TSTP Solution File: SEU217+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU217+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n003.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 08:47:45 EDT 2022
% Result : Theorem 8.13s 2.42s
% Output : Proof 13.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU217+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 00:01:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 A Theorem Prover for First-Order Logic
% 0.51/0.59 (ePrincess v.1.0)
% 0.51/0.59
% 0.51/0.59 (c) Philipp Rümmer, 2009-2015
% 0.51/0.59 (c) Peter Backeman, 2014-2015
% 0.51/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.59 Bug reports to peter@backeman.se
% 0.51/0.59
% 0.51/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.59
% 0.51/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.76/1.19 Prover 0: Preprocessing ...
% 6.45/2.01 Prover 0: Warning: ignoring some quantifiers
% 6.79/2.05 Prover 0: Constructing countermodel ...
% 8.13/2.42 Prover 0: proved (1783ms)
% 8.13/2.42
% 8.13/2.42 No countermodel exists, formula is valid
% 8.13/2.42 % SZS status Theorem for theBenchmark
% 8.13/2.42
% 8.13/2.42 Generating proof ... Warning: ignoring some quantifiers
% 12.04/3.32 found it (size 8)
% 12.04/3.32
% 12.04/3.32 % SZS output start Proof for theBenchmark
% 12.04/3.32 Assumed formulas after preprocessing and simplification:
% 12.04/3.32 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v4 = v2) & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & apply(v3, v2) = v4 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & identity_relation(v1) = v3 & relation_empty_yielding(v5) & relation_empty_yielding(empty_set) & relation(v10) & relation(v9) & relation(v7) & relation(v5) & relation(empty_set) & function(v10) & empty(v9) & empty(v8) & empty(empty_set) & in(v2, v1) & ~ empty(v7) & ~ empty(v6) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v11, v12) = v13) | ~ (ordered_pair(v17, v15) = v18) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ relation(v11) | ~ in(v18, v12) | in(v16, v13) | ? [v19] : (ordered_pair(v14, v17) = v19 & ~ in(v19, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v11, v12) = v13) | ~ (ordered_pair(v14, v17) = v18) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ relation(v11) | ~ in(v18, v11) | in(v16, v13) | ? [v19] : (ordered_pair(v17, v15) = v19 & ~ in(v19, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v14) = v17) | ~ (identity_relation(v13) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ relation(v14) | ~ in(v15, v17) | in(v15, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v14) = v17) | ~ (identity_relation(v13) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ relation(v14) | ~ in(v15, v17) | in(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v14) = v17) | ~ (identity_relation(v13) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ relation(v14) | ~ in(v15, v14) | ~ in(v11, v13) | in(v15, v17)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ relation(v11) | ~ in(v16, v13) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v15) = v19 & ordered_pair(v14, v17) = v18 & in(v19, v12) & in(v18, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ in(v15, v16) | in(v12, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ in(v15, v16) | in(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (ordered_pair(v11, v12) = v15) | ~ in(v12, v14) | ~ in(v11, v13) | in(v15, v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v12, v14) = v16) | ~ (cartesian_product2(v11, v13) = v15) | ~ subset(v13, v14) | ~ subset(v11, v12) | subset(v15, v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v11, v12) = v13) | ~ (ordered_pair(v15, v16) = v14) | ~ in(v16, v12) | ~ in(v15, v11) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse_image(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v11) | ~ in(v16, v11) | ~ in(v15, v12) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_image(v11, v12) = v13) | ~ (ordered_pair(v15, v14) = v16) | ~ relation(v11) | ~ in(v16, v11) | ~ in(v15, v12) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ in(v16, v13) | in(v16, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ in(v16, v13) | in(v15, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ in(v16, v12) | ~ in(v15, v11) | in(v16, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v11) | ~ in(v16, v13) | in(v16, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v11) | ~ in(v16, v13) | in(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom_restriction(v11, v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v11) | ~ in(v16, v11) | ~ in(v14, v12) | in(v16, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v14) = v15) | ~ (identity_relation(v11) = v12) | ~ relation(v12) | ~ function(v12) | ~ in(v14, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (identity_relation(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ in(v15, v12)) & ! [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] : (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] : (union_of_subsets(v11, v18) = v19 & complements_of_subsets(v11, v12) = v18 & powerset(v16) = v17 & powerset(v11) = v16 & (v19 = v15 | ~ element(v12, v17)))) & ! [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] : (meet_of_subsets(v11, v18) = v19 & complements_of_subsets(v11, v12) = v18 & powerset(v16) = v17 & powerset(v11) = v16 & (v19 = v15 | ~ element(v12, v17)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = empty_set | ~ (subset_complement(v11, v13) = v14) | ~ (powerset(v11) = v12) | ~ element(v15, v11) | ~ element(v13, v12) | in(v15, v14) | in(v15, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v13, v12) = v14) | ~ (apply(v14, v11) = v15) | ~ relation(v13) | ~ relation(v12) | ~ function(v13) | ~ function(v12) | ? [v16] : ? [v17] : ? [v18] : (relation_dom(v14) = v16 & apply(v13, v11) = v17 & apply(v12, v17) = v18 & (v18 = v15 | ~ in(v11, v16)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse(v11) = v12) | ~ (ordered_pair(v14, v13) = v15) | ~ relation(v12) | ~ relation(v11) | ~ in(v15, v11) | ? [v16] : (ordered_pair(v13, v14) = v16 & in(v16, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse(v11) = v12) | ~ (ordered_pair(v14, v13) = v15) | ~ relation(v12) | ~ relation(v11) | in(v15, v11) | ? [v16] : (ordered_pair(v13, v14) = v16 & ~ in(v16, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | ~ in(v15, v12) | ? [v16] : (ordered_pair(v14, v13) = v16 & in(v16, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ relation(v11) | in(v15, v12) | ? [v16] : (ordered_pair(v14, v13) = v16 & ~ in(v16, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_field(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ in(v14, v13) | in(v12, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_field(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ in(v14, v13) | in(v11, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_complement(v11, v14) = v15) | ~ (powerset(v11) = v13) | ~ disjoint(v12, v14) | ~ element(v14, v13) | ~ element(v12, v13) | subset(v12, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_complement(v11, v14) = v15) | ~ (powerset(v11) = v13) | ~ element(v14, v13) | ~ element(v12, v13) | ~ subset(v12, v15) | disjoint(v12, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ in(v14, v13) | in(v12, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ in(v14, v13) | ? [v16] : (relation_dom(v13) = v16 & in(v11, v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v11) = v12) | ~ (ordered_pair(v14, v13) = v15) | ~ relation(v11) | ~ in(v15, v11) | in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v14) = v15) | ~ (singleton(v13) = v14) | ~ subset(v11, v12) | subset(v11, v15) | in(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v13) = v15) | ~ (set_difference(v11, v13) = v14) | ~ subset(v11, v12) | subset(v14, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v13) = v15) | ~ (powerset(v11) = v14) | ~ element(v13, v14) | ~ element(v12, v14) | subset_difference(v11, v12, v13) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ function(v13) | ? [v16] : (apply(v13, v11) = v16 & ( ~ (v16 = v12) | ~ in(v11, v15) | in(v14, v13)) & ( ~ in(v14, v13) | (v16 = v12 & in(v11, v15))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ in(v14, v13) | in(v11, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v13) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ in(v14, v13) | ? [v16] : (relation_rng(v13) = v16 & in(v12, v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v12) = v13) | ~ (apply(v14, v11) = v15) | ~ relation(v14) | ~ relation(v12) | ~ function(v14) | ~ function(v12) | ? [v16] : ? [v17] : ? [v18] : (relation_composition(v14, v12) = v16 & relation_dom(v16) = v17 & relation_dom(v14) = v18 & ( ~ in(v15, v13) | ~ in(v11, v18) | in(v11, v17)) & ( ~ in(v11, v17) | (in(v15, v13) & in(v11, v18))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v12) = v13) | ~ (relation_image(v12, v14) = v15) | ~ (set_intersection2(v13, v11) = v14) | ~ relation(v12) | relation_image(v12, v11) = v15) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v11) | ~ function(v11) | ~ in(v13, v12) | ? [v16] : (apply(v11, v13) = v16 & ( ~ (v16 = v14) | in(v15, v11)) & (v16 = v14 | ~ in(v15, v11)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v11) | ~ in(v15, v11) | in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (apply(v13, v11) = v15) | ~ (ordered_pair(v11, v12) = v14) | ~ relation(v13) | ~ function(v13) | ? [v16] : (relation_dom(v13) = v16 & ( ~ (v15 = v12) | ~ in(v11, v16) | in(v14, v13)) & ( ~ in(v14, v13) | (v15 = v12 & in(v11, v16))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (apply(v13, v11) = v14) | ~ (apply(v12, v14) = v15) | ~ relation(v13) | ~ relation(v12) | ~ function(v13) | ~ function(v12) | ? [v16] : ? [v17] : ? [v18] : (relation_composition(v13, v12) = v16 & relation_dom(v16) = v17 & apply(v16, v11) = v18 & (v18 = v15 | ~ in(v11, v17)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v13, v12) = v15) | ~ (cartesian_product2(v13, v11) = v14) | ~ subset(v11, v12) | subset(v14, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v13, v12) = v15) | ~ (cartesian_product2(v13, v11) = v14) | ~ subset(v11, v12) | ? [v16] : ? [v17] : (cartesian_product2(v12, v13) = v17 & cartesian_product2(v11, v13) = v16 & subset(v16, v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v13, v12) = v15) | ~ (cartesian_product2(v11, v13) = v14) | ~ subset(v11, v12) | ? [v16] : ? [v17] : (cartesian_product2(v13, v11) = v17 & cartesian_product2(v12, v13) = v16 & subset(v17, v15) & subset(v14, v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v13, v11) = v15) | ~ (cartesian_product2(v12, v13) = v14) | ~ subset(v11, v12) | ? [v16] : ? [v17] : (cartesian_product2(v13, v12) = v17 & cartesian_product2(v11, v13) = v16 & subset(v16, v14) & subset(v15, v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (cartesian_product2(v11, v13) = v14) | ~ subset(v11, v12) | subset(v14, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v15) | ~ (cartesian_product2(v11, v13) = v14) | ~ subset(v11, v12) | ? [v16] : ? [v17] : (cartesian_product2(v13, v12) = v17 & cartesian_product2(v13, v11) = v16 & subset(v16, v17))) & ! [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] : ( ~ (relation_inverse_image(v13, v12) = v15) | ~ (relation_inverse_image(v13, v11) = v14) | ~ subset(v11, v12) | ~ relation(v13) | subset(v14, v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng_restriction(v11, v14) = v15) | ~ (relation_dom_restriction(v13, v12) = v14) | ~ relation(v13) | ? [v16] : (relation_rng_restriction(v11, v13) = v16 & relation_dom_restriction(v16, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng_restriction(v11, v13) = v14) | ~ (relation_dom_restriction(v14, v12) = v15) | ~ relation(v13) | ? [v16] : (relation_rng_restriction(v11, v16) = v15 & relation_dom_restriction(v13, v12) = v16)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (identity_relation(v11) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ relation(v12) | ~ in(v15, v12) | in(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (ordered_pair(v13, v14) = v15) | ~ subset(v11, v12) | ~ relation(v12) | ~ relation(v11) | ~ in(v15, v11) | in(v15, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v15) | ~ (set_intersection2(v11, v13) = v14) | ~ subset(v11, v12) | subset(v14, v15)) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v12) = v15) | ~ (relation_dom(v12) = v13) | ~ relation(v14) | ~ relation(v12) | ~ function(v14) | ~ function(v12) | ? [v16] : ? [v17] : ? [v18] : (relation_dom(v15) = v16 & relation_dom(v14) = v17 & apply(v14, v11) = v18 & ( ~ in(v18, v13) | ~ in(v11, v17) | in(v11, v16)) & ( ~ in(v11, v16) | (in(v18, v13) & in(v11, v17))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ (relation_dom(v12) = v13) | ~ relation(v14) | ~ relation(v12) | ~ function(v14) | ~ function(v12) | ? [v16] : ? [v17] : ? [v18] : (relation_composition(v14, v12) = v16 & relation_dom(v16) = v17 & apply(v14, v11) = v18 & ( ~ in(v18, v13) | ~ in(v11, v15) | in(v11, v17)) & ( ~ in(v11, v17) | (in(v18, v13) & in(v11, v15))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_composition(v11, v12) = v13) | ~ relation(v14) | ~ relation(v12) | ~ relation(v11) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v15, v16) = v17 & ( ~ in(v17, v14) | ( ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v16) = v22) | ~ in(v22, v12) | ? [v23] : (ordered_pair(v15, v21) = v23 & ~ in(v23, v11))) & ! [v21] : ! [v22] : ( ~ (ordered_pair(v15, v21) = v22) | ~ in(v22, v11) | ? [v23] : (ordered_pair(v21, v16) = v23 & ~ in(v23, v12))))) & (in(v17, v14) | (ordered_pair(v18, v16) = v20 & ordered_pair(v15, v18) = v19 & in(v20, v12) & in(v19, v11))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v14) | ~ relation(v12) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v15, v16) = v17 & ( ~ in(v17, v14) | ~ in(v17, v12) | ~ in(v16, v11)) & (in(v17, v14) | (in(v17, v12) & in(v16, v11))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_dom_restriction(v11, v12) = v14) | ~ relation(v13) | ~ relation(v11) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v15, v16) = v17 & ( ~ in(v17, v13) | ~ in(v17, v11) | ~ in(v15, v12)) & (in(v17, v13) | (in(v17, v11) & in(v15, v12))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | v14 = v11 | ~ (unordered_pair(v11, v12) = v13) | ~ in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (complements_of_subsets(v11, v13) = v14) | ~ (complements_of_subsets(v11, v12) = v13) | ? [v15] : ? [v16] : (powerset(v15) = v16 & powerset(v11) = v15 & ~ element(v12, v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (subset_complement(v11, v13) = v14) | ~ (subset_complement(v11, v12) = v13) | ? [v15] : (powerset(v11) = v15 & ~ element(v12, v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (set_difference(v12, v11) = v13) | ~ (set_union2(v11, v13) = v14) | ~ subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v11) = v13) | ~ (set_union2(v13, v12) = v14) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_difference(v11, v13) = v14) | ~ (singleton(v12) = v13) | in(v12, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = empty_set | ~ (relation_dom(v11) = v12) | ~ (apply(v11, v13) = v14) | ~ relation(v11) | ~ function(v11) | in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v11) = v14) | ~ (unordered_pair(v12, v13) = v14)) & ! [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 | ~ (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 | ~ (apply(v14, v13) = v12) | ~ (apply(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 | ~ (singleton(v12) = v14) | ~ (singleton(v11) = v13) | ~ subset(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (singleton(v11) = v14) | ~ (unordered_pair(v12, v13) = v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_inverse_image(v14, v13) = v12) | ~ (relation_inverse_image(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_image(v14, v13) = v12) | ~ (relation_image(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_rng_restriction(v14, v13) = v12) | ~ (relation_rng_restriction(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (relation_dom_restriction(v14, v13) = v12) | ~ (relation_dom_restriction(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (ordered_pair(v14, v13) = v12) | ~ (ordered_pair(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 = empty_set | ~ (meet_of_subsets(v11, v13) = v14) | ~ (complements_of_subsets(v11, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (subset_difference(v11, v17, v18) = v19 & union_of_subsets(v11, v12) = v18 & cast_to_subset(v11) = v17 & powerset(v15) = v16 & powerset(v11) = v15 & (v19 = v14 | ~ element(v12, v16)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = empty_set | ~ (union_of_subsets(v11, v13) = v14) | ~ (complements_of_subsets(v11, v12) = v13) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (subset_difference(v11, v17, v18) = v19 & meet_of_subsets(v11, v12) = v18 & cast_to_subset(v11) = v17 & powerset(v15) = v16 & powerset(v11) = v15 & (v19 = v14 | ~ element(v12, v16)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = empty_set | ~ (set_meet(v11) = v12) | ~ in(v14, v11) | ~ in(v13, v12) | in(v13, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_difference(v11, v12, v13) = v14) | ? [v15] : ? [v16] : (set_difference(v12, v13) = v16 & powerset(v11) = v15 & (v16 = v14 | ~ element(v13, v15) | ~ element(v12, v15)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_difference(v11, v12, v13) = v14) | ? [v15] : (powerset(v11) = v15 & ( ~ element(v13, v15) | ~ element(v12, v15) | element(v14, v15)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v12) = v14) | ~ (identity_relation(v11) = v13) | ~ relation(v12) | relation_dom_restriction(v12, v11) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v11, v13) = v14) | ~ (relation_rng(v11) = v12) | ~ relation(v13) | ~ relation(v11) | ? [v15] : (relation_rng(v14) = v15 & relation_image(v13, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v11, v13) = v14) | ~ (relation_dom(v11) = v12) | ~ relation(v13) | ~ relation(v11) | ? [v15] : (relation_dom(v14) = v15 & subset(v15, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v11, v13) = v14) | ~ in(v12, v14) | ~ in(v12, v13) | ? [v15] : (powerset(v11) = v15 & ~ element(v13, v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v12) = v13) | ~ (set_intersection2(v13, v11) = v14) | ~ relation(v12) | ? [v15] : (relation_rng(v15) = v14 & relation_rng_restriction(v11, v12) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v11) = v13) | ~ (relation_dom(v11) = v12) | ~ (cartesian_product2(v12, v13) = v14) | ~ relation(v11) | subset(v11, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v11) = v13) | ~ (relation_dom(v11) = v12) | ~ (set_union2(v12, v13) = v14) | ~ relation(v11) | relation_field(v11) = v14) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v11) = v12) | ~ (relation_image(v13, v12) = v14) | ~ relation(v13) | ~ relation(v11) | ? [v15] : (relation_composition(v11, v13) = v15 & relation_rng(v15) = 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, v13) | ~ in(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v12) = v13) | ~ in(v14, v13) | in(v14, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v11, v12) = v13) | ~ in(v14, v11) | in(v14, v13) | in(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v12) = v14) | ~ (powerset(v11) = v13) | ? [v15] : ? [v16] : (union_of_subsets(v11, v12) = v16 & powerset(v13) = v15 & (v16 = v14 | ~ element(v12, v15)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v11) = v12) | ~ in(v14, v11) | ~ in(v13, v14) | in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ (set_intersection2(v13, v11) = v14) | ~ relation(v12) | ? [v15] : (relation_dom(v15) = v14 & relation_dom_restriction(v12, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v11, v12) = v13) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v15, v16) = v14 & in(v16, v12) & in(v15, v11))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ empty(v13) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | ~ in(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v11) = v13) | ~ (set_meet(v12) = v14) | ? [v15] : ? [v16] : (meet_of_subsets(v11, v12) = v16 & powerset(v13) = v15 & (v16 = v14 | ~ element(v12, v15)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v11) = v13) | ~ element(v12, v13) | ~ in(v14, v12) | in(v14, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse_image(v11, v12) = v13) | ~ relation(v11) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v11) & in(v15, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_image(v11, v12) = v13) | ~ relation(v11) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v15, v14) = v16 & in(v16, v11) & in(v15, v12))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (identity_relation(v11) = v12) | ~ (ordered_pair(v13, v13) = v14) | ~ relation(v12) | ~ in(v13, v11) | in(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | ~ subset(v11, v13) | ~ subset(v11, v12) | subset(v11, v14)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ disjoint(v11, v12) | ~ in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ in(v14, v13) | in(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ in(v14, v13) | in(v14, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) | ~ in(v14, v12) | ~ in(v14, v11) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v13) = v14) | ~ subset(v13, v12) | ~ subset(v11, v12) | subset(v14, v12)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ in(v14, v13) | in(v14, v12) | in(v14, v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ in(v14, v12) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v11, v12) = v13) | ~ in(v14, v11) | in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v11, v12) = v14) | ~ subset(v14, v13) | in(v12, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v11, v12) = v14) | ~ subset(v14, v13) | in(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v11, v12) = v14) | ~ in(v12, v13) | ~ in(v11, v13) | subset(v14, v13)) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_difference(v12, v13) = v14) | ? [v15] : (( ~ in(v15, v12) | ~ in(v15, v11) | in(v15, v13)) & (in(v15, v11) | (in(v15, v12) & ~ in(v15, v13))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (cartesian_product2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (( ~ in(v15, v11) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v20) = v15) | ~ in(v20, v13) | ~ in(v19, v12))) & (in(v15, v11) | (v18 = v15 & ordered_pair(v16, v17) = v15 & in(v17, v13) & in(v16, v12))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (relation_inverse_image(v12, v13) = v14) | ~ relation(v12) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v11) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v15, v18) = v19) | ~ in(v19, v12) | ~ in(v18, v13))) & (in(v15, v11) | (ordered_pair(v15, v16) = v17 & in(v17, v12) & in(v16, v13))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (relation_image(v12, v13) = v14) | ~ relation(v12) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v11) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v15) = v19) | ~ in(v19, v12) | ~ in(v18, v13))) & (in(v15, v11) | (ordered_pair(v16, v15) = v17 & in(v17, v12) & in(v16, v13))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_intersection2(v12, v13) = v14) | ? [v15] : (( ~ in(v15, v13) | ~ in(v15, v12) | ~ in(v15, v11)) & (in(v15, v11) | (in(v15, v13) & in(v15, v12))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (set_union2(v12, v13) = v14) | ? [v15] : (( ~ in(v15, v11) | ( ~ in(v15, v13) & ~ in(v15, v12))) & (in(v15, v13) | in(v15, v12) | in(v15, v11)))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (unordered_pair(v12, v13) = v14) | ? [v15] : ((v15 = v13 | v15 = v12 | in(v15, v11)) & ( ~ in(v15, v11) | ( ~ (v15 = v13) & ~ (v15 = v12))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v12) = v14) | ~ relation(v13) | ~ relation(v12) | ~ function(v13) | ~ function(v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (relation_dom(v14) = v15 & apply(v14, v11) = v16 & apply(v13, v11) = v17 & apply(v12, v17) = v18 & (v18 = v16 | ~ in(v11, v15)))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse_image(v13, v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (relation_rng(v13) = v15 & ( ~ in(v11, v14) | (ordered_pair(v11, v16) = v17 & in(v17, v13) & in(v16, v15) & in(v16, v12))) & (in(v11, v14) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v11, v18) = v19) | ~ in(v19, v13) | ~ in(v18, v15) | ~ in(v18, v12))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_image(v13, v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (relation_dom(v13) = v15 & ( ~ in(v11, v14) | (ordered_pair(v16, v11) = v17 & in(v17, v13) & in(v16, v15) & in(v16, v12))) & (in(v11, v14) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v11) = v19) | ~ in(v19, v13) | ~ in(v18, v15) | ~ in(v18, v12))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_rng(v14) = v15 & relation_rng(v13) = v16 & ( ~ in(v11, v16) | ~ in(v11, v12) | in(v11, v15)) & ( ~ in(v11, v15) | (in(v11, v16) & in(v11, v12))))) & ? [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v13, v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_dom(v14) = v15 & relation_dom(v13) = v16 & ( ~ in(v11, v16) | ~ in(v11, v12) | in(v11, v15)) & ( ~ in(v11, v15) | (in(v11, v16) & in(v11, v12))))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_inverse(v11) = v12) | ~ relation(v13) | ~ relation(v11) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v15, v14) = v17 & ordered_pair(v14, v15) = v16 & ( ~ in(v17, v11) | ~ in(v16, v13)) & (in(v17, v11) | in(v16, v13)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (relation_dom(v12) = v11) | ~ (identity_relation(v11) = v13) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : ( ~ (v15 = v14) & apply(v12, v14) = v15 & in(v14, v11))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (identity_relation(v11) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & ( ~ (v15 = v14) | ~ in(v16, v12) | ~ in(v14, v11)) & (in(v16, v12) | (v15 = v14 & in(v14, v11))))) & ! [v11] : ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v11, v12) = v13) | ~ subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | v11 = empty_set | ~ (singleton(v12) = v13) | ~ subset(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_difference(v11, v12) = v13) | ~ disjoint(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_dom(v12) = v13) | ~ (identity_relation(v11) = v12) | ~ relation(v12) | ~ function(v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v11) = v12) | ~ in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (set_intersection2(v11, v12) = v13) | ~ subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_difference(v11, v12) = v13) | ~ subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_intersection2(v11, v12) = v13) | ~ disjoint(v11, v12)) & ! [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 | ~ (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 | ~ (identity_relation(v13) = v12) | ~ (identity_relation(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (meet_of_subsets(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (powerset(v14) = v15 & powerset(v11) = v14 & set_meet(v12) = v16 & (v16 = v13 | ~ element(v12, v15)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (meet_of_subsets(v11, v12) = v13) | ? [v14] : ? [v15] : (powerset(v14) = v15 & powerset(v11) = v14 & ( ~ element(v12, v15) | element(v13, v14)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union_of_subsets(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (union(v12) = v16 & powerset(v14) = v15 & powerset(v11) = v14 & (v16 = v13 | ~ element(v12, v15)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union_of_subsets(v11, v12) = v13) | ? [v14] : ? [v15] : (powerset(v14) = v15 & powerset(v11) = v14 & ( ~ element(v12, v15) | element(v13, v14)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (complements_of_subsets(v11, v12) = v13) | ? [v14] : ? [v15] : (powerset(v14) = v15 & powerset(v11) = v14 & ( ~ element(v12, v15) | element(v13, v15)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (complements_of_subsets(v11, v12) = v13) | ? [v14] : ? [v15] : (powerset(v14) = v15 & powerset(v11) = v14 & ( ~ element(v12, v15) | ( ! [v16] : ! [v17] : ( ~ (subset_complement(v11, v16) = v17) | ~ element(v16, v14) | ~ element(v13, v15) | ~ in(v17, v12) | in(v16, v13)) & ! [v16] : ! [v17] : ( ~ (subset_complement(v11, v16) = v17) | ~ element(v16, v14) | ~ element(v13, v15) | ~ in(v16, v13) | in(v17, v12)) & ! [v16] : (v16 = v13 | ~ element(v16, v15) | ? [v17] : ? [v18] : (subset_complement(v11, v17) = v18 & element(v17, v14) & ( ~ in(v18, v12) | ~ in(v17, v16)) & (in(v18, v12) | in(v17, v16)))))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v12, v11) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ~ function(v12) | ~ function(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ~ function(v12) | ~ function(v11) | function(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | ? [v14] : ? [v15] : (relation_rng(v13) = v14 & relation_rng(v12) = v15 & subset(v14, v15))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_composition(v11, v12) = v13) | ~ relation(v12) | ~ empty(v11) | empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset_complement(v11, v12) = v13) | ? [v14] : ? [v15] : (set_difference(v11, v12) = v15 & powerset(v11) = v14 & (v15 = v13 | ~ element(v12, v14)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (subset_complement(v11, v12) = v13) | ? [v14] : (powerset(v11) = v14 & ( ~ element(v12, v14) | element(v13, v14)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ~ relation(v11) | ? [v14] : ? [v15] : (relation_composition(v11, v12) = v14 & relation_rng(v14) = v15 & subset(v15, v13))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ in(v13, v12) | ? [v14] : ? [v15] : (ordered_pair(v14, v13) = v15 & in(v15, v11))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v13) = v11) | ~ (singleton(v12) = v13) | ~ in(v12, v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v12) = v13) | subset(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v12) = v13) | ? [v14] : ? [v15] : (subset_complement(v11, v12) = v15 & powerset(v11) = v14 & (v15 = v13 | ~ element(v12, v14)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_difference(v11, v12) = v13) | ? [v14] : (set_difference(v14, v12) = v13 & set_union2(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v12) = v13) | ~ in(v11, v12) | subset(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (union(v11) = v12) | ~ in(v13, v12) | ? [v14] : (in(v14, v11) & in(v13, v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom(v11) = v12) | ~ (relation_image(v11, v12) = v13) | ~ relation(v11) | relation_rng(v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ in(v13, v12) | ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & in(v15, v11))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (apply(v12, v11) = v13) | ~ relation(v12) | ~ function(v12) | ? [v14] : (relation_dom(v12) = v14 & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v12, v15) = v16) | ~ (apply(v16, v11) = v17) | ~ relation(v15) | ~ function(v15) | ~ in(v11, v14) | apply(v15, v13) = v17) & ! [v15] : ! [v16] : ( ~ (apply(v15, v13) = v16) | ~ relation(v15) | ~ function(v15) | ~ in(v11, v14) | ? [v17] : (relation_composition(v12, v15) = v17 & apply(v17, v11) = v16)))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (cartesian_product2(v11, v12) = v13) | ~ empty(v13) | empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ element(v11, v13) | subset(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ subset(v11, v12) | element(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v11) = v12) | ~ subset(v13, v11) | in(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v11) = v12) | ~ in(v13, v12) | subset(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v13) | ~ disjoint(v13, v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v13) | ~ subset(v13, v12) | in(v11, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v11) = v13) | ~ in(v11, v12) | subset(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_inverse_image(v12, v11) = v13) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & subset(v13, v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_image(v12, v11) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_dom(v12) = v14 & relation_image(v12, v15) = v13 & set_intersection2(v14, v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_image(v12, v11) = v13) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & subset(v13, v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v12) | subset(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v12) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_rng(v13) = v14 & relation_rng(v12) = v15 & set_intersection2(v15, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_rng(v13) = v14 & relation_rng(v12) = v15 & subset(v14, v15))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_rng_restriction(v11, v12) = v13) | ~ relation(v12) | ? [v14] : (relation_rng(v13) = v14 & subset(v14, v11))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom_restriction(v12, v11) = v13) | ~ relation(v12) | subset(v13, v12)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom_restriction(v12, v11) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_rng(v13) = v14 & relation_rng(v12) = v15 & subset(v14, v15))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom_restriction(v12, v11) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_dom(v13) = v14 & relation_dom(v12) = v15 & set_intersection2(v15, v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom_restriction(v12, v11) = v13) | ~ relation(v12) | ? [v14] : (relation_composition(v14, v12) = v13 & identity_relation(v11) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (relation_dom_restriction(v11, v12) = v13) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) | ? [v14] : ? [v15] : (singleton(v11) = v15 & unordered_pair(v14, v15) = v13 & unordered_pair(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v12, v11) = v13) | set_intersection2(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | set_intersection2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | disjoint(v11, v12) | ? [v14] : in(v14, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | subset(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | ? [v14] : (set_difference(v11, v14) = v13 & set_difference(v11, v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | ~ empty(v13) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v12, v11) = v13) | set_union2(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ relation(v12) | ~ relation(v11) | relation(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ~ empty(v13) | empty(v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | subset(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (set_union2(v11, v12) = v13) | ? [v14] : (set_difference(v12, v11) = v14 & set_union2(v11, v14) = v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v12, v11) = v13) | unordered_pair(v11, v12) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | ~ empty(v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | in(v12, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | in(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ disjoint(v12, v13) | ~ subset(v11, v12) | disjoint(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ disjoint(v11, v12) | ~ in(v13, v12) | ~ in(v13, v11)) & ! [v11] : ! [v12] : ! [v13] : ( ~ subset(v12, v13) | ~ subset(v11, v12) | subset(v11, v13)) & ! [v11] : ! [v12] : ! [v13] : ( ~ subset(v11, v12) | ~ in(v13, v11) | in(v13, v12)) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | v12 = empty_set | ~ (set_meet(v12) = v13) | ? [v14] : ? [v15] : (( ~ in(v14, v11) | (in(v15, v12) & ~ in(v14, v15))) & (in(v14, v11) | ! [v16] : ( ~ in(v16, v12) | in(v14, v16))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : ? [v16] : (( ~ in(v14, v11) | ! [v17] : ! [v18] : ( ~ (ordered_pair(v17, v14) = v18) | ~ in(v18, v12))) & (in(v14, v11) | (ordered_pair(v15, v14) = v16 & in(v16, v12))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (union(v12) = v13) | ? [v14] : ? [v15] : (( ~ in(v14, v11) | ! [v16] : ( ~ in(v16, v12) | ~ in(v14, v16))) & (in(v14, v11) | (in(v15, v12) & in(v14, v15))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : ? [v16] : (( ~ in(v14, v11) | ! [v17] : ! [v18] : ( ~ (ordered_pair(v14, v17) = v18) | ~ in(v18, v12))) & (in(v14, v11) | (ordered_pair(v14, v15) = v16 & in(v16, v12))))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (powerset(v12) = v13) | ? [v14] : (( ~ subset(v14, v12) | ~ in(v14, v11)) & (subset(v14, v12) | in(v14, v11)))) & ? [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (singleton(v12) = v13) | ? [v14] : (( ~ (v14 = v12) | ~ in(v12, v11)) & (v14 = v12 | in(v14, v11)))) & ? [v11] : ! [v12] : ! [v13] : (v12 = empty_set | ~ (set_meet(v12) = v13) | in(v11, v13) | ? [v14] : (in(v14, v12) & ~ in(v11, v14))) & ? [v11] : ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | element(v11, v13) | ? [v14] : (in(v14, v11) & ~ in(v14, v12))) & ? [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | disjoint(v13, v11) | in(v12, v11)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (set_difference(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (cast_to_subset(v11) = v12)) & ! [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 = v11 | ~ subset(v12, v11) | ~ subset(v11, v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ subset(v11, v12) | proper_subset(v11, v12)) & ! [v11] : ! [v12] : (v12 = v11 | ~ relation(v12) | ~ relation(v11) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & ( ~ in(v15, v12) | ~ in(v15, v11)) & (in(v15, v12) | in(v15, v11)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ empty(v12) | ~ empty(v11)) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (complements_of_subsets(v11, v12) = empty_set) | ? [v13] : ? [v14] : (powerset(v13) = v14 & powerset(v11) = v13 & ~ element(v12, v14))) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_difference(empty_set, v11) = v12)) & ! [v11] : ! [v12] : (v12 = empty_set | ~ (set_intersection2(v11, empty_set) = v12)) & ! [v11] : ! [v12] : (v11 = empty_set | ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : ( ~ (v13 = empty_set) & relation_dom(v11) = v13)) & ! [v11] : ! [v12] : (v11 = empty_set | ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : ( ~ (v13 = empty_set) & relation_rng(v11) = v13)) & ! [v11] : ! [v12] : (v11 = empty_set | ~ (relation_inverse_image(v12, v11) = empty_set) | ~ relation(v12) | ? [v13] : (relation_rng(v12) = v13 & ~ subset(v11, v13))) & ! [v11] : ! [v12] : ( ~ (relation_inverse(v11) = v12) | ~ relation(v11) | relation_inverse(v12) = v11) & ! [v11] : ! [v12] : ( ~ (relation_inverse(v11) = v12) | ~ relation(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_inverse(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_rng(v12) = v14 & relation_rng(v11) = v13 & relation_dom(v12) = v13 & relation_dom(v11) = v14)) & ! [v11] : ! [v12] : ( ~ (relation_field(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_rng(v11) = v14 & relation_dom(v11) = v13 & set_union2(v13, v14) = v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_inverse(v11) = v13 & relation_rng(v13) = v14 & relation_dom(v13) = v12 & relation_dom(v11) = v14)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & relation_image(v11, v13) = v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v11) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_rng(v15) = v17 & relation_rng(v14) = v16 & (v17 = v12 | ~ subset(v13, v16)))) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ subset(v13, v15) | ~ relation(v14) | ? [v16] : (relation_composition(v14, v11) = v16 & relation_rng(v16) = v12)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & ! [v14] : ! [v15] : ( ~ (relation_composition(v11, v14) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_dom(v15) = v17 & relation_dom(v14) = v16 & (v17 = v13 | ~ subset(v12, v16)))) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ subset(v12, v15) | ~ relation(v14) | ? [v16] : (relation_composition(v11, v14) = v16 & relation_dom(v16) = v13)))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | subset(v12, v15)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | ? [v16] : (relation_dom(v14) = v16 & subset(v13, v16))) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | subset(v13, v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | ? [v16] : (relation_rng(v14) = v16 & subset(v12, v16))))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_dom(v11) = v13 & ( ~ (v13 = empty_set) | v12 = empty_set) & ( ~ (v12 = empty_set) | v13 = empty_set))) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_rng(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (set_difference(v11, v12) = v11) | disjoint(v11, v12)) & ! [v11] : ! [v12] : ( ~ (set_difference(v11, v12) = empty_set) | subset(v11, v12)) & ! [v11] : ! [v12] : ( ~ (cast_to_subset(v11) = v12) | ? [v13] : (powerset(v11) = v13 & element(v12, v13))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ~ empty(v12) | empty(v11)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : ? [v14] : (relation_inverse(v11) = v14 & relation_rng(v14) = v12 & relation_rng(v11) = v13 & relation_dom(v14) = v13)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v11) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_rng(v15) = v17 & relation_rng(v14) = v16 & (v17 = v13 | ~ subset(v12, v16)))) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ subset(v12, v15) | ~ relation(v14) | ? [v16] : (relation_composition(v14, v11) = v16 & relation_rng(v16) = v13)))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & ! [v14] : ! [v15] : ( ~ (relation_composition(v11, v14) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_dom(v15) = v17 & relation_dom(v14) = v16 & (v17 = v12 | ~ subset(v13, v16)))) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ subset(v13, v15) | ~ relation(v14) | ? [v16] : (relation_composition(v11, v14) = v16 & relation_dom(v16) = v12)))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | subset(v13, v15)) & ! [v14] : ! [v15] : ( ~ (relation_rng(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | ? [v16] : (relation_dom(v14) = v16 & subset(v12, v16))) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | subset(v12, v15)) & ! [v14] : ! [v15] : ( ~ (relation_dom(v14) = v15) | ~ subset(v11, v14) | ~ relation(v14) | ? [v16] : (relation_rng(v14) = v16 & subset(v13, v16))))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ relation(v11) | ? [v13] : (relation_rng(v11) = v13 & ( ~ (v13 = empty_set) | v12 = empty_set) & ( ~ (v12 = empty_set) | v13 = empty_set))) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (relation_dom(v11) = v12) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | union(v12) = v11) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | empty(v11) | ? [v13] : (element(v13, v12) & ~ empty(v13))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (cast_to_subset(v11) = v13 & element(v13, v12))) & ! [v11] : ! [v12] : ( ~ (powerset(v11) = v12) | ? [v13] : (element(v13, v12) & empty(v13))) & ! [v11] : ! [v12] : ( ~ (singleton(v12) = v11) | subset(v11, v11)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | ~ empty(v12)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | unordered_pair(v11, v11) = v12) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | subset(empty_set, v12)) & ! [v11] : ! [v12] : ( ~ (singleton(v11) = v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation_rng(v12) = v11) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation_dom(v12) = v11) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | relation(v12)) & ! [v11] : ! [v12] : ( ~ (identity_relation(v11) = v12) | function(v12)) & ! [v11] : ! [v12] : ( ~ (set_intersection2(v11, v12) = empty_set) | disjoint(v11, v12)) & ! [v11] : ! [v12] : ( ~ (unordered_pair(v11, v11) = v12) | singleton(v11) = v12) & ! [v11] : ! [v12] : ( ~ disjoint(v11, v12) | disjoint(v12, v11)) & ! [v11] : ! [v12] : ( ~ element(v12, v11) | ~ empty(v11) | empty(v12)) & ! [v11] : ! [v12] : ( ~ element(v12, v11) | empty(v11) | in(v12, v11)) & ! [v11] : ! [v12] : ( ~ element(v11, v12) | empty(v12) | in(v11, v12)) & ! [v11] : ! [v12] : ( ~ subset(v11, v12) | ~ proper_subset(v12, v11)) & ! [v11] : ! [v12] : ( ~ relation(v12) | ~ relation(v11) | subset(v11, v12) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & in(v15, v11) & ~ in(v15, v12))) & ! [v11] : ! [v12] : ( ~ relation(v11) | ~ in(v12, v11) | ? [v13] : ? [v14] : ordered_pair(v13, v14) = v12) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ empty(v11) | element(v12, v11)) & ! [v11] : ! [v12] : ( ~ empty(v12) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ proper_subset(v12, v11) | ~ proper_subset(v11, v12)) & ! [v11] : ! [v12] : ( ~ proper_subset(v11, v12) | subset(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | ~ in(v11, v12)) & ! [v11] : ! [v12] : ( ~ in(v12, v11) | element(v12, v11) | empty(v11)) & ! [v11] : ! [v12] : ( ~ in(v11, v12) | element(v11, v12)) & ! [v11] : (v11 = empty_set | ~ (relation_rng(v11) = empty_set) | ~ relation(v11)) & ! [v11] : (v11 = empty_set | ~ (relation_dom(v11) = empty_set) | ~ relation(v11)) & ! [v11] : (v11 = empty_set | ~ (set_meet(empty_set) = v11)) & ! [v11] : (v11 = empty_set | ~ subset(v11, empty_set)) & ! [v11] : (v11 = empty_set | ~ relation(v11) | ? [v12] : ? [v13] : ? [v14] : (ordered_pair(v12, v13) = v14 & in(v14, v11))) & ! [v11] : (v11 = empty_set | ~ empty(v11)) & ! [v11] : ~ (singleton(v11) = empty_set) & ! [v11] : ( ~ empty(v11) | relation(v11)) & ! [v11] : ( ~ empty(v11) | function(v11)) & ! [v11] : ~ proper_subset(v11, v11) & ! [v11] : ~ in(v11, empty_set) & ? [v11] : ? [v12] : (v12 = v11 | ? [v13] : (( ~ in(v13, v12) | ~ in(v13, v11)) & (in(v13, v12) | in(v13, v11)))) & ? [v11] : ? [v12] : (disjoint(v11, v12) | ? [v13] : (in(v13, v12) & in(v13, v11))) & ? [v11] : ? [v12] : element(v12, v11) & ? [v11] : ? [v12] : (subset(v11, v12) | ? [v13] : (in(v13, v11) & ~ in(v13, v12))) & ? [v11] : ? [v12] : (in(v11, v12) & ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ in(v13, v12) | in(v14, v12)) & ! [v13] : ! [v14] : ( ~ subset(v14, v13) | ~ in(v13, v12) | in(v14, v12)) & ! [v13] : ( ~ subset(v13, v12) | are_equipotent(v13, v12) | in(v13, v12))) & ? [v11] : ? [v12] : (in(v11, v12) & ! [v13] : ! [v14] : ( ~ subset(v14, v13) | ~ in(v13, v12) | in(v14, v12)) & ! [v13] : ( ~ subset(v13, v12) | are_equipotent(v13, v12) | in(v13, v12)) & ! [v13] : ( ~ in(v13, v12) | ? [v14] : (in(v14, v12) & ! [v15] : ( ~ subset(v15, v13) | in(v15, v14))))) & ? [v11] : (v11 = empty_set | ? [v12] : in(v12, v11)) & ? [v11] : subset(v11, v11) & ? [v11] : subset(empty_set, v11) & ? [v11] : (relation(v11) | ? [v12] : (in(v12, v11) & ! [v13] : ! [v14] : ~ (ordered_pair(v13, v14) = v12))))
% 12.68/3.43 | 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:
% 12.68/3.43 | (1) ~ (all_0_6_6 = all_0_8_8) & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & apply(all_0_7_7, all_0_8_8) = all_0_6_6 & powerset(empty_set) = all_0_10_10 & singleton(empty_set) = all_0_10_10 & identity_relation(all_0_9_9) = all_0_7_7 & relation_empty_yielding(all_0_5_5) & relation_empty_yielding(empty_set) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_5_5) & relation(empty_set) & function(all_0_0_0) & empty(all_0_1_1) & empty(all_0_2_2) & empty(empty_set) & in(all_0_8_8, all_0_9_9) & ~ empty(all_0_3_3) & ~ empty(all_0_4_4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) & ! [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] : (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] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [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] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ element(v3, v2) | ~ element(v1, v2) | ~ subset(v1, v4) | disjoint(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6))) & ! [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] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [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 | ~ (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 | ~ (apply(v3, v2) = v1) | ~ (apply(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 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (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 = empty_set | ~ (meet_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = 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, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (set_meet(v1) = v3) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & ( ~ in(v6, v0) | ~ in(v5, v2)) & (in(v6, v0) | in(v5, v2)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0))))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [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 | ~ (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 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v5 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5)))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [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 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) & ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1))) & ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v1) & ! [v4] : ( ~ subset(v4, v2) | in(v4, v3))))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) & ? [v0] : subset(v0, v0) & ? [v0] : subset(empty_set, v0) & ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 12.92/3.48 |
% 12.92/3.48 | Applying alpha-rule on (1) yields:
% 12.92/3.48 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 12.92/3.48 | (3) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 12.92/3.48 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 12.92/3.48 | (5) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3)))
% 12.92/3.49 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3)
% 12.92/3.49 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1))
% 12.92/3.49 | (8) relation_dom(empty_set) = empty_set
% 12.92/3.49 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3)
% 12.92/3.49 | (10) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 12.92/3.49 | (11) powerset(empty_set) = all_0_10_10
% 12.92/3.49 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ element(v3, v2) | ~ element(v1, v2) | ~ subset(v1, v4) | disjoint(v1, v3))
% 12.92/3.49 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1)))
% 12.92/3.49 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 12.92/3.49 | (15) ! [v0] : ~ (singleton(v0) = empty_set)
% 12.92/3.49 | (16) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0))
% 12.92/3.49 | (17) empty(all_0_1_1)
% 12.92/3.49 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1)))
% 12.92/3.49 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 12.92/3.49 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 12.92/3.49 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3))
% 12.92/3.49 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2))
% 12.92/3.49 | (23) empty(empty_set)
% 12.92/3.49 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5)))))
% 12.92/3.49 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5))))
% 12.92/3.49 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1)))
% 12.92/3.49 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 12.92/3.49 | (28) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 12.92/3.49 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4)))
% 12.92/3.49 | (30) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 12.92/3.49 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 12.92/3.49 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 12.92/3.49 | (33) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1)))))
% 12.92/3.49 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 12.92/3.49 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5)))
% 12.92/3.49 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6)))
% 12.92/3.49 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 12.92/3.49 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0)))
% 12.92/3.49 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 12.92/3.49 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 12.92/3.49 | (41) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 12.92/3.49 | (42) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1)))))
% 12.92/3.49 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 12.92/3.49 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2))
% 12.92/3.49 | (45) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0))
% 12.92/3.49 | (46) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 12.92/3.49 | (47) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 12.92/3.49 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 12.92/3.49 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 12.92/3.49 | (50) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6)))))
% 12.92/3.49 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6)))
% 12.92/3.49 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 12.92/3.49 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1))
% 12.92/3.50 | (54) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 12.92/3.50 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3))
% 12.92/3.50 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 12.92/3.50 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 12.92/3.50 | (58) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 12.92/3.50 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0))
% 12.92/3.50 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 12.92/3.50 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4)
% 12.92/3.50 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 12.92/3.50 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 12.92/3.50 | (64) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 12.92/3.50 | (65) ! [v0] : ~ proper_subset(v0, v0)
% 12.92/3.50 | (66) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 12.92/3.50 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4))
% 12.92/3.50 | (68) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 12.92/3.50 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 12.92/3.50 | (70) in(all_0_8_8, all_0_9_9)
% 12.92/3.50 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0)))
% 12.92/3.50 | (72) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 12.92/3.50 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2))
% 12.92/3.50 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1))
% 12.92/3.50 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 12.92/3.50 | (76) relation_empty_yielding(all_0_5_5)
% 12.92/3.50 | (77) ? [v0] : ? [v1] : element(v1, v0)
% 12.92/3.50 | (78) identity_relation(all_0_9_9) = all_0_7_7
% 12.92/3.50 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 12.92/3.50 | (80) ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v1) & ! [v4] : ( ~ subset(v4, v2) | in(v4, v3)))))
% 12.92/3.50 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2))
% 12.92/3.50 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 12.92/3.50 | (83) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2)))
% 12.92/3.50 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 12.92/3.50 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0))
% 12.92/3.50 | (86) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2))))
% 12.92/3.50 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 12.92/3.50 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0))
% 12.92/3.50 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3))
% 12.92/3.50 | (90) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 12.92/3.50 | (91) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set)))
% 12.92/3.50 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0)))
% 12.92/3.50 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 12.92/3.50 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1)))
% 12.92/3.50 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 12.92/3.50 | (96) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set)))
% 12.92/3.50 | (97) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5)))))
% 12.92/3.50 | (98) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2))))
% 12.92/3.50 | (99) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 12.92/3.50 | (100) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 12.92/3.51 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5))))))))
% 12.92/3.51 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 12.92/3.51 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 12.92/3.51 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2))
% 12.92/3.51 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 12.92/3.51 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 12.92/3.51 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 12.92/3.51 | (108) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 12.92/3.51 | (109) ~ (all_0_6_6 = all_0_8_8)
% 12.92/3.51 | (110) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 12.92/3.51 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 12.92/3.51 | (112) relation(all_0_3_3)
% 12.92/3.51 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 12.92/3.51 | (114) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1)))
% 12.92/3.51 | (115) relation(all_0_5_5)
% 12.92/3.51 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1)))
% 12.92/3.51 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 12.92/3.51 | (118) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5))))
% 12.92/3.51 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 12.92/3.51 | (120) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 12.92/3.51 | (121) relation_empty_yielding(empty_set)
