7 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 104.31/53.93 | (78) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 104.31/53.93 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 104.31/53.93 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 104.31/53.93 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 104.31/53.93 | (82) ! [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)))))
% 104.31/53.93 | (83) ! [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))
% 104.31/53.93 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 104.31/53.93 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 104.31/53.93 | (86) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 104.31/53.93 | (87) ! [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)))
% 104.31/53.94 | (88) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 104.31/53.94 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 104.31/53.94 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 104.31/53.94 | (91) ! [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))
% 104.31/53.94 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 104.31/53.94 | (93) ! [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)))
% 104.31/53.94 | (94) empty(all_0_1_1) = 0
% 104.31/53.94 | (95) ! [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))
% 104.31/53.94 | (96) ? [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))))
% 104.31/53.94 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 104.31/53.94 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 104.31/53.94 | (99) ? [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))))
% 104.31/53.94 | (100) ! [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)))
% 104.31/53.94 | (101) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 104.31/53.94 | (102) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 104.31/53.94 | (103) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 104.31/53.94 | (104) ? [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)))))
% 104.31/53.94 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 104.31/53.94 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 104.31/53.94 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0))
% 104.31/53.94 | (108) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 104.31/53.94 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 104.31/53.94 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 104.31/53.94 | (111) ! [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))
% 104.31/53.94 | (112) ? [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)))
% 104.31/53.94 | (113) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 104.31/53.94 | (114) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 104.31/53.94 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v3) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ordered_pair(v13, v5) = v15 & in(v15, v1) = v16))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0)))))
% 104.31/53.94 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 104.31/53.94 | (117) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 104.31/53.94 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 104.31/53.94 | (119) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 104.31/53.94 | (120) ! [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))
% 104.31/53.94 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 104.31/53.94 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 104.31/53.94 | (123) ! [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))
% 104.31/53.94 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 104.31/53.94 | (125) ! [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))))
% 104.31/53.94 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse(v0) = v1) | ~ (relation(v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ordered_pair(v3, v2) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & relation(v0) = v6)))
% 104.31/53.94 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 104.31/53.94 | (128) ? [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)))
% 104.31/53.94 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 104.31/53.94 | (130) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v1) = v6 & relation_rng(v0) = v3 & relation_dom(v1) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v3))))
% 104.31/53.94 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0)
% 104.31/53.94 | (132) ! [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))
% 104.31/53.94 | (133) ! [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))
