TSTP Solution File: SEU230+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 08:47:56 EDT 2022
% Result : Theorem 14.90s 3.93s
% Output : Proof 23.80s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU230+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.11/0.33 % Computer : n023.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Mon Jun 20 12:16:18 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.48/0.57 ____ _
% 0.48/0.57 ___ / __ \_____(_)___ ________ __________
% 0.48/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.48/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.48/0.57
% 0.48/0.57 A Theorem Prover for First-Order Logic
% 0.48/0.57 (ePrincess v.1.0)
% 0.48/0.57
% 0.48/0.57 (c) Philipp Rümmer, 2009-2015
% 0.48/0.57 (c) Peter Backeman, 2014-2015
% 0.48/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.57 Bug reports to peter@backeman.se
% 0.48/0.57
% 0.48/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.57
% 0.48/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.48/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.78/1.17 Prover 0: Preprocessing ...
% 7.49/2.19 Prover 0: Warning: ignoring some quantifiers
% 7.49/2.25 Prover 0: Constructing countermodel ...
% 14.90/3.93 Prover 0: proved (3309ms)
% 14.90/3.93
% 14.90/3.93 No countermodel exists, formula is valid
% 14.90/3.93 % SZS status Theorem for theBenchmark
% 14.90/3.93
% 14.90/3.93 Generating proof ... Warning: ignoring some quantifiers
% 22.12/5.71 found it (size 9)
% 22.12/5.71
% 22.12/5.71 % SZS output start Proof for theBenchmark
% 22.12/5.71 Assumed formulas after preprocessing and simplification:
% 22.12/5.71 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(empty_set) = empty_set & powerset(empty_set) = v0 & singleton(empty_set) = v0 & succ(v1) = v2 & relation_dom(empty_set) = empty_set & relation_empty_yielding(v4) & relation_empty_yielding(v3) & relation_empty_yielding(empty_set) & one_to_one(v5) & relation(v11) & relation(v10) & relation(v8) & relation(v7) & relation(v5) & relation(v4) & relation(v3) & relation(empty_set) & function(v11) & function(v8) & function(v5) & function(v3) & empty(v10) & empty(v9) & empty(v8) & empty(empty_set) & ~ empty(v7) & ~ empty(v6) & ~ in(v1, v2) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v12, v13) = v14) | ~ (ordered_pair(v18, v16) = v19) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v13) | ~ relation(v12) | ~ in(v19, v13) | in(v17, v14) | ? [v20] : (ordered_pair(v15, v18) = v20 & ~ in(v20, v12))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v12, v13) = v14) | ~ (ordered_pair(v15, v18) = v19) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v13) | ~ relation(v12) | ~ in(v19, v12) | in(v17, v14) | ? [v20] : (ordered_pair(v18, v16) = v20 & ~ in(v20, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v15) = v18) | ~ (identity_relation(v14) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ relation(v15) | ~ in(v16, v18) | in(v16, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v15) = v18) | ~ (identity_relation(v14) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ relation(v15) | ~ in(v16, v18) | in(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v15) = v18) | ~ (identity_relation(v14) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ relation(v15) | ~ in(v16, v15) | ~ in(v12, v14) | in(v16, v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v13) | ~ relation(v12) | ~ in(v17, v14) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v16) = v20 & ordered_pair(v15, v18) = v19 & in(v20, v13) & in(v19, v12))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v14, v15) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ in(v16, v17) | in(v13, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v14, v15) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ in(v16, v17) | in(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v14, v15) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ in(v13, v15) | ~ in(v12, v14) | in(v16, v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v13, v15) = v17) | ~ (cartesian_product2(v12, v14) = v16) | ~ subset(v14, v15) | ~ subset(v12, v13) | subset(v16, v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ (ordered_pair(v16, v17) = v15) | ~ in(v17, v13) | ~ in(v16, v12) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v12, v14) = v15) | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v16) = v17) | ~ relation(v12) | ~ function(v12) | ~ in(v17, v14) | ~ in(v16, v13) | in(v16, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v12, v14) = v15) | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v16) = v17) | ~ relation(v12) | ~ function(v12) | ~ in(v16, v15) | in(v17, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v12, v14) = v15) | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v16) = v17) | ~ relation(v12) | ~ function(v12) | ~ in(v16, v15) | in(v16, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v12) | ~ in(v17, v12) | ~ in(v16, v13) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v13) | ~ in(v17, v14) | in(v17, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v13) | ~ in(v17, v14) | in(v16, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v13) | ~ in(v17, v13) | ~ in(v16, v12) | in(v17, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ (relation_dom(v13) = v14) | ~ (set_intersection2(v16, v12) = v17) | ~ relation(v15) | ~ relation(v13) | ~ function(v15) | ~ function(v13) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_dom_restriction(v15, v12) = v18 & ( ~ (v18 = v13) | (v17 = v14 & ! [v22] : ! [v23] : ( ~ (apply(v15, v22) = v23) | ~ in(v22, v14) | apply(v13, v22) = v23) & ! [v22] : ! [v23] : ( ~ (apply(v13, v22) = v23) | ~ in(v22, v14) | apply(v15, v22) = v23))) & ( ~ (v17 = v14) | v18 = v13 | ( ~ (v21 = v20) & apply(v15, v19) = v21 & apply(v13, v19) = v20 & in(v19, v14))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v12) = v13) | ~ (relation_image(v12, v14) = v15) | ~ (apply(v12, v17) = v16) | ~ relation(v12) | ~ function(v12) | ~ in(v17, v14) | ~ in(v17, v13) | in(v16, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v12, v13) = v14) | ~ (ordered_pair(v16, v15) = v17) | ~ relation(v12) | ~ in(v17, v12) | ~ in(v16, v13) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v12) | ~ in(v17, v14) | in(v17, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v12) | ~ in(v17, v14) | in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ relation(v14) | ~ relation(v12) | ~ in(v17, v12) | ~ in(v15, v13) | in(v17, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v15 | ~ (relation_dom(v13) = v14) | ~ (apply(v13, v15) = v16) | ~ (identity_relation(v12) = v13) | ~ relation(v13) | ~ function(v13) | ~ in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v14 | v16 = v13 | v16 = v12 | ~ (unordered_triple(v12, v13, v14) = v15) | ~ in(v16, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v15) = v16) | ~ (apply(v12, v14) = v16) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ~ in(v15, v13) | ~ in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (identity_relation(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ in(v16, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v13 | ~ (ordered_pair(v14, v15) = v16) | ~ (ordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v12 | v14 = v12 | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v12 | ~ (ordered_pair(v14, v15) = v16) | ~ (ordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (subset_difference(v16, v15, v14) = v13) | ~ (subset_difference(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (unordered_triple(v16, v15, v14) = v13) | ~ (unordered_triple(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = empty_set | ~ (subset_difference(v12, v14, v15) = v16) | ~ (meet_of_subsets(v12, v13) = v15) | ~ (cast_to_subset(v12) = v14) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (union_of_subsets(v12, v19) = v20 & complements_of_subsets(v12, v13) = v19 & powerset(v17) = v18 & powerset(v12) = v17 & (v20 = v16 | ~ element(v13, v18)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = empty_set | ~ (subset_difference(v12, v14, v15) = v16) | ~ (union_of_subsets(v12, v13) = v15) | ~ (cast_to_subset(v12) = v14) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (meet_of_subsets(v12, v19) = v20 & complements_of_subsets(v12, v13) = v19 & powerset(v17) = v18 & powerset(v12) = v17 & (v20 = v16 | ~ element(v13, v18)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = empty_set | ~ (subset_complement(v12, v14) = v15) | ~ (powerset(v12) = v13) | ~ element(v16, v12) | ~ element(v14, v13) | in(v16, v15) | in(v16, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (function_inverse(v13) = v14) | ~ (relation_composition(v14, v13) = v15) | ~ (apply(v15, v12) = v16) | ~ one_to_one(v13) | ~ relation(v13) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_rng(v13) = v17 & apply(v14, v12) = v18 & apply(v13, v18) = v19 & ( ~ in(v12, v17) | (v19 = v12 & v16 = v12)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (function_inverse(v13) = v14) | ~ (apply(v14, v12) = v15) | ~ (apply(v13, v15) = v16) | ~ one_to_one(v13) | ~ relation(v13) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_composition(v14, v13) = v18 & relation_rng(v13) = v17 & apply(v18, v12) = v19 & ( ~ in(v12, v17) | (v19 = v12 & v16 = v12)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v14, v13) = v15) | ~ (apply(v15, v12) = v16) | ~ relation(v14) | ~ relation(v13) | ~ function(v14) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_dom(v15) = v17 & apply(v14, v12) = v18 & apply(v13, v18) = v19 & (v19 = v16 | ~ in(v12, v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse(v12) = v13) | ~ (ordered_pair(v15, v14) = v16) | ~ relation(v13) | ~ relation(v12) | ~ in(v16, v12) | ? [v17] : (ordered_pair(v14, v15) = v17 & in(v17, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse(v12) = v13) | ~ (ordered_pair(v15, v14) = v16) | ~ relation(v13) | ~ relation(v12) | in(v16, v12) | ? [v17] : (ordered_pair(v14, v15) = v17 & ~ in(v17, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | ~ in(v16, v13) | ? [v17] : (ordered_pair(v15, v14) = v17 & in(v17, v12))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ relation(v12) | in(v16, v13) | ? [v17] : (ordered_pair(v15, v14) = v17 & ~ in(v17, v12))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_field(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ in(v15, v14) | in(v13, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_field(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ in(v15, v14) | in(v12, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (subset_complement(v12, v15) = v16) | ~ (powerset(v12) = v14) | ~ disjoint(v13, v15) | ~ element(v15, v14) | ~ element(v13, v14) | subset(v13, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (subset_complement(v12, v15) = v16) | ~ (powerset(v12) = v14) | ~ element(v15, v14) | ~ element(v13, v14) | ~ subset(v13, v16) | disjoint(v13, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ in(v15, v14) | in(v13, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ in(v15, v14) | ? [v17] : (relation_dom(v14) = v17 & in(v12, v17))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng(v12) = v13) | ~ (ordered_pair(v15, v14) = v16) | ~ relation(v12) | ~ in(v16, v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_difference(v13, v15) = v16) | ~ (singleton(v14) = v15) | ~ subset(v12, v13) | subset(v12, v16) | in(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_difference(v13, v14) = v16) | ~ (set_difference(v12, v14) = v15) | ~ subset(v12, v13) | subset(v15, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_difference(v13, v14) = v16) | ~ (powerset(v12) = v15) | ~ element(v14, v15) | ~ element(v13, v15) | subset_difference(v12, v13, v14) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v14, v13) = v16) | ~ (cartesian_product2(v14, v12) = v15) | ~ subset(v12, v13) | subset(v15, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v14, v13) = v16) | ~ (cartesian_product2(v14, v12) = v15) | ~ subset(v12, v13) | ? [v17] : ? [v18] : (cartesian_product2(v13, v14) = v18 & cartesian_product2(v12, v14) = v17 & subset(v17, v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v14, v13) = v16) | ~ (cartesian_product2(v12, v14) = v15) | ~ subset(v12, v13) | ? [v17] : ? [v18] : (cartesian_product2(v14, v12) = v18 & cartesian_product2(v13, v14) = v17 & subset(v18, v16) & subset(v15, v17))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v14, v12) = v16) | ~ (cartesian_product2(v13, v14) = v15) | ~ subset(v12, v13) | ? [v17] : ? [v18] : (cartesian_product2(v14, v13) = v18 & cartesian_product2(v12, v14) = v17 & subset(v17, v15) & subset(v16, v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (cartesian_product2(v12, v14) = v15) | ~ subset(v12, v13) | subset(v15, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (cartesian_product2(v12, v14) = v15) | ~ subset(v12, v13) | ? [v17] : ? [v18] : (cartesian_product2(v14, v13) = v18 & cartesian_product2(v14, v12) = v17 & subset(v17, v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (singleton(v12) = v15) | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse_image(v14, v13) = v16) | ~ (relation_inverse_image(v14, v12) = v15) | ~ subset(v12, v13) | ~ relation(v14) | subset(v15, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng_restriction(v12, v15) = v16) | ~ (relation_dom_restriction(v14, v13) = v15) | ~ relation(v14) | ? [v17] : (relation_rng_restriction(v12, v14) = v17 & relation_dom_restriction(v17, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng_restriction(v12, v14) = v15) | ~ (relation_dom_restriction(v15, v13) = v16) | ~ relation(v14) | ? [v17] : (relation_rng_restriction(v12, v17) = v16 & relation_dom_restriction(v14, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ function(v14) | ? [v17] : (apply(v14, v12) = v17 & ( ~ (v17 = v13) | ~ in(v12, v16) | in(v15, v14)) & ( ~ in(v15, v14) | (v17 = v13 & in(v12, v16))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ in(v15, v14) | in(v12, v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v14) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ in(v15, v14) | ? [v17] : (relation_rng(v14) = v17 & in(v13, v17))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v13) = v14) | ~ (relation_image(v13, v15) = v16) | ~ (set_intersection2(v14, v12) = v15) | ~ relation(v13) | relation_image(v13, v12) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v13) = v14) | ~ (apply(v15, v12) = v16) | ~ relation(v15) | ~ relation(v13) | ~ function(v15) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_composition(v15, v13) = v17 & relation_dom(v17) = v18 & relation_dom(v15) = v19 & ( ~ in(v16, v14) | ~ in(v12, v19) | in(v12, v18)) & ( ~ in(v12, v18) | (in(v16, v14) & in(v12, v19))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v13) = v14) | ~ (relation_dom_restriction(v15, v12) = v16) | ~ relation(v15) | ~ relation(v13) | ~ function(v15) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_dom(v15) = v17 & set_intersection2(v17, v12) = v18 & ( ~ (v18 = v14) | v16 = v13 | ( ~ (v21 = v20) & apply(v15, v19) = v21 & apply(v13, v19) = v20 & in(v19, v14))) & ( ~ (v16 = v13) | (v18 = v14 & ! [v22] : ! [v23] : ( ~ (apply(v15, v22) = v23) | ~ in(v22, v14) | apply(v13, v22) = v23) & ! [v22] : ! [v23] : ( ~ (apply(v13, v22) = v23) | ~ in(v22, v14) | apply(v15, v22) = v23))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (relation_image(v12, v14) = v15) | ~ relation(v12) | ~ function(v12) | ~ in(v16, v15) | ? [v17] : (apply(v12, v17) = v16 & in(v17, v14) & in(v17, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v12) | ~ function(v12) | ~ in(v14, v13) | ? [v17] : (apply(v12, v14) = v17 & ( ~ (v17 = v15) | in(v16, v12)) & (v17 = v15 | ~ in(v16, v12)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v12) | ~ in(v16, v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (apply(v15, v13) = v16) | ~ (relation_dom_restriction(v14, v12) = v15) | ~ relation(v14) | ~ function(v14) | ~ in(v13, v12) | apply(v14, v13) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (apply(v15, v13) = v16) | ~ (relation_dom_restriction(v14, v12) = v15) | ~ relation(v14) | ~ function(v14) | ? [v17] : ? [v18] : (relation_dom(v15) = v17 & apply(v14, v13) = v18 & (v18 = v16 | ~ in(v13, v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (apply(v14, v13) = v16) | ~ (relation_dom_restriction(v14, v12) = v15) | ~ relation(v14) | ~ function(v14) | ? [v17] : ? [v18] : (relation_dom(v15) = v17 & apply(v15, v13) = v18 & (v18 = v16 | ~ in(v13, v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (apply(v14, v12) = v16) | ~ (ordered_pair(v12, v13) = v15) | ~ relation(v14) | ~ function(v14) | ? [v17] : (relation_dom(v14) = v17 & ( ~ (v16 = v13) | ~ in(v12, v17) | in(v15, v14)) & ( ~ in(v15, v14) | (v16 = v13 & in(v12, v17))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (apply(v14, v12) = v15) | ~ (apply(v13, v15) = v16) | ~ relation(v14) | ~ relation(v13) | ~ function(v14) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_composition(v14, v13) = v17 & relation_dom(v17) = v18 & apply(v17, v12) = v19 & (v19 = v16 | ~ in(v12, v18)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (identity_relation(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ relation(v13) | ~ in(v16, v13) | in(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (ordered_pair(v14, v15) = v16) | ~ subset(v12, v13) | ~ relation(v13) | ~ relation(v12) | ~ in(v16, v12) | in(v16, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_intersection2(v13, v14) = v16) | ~ (set_intersection2(v12, v14) = v15) | ~ subset(v12, v13) | subset(v15, v16)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v12 | ~ (unordered_triple(v13, v14, v15) = v16) | ? [v17] : ((v17 = v15 | v17 = v14 | v17 = v13 | in(v17, v12)) & ( ~ in(v17, v12) | ( ~ (v17 = v15) & ~ (v17 = v14) & ~ (v17 = v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v12 | ~ (relation_inverse_image(v13, v15) = v16) | ~ (relation_dom(v13) = v14) | ~ relation(v13) | ~ function(v13) | ? [v17] : ? [v18] : (apply(v13, v17) = v18 & ( ~ in(v18, v15) | ~ in(v17, v14) | ~ in(v17, v12)) & (in(v17, v12) | (in(v18, v15) & in(v17, v14))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = v12 | ~ (relation_dom(v13) = v14) | ~ (relation_image(v13, v15) = v16) | ~ relation(v13) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (( ~ in(v17, v12) | ! [v20] : ( ~ (apply(v13, v20) = v17) | ~ in(v20, v15) | ~ in(v20, v14))) & (in(v17, v12) | (v19 = v17 & apply(v13, v18) = v17 & in(v18, v15) & in(v18, v14))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v13) = v16) | ~ (relation_dom(v13) = v14) | ~ relation(v15) | ~ relation(v13) | ~ function(v15) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_dom(v16) = v17 & relation_dom(v15) = v18 & apply(v15, v12) = v19 & ( ~ in(v19, v14) | ~ in(v12, v18) | in(v12, v17)) & ( ~ in(v12, v17) | (in(v19, v14) & in(v12, v18))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ (relation_dom(v13) = v14) | ~ relation(v15) | ~ relation(v13) | ~ function(v15) | ~ function(v13) | ? [v17] : ? [v18] : ? [v19] : (relation_composition(v15, v13) = v17 & relation_dom(v17) = v18 & apply(v15, v12) = v19 & ( ~ in(v19, v14) | ~ in(v12, v16) | in(v12, v18)) & ( ~ in(v12, v18) | (in(v19, v14) & in(v12, v16))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_composition(v12, v13) = v14) | ~ relation(v15) | ~ relation(v13) | ~ relation(v12) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v16, v17) = v18 & ( ~ in(v18, v15) | ( ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v17) = v23) | ~ in(v23, v13) | ? [v24] : (ordered_pair(v16, v22) = v24 & ~ in(v24, v12))) & ! [v22] : ! [v23] : ( ~ (ordered_pair(v16, v22) = v23) | ~ in(v23, v12) | ? [v24] : (ordered_pair(v22, v17) = v24 & ~ in(v24, v13))))) & (in(v18, v15) | (ordered_pair(v19, v17) = v21 & ordered_pair(v16, v19) = v20 & in(v21, v13) & in(v20, v12))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v15) | ~ relation(v13) | ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v17) = v18 & ( ~ in(v18, v15) | ~ in(v18, v13) | ~ in(v17, v12)) & (in(v18, v15) | (in(v18, v13) & in(v17, v12))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_dom_restriction(v12, v13) = v15) | ~ relation(v14) | ~ relation(v12) | ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v17) = v18 & ( ~ in(v18, v14) | ~ in(v18, v12) | ~ in(v16, v13)) & (in(v18, v14) | (in(v18, v12) & in(v16, v13))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | v15 = v12 | ~ (unordered_pair(v12, v13) = v14) | ~ in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (complements_of_subsets(v12, v14) = v15) | ~ (complements_of_subsets(v12, v13) = v14) | ? [v16] : ? [v17] : (powerset(v16) = v17 & powerset(v12) = v16 & ~ element(v13, v17))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (subset_complement(v12, v14) = v15) | ~ (subset_complement(v12, v13) = v14) | ? [v16] : (powerset(v12) = v16 & ~ element(v13, v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (set_difference(v13, v12) = v14) | ~ (set_union2(v12, v14) = v15) | ~ subset(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v12) = v14) | ~ (set_union2(v14, v13) = v15) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (apply(v14, v13) = v15) | ~ (identity_relation(v12) = v14) | ~ in(v13, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_difference(v12, v14) = v15) | ~ (singleton(v13) = v14) | in(v13, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (relation_inverse_image(v13, v12) = v14) | ~ (relation_image(v13, v14) = v15) | ~ relation(v13) | ~ function(v13) | ? [v16] : (relation_rng(v13) = v16 & ~ subset(v12, v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = empty_set | ~ (relation_dom(v12) = v13) | ~ (apply(v12, v14) = v15) | ~ relation(v12) | ~ function(v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v12) = v15) | ~ (unordered_pair(v13, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (meet_of_subsets(v15, v14) = v13) | ~ (meet_of_subsets(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (union_of_subsets(v15, v14) = v13) | ~ (union_of_subsets(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (complements_of_subsets(v15, v14) = v13) | ~ (complements_of_subsets(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_composition(v15, v14) = v13) | ~ (relation_composition(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset_complement(v15, v14) = v13) | ~ (subset_complement(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_difference(v15, v14) = v13) | ~ (set_difference(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (cartesian_product2(v15, v14) = v13) | ~ (cartesian_product2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (singleton(v13) = v15) | ~ (singleton(v12) = v14) | ~ subset(v14, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (singleton(v12) = v15) | ~ (unordered_pair(v13, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_inverse_image(v15, v14) = v13) | ~ (relation_inverse_image(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_rng_restriction(v15, v14) = v13) | ~ (relation_rng_restriction(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_image(v15, v14) = v13) | ~ (relation_image(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (apply(v15, v14) = v13) | ~ (apply(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_dom_restriction(v15, v14) = v13) | ~ (relation_dom_restriction(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_intersection2(v15, v14) = v13) | ~ (set_intersection2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_union2(v15, v14) = v13) | ~ (set_union2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = empty_set | ~ (meet_of_subsets(v12, v14) = v15) | ~ (complements_of_subsets(v12, v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (subset_difference(v12, v18, v19) = v20 & union_of_subsets(v12, v13) = v19 & cast_to_subset(v12) = v18 & powerset(v16) = v17 & powerset(v12) = v16 & (v20 = v15 | ~ element(v13, v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = empty_set | ~ (union_of_subsets(v12, v14) = v15) | ~ (complements_of_subsets(v12, v13) = v14) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (subset_difference(v12, v18, v19) = v20 & meet_of_subsets(v12, v13) = v19 & cast_to_subset(v12) = v18 & powerset(v16) = v17 & powerset(v12) = v16 & (v20 = v15 | ~ element(v13, v17)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = empty_set | ~ (set_meet(v12) = v13) | ~ in(v15, v12) | ~ in(v14, v13) | in(v14, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_difference(v12, v13, v14) = v15) | ? [v16] : ? [v17] : (set_difference(v13, v14) = v17 & powerset(v12) = v16 & (v17 = v15 | ~ element(v14, v16) | ~ element(v13, v16)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_difference(v12, v13, v14) = v15) | ? [v16] : (powerset(v12) = v16 & ( ~ element(v14, v16) | ~ element(v13, v16) | element(v15, v16)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v13) = v15) | ~ (identity_relation(v12) = v14) | ~ relation(v13) | relation_dom_restriction(v13, v12) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v12, v14) = v15) | ~ (relation_rng(v12) = v13) | ~ relation(v14) | ~ relation(v12) | ? [v16] : (relation_rng(v15) = v16 & relation_image(v14, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v12, v14) = v15) | ~ (relation_dom(v12) = v13) | ~ relation(v14) | ~ relation(v12) | ? [v16] : (relation_dom(v15) = v16 & subset(v16, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset_complement(v12, v14) = v15) | ~ in(v13, v15) | ~ in(v13, v14) | ? [v16] : (powerset(v12) = v16 & ~ element(v14, v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v13) = v14) | ~ (set_intersection2(v14, v12) = v15) | ~ relation(v13) | ? [v16] : (relation_rng(v16) = v15 & relation_rng_restriction(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v12) = v14) | ~ (cartesian_product2(v13, v14) = v15) | ~ (relation_dom(v12) = v13) | ~ relation(v12) | subset(v12, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v12) = v14) | ~ (relation_dom(v12) = v13) | ~ (set_union2(v13, v14) = v15) | ~ relation(v12) | relation_field(v12) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v12) = v13) | ~ (relation_image(v14, v13) = v15) | ~ relation(v14) | ~ relation(v12) | ? [v16] : (relation_composition(v12, v14) = v16 & relation_rng(v16) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v14, v13) = v15) | ~ (set_union2(v12, v13) = v14) | set_difference(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v13, v12) = v14) | ~ (set_union2(v12, v14) = v15) | set_union2(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v14) = v15) | ~ (set_difference(v12, v13) = v14) | set_intersection2(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v13) = v14) | ~ in(v15, v14) | ~ in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v13) = v14) | ~ in(v15, v12) | in(v15, v14) | in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (union(v13) = v15) | ~ (powerset(v12) = v14) | ? [v16] : ? [v17] : (union_of_subsets(v12, v13) = v17 & powerset(v14) = v16 & (v17 = v15 | ~ element(v13, v16)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (union(v12) = v13) | ~ in(v15, v12) | ~ in(v14, v15) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ in(v15, v14) | ? [v16] : ? [v17] : (ordered_pair(v16, v17) = v15 & in(v17, v13) & in(v16, v12))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | ~ empty(v14) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ element(v13, v15) | ~ in(v12, v13) | element(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v14) | ~ (set_meet(v13) = v15) | ? [v16] : ? [v17] : (meet_of_subsets(v12, v13) = v17 & powerset(v14) = v16 & (v17 = v15 | ~ element(v13, v16)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (powerset(v12) = v14) | ~ element(v13, v14) | ~ in(v15, v13) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_triple(v12, v13, v14) = v15) | in(v14, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_triple(v12, v13, v14) = v15) | in(v13, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_triple(v12, v13, v14) = v15) | in(v12, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse_image(v13, v14) = v15) | ~ (relation_image(v13, v12) = v14) | ~ relation(v13) | subset(v12, v15) | ? [v16] : (relation_dom(v13) = v16 & ~ subset(v12, v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse_image(v13, v12) = v14) | ~ (relation_image(v13, v14) = v15) | ~ relation(v13) | ~ function(v13) | subset(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse_image(v12, v13) = v14) | ~ relation(v12) | ~ in(v15, v14) | ? [v16] : ? [v17] : (ordered_pair(v15, v16) = v17 & in(v17, v12) & in(v16, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v13) = v14) | ~ (set_intersection2(v14, v12) = v15) | ~ relation(v13) | ? [v16] : (relation_dom(v16) = v15 & relation_dom_restriction(v13, v12) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_image(v12, v13) = v14) | ~ relation(v12) | ~ in(v15, v14) | ? [v16] : ? [v17] : (ordered_pair(v16, v15) = v17 & in(v17, v12) & in(v16, v13))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (identity_relation(v12) = v13) | ~ (ordered_pair(v14, v14) = v15) | ~ relation(v13) | ~ in(v14, v12) | in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v13, v14) = v15) | ~ subset(v12, v14) | ~ subset(v12, v13) | subset(v12, v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ disjoint(v12, v13) | ~ in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ in(v15, v13) | ~ in(v15, v12) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v14) = v15) | ~ subset(v14, v13) | ~ subset(v12, v13) | subset(v15, v13)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v13) = v14) | ~ in(v15, v14) | in(v15, v13) | in(v15, v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v13) = v14) | ~ in(v15, v13) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_union2(v12, v13) = v14) | ~ in(v15, v12) | in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v12, v13) = v15) | ~ subset(v15, v14) | in(v13, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v12, v13) = v15) | ~ subset(v15, v14) | in(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (unordered_pair(v12, v13) = v15) | ~ in(v13, v14) | ~ in(v12, v14) | subset(v15, v14)) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_difference(v13, v14) = v15) | ? [v16] : (( ~ in(v16, v13) | ~ in(v16, v12) | in(v16, v14)) & (in(v16, v12) | (in(v16, v13) & ~ in(v16, v14))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (cartesian_product2(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ~ in(v16, v12) | ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v21) = v16) | ~ in(v21, v14) | ~ in(v20, v13))) & (in(v16, v12) | (v19 = v16 & ordered_pair(v17, v18) = v16 & in(v18, v14) & in(v17, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (relation_inverse_image(v13, v14) = v15) | ~ relation(v13) | ? [v16] : ? [v17] : ? [v18] : (( ~ in(v16, v12) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v16, v19) = v20) | ~ in(v20, v13) | ~ in(v19, v14))) & (in(v16, v12) | (ordered_pair(v16, v17) = v18 & in(v18, v13) & in(v17, v14))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (relation_image(v13, v14) = v15) | ~ relation(v13) | ? [v16] : ? [v17] : ? [v18] : (( ~ in(v16, v12) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v16) = v20) | ~ in(v20, v13) | ~ in(v19, v14))) & (in(v16, v12) | (ordered_pair(v17, v16) = v18 & in(v18, v13) & in(v17, v14))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_intersection2(v13, v14) = v15) | ? [v16] : (( ~ in(v16, v14) | ~ in(v16, v13) | ~ in(v16, v12)) & (in(v16, v12) | (in(v16, v14) & in(v16, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_union2(v13, v14) = v15) | ? [v16] : (( ~ in(v16, v12) | ( ~ in(v16, v14) & ~ in(v16, v13))) & (in(v16, v14) | in(v16, v13) | in(v16, v12)))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (unordered_pair(v13, v14) = v15) | ? [v16] : ((v16 = v14 | v16 = v13 | in(v16, v12)) & ( ~ in(v16, v12) | ( ~ (v16 = v14) & ~ (v16 = v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v13) = v15) | ~ relation(v14) | ~ relation(v13) | ~ function(v14) | ~ function(v13) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (relation_dom(v15) = v16 & apply(v15, v12) = v17 & apply(v14, v12) = v18 & apply(v13, v18) = v19 & (v19 = v17 | ~ in(v12, v16)))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse_image(v14, v13) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : ? [v18] : (relation_rng(v14) = v16 & ( ~ in(v12, v15) | (ordered_pair(v12, v17) = v18 & in(v18, v14) & in(v17, v16) & in(v17, v13))) & (in(v12, v15) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v12, v19) = v20) | ~ in(v20, v14) | ~ in(v19, v16) | ~ in(v19, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng_restriction(v13, v14) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_rng(v15) = v16 & relation_rng(v14) = v17 & ( ~ in(v12, v17) | ~ in(v12, v13) | in(v12, v16)) & ( ~ in(v12, v16) | (in(v12, v17) & in(v12, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_image(v14, v13) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : ? [v18] : (relation_dom(v14) = v16 & ( ~ in(v12, v15) | (ordered_pair(v17, v12) = v18 & in(v18, v14) & in(v17, v16) & in(v17, v13))) & (in(v12, v15) | ! [v19] : ! [v20] : ( ~ (ordered_pair(v19, v12) = v20) | ~ in(v20, v14) | ~ in(v19, v16) | ~ in(v19, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v14, v13) = v15) | ~ relation(v14) | ~ function(v14) | ? [v16] : ? [v17] : (relation_dom(v15) = v16 & relation_dom(v14) = v17 & ( ~ in(v12, v17) | ~ in(v12, v13) | in(v12, v16)) & ( ~ in(v12, v16) | (in(v12, v17) & in(v12, v13))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom_restriction(v14, v13) = v15) | ~ relation(v14) | ? [v16] : ? [v17] : (relation_dom(v15) = v16 & relation_dom(v14) = v17 & ( ~ in(v12, v17) | ~ in(v12, v13) | in(v12, v16)) & ( ~ in(v12, v16) | (in(v12, v17) & in(v12, v13))))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_inverse(v12) = v13) | ~ relation(v14) | ~ relation(v12) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v15) = v18 & ordered_pair(v15, v16) = v17 & ( ~ in(v18, v12) | ~ in(v17, v14)) & (in(v18, v12) | in(v17, v14)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_dom(v13) = v12) | ~ (identity_relation(v12) = v14) | ~ relation(v13) | ~ function(v13) | ? [v15] : ? [v16] : ( ~ (v16 = v15) & apply(v13, v15) = v16 & in(v15, v12))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (identity_relation(v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v15, v16) = v17 & ( ~ (v16 = v15) | ~ in(v17, v13) | ~ in(v15, v12)) & (in(v17, v13) | (v16 = v15 & in(v15, v12))))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v12, v13) = v14) | ~ subset(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | v12 = empty_set | ~ (singleton(v13) = v14) | ~ subset(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (set_difference(v12, v13) = v14) | ~ disjoint(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v12) = v13) | ~ in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_dom(v13) = v14) | ~ (identity_relation(v12) = v13) | ~ relation(v13) | ~ function(v13)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (set_intersection2(v12, v13) = v14) | ~ subset(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : (v14 = empty_set | ~ (set_difference(v12, v13) = v14) | ~ subset(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : (v14 = empty_set | ~ (set_intersection2(v12, v13) = v14) | ~ disjoint(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (function_inverse(v14) = v13) | ~ (function_inverse(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_inverse(v14) = v13) | ~ (relation_inverse(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_field(v14) = v13) | ~ (relation_field(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_rng(v14) = v13) | ~ (relation_rng(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (union(v14) = v13) | ~ (union(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (cast_to_subset(v14) = v13) | ~ (cast_to_subset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (set_meet(v14) = v13) | ~ (set_meet(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (succ(v14) = v13) | ~ (succ(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (identity_relation(v14) = v13) | ~ (identity_relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (meet_of_subsets(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (powerset(v15) = v16 & powerset(v12) = v15 & set_meet(v13) = v17 & (v17 = v14 | ~ element(v13, v16)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (meet_of_subsets(v12, v13) = v14) | ? [v15] : ? [v16] : (powerset(v15) = v16 & powerset(v12) = v15 & ( ~ element(v13, v16) | element(v14, v15)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (union_of_subsets(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (union(v13) = v17 & powerset(v15) = v16 & powerset(v12) = v15 & (v17 = v14 | ~ element(v13, v16)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (union_of_subsets(v12, v13) = v14) | ? [v15] : ? [v16] : (powerset(v15) = v16 & powerset(v12) = v15 & ( ~ element(v13, v16) | element(v14, v15)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (complements_of_subsets(v12, v13) = v14) | ? [v15] : ? [v16] : (powerset(v15) = v16 & powerset(v12) = v15 & ( ~ element(v13, v16) | element(v14, v16)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (complements_of_subsets(v12, v13) = v14) | ? [v15] : ? [v16] : (powerset(v15) = v16 & powerset(v12) = v15 & ( ~ element(v13, v16) | ( ! [v17] : ! [v18] : ( ~ (subset_complement(v12, v17) = v18) | ~ element(v17, v15) | ~ element(v14, v16) | ~ in(v18, v13) | in(v17, v14)) & ! [v17] : ! [v18] : ( ~ (subset_complement(v12, v17) = v18) | ~ element(v17, v15) | ~ element(v14, v16) | ~ in(v17, v14) | in(v18, v13)) & ! [v17] : (v17 = v14 | ~ element(v17, v16) | ? [v18] : ? [v19] : (subset_complement(v12, v18) = v19 & element(v18, v15) & ( ~ in(v19, v13) | ~ in(v18, v17)) & (in(v19, v13) | in(v18, v17)))))))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v12) = v14) | ~ relation(v13) | ~ empty(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v12) = v14) | ~ relation(v13) | ~ empty(v12) | empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | ~ function(v13) | ~ function(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | ~ function(v13) | ~ function(v12) | function(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | ? [v15] : ? [v16] : (relation_rng(v14) = v15 & relation_rng(v13) = v16 & subset(v15, v16))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ~ relation(v13) | ~ empty(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ~ relation(v13) | ~ empty(v12) | empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v12, v13) = v14) | ? [v15] : ? [v16] : (set_difference(v12, v13) = v16 & powerset(v12) = v15 & (v16 = v14 | ~ element(v13, v15)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset_complement(v12, v13) = v14) | ? [v15] : (powerset(v12) = v15 & ( ~ element(v13, v15) | element(v14, v15)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v13) = v14) | ~ relation(v13) | ~ relation(v12) | ? [v15] : ? [v16] : (relation_composition(v12, v13) = v15 & relation_rng(v15) = v16 & subset(v16, v14))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v15, v14) = v16 & in(v16, v12))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v14) = v12) | ~ (singleton(v13) = v14) | ~ in(v13, v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v13) = v14) | subset(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v13) = v14) | ? [v15] : ? [v16] : (subset_complement(v12, v13) = v16 & powerset(v12) = v15 & (v16 = v14 | ~ element(v13, v15)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v13) = v14) | ? [v15] : (set_difference(v15, v13) = v14 & set_union2(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v13) = v14) | ~ in(v12, v13) | subset(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v12) = v13) | ~ in(v14, v13) | ? [v15] : (in(v15, v12) & in(v14, v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ empty(v14) | empty(v13) | empty(v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ element(v12, v14) | subset(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | ~ subset(v12, v13) | element(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ subset(v14, v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ in(v14, v13) | subset(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v12) = v14) | ~ disjoint(v14, v13) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v12) = v14) | ~ subset(v14, v13) | in(v12, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v12) = v14) | ~ in(v12, v13) | subset(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v12) = v13) | ~ (set_union2(v12, v13) = v14) | succ(v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_inverse_image(v13, v12) = v14) | ~ relation(v13) | ? [v15] : (relation_dom(v13) = v15 & subset(v14, v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v13) | subset(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v13) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_rng(v14) = v15 & relation_rng(v13) = v16 & set_intersection2(v16, v12) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_rng(v14) = v15 & relation_rng(v13) = v16 & subset(v15, v16))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ relation(v13) | ? [v15] : (relation_rng(v14) = v15 & subset(v15, v12))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ (relation_image(v12, v13) = v14) | ~ relation(v12) | relation_rng(v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ in(v14, v13) | ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v12))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_image(v13, v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_dom(v13) = v15 & relation_image(v13, v16) = v14 & set_intersection2(v15, v12) = v16)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_image(v13, v12) = v14) | ~ relation(v13) | ? [v15] : (relation_rng(v13) = v15 & subset(v14, v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (apply(v13, v12) = v14) | ~ relation(v13) | ~ function(v13) | ? [v15] : (relation_dom(v13) = v15 & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v13, v16) = v17) | ~ (apply(v17, v12) = v18) | ~ relation(v16) | ~ function(v16) | ~ in(v12, v15) | apply(v16, v14) = v18) & ! [v16] : ! [v17] : ( ~ (apply(v16, v14) = v17) | ~ relation(v16) | ~ function(v16) | ~ in(v12, v15) | ? [v18] : (relation_composition(v13, v16) = v18 & apply(v18, v12) = v17)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v13, v12) = v14) | ~ relation(v13) | subset(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v13, v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_rng(v14) = v15 & relation_rng(v13) = v16 & subset(v15, v16))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v13, v12) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : (relation_dom(v14) = v15 & relation_dom(v13) = v16 & set_intersection2(v16, v12) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v13, v12) = v14) | ~ relation(v13) | ? [v15] : (relation_composition(v15, v13) = v14 & identity_relation(v12) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ relation_empty_yielding(v12) | ~ relation(v12) | relation_empty_yielding(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ relation_empty_yielding(v12) | ~ relation(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ relation(v12) | ~ function(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ relation(v12) | ~ function(v12) | function(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ relation(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ~ empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ? [v16] : (singleton(v12) = v16 & unordered_pair(v15, v16) = v14 & unordered_pair(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v13, v12) = v14) | set_intersection2(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | set_intersection2(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | disjoint(v12, v13) | ? [v15] : in(v15, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | subset(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | ? [v15] : (set_difference(v12, v15) = v14 & set_difference(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v13, v12) = v14) | ~ empty(v14) | empty(v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v13, v12) = v14) | set_union2(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ~ relation(v13) | ~ relation(v12) | relation(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ~ empty(v14) | empty(v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | set_union2(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | subset(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ? [v15] : (set_difference(v13, v12) = v15 & set_union2(v12, v15) = v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v13, v12) = v14) | unordered_pair(v12, v13) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | ~ empty(v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | in(v13, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | in(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ disjoint(v13, v14) | ~ subset(v12, v13) | disjoint(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ disjoint(v12, v13) | ~ in(v14, v13) | ~ in(v14, v12)) & ! [v12] : ! [v13] : ! [v14] : ( ~ subset(v13, v14) | ~ subset(v12, v13) | subset(v12, v14)) & ! [v12] : ! [v13] : ! [v14] : ( ~ subset(v12, v13) | ~ in(v14, v12) | in(v14, v13)) & ! [v12] : ! [v13] : ! [v14] : ( ~ in(v14, v12) | ~ in(v13, v14) | ~ in(v12, v13)) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | v13 = empty_set | ~ (set_meet(v13) = v14) | ? [v15] : ? [v16] : (( ~ in(v15, v12) | (in(v16, v13) & ~ in(v15, v16))) & (in(v15, v12) | ! [v17] : ( ~ in(v17, v13) | in(v15, v17))))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_rng(v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v12) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v18, v15) = v19) | ~ in(v19, v13))) & (in(v15, v12) | (ordered_pair(v16, v15) = v17 & in(v17, v13))))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (union(v13) = v14) | ? [v15] : ? [v16] : (( ~ in(v15, v12) | ! [v17] : ( ~ in(v17, v13) | ~ in(v15, v17))) & (in(v15, v12) | (in(v16, v13) & in(v15, v16))))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (powerset(v13) = v14) | ? [v15] : (( ~ subset(v15, v13) | ~ in(v15, v12)) & (subset(v15, v13) | in(v15, v12)))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v13) = v14) | ? [v15] : (( ~ (v15 = v13) | ~ in(v13, v12)) & (v15 = v13 | in(v15, v12)))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_dom(v13) = v14) | ~ relation(v13) | ? [v15] : ? [v16] : ? [v17] : (( ~ in(v15, v12) | ! [v18] : ! [v19] : ( ~ (ordered_pair(v15, v18) = v19) | ~ in(v19, v13))) & (in(v15, v12) | (ordered_pair(v15, v16) = v17 & in(v17, v13))))) & ? [v12] : ! [v13] : ! [v14] : (v13 = empty_set | ~ (set_meet(v13) = v14) | in(v12, v14) | ? [v15] : (in(v15, v13) & ~ in(v12, v15))) & ? [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v13) = v14) | element(v12, v14) | ? [v15] : (in(v15, v12) & ~ in(v15, v13))) & ? [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v13) = v14) | disjoint(v14, v12) | in(v13, v12)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_difference(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (cast_to_subset(v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_intersection2(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ subset(v13, v12) | ~ subset(v12, v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ subset(v12, v13) | proper_subset(v12, v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ relation(v13) | ~ relation(v12) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & ( ~ in(v16, v13) | ~ in(v16, v12)) & (in(v16, v13) | in(v16, v12)))) & ! [v12] : ! [v13] : (v13 = v12 | ~ empty(v13) | ~ empty(v12)) & ! [v12] : ! [v13] : (v13 = empty_set | ~ (complements_of_subsets(v12, v13) = empty_set) | ? [v14] : ? [v15] : (powerset(v14) = v15 & powerset(v12) = v14 & ~ element(v13, v15))) & ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_difference(empty_set, v12) = v13)) & ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_intersection2(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v12 = empty_set | ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : ( ~ (v14 = empty_set) & relation_dom(v12) = v14)) & ! [v12] : ! [v13] : (v12 = empty_set | ~ (relation_inverse_image(v13, v12) = empty_set) | ~ relation(v13) | ? [v14] : (relation_rng(v13) = v14 & ~ subset(v12, v14))) & ! [v12] : ! [v13] : (v12 = empty_set | ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : ( ~ (v14 = empty_set) & relation_rng(v12) = v14)) & ! [v12] : ! [v13] : ( ~ (function_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | relation_inverse(v12) = v13) & ! [v12] : ! [v13] : ( ~ (function_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | one_to_one(v13)) & ! [v12] : ! [v13] : ( ~ (function_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : (relation_rng(v13) = v15 & relation_rng(v12) = v14 & relation_dom(v13) = v14 & relation_dom(v12) = v15)) & ! [v12] : ! [v13] : ( ~ (function_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : (relation_rng(v12) = v14 & relation_dom(v12) = v15 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom(v13) = v16) | ~ (apply(v13, v17) = v19) | ~ (apply(v12, v18) = v17) | ~ relation(v13) | ~ function(v13) | ~ in(v18, v15)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_dom(v13) = v16) | ~ (apply(v13, v17) = v18) | ~ (apply(v12, v18) = v19) | ~ relation(v13) | ~ function(v13) | ~ in(v17, v14)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v13) = v16) | ~ (apply(v13, v17) = v19) | ~ (apply(v12, v18) = v17) | ~ relation(v13) | ~ function(v13) | ~ in(v18, v15) | in(v17, v14)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v13) = v16) | ~ (apply(v13, v17) = v18) | ~ (apply(v12, v18) = v19) | ~ relation(v13) | ~ function(v13) | ~ in(v17, v14) | in(v18, v15)) & ! [v16] : (v16 = v14 | ~ (relation_dom(v13) = v16) | ~ relation(v13) | ~ function(v13)) & ! [v16] : (v16 = v13 | ~ (relation_dom(v16) = v14) | ~ relation(v16) | ~ function(v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v16, v17) = v19 & apply(v12, v18) = v20 & ((v20 = v17 & in(v18, v15) & ( ~ (v19 = v18) | ~ in(v17, v14))) | (v19 = v18 & in(v17, v14) & ( ~ (v20 = v17) | ~ in(v18, v15)))))))) & ! [v12] : ! [v13] : ( ~ (function_inverse(v12) = v13) | ~ relation(v12) | ~ function(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (function_inverse(v12) = v13) | ~ relation(v12) | ~ function(v12) | function(v13)) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | function_inverse(v12) = v13) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | function(v13)) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ relation(v12) | relation_inverse(v13) = v12) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ relation(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_rng(v13) = v15 & relation_rng(v12) = v14 & relation_dom(v13) = v14 & relation_dom(v12) = v15)) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ empty(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ~ empty(v12) | empty(v13)) & ! [v12] : ! [v13] : ( ~ (relation_field(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_rng(v12) = v15 & relation_dom(v12) = v14 & set_union2(v14, v15) = v13)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : (function_inverse(v12) = v14 & relation_rng(v14) = v15 & relation_dom(v14) = v13 & relation_dom(v12) = v15)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : (function_inverse(v12) = v14 & relation_dom(v12) = v15 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v19) | ~ (apply(v12, v18) = v17) | ~ relation(v14) | ~ function(v14) | ~ in(v18, v15)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v18) | ~ (apply(v12, v18) = v19) | ~ relation(v14) | ~ function(v14) | ~ in(v17, v13)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v19) | ~ (apply(v12, v18) = v17) | ~ relation(v14) | ~ function(v14) | ~ in(v18, v15) | in(v17, v13)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v18) | ~ (apply(v12, v18) = v19) | ~ relation(v14) | ~ function(v14) | ~ in(v17, v13) | in(v18, v15)) & ! [v16] : (v16 = v14 | ~ (relation_dom(v16) = v13) | ~ relation(v16) | ~ function(v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v16, v17) = v19 & apply(v12, v18) = v20 & ((v20 = v17 & in(v18, v15) & ( ~ (v19 = v18) | ~ in(v17, v13))) | (v19 = v18 & in(v17, v13) & ( ~ (v20 = v17) | ~ in(v18, v15)))))) & ! [v16] : (v16 = v13 | ~ (relation_dom(v14) = v16) | ~ relation(v14) | ~ function(v14)))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ~ function(v12) | ? [v14] : (relation_dom(v12) = v14 & ! [v15] : ! [v16] : ( ~ (apply(v12, v16) = v15) | ~ in(v16, v14) | in(v15, v13)) & ! [v15] : ( ~ in(v15, v13) | ? [v16] : (apply(v12, v16) = v15 & in(v16, v14))) & ? [v15] : (v15 = v13 | ? [v16] : ? [v17] : ? [v18] : (( ~ in(v16, v15) | ! [v19] : ( ~ (apply(v12, v19) = v16) | ~ in(v19, v14))) & (in(v16, v15) | (v18 = v16 & apply(v12, v17) = v16 & in(v17, v14))))))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ~ empty(v13) | empty(v12)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_inverse(v12) = v14 & relation_rng(v14) = v15 & relation_dom(v14) = v13 & relation_dom(v12) = v15)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & relation_image(v12, v14) = v13)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v12) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & (v18 = v13 | ~ subset(v14, v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ subset(v14, v16) | ~ relation(v15) | ? [v17] : (relation_composition(v15, v12) = v17 & relation_rng(v17) = v13)))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & ! [v15] : ! [v16] : ( ~ (relation_composition(v12, v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_dom(v16) = v18 & relation_dom(v15) = v17 & (v18 = v14 | ~ subset(v13, v17)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ subset(v13, v16) | ~ relation(v15) | ? [v17] : (relation_composition(v12, v15) = v17 & relation_dom(v17) = v14)))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | subset(v13, v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & subset(v14, v17))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | subset(v14, v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & subset(v13, v17))))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_dom(v12) = v14 & ( ~ (v14 = empty_set) | v13 = empty_set) & ( ~ (v13 = empty_set) | v14 = empty_set))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ empty(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ~ empty(v12) | empty(v13)) & ! [v12] : ! [v13] : ( ~ (set_difference(v12, v13) = v12) | disjoint(v12, v13)) & ! [v12] : ! [v13] : ( ~ (set_difference(v12, v13) = empty_set) | subset(v12, v13)) & ! [v12] : ! [v13] : ( ~ (cast_to_subset(v12) = v13) | ? [v14] : (powerset(v12) = v14 & element(v13, v14))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | union(v13) = v12) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | empty(v12) | ? [v14] : (element(v14, v13) & ~ empty(v14))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (cast_to_subset(v12) = v14 & element(v14, v13))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (element(v14, v13) & empty(v14))) & ! [v12] : ! [v13] : ( ~ (singleton(v13) = v12) | subset(v12, v12)) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | unordered_pair(v12, v12) = v13) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | subset(empty_set, v13)) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | in(v12, v13)) & ! [v12] : ! [v13] : ( ~ (succ(v12) = v13) | ~ empty(v13)) & ! [v12] : ! [v13] : ( ~ (succ(v12) = v13) | ? [v14] : (singleton(v12) = v14 & set_union2(v12, v14) = v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : (function_inverse(v12) = v15 & relation_rng(v15) = v13 & relation_rng(v12) = v14 & relation_dom(v15) = v14)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ one_to_one(v12) | ~ relation(v12) | ~ function(v12) | ? [v14] : ? [v15] : (function_inverse(v12) = v14 & relation_rng(v12) = v15 & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v19) | ~ (apply(v12, v18) = v17) | ~ relation(v14) | ~ function(v14) | ~ in(v18, v13)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v18) | ~ (apply(v12, v18) = v19) | ~ relation(v14) | ~ function(v14) | ~ in(v17, v15)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v19) | ~ (apply(v12, v18) = v17) | ~ relation(v14) | ~ function(v14) | ~ in(v18, v13) | in(v17, v15)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v14) = v16) | ~ (apply(v14, v17) = v18) | ~ (apply(v12, v18) = v19) | ~ relation(v14) | ~ function(v14) | ~ in(v17, v15) | in(v18, v13)) & ! [v16] : (v16 = v15 | ~ (relation_dom(v14) = v16) | ~ relation(v14) | ~ function(v14)) & ! [v16] : (v16 = v14 | ~ (relation_dom(v16) = v15) | ~ relation(v16) | ~ function(v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (apply(v16, v17) = v19 & apply(v12, v18) = v20 & ((v20 = v17 & in(v18, v13) & ( ~ (v19 = v18) | ~ in(v17, v15))) | (v19 = v18 & in(v17, v15) & ( ~ (v20 = v17) | ~ in(v18, v13)))))))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ function(v12) | one_to_one(v12) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v15 = v14) & apply(v12, v15) = v16 & apply(v12, v14) = v16 & in(v15, v13) & in(v14, v13))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ function(v12) | ? [v14] : (relation_rng(v12) = v14 & ! [v15] : ! [v16] : ( ~ (apply(v12, v16) = v15) | ~ in(v16, v13) | in(v15, v14)) & ! [v15] : ( ~ in(v15, v14) | ? [v16] : (apply(v12, v16) = v15 & in(v16, v13))) & ? [v15] : (v15 = v14 | ? [v16] : ? [v17] : ? [v18] : (( ~ in(v16, v15) | ! [v19] : ( ~ (apply(v12, v19) = v16) | ~ in(v19, v13))) & (in(v16, v15) | (v18 = v16 & apply(v12, v17) = v16 & in(v17, v13))))))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ~ empty(v13) | empty(v12)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : ? [v15] : (relation_inverse(v12) = v15 & relation_rng(v15) = v13 & relation_rng(v12) = v14 & relation_dom(v15) = v14)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & ! [v15] : ! [v16] : ( ~ (relation_composition(v15, v12) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & (v18 = v14 | ~ subset(v13, v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ subset(v13, v16) | ~ relation(v15) | ? [v17] : (relation_composition(v15, v12) = v17 & relation_rng(v17) = v14)))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & ! [v15] : ! [v16] : ( ~ (relation_composition(v12, v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_dom(v16) = v18 & relation_dom(v15) = v17 & (v18 = v13 | ~ subset(v14, v17)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ subset(v14, v16) | ~ relation(v15) | ? [v17] : (relation_composition(v12, v15) = v17 & relation_dom(v17) = v13)))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | subset(v14, v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & subset(v13, v17))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | subset(v13, v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ subset(v12, v15) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & subset(v14, v17))))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ relation(v12) | ? [v14] : (relation_rng(v12) = v14 & ( ~ (v14 = empty_set) | v13 = empty_set) & ( ~ (v13 = empty_set) | v14 = empty_set))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ empty(v12) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ~ empty(v12) | empty(v13)) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation_rng(v13) = v12) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation_dom(v13) = v12) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation(v13)) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | function(v13)) & ! [v12] : ! [v13] : ( ~ (set_intersection2(v12, v13) = empty_set) | disjoint(v12, v13)) & ! [v12] : ! [v13] : ( ~ (unordered_pair(v12, v12) = v13) | singleton(v12) = v13) & ! [v12] : ! [v13] : ( ~ disjoint(v12, v13) | disjoint(v13, v12)) & ! [v12] : ! [v13] : ( ~ element(v13, v12) | ~ empty(v12) | empty(v13)) & ! [v12] : ! [v13] : ( ~ element(v13, v12) | empty(v12) | in(v13, v12)) & ! [v12] : ! [v13] : ( ~ element(v12, v13) | empty(v13) | in(v12, v13)) & ! [v12] : ! [v13] : ( ~ subset(v12, v13) | ~ proper_subset(v13, v12)) & ! [v12] : ! [v13] : ( ~ relation(v13) | ~ relation(v12) | subset(v12, v13) | ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v15) = v16 & in(v16, v12) & ~ in(v16, v13))) & ! [v12] : ! [v13] : ( ~ relation(v12) | ~ in(v13, v12) | ? [v14] : ? [v15] : ordered_pair(v14, v15) = v13) & ! [v12] : ! [v13] : ( ~ empty(v13) | ~ empty(v12) | element(v13, v12)) & ! [v12] : ! [v13] : ( ~ empty(v13) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ proper_subset(v13, v12) | ~ proper_subset(v12, v13)) & ! [v12] : ! [v13] : ( ~ proper_subset(v12, v13) | subset(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | ~ in(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v13, v12) | element(v13, v12) | empty(v12)) & ! [v12] : ! [v13] : ( ~ in(v12, v13) | element(v12, v13)) & ! [v12] : ! [v13] : ( ~ in(v12, v13) | ? [v14] : (in(v14, v13) & ! [v15] : ( ~ in(v15, v14) | ~ in(v15, v13)))) & ! [v12] : (v12 = empty_set | ~ (relation_rng(v12) = empty_set) | ~ relation(v12)) & ! [v12] : (v12 = empty_set | ~ (set_meet(empty_set) = v12)) & ! [v12] : (v12 = empty_set | ~ (relation_dom(v12) = empty_set) | ~ relation(v12)) & ! [v12] : (v12 = empty_set | ~ subset(v12, empty_set)) & ! [v12] : (v12 = empty_set | ~ relation(v12) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & in(v15, v12))) & ! [v12] : (v12 = empty_set | ~ empty(v12)) & ! [v12] : ~ (singleton(v12) = empty_set) & ! [v12] : ( ~ relation(v12) | ~ function(v12) | ~ empty(v12) | one_to_one(v12)) & ! [v12] : ( ~ empty(v12) | relation(v12)) & ! [v12] : ( ~ empty(v12) | function(v12)) & ! [v12] : ~ proper_subset(v12, v12) & ! [v12] : ~ in(v12, empty_set) & ? [v12] : ? [v13] : (v13 = v12 | ? [v14] : (( ~ in(v14, v13) | ~ in(v14, v12)) & (in(v14, v13) | in(v14, v12)))) & ? [v12] : ? [v13] : (disjoint(v12, v13) | ? [v14] : (in(v14, v13) & in(v14, v12))) & ? [v12] : ? [v13] : element(v13, v12) & ? [v12] : ? [v13] : (subset(v12, v13) | ? [v14] : (in(v14, v12) & ~ in(v14, v13))) & ? [v12] : ? [v13] : (in(v12, v13) & ! [v14] : ! [v15] : ( ~ (powerset(v14) = v15) | ~ in(v14, v13) | in(v15, v13)) & ! [v14] : ! [v15] : ( ~ subset(v15, v14) | ~ in(v14, v13) | in(v15, v13)) & ! [v14] : ( ~ subset(v14, v13) | are_equipotent(v14, v13) | in(v14, v13))) & ? [v12] : ? [v13] : (in(v12, v13) & ! [v14] : ! [v15] : ( ~ subset(v15, v14) | ~ in(v14, v13) | in(v15, v13)) & ! [v14] : ( ~ subset(v14, v13) | are_equipotent(v14, v13) | in(v14, v13)) & ! [v14] : ( ~ in(v14, v13) | ? [v15] : (in(v15, v13) & ! [v16] : ( ~ subset(v16, v14) | in(v16, v15))))) & ? [v12] : (v12 = empty_set | ? [v13] : in(v13, v12)) & ? [v12] : subset(v12, v12) & ? [v12] : subset(empty_set, v12) & ? [v12] : (relation(v12) | ? [v13] : (in(v13, v12) & ! [v14] : ! [v15] : ~ (ordered_pair(v14, v15) = v13))))
% 22.74/5.86 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 22.74/5.86 | (1) relation_rng(empty_set) = empty_set & powerset(empty_set) = all_0_11_11 & singleton(empty_set) = all_0_11_11 & succ(all_0_10_10) = all_0_9_9 & relation_dom(empty_set) = empty_set & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(all_0_8_8) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_8_8) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_8_8) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ~ in(all_0_10_10, all_0_9_9) & ! [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, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v4, v1) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v4, v1)) & ! [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_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(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ (apply(v0, v5) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v5, v1) | in(v4, v3)) & ! [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_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] : (v4 = v2 | v4 = v1 | v4 = v0 | ~ (unordered_triple(v0, v1, v2) = v3) | ~ in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1)) & ! [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 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(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] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v6 & relation_rng(v1) = v5 & apply(v6, v0) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [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] : ( ~ (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] : ( ~ (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) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [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_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | ? [v5] : (apply(v0, v5) = v4 & in(v5, v2) & in(v5, v1))) & ! [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(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ~ in(v1, v0) | apply(v2, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v2, v1) = v6 & (v6 = v4 | ~ in(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v3, v1) = v6 & (v6 = v4 | ~ in(v1, v5)))) & ! [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] : ( ~ (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] : (v4 = v0 | ~ (unordered_triple(v1, v2, v3) = v4) | ? [v5] : ((v5 = v3 | v5 = v2 | v5 = v1 | in(v5, v0)) & ( ~ in(v5, v0) | ( ~ (v5 = v3) & ~ (v5 = v2) & ~ (v5 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_inverse_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : (apply(v1, v5) = v6 & ( ~ in(v6, v3) | ~ in(v5, v2) | ~ in(v5, v0)) & (in(v5, v0) | (in(v6, v3) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (( ~ in(v5, v0) | ! [v8] : ( ~ (apply(v1, v8) = v5) | ~ in(v8, v3) | ~ in(v8, v2))) & (in(v5, v0) | (v7 = v5 & apply(v1, v6) = v5 & in(v6, v3) & in(v6, v2))))) & ? [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 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | ? [v4] : (relation_rng(v1) = v4 & ~ subset(v0, v4))) & ! [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 | ~ (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_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(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 | ~ (apply(v3, v2) = v1) | ~ (apply(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) | ~ (cartesian_product2(v1, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ 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] : ( ~ (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] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | subset(v0, v3) | ? [v4] : (relation_dom(v1) = v4 & ~ subset(v0, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | subset(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_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] : ( ~ (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_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_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_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ~ function(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] : ! [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 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(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 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [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 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(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] : ( ~ (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] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(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(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] : ( ~ (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] : ( ~ (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] : ( ~ (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_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) & ! [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] : ( ~ in(v2, v0) | ~ in(v1, v2) | ~ in(v0, 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 | ~ (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] : (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] : (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_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3)))))))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [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_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [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) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2))))))) & ! [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] : ( ~ (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] : ( ~ (succ(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1)))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & in(v3, v1) & in(v2, v1))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1))))))) & ! [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] : ( ~ (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] : ! [v1] : ( ~ in(v0, v1) | ? [v2] : (in(v2, v1) & ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1)))) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(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] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [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)))
% 23.43/5.93 |
% 23.43/5.93 | Applying alpha-rule on (1) yields:
% 23.43/5.93 | (2) ! [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))))
% 23.43/5.93 | (3) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1)
% 23.43/5.93 | (4) function(all_0_0_0)
% 23.43/5.93 | (5) ? [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)))))
% 23.43/5.93 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 23.43/5.93 | (7) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2)))
% 23.43/5.93 | (8) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2))))
% 23.43/5.93 | (9) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 23.43/5.93 | (10) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 23.43/5.93 | (11) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 23.43/5.93 | (12) empty(all_0_1_1)
% 23.49/5.93 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 23.49/5.93 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1))
% 23.49/5.94 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 23.49/5.94 | (16) ? [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)))))
% 23.49/5.94 | (17) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1)))
% 23.49/5.94 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 23.49/5.94 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4)))
% 23.49/5.94 | (20) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 23.49/5.94 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 23.49/5.94 | (22) ! [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))
% 23.49/5.94 | (23) ! [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))
% 23.49/5.94 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 23.49/5.94 | (25) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 23.49/5.94 | (26) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 23.49/5.94 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ in(v2, v0) | ~ in(v1, v2) | ~ in(v0, v1))
% 23.49/5.94 | (28) one_to_one(all_0_6_6)
% 23.49/5.94 | (29) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0))
% 23.49/5.94 | (30) relation(all_0_7_7)
% 23.49/5.94 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 23.49/5.94 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 23.49/5.94 | (33) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 23.49/5.94 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 23.49/5.94 | (35) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1))
% 23.49/5.94 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 23.49/5.94 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 23.49/5.94 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 23.49/5.94 | (39) ! [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)))))
% 23.49/5.94 | (40) ! [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))
% 23.49/5.94 | (41) ? [v0] : subset(empty_set, v0)
% 23.49/5.94 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3)))
% 23.49/5.94 | (43) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 23.49/5.94 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 23.49/5.94 | (45) ! [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))))
% 23.49/5.94 | (46) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 23.49/5.94 | (47) powerset(empty_set) = all_0_11_11
% 23.49/5.94 | (48) ! [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)))))
% 23.49/5.94 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1))
% 23.49/5.94 | (50) ? [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)))))
% 23.49/5.94 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 23.49/5.94 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 23.49/5.94 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 23.49/5.94 | (54) ! [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))
% 23.49/5.94 | (55) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 23.49/5.94 | (56) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 23.49/5.94 | (57) ! [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))
% 23.49/5.94 | (58) function(all_0_6_6)
% 23.49/5.94 | (59) ! [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))
% 23.49/5.94 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 23.49/5.94 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 23.49/5.94 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 23.49/5.94 | (63) ? [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)))))
% 23.49/5.94 | (64) ! [v0] : ~ proper_subset(v0, v0)
% 23.49/5.94 | (65) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 23.49/5.94 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 23.49/5.95 | (67) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0))
% 23.49/5.95 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 23.49/5.95 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2))
% 23.49/5.95 | (70) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 23.49/5.95 | (71) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v1) | in(v3, v2)) & ! [v3] : ( ~ in(v3, v2) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v1))) & ? [v3] : (v3 = v2 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v1))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v1)))))))
% 23.49/5.95 | (72) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ~ empty(v1))
% 23.49/5.95 | (73) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 23.49/5.95 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 23.49/5.95 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 23.49/5.95 | (76) ! [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)))
% 23.49/5.95 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 23.49/5.95 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 23.49/5.95 | (79) relation(all_0_6_6)
% 23.49/5.95 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3))
% 23.49/5.95 | (81) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 23.49/5.95 | (82) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 23.49/5.95 | (83) relation_empty_yielding(all_0_8_8)
% 23.49/5.95 | (84) relation(all_0_0_0)
% 23.49/5.95 | (85) singleton(empty_set) = all_0_11_11
% 23.49/5.95 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 23.49/5.95 | (87) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 23.49/5.95 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 23.49/5.95 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 23.49/5.95 | (90) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3))
% 23.49/5.95 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 23.49/5.95 | (92) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 23.49/5.95 | (93) ! [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)))))
% 23.49/5.95 | (94) ! [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))
% 23.49/5.95 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (unordered_triple(v4, v3, v2) = v1) | ~ (unordered_triple(v4, v3, v2) = v0))
% 23.49/5.95 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 23.49/5.95 | (97) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 23.49/5.95 | (98) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 23.49/5.95 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v1, v3))
% 23.49/5.95 | (100) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1))
% 23.49/5.95 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 23.49/5.95 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0))
% 23.49/5.95 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 23.49/5.95 | (104) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ~ function(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)))))
% 23.49/5.95 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0)))
% 23.49/5.95 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 23.49/5.95 | (107) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1))
% 23.49/5.95 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 23.49/5.95 | (109) ! [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))
% 23.49/5.95 | (110) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 23.49/5.95 | (111) ! [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))))
% 23.49/5.95 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 23.49/5.95 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0))
% 23.49/5.95 | (114) ! [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)))
% 23.49/5.95 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2))
% 23.49/5.95 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1))
% 23.49/5.95 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 23.49/5.95 | (118) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2))
% 23.49/5.95 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v2, v1) = v6 & (v6 = v4 | ~ in(v1, v5))))