% 12.92/3.51 | (122) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 12.92/3.51 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2))
% 12.92/3.51 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4))))
% 12.92/3.51 | (125) ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0))))
% 12.92/3.51 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 12.92/3.51 | (127) ! [v0] : ( ~ empty(v0) | function(v0))
% 12.92/3.51 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 12.92/3.51 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v6)))
% 12.92/3.51 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 12.92/3.51 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 12.92/3.51 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 12.92/3.51 | (133) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1)))))
% 12.92/3.51 | (134) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 12.92/3.51 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3))))
% 12.92/3.51 | (136) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 12.92/3.51 | (137) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 12.92/3.51 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 12.92/3.51 | (139) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2))
% 12.92/3.51 | (140) ? [v0] : subset(empty_set, v0)
% 12.92/3.51 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 12.92/3.51 | (142) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1)))))
% 12.92/3.51 | (143) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_dom(v1) = v0) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : ( ~ (v4 = v3) & apply(v1, v3) = v4 & in(v3, v0)))
% 12.92/3.51 | (144) relation_rng(empty_set) = empty_set
% 12.92/3.51 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0))
% 12.92/3.51 | (146) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 12.92/3.51 | (147) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 12.92/3.51 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 12.92/3.51 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1))
% 13.18/3.51 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2))
% 13.18/3.51 | (151) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 13.18/3.51 | (152) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4)))))
% 13.18/3.52 | (153) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0))
% 13.18/3.52 | (154) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 13.18/3.52 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 13.18/3.52 | (156) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 13.18/3.52 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2))
% 13.18/3.52 | (158) ! [v0] : ( ~ empty(v0) | relation(v0))
% 13.18/3.52 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 13.18/3.52 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 13.18/3.52 | (161) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2)))
% 13.18/3.52 | (162) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 13.18/3.52 | (163) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 13.18/3.52 | (164) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3))
% 13.18/3.52 | (165) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 13.18/3.52 | (166) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1))))
% 13.18/3.52 | (167) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 13.18/3.52 | (168) empty(all_0_2_2)
% 13.18/3.52 | (169) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 13.18/3.52 | (170) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 13.18/3.52 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 13.18/3.52 | (172) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 13.18/3.52 | (173) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 13.18/3.52 | (174) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 13.18/3.52 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4))
% 13.18/3.52 | (176) relation(empty_set)
% 13.18/3.52 | (177) ! [v0] : ~ in(v0, empty_set)
% 13.18/3.52 | (178) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 13.18/3.52 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 13.18/3.52 | (180) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1)))
% 13.18/3.52 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0)))))
% 13.18/3.52 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 13.18/3.52 | (183) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 13.18/3.52 | (184) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 13.18/3.52 | (185) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4))
% 13.18/3.52 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 13.18/3.52 | (187) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 13.18/3.52 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 13.18/3.52 | (189) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 13.18/3.52 | (190) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 13.18/3.52 | (191) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 13.18/3.52 | (192) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2)))
% 13.18/3.52 | (193) function(all_0_0_0)
% 13.18/3.52 | (194) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 13.18/3.52 | (195) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4))))
% 13.18/3.52 | (196) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 13.18/3.52 | (197) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 13.18/3.52 | (198) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 13.18/3.52 | (199) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 13.18/3.52 | (200) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 13.18/3.52 | (201) ~ empty(all_0_3_3)
% 13.18/3.52 | (202) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 13.18/3.52 | (203) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4))))
% 13.18/3.52 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 13.18/3.52 | (205) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 13.18/3.52 | (206) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 13.18/3.52 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 13.18/3.52 | (208) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2))
% 13.18/3.52 | (209) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 13.18/3.53 | (210) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 13.18/3.53 | (211) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 13.18/3.53 | (212) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1))
% 13.18/3.53 | (213) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4))
% 13.18/3.53 | (214) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 13.18/3.53 | (215) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 13.18/3.53 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4)))
% 13.18/3.53 | (217) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4))
% 13.18/3.53 | (218) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (set_meet(v1) = v3) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4))))
% 13.18/3.53 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 13.18/3.53 | (220) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 13.18/3.53 | (221) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v5 & (v5 = v2 | ~ element(v1, v4))))
% 13.18/3.53 | (222) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1))
% 13.18/3.53 | (223) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5)))))
% 13.18/3.53 | (224) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & ( ~ (v4 = v3) | ~ in(v5, v1) | ~ in(v3, v0)) & (in(v5, v1) | (v4 = v3 & in(v3, v0)))))
% 13.18/3.53 | (225) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1))
% 13.18/3.53 | (226) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4))
% 13.18/3.53 | (227) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1))
% 13.18/3.53 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 13.18/3.53 | (229) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0))
% 13.18/3.53 | (230) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 13.18/3.53 | (231) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 13.18/3.53 | (232) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3)))
% 13.18/3.53 | (233) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4)))))
% 13.18/3.53 | (234) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3)))
% 13.18/3.53 | (235) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3))
% 13.18/3.53 | (236) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 13.18/3.53 | (237) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 13.18/3.53 | (238) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 13.18/3.53 | (239) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0)))
% 13.18/3.53 | (240) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 13.18/3.53 | (241) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6))
% 13.18/3.53 | (242) ~ empty(all_0_4_4)
% 13.18/3.53 | (243) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5))
% 13.18/3.53 | (244) ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)))
% 13.18/3.53 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 13.18/3.53 | (246) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 13.18/3.53 | (247) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1))))
% 13.18/3.53 | (248) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1)))))
% 13.18/3.53 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6))))
% 13.18/3.53 | (250) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 13.18/3.53 | (251) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 13.18/3.53 | (252) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 13.18/3.53 | (253) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 13.18/3.53 | (254) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 13.18/3.53 | (255) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 13.18/3.53 | (256) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1))