% 104.31/53.95 | (134) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 104.31/53.95 | (135) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 104.31/53.95 | (136) ! [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))))
% 104.31/53.95 | (137) ! [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)))
% 104.31/53.95 | (138) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 104.31/53.95 | (139) ! [v0] : ~ (in(v0, empty_set) = 0)
% 104.31/53.95 | (140) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 104.31/53.95 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0))))
% 104.31/53.95 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 104.31/53.95 | (143) ! [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))
% 104.31/53.95 | (144) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 104.31/53.95 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 104.31/53.95 | (146) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 104.31/53.95 | (147) ! [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)))))
% 104.31/53.95 | (148) empty(all_0_3_3) = all_0_2_2
% 104.31/53.95 | (149) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 104.31/53.95 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v6 & ordered_pair(v0, v1) = v7 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 104.31/53.95 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4))
% 104.31/53.95 | (152) ? [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)))
% 104.31/53.95 | (153) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 104.31/53.95 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 104.31/53.95 | (155) empty(all_0_0_0) = 0
% 104.31/53.95 | (156) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 104.31/53.95 | (157) ! [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))
% 104.31/53.95 | (158) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 104.31/53.95 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2))
% 104.31/53.95 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 104.31/53.95 | (161) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 104.31/53.95 | (162) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 104.31/53.95 | (163) ? [v0] : ? [v1] : element(v1, v0) = 0
% 104.31/53.95 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 104.31/53.95 | (165) ! [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))
% 104.31/53.95 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 104.31/53.95 | (167) ! [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))
% 104.31/53.95 | (168) ! [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))
% 104.31/53.95 | (169) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 104.31/53.95 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 104.31/53.95 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 104.31/53.95 | (172) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 104.31/53.95 | (173) ! [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)))
% 104.31/53.95 | (174) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 104.31/53.95 | (175) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 104.31/53.95 | (176) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 104.31/53.95 | (177) ! [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))
% 104.31/53.95 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6)))
% 104.31/53.95 | (179) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 104.31/53.95 | (180) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 104.31/53.95 | (181) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 104.31/53.95 | (182) ! [v0] : ~ (singleton(v0) = empty_set)
% 104.31/53.95 | (183) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 104.31/53.95 | (184) ? [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)))))
% 104.31/53.95 | (185) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 104.31/53.95 | (186) ? [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))))
% 104.31/53.95 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (relation(v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | ( ~ (v5 = 0) & relation(v0) = v5)))
% 104.31/53.96 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 104.31/53.96 | (189) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 104.31/53.96 | (190) ! [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))))
% 104.31/53.96 | (191) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 104.31/53.96 | (192) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 104.31/53.96 | (193) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 104.31/53.96 | (194) ! [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))))