% 23.49/5.96 | (120) ! [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))
% 23.49/5.96 | (121) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 23.49/5.96 | (122) ! [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))
% 23.49/5.96 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 23.49/5.96 | (124) ! [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)
% 23.49/5.96 | (125) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 23.49/5.96 | (126) ! [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))))
% 23.49/5.96 | (127) ! [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)))))
% 23.49/5.96 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 23.49/5.96 | (129) ? [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)))))
% 23.49/5.96 | (130) ! [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)))
% 23.49/5.96 | (131) ! [v0] : ( ~ empty(v0) | function(v0))
% 23.49/5.96 | (132) ? [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)))))
% 23.49/5.96 | (133) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 23.49/5.96 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 23.49/5.96 | (135) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2)))
% 23.49/5.96 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 23.49/5.96 | (137) ! [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))
% 23.49/5.96 | (138) ! [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))))
% 23.49/5.96 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11)))))
% 23.49/5.96 | (140) relation(all_0_4_4)
% 23.49/5.96 | (141) ? [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)))))
% 23.49/5.96 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 23.49/5.96 | (143) ~ empty(all_0_5_5)
% 23.49/5.96 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 23.49/5.96 | (145) ! [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))))
% 23.49/5.96 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 23.49/5.96 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 23.49/5.96 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 23.49/5.96 | (149) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 23.49/5.96 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 23.49/5.96 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 23.49/5.96 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 23.49/5.96 | (153) ! [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))))
% 23.49/5.96 | (154) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 23.49/5.96 | (155) ! [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))
% 23.49/5.96 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4)))
% 23.49/5.96 | (157) relation_rng(empty_set) = empty_set
% 23.49/5.96 | (158) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0)))
% 23.49/5.96 | (159) ! [v0] : ( ~ empty(v0) | relation(v0))
% 23.49/5.96 | (160) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 23.49/5.96 | (161) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 23.49/5.96 | (162) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0)
% 23.49/5.96 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 23.49/5.96 | (164) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2)
% 23.49/5.96 | (165) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 23.49/5.96 | (166) ! [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))))
% 23.49/5.96 | (167) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 23.49/5.96 | (168) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 23.49/5.96 | (169) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 23.49/5.97 | (170) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1))))))))
% 23.49/5.97 | (171) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 23.49/5.97 | (172) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 23.49/5.97 | (173) ! [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))
% 23.49/5.97 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 23.49/5.97 | (175) ! [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))
% 23.49/5.97 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v6 & relation_rng(v1) = v5 & apply(v6, v0) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 23.49/5.97 | (177) ! [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)))
% 23.49/5.97 | (178) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3))))))))
% 23.49/5.97 | (179) ! [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))
% 23.49/5.97 | (180) ! [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)))
% 23.49/5.97 | (181) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 23.49/5.97 | (182) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (succ(v2) = v1) | ~ (succ(v2) = v0))
% 23.49/5.97 | (183) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 23.49/5.97 | (184) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 23.49/5.97 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 23.49/5.97 | (186) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 23.49/5.97 | (187) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2))
% 23.49/5.97 | (188) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 23.49/5.97 | (189) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 23.49/5.97 | (190) ! [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))))
% 23.49/5.97 | (191) ! [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))))))))
% 23.49/5.97 | (192) ! [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))
% 23.49/5.97 | (193) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v0, v3))
% 23.49/5.97 | (194) ? [v0] : subset(v0, v0)
% 23.49/5.97 | (195) ! [v0] : ! [v1] : ( ~ (succ(v0) = v1) | ? [v2] : (singleton(v0) = v2 & set_union2(v0, v2) = v1))
% 23.49/5.97 | (196) ? [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)))))
% 23.49/5.97 | (197) ! [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)))
% 23.49/5.97 | (198) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2))
% 23.49/5.97 | (199) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1))
% 23.49/5.97 | (200) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 23.49/5.97 | (201) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 23.49/5.97 | (202) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 23.49/5.97 | (203) ! [v0] : ~ in(v0, empty_set)
% 23.49/5.97 | (204) ? [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)))
% 23.49/5.97 | (205) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 23.49/5.97 | (206) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 23.49/5.97 | (207) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 23.49/5.97 | (208) ! [v0] : ~ (singleton(v0) = empty_set)
% 23.49/5.98 | (209) ! [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))))
% 23.49/5.98 | (210) ! [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))))
% 23.49/5.98 | (211) empty(all_0_2_2)
% 23.49/5.98 | (212) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 23.49/5.98 | (213) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 23.49/5.98 | (214) ! [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))
% 23.49/5.98 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 23.49/5.98 | (216) ! [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)))
% 23.49/5.98 | (217) function(all_0_3_3)
% 23.49/5.98 | (218) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 23.49/5.98 | (219) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 23.49/5.98 | (220) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 23.49/5.98 | (221) ? [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)))))
% 23.49/5.98 | (222) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 23.49/5.98 | (223) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 23.49/5.98 | (224) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v1) | ~ (set_union2(v0, v1) = v2) | succ(v0) = v2)
% 23.49/5.98 | (225) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 23.49/5.98 | (226) ! [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))
% 23.49/5.98 | (227) ! [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)))
% 23.49/5.98 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 23.49/5.98 | (229) ? [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)))))
% 23.49/5.98 | (230) ! [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)))
% 23.49/5.98 | (231) ! [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)))
% 23.49/5.98 | (232) ! [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))
% 23.49/5.98 | (233) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 23.49/5.98 | (234) ! [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)))))
% 23.49/5.98 | (235) ? [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)))))
% 23.49/5.98 | (236) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ (apply(v0, v5) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v5, v1) | in(v4, v3))
% 23.49/5.98 | (237) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | ? [v4] : (relation_rng(v1) = v4 & ~ subset(v0, v4)))
% 23.49/5.98 | (238) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0))
% 23.49/5.98 | (239) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 23.49/5.98 | (240) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 23.49/5.98 | (241) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 23.49/5.98 | (242) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 23.49/5.98 | (243) ~ empty(all_0_4_4)
% 23.49/5.98 | (244) empty(empty_set)
% 23.49/5.98 | (245) ! [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))
% 23.49/5.98 | (246) ? [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))))
% 23.49/5.98 | (247) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 23.49/5.98 | (248) ! [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))
% 23.49/5.98 | (249) ? [v0] : ? [v1] : element(v1, v0)
% 23.49/5.98 | (250) relation_dom(empty_set) = empty_set
% 23.49/5.98 | (251) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 23.49/5.98 | (252) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 23.49/5.98 | (253) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 23.49/5.98 | (254) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3))
% 23.49/5.98 | (255) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 23.49/5.98 | (256) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 23.49/5.98 | (257) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 23.49/5.98 | (258) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 23.49/5.98 | (259) ! [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)))
% 23.49/5.98 | (260) empty(all_0_3_3)
% 23.49/5.98 | (261) ! [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)))
% 23.49/5.99 | (262) ! [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))))
% 23.49/5.99 | (263) ? [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)))))
% 23.49/5.99 | (264) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1))
% 23.49/5.99 | (265) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1))
% 23.49/5.99 | (266) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0))
% 23.49/5.99 | (267) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ function(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (apply(v0, v4) = v3) | ~ in(v4, v2) | in(v3, v1)) & ! [v3] : ( ~ in(v3, v1) | ? [v4] : (apply(v0, v4) = v3 & in(v4, v2))) & ? [v3] : (v3 = v1 | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v3) | ! [v7] : ( ~ (apply(v0, v7) = v4) | ~ in(v7, v2))) & (in(v4, v3) | (v6 = v4 & apply(v0, v5) = v4 & in(v5, v2)))))))
% 23.49/5.99 | (268) ? [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)))))
% 23.49/5.99 | (269) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 23.49/5.99 | (270) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ~ function(v1) | subset(v3, v0))
% 23.49/5.99 | (271) relation_empty_yielding(empty_set)
% 23.49/5.99 | (272) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 23.49/5.99 | (273) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 23.49/5.99 | (274) ! [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))))
% 23.49/5.99 | (275) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3)))
% 23.49/5.99 | (276) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 23.49/5.99 | (277) ! [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))
% 23.49/5.99 | (278) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 23.49/5.99 | (279) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_inverse_image(v1, v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : (apply(v1, v5) = v6 & ( ~ in(v6, v3) | ~ in(v5, v2) | ~ in(v5, v0)) & (in(v5, v0) | (in(v6, v3) & in(v5, v2)))))
% 23.49/5.99 | (280) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1))
% 23.49/5.99 | (281) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 23.49/5.99 | (282) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 23.49/5.99 | (283) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 23.49/5.99 | (284) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 23.49/5.99 | (285) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 23.49/5.99 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 23.49/5.99 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v5, v2))