% 13.18/3.53 | (257) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 13.18/3.53 | (258) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 13.18/3.54 | (259) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 13.18/3.54 | (260) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 13.18/3.54 | (261) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4))))
% 13.18/3.54 | (262) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1)))))
% 13.18/3.54 | (263) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0)
% 13.18/3.54 | (264) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2)))))
% 13.18/3.54 | (265) relation(all_0_0_0)
% 13.18/3.54 | (266) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 13.18/3.54 | (267) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0))))
% 13.18/3.54 | (268) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1)))))
% 13.18/3.54 | (269) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 13.18/3.54 | (270) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2)))))
% 13.18/3.54 | (271) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 13.18/3.54 | (272) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 13.18/3.54 | (273) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0))
% 13.18/3.54 | (274) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1))
% 13.18/3.54 | (275) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1)))
% 13.18/3.54 | (276) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 13.18/3.54 | (277) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0)))
% 13.18/3.54 | (278) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 13.18/3.54 | (279) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3))
% 13.18/3.54 | (280) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 13.18/3.54 | (281) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3)))
% 13.18/3.54 | (282) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2))
% 13.18/3.54 | (283) relation(all_0_1_1)
% 13.18/3.54 | (284) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0)))))
% 13.18/3.54 | (285) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5))
% 13.18/3.54 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 13.18/3.54 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0))
% 13.18/3.54 | (288) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2))
% 13.18/3.54 | (289) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1)))
% 13.18/3.54 | (290) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 13.18/3.54 | (291) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 13.18/3.54 | (292) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 13.18/3.54 | (293) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 13.18/3.54 | (294) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 13.18/3.54 | (295) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2)
% 13.18/3.54 | (296) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5))))
% 13.18/3.54 | (297) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (meet_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5))))
% 13.18/3.54 | (298) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 13.18/3.54 | (299) ! [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] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6))))
% 13.18/3.54 | (300) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 13.18/3.54 | (301) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 13.18/3.54 | (302) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0)))
% 13.18/3.54 | (303) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 13.18/3.55 | (304) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 13.18/3.55 | (305) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 13.18/3.55 | (306) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3))
% 13.18/3.55 | (307) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 13.18/3.55 | (308) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 13.18/3.55 | (309) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 13.18/3.55 | (310) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 13.18/3.55 | (311) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3))
% 13.18/3.55 | (312) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 13.18/3.55 | (313) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 13.18/3.55 | (314) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1)))))
% 13.18/3.55 | (315) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5))
% 13.18/3.55 | (316) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3))
% 13.18/3.55 | (317) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0))
% 13.18/3.55 | (318) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5)))))
% 13.18/3.55 | (319) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5)))
% 13.18/3.55 | (320) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 13.18/3.55 | (321) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5)))
% 13.18/3.55 | (322) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4))
% 13.18/3.55 | (323) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 13.18/3.55 | (324) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 13.18/3.55 | (325) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 13.18/3.55 | (326) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 13.18/3.55 | (327) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 13.18/3.55 | (328) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 13.18/3.55 | (329) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3)))
% 13.18/3.55 | (330) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0)))
% 13.18/3.55 | (331) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4)
% 13.18/3.55 | (332) singleton(empty_set) = all_0_10_10
% 13.18/3.55 | (333) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 13.18/3.55 | (334) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1))
% 13.18/3.55 | (335) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1)))))
% 13.18/3.55 | (336) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1))
% 13.18/3.55 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5)))
% 13.18/3.55 | (338) apply(all_0_7_7, all_0_8_8) = all_0_6_6
% 13.18/3.55 | (339) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 13.18/3.55 | (340) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2)))))
% 13.18/3.55 | (341) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 13.18/3.55 | (342) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 13.18/3.55 | (343) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 13.18/3.55 | (344) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0))
% 13.18/3.55 | (345) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 13.18/3.55 | (346) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1))
% 13.18/3.55 | (347) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 13.18/3.55 | (348) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 13.18/3.55 | (349) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 13.18/3.55 | (350) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 13.18/3.55 | (351) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 13.18/3.55 | (352) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7)))))
% 13.18/3.55 | (353) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 13.18/3.56 | (354) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4)))))
% 13.18/3.56 | (355) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4))))
% 13.18/3.56 | (356) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v3) = v6 & ordered_pair(v3, v4) = v5 & ( ~ in(v6, v0) | ~ in(v5, v2)) & (in(v6, v0) | in(v5, v2))))
% 13.18/3.56 | (357) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0))
% 13.18/3.56 | (358) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 13.18/3.56 | (359) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 13.18/3.56 | (360) ! [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] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6))))
% 13.18/3.56 | (361) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 13.18/3.56 | (362) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 13.18/3.56 | (363) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 13.18/3.56 | (364) ? [v0] : subset(v0, v0)
% 13.18/3.56 |
% 13.18/3.56 | Instantiating formula (308) with all_0_7_7, all_0_9_9 and discharging atoms identity_relation(all_0_9_9) = all_0_7_7, yields:
% 13.18/3.56 | (365) relation_dom(all_0_7_7) = all_0_9_9
% 13.18/3.56 |
% 13.18/3.56 | Instantiating formula (220) with all_0_7_7, all_0_9_9 and discharging atoms identity_relation(all_0_9_9) = all_0_7_7, yields:
% 13.18/3.56 | (366) relation(all_0_7_7)
% 13.18/3.56 |
% 13.18/3.56 | Instantiating formula (167) with all_0_7_7, all_0_9_9 and discharging atoms identity_relation(all_0_9_9) = all_0_7_7, yields:
% 13.18/3.56 | (367) function(all_0_7_7)
% 13.18/3.56 |
% 13.18/3.56 | Instantiating formula (287) with all_0_6_6, all_0_8_8, all_0_9_9, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_7_7) = all_0_9_9, apply(all_0_7_7, all_0_8_8) = all_0_6_6, identity_relation(all_0_9_9) = all_0_7_7, relation(all_0_7_7), function(all_0_7_7), in(all_0_8_8, all_0_9_9), yields:
% 13.18/3.56 | (368) all_0_6_6 = all_0_8_8
% 13.18/3.56 |
% 13.18/3.56 | Equations (368) can reduce 109 to:
% 13.18/3.56 | (369) $false
% 13.18/3.56 |
% 13.18/3.56 |-The branch is then unsatisfiable
% 13.18/3.56 % SZS output end Proof for theBenchmark
% 13.18/3.56
% 13.18/3.56 2966ms
%------------------------------------------------------------------------------