% 104.31/53.96 | (195) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 104.31/53.96 | (196) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 104.31/53.96 | (197) ~ (all_0_4_4 = 0)
% 104.31/53.96 | (198) empty(empty_set) = 0
% 104.31/53.96 | (199) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 104.31/53.96 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 104.31/53.96 | (201) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 104.31/53.96 | (202) ! [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))
% 104.31/53.96 | (203) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 104.31/53.96 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 104.31/53.96 | (205) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 104.31/53.96 | (206) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 104.31/53.96 | (207) ! [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))
% 104.31/53.96 | (208) ? [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)))))
% 104.31/53.96 | (209) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 104.31/53.96 | (210) ! [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))
% 104.31/53.96 | (211) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 104.31/53.96 | (212) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 104.31/53.96 | (213) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 104.31/53.96 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 104.31/53.96 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 104.31/53.96 | (216) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 104.31/53.96 | (217) ! [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))
% 104.31/53.96 | (218) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 104.31/53.96 | (219) ~ (all_0_2_2 = 0)
% 104.31/53.96 | (220) ? [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))))
% 104.31/53.96 | (221) ! [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))))
% 104.31/53.96 | (222) ! [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))))
% 104.31/53.96 | (223) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 104.31/53.96 |
% 104.31/53.96 | Instantiating formula (149) with all_0_1_1, all_0_0_0 and discharging atoms empty(all_0_0_0) = 0, empty(all_0_1_1) = 0, yields:
% 104.31/53.96 | (224) all_0_0_0 = all_0_1_1
% 104.31/53.96 |
% 104.31/53.96 | Instantiating formula (149) with empty_set, all_0_0_0 and discharging atoms empty(all_0_0_0) = 0, empty(empty_set) = 0, yields:
% 104.31/53.96 | (225) all_0_0_0 = empty_set
% 104.31/53.96 |
% 104.31/53.96 | Combining equations (225,224) yields a new equation:
% 104.31/53.96 | (226) all_0_1_1 = empty_set
% 104.31/53.96 |
% 104.31/53.96 | Combining equations (226,224) yields a new equation:
% 104.31/53.96 | (225) all_0_0_0 = empty_set
% 104.31/53.96 |
% 104.31/53.96 | From (225) and (58) follows:
% 104.31/53.96 | (228) relation(empty_set) = 0
% 104.31/53.96 |
% 104.31/53.96 | Instantiating formula (129) with all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 104.31/53.96 | (229) ? [v0] : ? [v1] : ? [v2] : (relation(all_0_6_6) = v2 & relation(all_0_7_7) = v1 & relation(all_0_9_9) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2 = 0))
% 104.31/53.96 |
% 104.31/53.96 | Instantiating formula (40) with all_0_4_4, all_0_8_8, all_0_5_5 and discharging atoms subset(all_0_5_5, all_0_8_8) = all_0_4_4, yields:
% 104.31/53.96 | (230) all_0_4_4 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = 0 & in(v0, all_0_8_8) = v1)
% 104.31/53.96 |
% 104.31/53.96 | Instantiating (229) with all_72_0_39, all_72_1_40, all_72_2_41 yields:
% 104.31/53.96 | (231) relation(all_0_6_6) = all_72_0_39 & relation(all_0_7_7) = all_72_1_40 & relation(all_0_9_9) = all_72_2_41 & ( ~ (all_72_1_40 = 0) | ~ (all_72_2_41 = 0) | all_72_0_39 = 0)
% 104.31/53.97 |
% 104.31/53.97 | Applying alpha-rule on (231) yields:
% 104.31/53.97 | (232) relation(all_0_6_6) = all_72_0_39
% 104.31/53.97 | (233) relation(all_0_7_7) = all_72_1_40
% 104.31/53.97 | (234) relation(all_0_9_9) = all_72_2_41
% 104.31/53.97 | (235) ~ (all_72_1_40 = 0) | ~ (all_72_2_41 = 0) | all_72_0_39 = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (230), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (236) all_0_4_4 = 0
% 104.31/53.97 |
% 104.31/53.97 | Equations (236) can reduce 197 to:
% 104.31/53.97 | (237) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (197) ~ (all_0_4_4 = 0)
% 104.31/53.97 | (239) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_5_5) = 0 & in(v0, all_0_8_8) = v1)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating (239) with all_85_0_44, all_85_1_45 yields:
% 104.31/53.97 | (240) ~ (all_85_0_44 = 0) & in(all_85_1_45, all_0_5_5) = 0 & in(all_85_1_45, all_0_8_8) = all_85_0_44
% 104.31/53.97 |
% 104.31/53.97 | Applying alpha-rule on (240) yields:
% 104.31/53.97 | (241) ~ (all_85_0_44 = 0)
% 104.31/53.97 | (242) in(all_85_1_45, all_0_5_5) = 0
% 104.31/53.97 | (243) in(all_85_1_45, all_0_8_8) = all_85_0_44
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_7_7, all_72_0_39, 0 and discharging atoms relation(all_0_7_7) = 0, yields:
% 104.31/53.97 | (244) all_72_0_39 = 0 | ~ (relation(all_0_7_7) = all_72_0_39)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_9_9, all_72_0_39, 0 and discharging atoms relation(all_0_9_9) = 0, yields:
% 104.31/53.97 | (245) all_72_0_39 = 0 | ~ (relation(all_0_9_9) = all_72_0_39)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with empty_set, all_72_0_39, 0 and discharging atoms relation(empty_set) = 0, yields:
% 104.31/53.97 | (246) all_72_0_39 = 0 | ~ (relation(empty_set) = all_72_0_39)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_7_7, all_72_1_40, 0 and discharging atoms relation(all_0_7_7) = all_72_1_40, relation(all_0_7_7) = 0, yields:
% 104.31/53.97 | (247) all_72_1_40 = 0
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_9_9, all_72_1_40, 0 and discharging atoms relation(all_0_9_9) = 0, yields:
% 104.31/53.97 | (248) all_72_1_40 = 0 | ~ (relation(all_0_9_9) = all_72_1_40)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with empty_set, all_72_1_40, 0 and discharging atoms relation(empty_set) = 0, yields:
% 104.31/53.97 | (249) all_72_1_40 = 0 | ~ (relation(empty_set) = all_72_1_40)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_7_7, all_72_1_40, all_72_0_39 and discharging atoms relation(all_0_7_7) = all_72_1_40, yields:
% 104.31/53.97 | (250) all_72_0_39 = all_72_1_40 | ~ (relation(all_0_7_7) = all_72_0_39)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_9_9, all_72_2_41, 0 and discharging atoms relation(all_0_9_9) = all_72_2_41, relation(all_0_9_9) = 0, yields:
% 104.31/53.97 | (251) all_72_2_41 = 0
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with empty_set, all_72_2_41, 0 and discharging atoms relation(empty_set) = 0, yields:
% 104.31/53.97 | (252) all_72_2_41 = 0 | ~ (relation(empty_set) = all_72_2_41)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_9_9, all_72_2_41, all_72_0_39 and discharging atoms relation(all_0_9_9) = all_72_2_41, yields:
% 104.31/53.97 | (253) all_72_0_39 = all_72_2_41 | ~ (relation(all_0_9_9) = all_72_0_39)
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (169) with all_0_9_9, all_72_2_41, all_72_1_40 and discharging atoms relation(all_0_9_9) = all_72_2_41, yields:
% 104.31/53.97 | (254) all_72_1_40 = all_72_2_41 | ~ (relation(all_0_9_9) = all_72_1_40)
% 104.31/53.97 |
% 104.31/53.97 | From (247) and (233) follows:
% 104.31/53.97 | (4) relation(all_0_7_7) = 0
% 104.31/53.97 |
% 104.31/53.97 | From (251) and (234) follows:
% 104.31/53.97 | (54) relation(all_0_9_9) = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (235), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (257) ~ (all_72_1_40 = 0)
% 104.31/53.97 |
% 104.31/53.97 | Equations (247) can reduce 257 to:
% 104.31/53.97 | (237) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (247) all_72_1_40 = 0
% 104.31/53.97 | (260) ~ (all_72_2_41 = 0) | all_72_0_39 = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (260), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (261) ~ (all_72_2_41 = 0)
% 104.31/53.97 |
% 104.31/53.97 | Equations (251) can reduce 261 to:
% 104.31/53.97 | (237) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (251) all_72_2_41 = 0
% 104.31/53.97 | (264) all_72_0_39 = 0
% 104.31/53.97 |
% 104.31/53.97 | From (264) and (232) follows:
% 104.31/53.97 | (265) relation(all_0_6_6) = 0
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (93) with all_85_1_45, all_0_5_5, all_0_6_6 and discharging atoms relation_dom(all_0_6_6) = all_0_5_5, in(all_85_1_45, all_0_5_5) = 0, yields:
% 104.31/53.97 | (266) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & ordered_pair(all_85_1_45, v0) = v1 & in(v1, all_0_6_6) = 0) | ( ~ (v0 = 0) & relation(all_0_6_6) = v0))
% 104.31/53.97 |
% 104.31/53.97 | Instantiating (266) with all_137_0_64, all_137_1_65, all_137_2_66 yields:
% 104.31/53.97 | (267) (all_137_0_64 = 0 & ordered_pair(all_85_1_45, all_137_2_66) = all_137_1_65 & in(all_137_1_65, all_0_6_6) = 0) | ( ~ (all_137_2_66 = 0) & relation(all_0_6_6) = all_137_2_66)
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (267), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (268) all_137_0_64 = 0 & ordered_pair(all_85_1_45, all_137_2_66) = all_137_1_65 & in(all_137_1_65, all_0_6_6) = 0