% 23.49/5.99 | (288) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 23.49/5.99 | (289) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 23.49/5.99 | (290) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1))
% 23.49/5.99 | (291) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1))
% 23.49/5.99 | (292) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 23.49/5.99 | (293) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3)))
% 23.49/5.99 | (294) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 23.49/5.99 | (295) succ(all_0_10_10) = all_0_9_9
% 23.49/5.99 | (296) ! [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))
% 23.49/5.99 | (297) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 23.49/5.99 | (298) ! [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))
% 23.49/5.99 | (299) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 23.49/5.99 | (300) ! [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))
% 23.49/5.99 | (301) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 23.49/5.99 | (302) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 23.49/5.99 | (303) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 23.49/5.99 | (304) ? [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))))
% 23.49/5.99 | (305) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 23.49/5.99 | (306) relation(all_0_3_3)
% 23.49/5.99 | (307) ! [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))
% 23.49/5.99 | (308) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 23.49/5.99 | (309) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2))
% 23.49/6.00 | (310) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v3, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ~ in(v1, v0) | apply(v2, v1) = v4)
% 23.49/6.00 | (311) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | in(v4, v1))
% 23.49/6.00 | (312) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 23.49/6.00 | (313) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3)))
% 23.49/6.00 | (314) relation(all_0_1_1)
% 23.49/6.00 | (315) ? [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)))))
% 23.49/6.00 | (316) ! [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))))
% 23.49/6.00 | (317) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 23.49/6.00 | (318) relation_empty_yielding(all_0_7_7)
% 23.49/6.00 | (319) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 23.49/6.00 | (320) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 23.49/6.00 | (321) ! [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)))
% 23.49/6.00 | (322) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 23.49/6.00 | (323) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 23.49/6.00 | (324) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 23.49/6.00 | (325) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3)
% 23.49/6.00 | (326) ~ in(all_0_10_10, all_0_9_9)
% 23.49/6.00 | (327) ! [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)))))
% 23.49/6.00 | (328) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 23.49/6.00 | (329) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 23.49/6.00 | (330) ? [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)))))
% 23.49/6.00 | (331) ? [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)))))
% 23.49/6.00 | (332) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (( ~ in(v5, v0) | ! [v8] : ( ~ (apply(v1, v8) = v5) | ~ in(v8, v3) | ~ in(v8, v2))) & (in(v5, v0) | (v7 = v5 & apply(v1, v6) = v5 & in(v6, v3) & in(v6, v2)))))
% 23.49/6.00 | (333) ! [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)
% 23.49/6.00 | (334) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 23.49/6.00 | (335) ! [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)))
% 23.49/6.00 | (336) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3))))
% 23.49/6.00 | (337) ! [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))))
% 23.49/6.00 | (338) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1))
% 23.49/6.00 | (339) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 23.49/6.00 | (340) ! [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)))
% 23.49/6.00 | (341) ! [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)))
% 23.49/6.00 | (342) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 23.49/6.00 | (343) ! [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))
% 23.49/6.00 | (344) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (cartesian_product2(v1, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v0) | subset(v0, v3))
% 23.49/6.00 | (345) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 23.49/6.00 | (346) ! [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))
% 23.49/6.00 | (347) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 23.49/6.00 | (348) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 23.49/6.00 | (349) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3)))
% 23.49/6.00 | (350) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 23.49/6.00 | (351) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0))
% 23.49/6.00 | (352) ! [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))))
% 23.49/6.01 | (353) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v1) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : ? [v6] : (relation_dom(v3) = v5 & apply(v3, v1) = v6 & (v6 = v4 | ~ in(v1, v5))))
% 23.49/6.01 | (354) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 23.49/6.01 | (355) relation(all_0_8_8)
% 23.49/6.01 | (356) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2))
% 23.49/6.01 | (357) ! [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))))
% 23.49/6.01 | (358) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1))
% 23.49/6.01 | (359) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | v4 = v1 | v4 = v0 | ~ (unordered_triple(v0, v1, v2) = v3) | ~ in(v4, v3))
% 23.49/6.01 | (360) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0))
% 23.49/6.01 | (361) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0))
% 23.49/6.01 | (362) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3)
% 23.49/6.01 | (363) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1))
% 23.49/6.01 | (364) ! [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)))
% 23.49/6.01 | (365) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2))
% 23.49/6.01 | (366) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 23.49/6.01 | (367) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 23.49/6.01 | (368) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 23.49/6.01 | (369) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 23.49/6.01 | (370) ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v0 | ~ (unordered_triple(v1, v2, v3) = v4) | ? [v5] : ((v5 = v3 | v5 = v2 | v5 = v1 | in(v5, v0)) & ( ~ in(v5, v0) | ( ~ (v5 = v3) & ~ (v5 = v2) & ~ (v5 = v1)))))
% 23.49/6.01 | (371) ! [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)))
% 23.49/6.01 | (372) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0))
% 23.49/6.01 | (373) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 23.80/6.01 | (374) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_triple(v0, v1, v2) = v3) | in(v2, v3))
% 23.80/6.01 | (375) ! [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))
% 23.80/6.01 | (376) function(all_0_8_8)
% 23.80/6.01 | (377) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 23.80/6.01 | (378) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2))
% 23.80/6.01 | (379) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 23.80/6.01 | (380) ! [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)))))
% 23.80/6.01 | (381) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1)
% 23.80/6.01 | (382) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 23.80/6.01 | (383) ! [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))
% 23.80/6.01 | (384) ! [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))
% 23.80/6.01 | (385) ? [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)))))
% 23.80/6.01 | (386) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 23.80/6.01 | (387) relation(empty_set)
% 23.80/6.01 | (388) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 23.80/6.01 | (389) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 23.80/6.01 | (390) ! [v0] : ! [v1] : ( ~ in(v0, v1) | ? [v2] : (in(v2, v1) & ! [v3] : ( ~ in(v3, v2) | ~ in(v3, v1))))
% 23.80/6.01 | (391) ! [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))))
% 23.80/6.01 | (392) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1))
% 23.80/6.01 | (393) ! [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)))
% 23.80/6.01 | (394) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0))
% 23.80/6.01 | (395) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 23.80/6.01 | (396) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 23.80/6.01 | (397) ! [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)))
% 23.80/6.01 | (398) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1)))
% 23.80/6.01 | (399) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 23.80/6.02 | (400) ! [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)))
% 23.80/6.02 | (401) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 23.80/6.02 | (402) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 23.80/6.02 | (403) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2)))))
% 23.80/6.02 | (404) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4))))
% 23.80/6.02 | (405) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 23.80/6.02 | (406) ! [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)))))
% 23.80/6.02 | (407) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1)))
% 23.80/6.02 | (408) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 23.80/6.02 | (409) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & in(v3, v1) & in(v2, v1)))
% 23.80/6.02 | (410) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 23.80/6.02 | (411) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 23.80/6.02 | (412) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 23.80/6.02 | (413) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v3) | ? [v5] : (apply(v0, v5) = v4 & in(v5, v2) & in(v5, v1)))
% 23.80/6.02 | (414) ! [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)))
% 23.80/6.02 | (415) ! [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))))
% 23.80/6.02 | (416) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 23.80/6.02 | (417) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 23.80/6.02 | (418) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 23.80/6.02 | (419) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 23.80/6.02 | (420) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 23.80/6.02 | (421) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 23.80/6.02 | (422) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | subset(v0, v3) | ? [v4] : (relation_dom(v1) = v4 & ~ subset(v0, v4)))
% 23.80/6.02 | (423) ! [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)))))
% 23.80/6.02 | (424) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 23.80/6.02 | (425) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v5, v2) | ~ in(v4, v1) | in(v4, v3))
% 23.80/6.02 | (426) ! [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)))
% 23.80/6.02 | (427) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3))
% 23.80/6.02 |
% 23.80/6.02 | Instantiating formula (195) with all_0_9_9, all_0_10_10 and discharging atoms succ(all_0_10_10) = all_0_9_9, yields:
% 23.80/6.02 | (428) ? [v0] : (singleton(all_0_10_10) = v0 & set_union2(all_0_10_10, v0) = all_0_9_9)
% 23.80/6.02 |
% 23.80/6.02 | Instantiating (428) with all_116_0_71 yields:
% 23.80/6.02 | (429) singleton(all_0_10_10) = all_116_0_71 & set_union2(all_0_10_10, all_116_0_71) = all_0_9_9
% 23.80/6.02 |
% 23.80/6.02 | Applying alpha-rule on (429) yields:
% 23.80/6.02 | (430) singleton(all_0_10_10) = all_116_0_71
% 23.80/6.02 | (431) set_union2(all_0_10_10, all_116_0_71) = all_0_9_9
% 23.80/6.02 |
% 23.80/6.02 | Instantiating formula (288) with all_116_0_71, all_0_10_10 and discharging atoms singleton(all_0_10_10) = all_116_0_71, yields:
% 23.80/6.02 | (432) in(all_0_10_10, all_116_0_71)
% 23.80/6.02 |
% 23.80/6.02 | Instantiating formula (368) with all_0_9_9, all_0_10_10, all_116_0_71 and discharging atoms set_union2(all_0_10_10, all_116_0_71) = all_0_9_9, yields:
% 23.80/6.02 | (433) set_union2(all_116_0_71, all_0_10_10) = all_0_9_9
% 23.80/6.02 |
% 23.80/6.02 | Instantiating formula (202) with all_0_10_10, all_0_9_9, all_0_10_10, all_116_0_71 and discharging atoms set_union2(all_116_0_71, all_0_10_10) = all_0_9_9, in(all_0_10_10, all_116_0_71), ~ in(all_0_10_10, all_0_9_9), yields:
% 23.80/6.02 | (434) $false
% 23.80/6.02 |
% 23.80/6.03 |-The branch is then unsatisfiable
% 23.80/6.03 % SZS output end Proof for theBenchmark
% 23.80/6.03
% 23.80/6.03 5447ms
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