% 104.31/53.97 |
% 104.31/53.97 | Applying alpha-rule on (268) yields:
% 104.31/53.97 | (269) all_137_0_64 = 0
% 104.31/53.97 | (270) ordered_pair(all_85_1_45, all_137_2_66) = all_137_1_65
% 104.31/53.97 | (271) in(all_137_1_65, all_0_6_6) = 0
% 104.31/53.97 |
% 104.31/53.97 | Instantiating formula (178) with all_137_1_65, all_137_2_66, all_85_1_45, all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms relation_composition(all_0_9_9, all_0_7_7) = all_0_6_6, relation(all_0_6_6) = 0, relation(all_0_9_9) = 0, ordered_pair(all_85_1_45, all_137_2_66) = all_137_1_65, in(all_137_1_65, all_0_6_6) = 0, yields:
% 104.31/53.97 | (272) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & ordered_pair(v0, all_137_2_66) = v3 & ordered_pair(all_85_1_45, v0) = v1 & in(v3, all_0_7_7) = 0 & in(v1, all_0_9_9) = 0) | ( ~ (v0 = 0) & relation(all_0_7_7) = v0))
% 104.31/53.97 |
% 104.31/53.97 | Instantiating (272) with all_312_0_116, all_312_1_117, all_312_2_118, all_312_3_119, all_312_4_120 yields:
% 104.31/53.97 | (273) (all_312_0_116 = 0 & all_312_2_118 = 0 & ordered_pair(all_312_4_120, all_137_2_66) = all_312_1_117 & ordered_pair(all_85_1_45, all_312_4_120) = all_312_3_119 & in(all_312_1_117, all_0_7_7) = 0 & in(all_312_3_119, all_0_9_9) = 0) | ( ~ (all_312_4_120 = 0) & relation(all_0_7_7) = all_312_4_120)
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (273), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (274) all_312_0_116 = 0 & all_312_2_118 = 0 & ordered_pair(all_312_4_120, all_137_2_66) = all_312_1_117 & ordered_pair(all_85_1_45, all_312_4_120) = all_312_3_119 & in(all_312_1_117, all_0_7_7) = 0 & in(all_312_3_119, all_0_9_9) = 0
% 104.31/53.97 |
% 104.31/53.97 | Applying alpha-rule on (274) yields:
% 104.31/53.97 | (275) in(all_312_3_119, all_0_9_9) = 0
% 104.31/53.97 | (276) all_312_2_118 = 0
% 104.31/53.97 | (277) in(all_312_1_117, all_0_7_7) = 0
% 104.31/53.97 | (278) ordered_pair(all_85_1_45, all_312_4_120) = all_312_3_119
% 104.31/53.97 | (279) ordered_pair(all_312_4_120, all_137_2_66) = all_312_1_117
% 104.31/53.97 | (280) all_312_0_116 = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (246), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (281) ~ (relation(empty_set) = all_72_0_39)
% 104.31/53.97 |
% 104.31/53.97 | From (264) and (281) follows:
% 104.31/53.97 | (282) ~ (relation(empty_set) = 0)
% 104.31/53.97 |
% 104.31/53.97 | Using (228) and (282) yields:
% 104.31/53.97 | (283) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (284) relation(empty_set) = all_72_0_39
% 104.31/53.97 | (264) all_72_0_39 = 0
% 104.31/53.97 |
% 104.31/53.97 | From (264) and (284) follows:
% 104.31/53.97 | (228) relation(empty_set) = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (252), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (287) ~ (relation(empty_set) = all_72_2_41)
% 104.31/53.97 |
% 104.31/53.97 | From (251) and (287) follows:
% 104.31/53.97 | (282) ~ (relation(empty_set) = 0)
% 104.31/53.97 |
% 104.31/53.97 | Using (228) and (282) yields:
% 104.31/53.97 | (283) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (290) relation(empty_set) = all_72_2_41
% 104.31/53.97 | (251) all_72_2_41 = 0
% 104.31/53.97 |
% 104.31/53.97 | From (251) and (290) follows:
% 104.31/53.97 | (228) relation(empty_set) = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (249), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (293) ~ (relation(empty_set) = all_72_1_40)
% 104.31/53.97 |
% 104.31/53.97 | From (247) and (293) follows:
% 104.31/53.97 | (282) ~ (relation(empty_set) = 0)
% 104.31/53.97 |
% 104.31/53.97 | Using (228) and (282) yields:
% 104.31/53.97 | (283) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (296) relation(empty_set) = all_72_1_40
% 104.31/53.97 | (247) all_72_1_40 = 0
% 104.31/53.97 |
% 104.31/53.97 +-Applying beta-rule and splitting (248), into two cases.
% 104.31/53.97 |-Branch one:
% 104.31/53.97 | (298) ~ (relation(all_0_9_9) = all_72_1_40)
% 104.31/53.97 |
% 104.31/53.97 | From (247) and (298) follows:
% 104.31/53.97 | (299) ~ (relation(all_0_9_9) = 0)
% 104.31/53.97 |
% 104.31/53.97 | Using (54) and (299) yields:
% 104.31/53.97 | (283) $false
% 104.31/53.97 |
% 104.31/53.97 |-The branch is then unsatisfiable
% 104.31/53.97 |-Branch two:
% 104.31/53.97 | (301) relation(all_0_9_9) = all_72_1_40
% 104.31/53.97 | (247) all_72_1_40 = 0
% 104.31/53.97 |
% 104.31/53.97 | From (247) and (301) follows:
% 104.31/53.97 | (54) relation(all_0_9_9) = 0
% 104.31/53.97 |
% 104.31/53.98 +-Applying beta-rule and splitting (254), into two cases.
% 104.31/53.98 |-Branch one:
% 104.31/53.98 | (298) ~ (relation(all_0_9_9) = all_72_1_40)
% 104.31/53.98 |
% 104.31/53.98 | From (247) and (298) follows:
% 104.31/53.98 | (299) ~ (relation(all_0_9_9) = 0)
% 104.31/53.98 |
% 104.31/53.98 | Using (54) and (299) yields:
% 104.31/53.98 | (283) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (301) relation(all_0_9_9) = all_72_1_40
% 104.31/53.98 | (308) all_72_1_40 = all_72_2_41
% 104.31/53.98 |
% 104.31/53.98 | Combining equations (247,308) yields a new equation:
% 104.31/53.98 | (251) all_72_2_41 = 0
% 104.31/53.98 |
% 104.31/53.98 | Combining equations (251,308) yields a new equation:
% 104.31/53.98 | (247) all_72_1_40 = 0
% 104.31/53.98 |
% 104.31/53.98 | From (247) and (301) follows:
% 104.31/53.98 | (54) relation(all_0_9_9) = 0
% 104.31/53.98 |
% 104.31/53.98 +-Applying beta-rule and splitting (253), into two cases.
% 104.31/53.98 |-Branch one:
% 104.31/53.98 | (312) ~ (relation(all_0_9_9) = all_72_0_39)
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (312) follows:
% 104.31/53.98 | (299) ~ (relation(all_0_9_9) = 0)
% 104.31/53.98 |
% 104.31/53.98 | Using (54) and (299) yields:
% 104.31/53.98 | (283) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (315) relation(all_0_9_9) = all_72_0_39
% 104.31/53.98 | (316) all_72_0_39 = all_72_2_41
% 104.31/53.98 |
% 104.31/53.98 | Combining equations (264,316) yields a new equation:
% 104.31/53.98 | (251) all_72_2_41 = 0
% 104.31/53.98 |
% 104.31/53.98 | Combining equations (251,316) yields a new equation:
% 104.31/53.98 | (264) all_72_0_39 = 0
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (315) follows:
% 104.31/53.98 | (54) relation(all_0_9_9) = 0
% 104.31/53.98 |
% 104.31/53.98 +-Applying beta-rule and splitting (244), into two cases.
% 104.31/53.98 |-Branch one:
% 104.31/53.98 | (320) ~ (relation(all_0_7_7) = all_72_0_39)
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (320) follows:
% 104.31/53.98 | (321) ~ (relation(all_0_7_7) = 0)
% 104.31/53.98 |
% 104.31/53.98 | Using (4) and (321) yields:
% 104.31/53.98 | (283) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (323) relation(all_0_7_7) = all_72_0_39
% 104.31/53.98 | (264) all_72_0_39 = 0
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (323) follows:
% 104.31/53.98 | (4) relation(all_0_7_7) = 0
% 104.31/53.98 |
% 104.31/53.98 +-Applying beta-rule and splitting (250), into two cases.
% 104.31/53.98 |-Branch one:
% 104.31/53.98 | (320) ~ (relation(all_0_7_7) = all_72_0_39)
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (320) follows:
% 104.31/53.98 | (321) ~ (relation(all_0_7_7) = 0)
% 104.31/53.98 |
% 104.31/53.98 | Using (4) and (321) yields:
% 104.31/53.98 | (283) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (323) relation(all_0_7_7) = all_72_0_39
% 104.31/53.98 | (330) all_72_0_39 = all_72_1_40
% 104.31/53.98 |
% 104.31/53.98 | Combining equations (264,330) yields a new equation:
% 104.31/53.98 | (247) all_72_1_40 = 0
% 104.31/53.98 |
% 104.31/53.98 | Combining equations (247,330) yields a new equation:
% 104.31/53.98 | (264) all_72_0_39 = 0
% 104.31/53.98 |
% 104.31/53.98 +-Applying beta-rule and splitting (245), into two cases.
% 104.31/53.98 |-Branch one:
% 104.31/53.98 | (312) ~ (relation(all_0_9_9) = all_72_0_39)
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (312) follows:
% 104.31/53.98 | (299) ~ (relation(all_0_9_9) = 0)
% 104.31/53.98 |
% 104.31/53.98 | Using (54) and (299) yields:
% 104.31/53.98 | (283) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (315) relation(all_0_9_9) = all_72_0_39
% 104.31/53.98 | (264) all_72_0_39 = 0
% 104.31/53.98 |
% 104.31/53.98 | From (264) and (315) follows:
% 104.31/53.98 | (54) relation(all_0_9_9) = 0
% 104.31/53.98 |
% 104.31/53.98 | Instantiating formula (123) with all_312_3_119, all_312_4_120, all_85_0_44, all_85_1_45, all_0_8_8, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_8_8, ordered_pair(all_85_1_45, all_312_4_120) = all_312_3_119, in(all_312_3_119, all_0_9_9) = 0, in(all_85_1_45, all_0_8_8) = all_85_0_44, yields:
% 104.31/53.98 | (339) all_85_0_44 = 0 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 104.31/53.98 |
% 104.31/53.98 +-Applying beta-rule and splitting (339), into two cases.
% 104.31/53.98 |-Branch one:
% 104.31/53.98 | (340) all_85_0_44 = 0
% 104.31/53.98 |
% 104.31/53.98 | Equations (340) can reduce 241 to:
% 104.31/53.98 | (237) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (241) ~ (all_85_0_44 = 0)
% 104.31/53.98 | (343) ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 104.31/53.98 |
% 104.31/53.98 | Instantiating (343) with all_2376_0_1079 yields:
% 104.31/53.98 | (344) ~ (all_2376_0_1079 = 0) & relation(all_0_9_9) = all_2376_0_1079
% 104.31/53.98 |
% 104.31/53.98 | Applying alpha-rule on (344) yields:
% 104.31/53.98 | (345) ~ (all_2376_0_1079 = 0)
% 104.31/53.98 | (346) relation(all_0_9_9) = all_2376_0_1079
% 104.31/53.98 |
% 104.31/53.98 | Instantiating formula (169) with all_0_9_9, all_2376_0_1079, 0 and discharging atoms relation(all_0_9_9) = all_2376_0_1079, relation(all_0_9_9) = 0, yields:
% 104.31/53.98 | (347) all_2376_0_1079 = 0
% 104.31/53.98 |
% 104.31/53.98 | Equations (347) can reduce 345 to:
% 104.31/53.98 | (237) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (349) ~ (all_312_4_120 = 0) & relation(all_0_7_7) = all_312_4_120
% 104.31/53.98 |
% 104.31/53.98 | Applying alpha-rule on (349) yields:
% 104.31/53.98 | (350) ~ (all_312_4_120 = 0)
% 104.31/53.98 | (351) relation(all_0_7_7) = all_312_4_120
% 104.31/53.98 |
% 104.31/53.98 | Instantiating formula (169) with all_0_7_7, all_312_4_120, 0 and discharging atoms relation(all_0_7_7) = all_312_4_120, relation(all_0_7_7) = 0, yields:
% 104.31/53.98 | (352) all_312_4_120 = 0
% 104.31/53.98 |
% 104.31/53.98 | Equations (352) can reduce 350 to:
% 104.31/53.98 | (237) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 |-Branch two:
% 104.31/53.98 | (354) ~ (all_137_2_66 = 0) & relation(all_0_6_6) = all_137_2_66
% 104.31/53.98 |
% 104.31/53.98 | Applying alpha-rule on (354) yields:
% 104.31/53.98 | (355) ~ (all_137_2_66 = 0)
% 104.31/53.98 | (356) relation(all_0_6_6) = all_137_2_66
% 104.31/53.98 |
% 104.31/53.98 | Instantiating formula (169) with all_0_6_6, all_137_2_66, 0 and discharging atoms relation(all_0_6_6) = all_137_2_66, relation(all_0_6_6) = 0, yields:
% 104.31/53.98 | (357) all_137_2_66 = 0
% 104.31/53.98 |
% 104.31/53.98 | Equations (357) can reduce 355 to:
% 104.31/53.98 | (237) $false
% 104.31/53.98 |
% 104.31/53.98 |-The branch is then unsatisfiable
% 104.31/53.98 % SZS output end Proof for theBenchmark
% 104.31/53.98
% 104.31/53.98 53369ms
%------------------------------------------------------------------------------