TSTP Solution File: SEU225+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU225+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 08:47:52 EDT 2022
% Result : Theorem 19.19s 4.94s
% Output : Proof 30.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU225+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.33 % Computer : n024.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 15:54:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.58 (ePrincess v.1.0)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2015
% 0.20/0.58 (c) Peter Backeman, 2014-2015
% 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.58 Bug reports to peter@backeman.se
% 0.20/0.58
% 0.20/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.58
% 0.20/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.56/1.15 Prover 0: Preprocessing ...
% 7.22/2.10 Prover 0: Warning: ignoring some quantifiers
% 7.48/2.15 Prover 0: Constructing countermodel ...
% 19.19/4.94 Prover 0: proved (4314ms)
% 19.19/4.94
% 19.19/4.94 No countermodel exists, formula is valid
% 19.19/4.94 % SZS status Theorem for theBenchmark
% 19.19/4.94
% 19.19/4.94 Generating proof ... Warning: ignoring some quantifiers
% 28.74/7.28 found it (size 87)
% 28.74/7.28
% 28.74/7.28 % SZS output start Proof for theBenchmark
% 28.74/7.28 Assumed formulas after preprocessing and simplification:
% 28.74/7.28 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v6 = v5) & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & apply(v4, v2) = v5 & apply(v3, v2) = v6 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_dom_restriction(v3, v1) = v4 & relation_empty_yielding(v7) & relation_empty_yielding(empty_set) & one_to_one(v8) & relation(v14) & relation(v13) & relation(v11) & relation(v10) & relation(v8) & relation(v7) & relation(v3) & relation(empty_set) & function(v14) & function(v11) & function(v8) & function(v3) & empty(v13) & empty(v12) & empty(v11) & empty(empty_set) & in(v2, v1) & ~ empty(v10) & ~ empty(v9) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v21, v19) = v22) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v22, v16) | in(v20, v17) | ? [v23] : (ordered_pair(v18, v21) = v23 & ~ in(v23, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v18, v21) = v22) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v22, v15) | in(v20, v17) | ? [v23] : (ordered_pair(v21, v19) = v23 & ~ in(v23, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v21) | in(v19, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v21) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (identity_relation(v17) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ relation(v18) | ~ in(v19, v18) | ~ in(v15, v17) | in(v19, v21)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ relation(v15) | ~ in(v20, v17) | ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v19) = v23 & ordered_pair(v18, v21) = v22 & in(v23, v16) & in(v22, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v19) | ~ (relation_dom(v16) = v17) | ~ (set_intersection2(v19, v15) = v20) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_dom_restriction(v18, v15) = v21 & ( ~ (v21 = v16) | (v20 = v17 & ! [v25] : ! [v26] : ( ~ (apply(v18, v25) = v26) | ~ in(v25, v17) | apply(v16, v25) = v26) & ! [v25] : ! [v26] : ( ~ (apply(v16, v25) = v26) | ~ in(v25, v17) | apply(v18, v25) = v26))) & ( ~ (v20 = v17) | v21 = v16 | ( ~ (v24 = v23) & apply(v18, v22) = v24 & apply(v16, v22) = v23 & in(v22, v17))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ in(v19, v20) | in(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ in(v19, v20) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (ordered_pair(v15, v16) = v19) | ~ in(v16, v18) | ~ in(v15, v17) | in(v19, v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v16, v18) = v20) | ~ (cartesian_product2(v15, v17) = v19) | ~ subset(v17, v18) | ~ subset(v15, v16) | subset(v19, v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ (ordered_pair(v19, v20) = v18) | ~ in(v20, v16) | ~ in(v19, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v15, v16) = v17) | ~ (ordered_pair(v19, v18) = v20) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v19, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | in(v20, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | in(v19, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v16) | ~ in(v19, v15) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v17) | in(v20, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v15) | ~ in(v20, v15) | ~ in(v18, v16) | in(v20, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom(v16) = v17) | ~ (apply(v16, v18) = v19) | ~ (identity_relation(v15) = v16) | ~ relation(v16) | ~ function(v16) | ~ in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v18) = v19) | ~ (apply(v15, v17) = v19) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ~ in(v18, v16) | ~ in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v16 | ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v15 | v17 = v15 | ~ (unordered_pair(v17, v18) = v19) | ~ (unordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v15 | ~ (ordered_pair(v17, v18) = v19) | ~ (ordered_pair(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = v15 | ~ (subset_difference(v19, v18, v17) = v16) | ~ (subset_difference(v19, v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (subset_difference(v15, v17, v18) = v19) | ~ (meet_of_subsets(v15, v16) = v18) | ~ (cast_to_subset(v15) = v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (union_of_subsets(v15, v22) = v23 & complements_of_subsets(v15, v16) = v22 & powerset(v20) = v21 & powerset(v15) = v20 & (v23 = v19 | ~ element(v16, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (subset_difference(v15, v17, v18) = v19) | ~ (union_of_subsets(v15, v16) = v18) | ~ (cast_to_subset(v15) = v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (meet_of_subsets(v15, v22) = v23 & complements_of_subsets(v15, v16) = v22 & powerset(v20) = v21 & powerset(v15) = v20 & (v23 = v19 | ~ element(v16, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v15 = empty_set | ~ (subset_complement(v15, v17) = v18) | ~ (powerset(v15) = v16) | ~ element(v19, v15) | ~ element(v17, v16) | in(v19, v18) | in(v19, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (function_inverse(v16) = v17) | ~ (relation_composition(v17, v16) = v18) | ~ (apply(v18, v15) = v19) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_rng(v16) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & ( ~ in(v15, v20) | (v22 = v15 & v19 = v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (function_inverse(v16) = v17) | ~ (apply(v17, v15) = v18) | ~ (apply(v16, v18) = v19) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v17, v16) = v21 & relation_rng(v16) = v20 & apply(v21, v15) = v22 & ( ~ in(v15, v20) | (v22 = v15 & v19 = v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v16) = v18) | ~ (apply(v18, v15) = v19) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & (v22 = v19 | ~ in(v15, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v16) | ~ relation(v15) | in(v19, v15) | ? [v20] : (ordered_pair(v17, v18) = v20 & ~ in(v20, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ relation(v15) | in(v19, v16) | ? [v20] : (ordered_pair(v18, v17) = v20 & ~ in(v20, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_field(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_field(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v15, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v15, v18) = v19) | ~ (powerset(v15) = v17) | ~ disjoint(v16, v18) | ~ element(v18, v17) | ~ element(v16, v17) | subset(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v15, v18) = v19) | ~ (powerset(v15) = v17) | ~ element(v18, v17) | ~ element(v16, v17) | ~ subset(v16, v19) | disjoint(v16, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v16, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | ? [v20] : (relation_dom(v17) = v20 & in(v15, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v15) = v16) | ~ (ordered_pair(v18, v17) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v18) = v19) | ~ (singleton(v17) = v18) | ~ subset(v15, v16) | subset(v15, v19) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v19) | ~ (set_difference(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v19) | ~ (powerset(v15) = v18) | ~ element(v17, v18) | ~ element(v16, v18) | subset_difference(v15, v16, v17) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : (apply(v17, v15) = v20 & ( ~ (v20 = v16) | ~ in(v15, v19) | in(v18, v17)) & ( ~ in(v18, v17) | (v20 = v16 & in(v15, v19))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | in(v15, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ in(v18, v17) | ? [v20] : (relation_rng(v17) = v20 & in(v16, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (apply(v18, v15) = v19) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v18, v16) = v20 & relation_dom(v20) = v21 & relation_dom(v18) = v22 & ( ~ in(v19, v17) | ~ in(v15, v22) | in(v15, v21)) & ( ~ in(v15, v21) | (in(v19, v17) & in(v15, v22))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (relation_image(v16, v18) = v19) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | relation_image(v16, v15) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v16) = v17) | ~ (relation_dom_restriction(v18, v15) = v19) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_dom(v18) = v20 & set_intersection2(v20, v15) = v21 & ( ~ (v21 = v17) | v19 = v16 | ( ~ (v24 = v23) & apply(v18, v22) = v24 & apply(v16, v22) = v23 & in(v22, v17))) & ( ~ (v19 = v16) | (v21 = v17 & ! [v25] : ! [v26] : ( ~ (apply(v18, v25) = v26) | ~ in(v25, v17) | apply(v16, v25) = v26) & ! [v25] : ! [v26] : ( ~ (apply(v16, v25) = v26) | ~ in(v25, v17) | apply(v18, v25) = v26))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v15) | ~ function(v15) | ~ in(v17, v16) | ? [v20] : (apply(v15, v17) = v20 & ( ~ (v20 = v18) | in(v19, v15)) & (v20 = v18 | ~ in(v19, v15)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v15) | ~ in(v19, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v18, v16) = v19) | ~ (relation_dom_restriction(v17, v15) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : ? [v21] : (relation_dom(v18) = v20 & apply(v17, v16) = v21 & (v21 = v19 | ~ in(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v16) = v19) | ~ (relation_dom_restriction(v17, v15) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : ? [v21] : (relation_dom(v18) = v20 & apply(v18, v16) = v21 & (v21 = v19 | ~ in(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v15) = v19) | ~ (ordered_pair(v15, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v20] : (relation_dom(v17) = v20 & ( ~ (v19 = v16) | ~ in(v15, v20) | in(v18, v17)) & ( ~ in(v18, v17) | (v19 = v16 & in(v15, v20))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v17, v15) = v18) | ~ (apply(v16, v18) = v19) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v17, v16) = v20 & relation_dom(v20) = v21 & apply(v20, v15) = v22 & (v22 = v19 | ~ in(v15, v21)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v17, v15) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v17, v15) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v16, v17) = v21 & cartesian_product2(v15, v17) = v20 & subset(v20, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v16) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v15) = v21 & cartesian_product2(v16, v17) = v20 & subset(v21, v19) & subset(v18, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v15) = v19) | ~ (cartesian_product2(v16, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v16) = v21 & cartesian_product2(v15, v17) = v20 & subset(v20, v18) & subset(v19, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v19) | ~ (cartesian_product2(v15, v17) = v18) | ~ subset(v15, v16) | ? [v20] : ? [v21] : (cartesian_product2(v17, v16) = v21 & cartesian_product2(v17, v15) = v20 & subset(v20, v21))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v15) = v18) | ~ (unordered_pair(v17, v18) = v19) | ~ (unordered_pair(v15, v16) = v17) | ordered_pair(v15, v16) = v19) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v17, v16) = v19) | ~ (relation_inverse_image(v17, v15) = v18) | ~ subset(v15, v16) | ~ relation(v17) | subset(v18, v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v18) = v19) | ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v20] : (relation_rng_restriction(v15, v17) = v20 & relation_dom_restriction(v20, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v15, v17) = v18) | ~ (relation_dom_restriction(v18, v16) = v19) | ~ relation(v17) | ? [v20] : (relation_rng_restriction(v15, v20) = v19 & relation_dom_restriction(v17, v16) = v20)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v18) = v19) | ~ relation(v16) | ~ in(v19, v16) | in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ subset(v15, v16) | ~ relation(v16) | ~ relation(v15) | ~ in(v19, v15) | in(v19, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v19) | ~ (set_intersection2(v15, v17) = v18) | ~ subset(v15, v16) | subset(v18, v19)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v16) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v19) = v20 & relation_dom(v18) = v21 & apply(v18, v15) = v22 & ( ~ in(v22, v17) | ~ in(v15, v21) | in(v15, v20)) & ( ~ in(v15, v20) | (in(v22, v17) & in(v15, v21))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ function(v18) | ~ function(v16) | ? [v20] : ? [v21] : ? [v22] : (relation_composition(v18, v16) = v20 & relation_dom(v20) = v21 & apply(v18, v15) = v22 & ( ~ in(v22, v17) | ~ in(v15, v19) | in(v15, v21)) & ( ~ in(v15, v21) | (in(v22, v17) & in(v15, v19))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_composition(v15, v16) = v17) | ~ relation(v18) | ~ relation(v16) | ~ relation(v15) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ( ! [v25] : ! [v26] : ( ~ (ordered_pair(v25, v20) = v26) | ~ in(v26, v16) | ? [v27] : (ordered_pair(v19, v25) = v27 & ~ in(v27, v15))) & ! [v25] : ! [v26] : ( ~ (ordered_pair(v19, v25) = v26) | ~ in(v26, v15) | ? [v27] : (ordered_pair(v25, v20) = v27 & ~ in(v27, v16))))) & (in(v21, v18) | (ordered_pair(v22, v20) = v24 & ordered_pair(v19, v22) = v23 & in(v24, v16) & in(v23, v15))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ~ in(v21, v16) | ~ in(v20, v15)) & (in(v21, v18) | (in(v21, v16) & in(v20, v15))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_dom_restriction(v15, v16) = v18) | ~ relation(v17) | ~ relation(v15) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v17) | ~ in(v21, v15) | ~ in(v19, v16)) & (in(v21, v17) | (in(v21, v15) & in(v19, v16))))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | v18 = v15 | ~ (unordered_pair(v15, v16) = v17) | ~ in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (complements_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v15) = v19 & ~ element(v16, v20))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (subset_complement(v15, v17) = v18) | ~ (subset_complement(v15, v16) = v17) | ? [v19] : (powerset(v15) = v19 & ~ element(v16, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (set_difference(v16, v15) = v17) | ~ (set_union2(v15, v17) = v18) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (apply(v17, v16) = v18) | ~ (identity_relation(v15) = v17) | ~ in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (singleton(v15) = v17) | ~ (set_union2(v17, v16) = v18) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v15, v17) = v18) | ~ (singleton(v16) = v17) | in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = empty_set | ~ (relation_dom(v15) = v16) | ~ (apply(v15, v17) = v18) | ~ relation(v15) | ~ function(v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v15) = v18) | ~ (unordered_pair(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (meet_of_subsets(v18, v17) = v16) | ~ (meet_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (union_of_subsets(v18, v17) = v16) | ~ (union_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (complements_of_subsets(v18, v17) = v16) | ~ (complements_of_subsets(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_composition(v18, v17) = v16) | ~ (relation_composition(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (subset_complement(v18, v17) = v16) | ~ (subset_complement(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_difference(v18, v17) = v16) | ~ (set_difference(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (apply(v18, v17) = v16) | ~ (apply(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (cartesian_product2(v18, v17) = v16) | ~ (cartesian_product2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (singleton(v16) = v18) | ~ (singleton(v15) = v17) | ~ subset(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (singleton(v15) = v18) | ~ (unordered_pair(v16, v17) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_inverse_image(v18, v17) = v16) | ~ (relation_inverse_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_image(v18, v17) = v16) | ~ (relation_image(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_rng_restriction(v18, v17) = v16) | ~ (relation_rng_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (relation_dom_restriction(v18, v17) = v16) | ~ (relation_dom_restriction(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (ordered_pair(v18, v17) = v16) | ~ (ordered_pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_intersection2(v18, v17) = v16) | ~ (set_intersection2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (set_union2(v18, v17) = v16) | ~ (set_union2(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = v15 | ~ (unordered_pair(v18, v17) = v16) | ~ (unordered_pair(v18, v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = empty_set | ~ (meet_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset_difference(v15, v21, v22) = v23 & union_of_subsets(v15, v16) = v22 & cast_to_subset(v15) = v21 & powerset(v19) = v20 & powerset(v15) = v19 & (v23 = v18 | ~ element(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = empty_set | ~ (union_of_subsets(v15, v17) = v18) | ~ (complements_of_subsets(v15, v16) = v17) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (subset_difference(v15, v21, v22) = v23 & meet_of_subsets(v15, v16) = v22 & cast_to_subset(v15) = v21 & powerset(v19) = v20 & powerset(v15) = v19 & (v23 = v18 | ~ element(v16, v20)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v15 = empty_set | ~ (set_meet(v15) = v16) | ~ in(v18, v15) | ~ in(v17, v16) | in(v17, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_difference(v15, v16, v17) = v18) | ? [v19] : ? [v20] : (set_difference(v16, v17) = v20 & powerset(v15) = v19 & (v20 = v18 | ~ element(v17, v19) | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_difference(v15, v16, v17) = v18) | ? [v19] : (powerset(v15) = v19 & ( ~ element(v17, v19) | ~ element(v16, v19) | element(v18, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ (identity_relation(v15) = v17) | ~ relation(v16) | relation_dom_restriction(v16, v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v15, v17) = v18) | ~ (relation_rng(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_rng(v18) = v19 & relation_image(v17, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v15, v17) = v18) | ~ (relation_dom(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_dom(v18) = v19 & subset(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v15, v17) = v18) | ~ in(v16, v18) | ~ in(v16, v17) | ? [v19] : (powerset(v15) = v19 & ~ element(v17, v19))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v16) = v17) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | ? [v19] : (relation_rng(v19) = v18 & relation_rng_restriction(v15, v16) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v17) | ~ (relation_dom(v15) = v16) | ~ (cartesian_product2(v16, v17) = v18) | ~ relation(v15) | subset(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v17) | ~ (relation_dom(v15) = v16) | ~ (set_union2(v16, v17) = v18) | ~ relation(v15) | relation_field(v15) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v15) = v16) | ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ~ relation(v15) | ? [v19] : (relation_composition(v15, v17) = v19 & relation_rng(v19) = v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v17, v16) = v18) | ~ (set_union2(v15, v16) = v17) | set_difference(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v15) = v17) | ~ (set_union2(v15, v17) = v18) | set_union2(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v17) = v18) | ~ (set_difference(v15, v16) = v17) | set_intersection2(v15, v16) = v18) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v17) | ~ in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v15, v16) = v17) | ~ in(v18, v15) | in(v18, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v16) = v18) | ~ (powerset(v15) = v17) | ? [v19] : ? [v20] : (union_of_subsets(v15, v16) = v20 & powerset(v17) = v19 & (v20 = v18 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v15) = v16) | ~ in(v18, v15) | ~ in(v17, v18) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ (set_intersection2(v17, v15) = v18) | ~ relation(v16) | ? [v19] : (relation_dom(v19) = v18 & relation_dom_restriction(v16, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v20) = v18 & in(v20, v16) & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ empty(v17) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | ~ in(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v15) = v17) | ~ (set_meet(v16) = v18) | ? [v19] : ? [v20] : (meet_of_subsets(v15, v16) = v20 & powerset(v17) = v19 & (v20 = v18 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v15) = v17) | ~ element(v16, v17) | ~ in(v18, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v15, v16) = v17) | ~ relation(v15) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v15) & in(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v15, v16) = v17) | ~ relation(v15) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v18) = v20 & in(v20, v15) & in(v19, v16))) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (identity_relation(v15) = v16) | ~ (ordered_pair(v17, v17) = v18) | ~ relation(v16) | ~ in(v17, v15) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | ~ subset(v15, v17) | ~ subset(v15, v16) | subset(v15, v18)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ disjoint(v15, v16) | ~ in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v15, v16) = v17) | ~ in(v18, v16) | ~ in(v18, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v17) = v18) | ~ subset(v17, v16) | ~ subset(v15, v16) | subset(v18, v16)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v17) | in(v18, v16) | in(v18, v15)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v16) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v15, v16) = v17) | ~ in(v18, v15) | in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ subset(v18, v17) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ subset(v18, v17) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v15, v16) = v18) | ~ in(v16, v17) | ~ in(v15, v17) | subset(v18, v17)) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_difference(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v16) | ~ in(v19, v15) | in(v19, v17)) & (in(v19, v15) | (in(v19, v16) & ~ in(v19, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (cartesian_product2(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (( ~ in(v19, v15) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v24) = v19) | ~ in(v24, v17) | ~ in(v23, v16))) & (in(v19, v15) | (v22 = v19 & ordered_pair(v20, v21) = v19 & in(v21, v17) & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_inverse_image(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v15) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v19, v22) = v23) | ~ in(v23, v16) | ~ in(v22, v17))) & (in(v19, v15) | (ordered_pair(v19, v20) = v21 & in(v21, v16) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v15) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v19) = v23) | ~ in(v23, v16) | ~ in(v22, v17))) & (in(v19, v15) | (ordered_pair(v20, v19) = v21 & in(v21, v16) & in(v20, v17))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_intersection2(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v17) | ~ in(v19, v16) | ~ in(v19, v15)) & (in(v19, v15) | (in(v19, v17) & in(v19, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (set_union2(v16, v17) = v18) | ? [v19] : (( ~ in(v19, v15) | ( ~ in(v19, v17) & ~ in(v19, v16))) & (in(v19, v17) | in(v19, v16) | in(v19, v15)))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = v15 | ~ (unordered_pair(v16, v17) = v18) | ? [v19] : ((v19 = v17 | v19 = v16 | in(v19, v15)) & ( ~ in(v19, v15) | ( ~ (v19 = v17) & ~ (v19 = v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v19 & apply(v18, v15) = v20 & apply(v17, v15) = v21 & apply(v16, v21) = v22 & (v22 = v20 | ~ in(v15, v19)))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (relation_rng(v17) = v19 & ( ~ in(v15, v18) | (ordered_pair(v15, v20) = v21 & in(v21, v17) & in(v20, v19) & in(v20, v16))) & (in(v15, v18) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v15, v22) = v23) | ~ in(v23, v17) | ~ in(v22, v19) | ~ in(v22, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (relation_dom(v17) = v19 & ( ~ in(v15, v18) | (ordered_pair(v20, v15) = v21 & in(v21, v17) & in(v20, v19) & in(v20, v16))) & (in(v15, v18) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v15) = v23) | ~ in(v23, v17) | ~ in(v22, v19) | ~ in(v22, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ? [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & ( ~ in(v15, v20) | ~ in(v15, v16) | in(v15, v19)) & ( ~ in(v15, v19) | (in(v15, v20) & in(v15, v16))))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (relation_inverse(v15) = v16) | ~ relation(v17) | ~ relation(v15) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v18) = v21 & ordered_pair(v18, v19) = v20 & ( ~ in(v21, v15) | ~ in(v20, v17)) & (in(v21, v15) | in(v20, v17)))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (relation_dom(v16) = v15) | ~ (identity_relation(v15) = v17) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : ( ~ (v19 = v18) & apply(v16, v18) = v19 & in(v18, v15))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (identity_relation(v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & ( ~ (v19 = v18) | ~ in(v20, v16) | ~ in(v18, v15)) & (in(v20, v16) | (v19 = v18 & in(v18, v15))))) & ! [v15] : ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | v15 = empty_set | ~ (singleton(v16) = v17) | ~ subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (set_difference(v15, v16) = v17) | ~ disjoint(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_dom(v16) = v17) | ~ (identity_relation(v15) = v16) | ~ relation(v16) | ~ function(v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (singleton(v15) = v16) | ~ in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (set_intersection2(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_difference(v15, v16) = v17) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_intersection2(v15, v16) = v17) | ~ disjoint(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (function_inverse(v17) = v16) | ~ (function_inverse(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_inverse(v17) = v16) | ~ (relation_inverse(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_field(v17) = v16) | ~ (relation_field(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_rng(v17) = v16) | ~ (relation_rng(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (union(v17) = v16) | ~ (union(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (cast_to_subset(v17) = v16) | ~ (cast_to_subset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (relation_dom(v17) = v16) | ~ (relation_dom(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (powerset(v17) = v16) | ~ (powerset(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (singleton(v17) = v16) | ~ (singleton(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (set_meet(v17) = v16) | ~ (set_meet(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : (v16 = v15 | ~ (identity_relation(v17) = v16) | ~ (identity_relation(v17) = v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (meet_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (powerset(v18) = v19 & powerset(v15) = v18 & set_meet(v16) = v20 & (v20 = v17 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (meet_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : (union(v16) = v20 & powerset(v18) = v19 & powerset(v15) = v18 & (v20 = v17 | ~ element(v16, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (complements_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | element(v17, v19)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (complements_of_subsets(v15, v16) = v17) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v15) = v18 & ( ~ element(v16, v19) | ( ! [v20] : ! [v21] : ( ~ (subset_complement(v15, v20) = v21) | ~ element(v20, v18) | ~ element(v17, v19) | ~ in(v21, v16) | in(v20, v17)) & ! [v20] : ! [v21] : ( ~ (subset_complement(v15, v20) = v21) | ~ element(v20, v18) | ~ element(v17, v19) | ~ in(v20, v17) | in(v21, v16)) & ! [v20] : (v20 = v17 | ~ element(v20, v19) | ? [v21] : ? [v22] : (subset_complement(v15, v21) = v22 & element(v21, v18) & ( ~ in(v22, v16) | ~ in(v21, v20)) & (in(v22, v16) | in(v21, v20)))))))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ empty(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v16, v15) = v17) | ~ relation(v16) | ~ empty(v15) | empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ~ function(v16) | ~ function(v15) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ empty(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v15, v16) = v17) | ~ relation(v16) | ~ empty(v15) | empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v15, v16) = v17) | ? [v18] : ? [v19] : (set_difference(v15, v16) = v19 & powerset(v15) = v18 & (v19 = v17 | ~ element(v16, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v15, v16) = v17) | ? [v18] : (powerset(v15) = v18 & ( ~ element(v16, v18) | element(v17, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ relation(v15) | ? [v18] : ? [v19] : (relation_composition(v15, v16) = v18 & relation_rng(v18) = v19 & subset(v19, v17))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ in(v17, v16) | ? [v18] : ? [v19] : (ordered_pair(v18, v17) = v19 & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v17) = v15) | ~ (singleton(v16) = v17) | ~ in(v16, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : ? [v19] : (subset_complement(v15, v16) = v19 & powerset(v15) = v18 & (v19 = v17 | ~ element(v16, v18)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_difference(v15, v16) = v17) | ? [v18] : (set_difference(v18, v16) = v17 & set_union2(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union(v16) = v17) | ~ in(v15, v16) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (union(v15) = v16) | ~ in(v17, v16) | ? [v18] : (in(v18, v15) & in(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ (relation_image(v15, v16) = v17) | ~ relation(v15) | relation_rng(v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ in(v17, v16) | ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (apply(v16, v15) = v17) | ~ relation(v16) | ~ function(v16) | ? [v18] : (relation_dom(v16) = v18 & ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v16, v19) = v20) | ~ (apply(v20, v15) = v21) | ~ relation(v19) | ~ function(v19) | ~ in(v15, v18) | apply(v19, v17) = v21) & ! [v19] : ! [v20] : ( ~ (apply(v19, v17) = v20) | ~ relation(v19) | ~ function(v19) | ~ in(v15, v18) | ? [v21] : (relation_composition(v16, v19) = v21 & apply(v21, v15) = v20)))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v15, v16) = v17) | ~ empty(v17) | empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ element(v15, v17) | subset(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ subset(v15, v16) | element(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v15) = v16) | ~ subset(v17, v15) | in(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v15) = v16) | ~ in(v17, v16) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ disjoint(v17, v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ subset(v17, v16) | in(v15, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v15) = v17) | ~ in(v15, v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_inverse_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & subset(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v16) = v18 & relation_image(v16, v19) = v17 & set_intersection2(v18, v15) = v19)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_image(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & subset(v17, v18))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & set_intersection2(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v15, v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v17) = v18 & subset(v18, v15))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | subset(v17, v16)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v18 & relation_rng(v16) = v19 & subset(v18, v19))) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_dom(v17) = v18 & relation_dom(v16) = v19 & set_intersection2(v19, v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v16, v15) = v17) | ~ relation(v16) | ? [v18] : (relation_composition(v18, v16) = v17 & identity_relation(v15) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation_empty_yielding(v15) | ~ relation(v15) | relation_empty_yielding(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation_empty_yielding(v15) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | ~ function(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | ~ function(v15) | function(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v15, v16) = v17) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (ordered_pair(v15, v16) = v17) | ? [v18] : ? [v19] : (singleton(v15) = v19 & unordered_pair(v18, v19) = v17 & unordered_pair(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v16, v15) = v17) | set_intersection2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | set_intersection2(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | disjoint(v15, v16) | ? [v18] : in(v18, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | subset(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_intersection2(v15, v16) = v17) | ? [v18] : (set_difference(v15, v18) = v17 & set_difference(v15, v16) = v18)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v16, v15) = v17) | set_union2(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ relation(v16) | ~ relation(v15) | relation(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ~ empty(v17) | empty(v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | set_union2(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (set_union2(v15, v16) = v17) | ? [v18] : (set_difference(v16, v15) = v18 & set_union2(v15, v18) = v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v16, v15) = v17) | unordered_pair(v15, v16) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | ~ empty(v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | unordered_pair(v16, v15) = v17) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | in(v16, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ (unordered_pair(v15, v16) = v17) | in(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ disjoint(v16, v17) | ~ subset(v15, v16) | disjoint(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ disjoint(v15, v16) | ~ in(v17, v16) | ~ in(v17, v15)) & ! [v15] : ! [v16] : ! [v17] : ( ~ subset(v16, v17) | ~ subset(v15, v16) | subset(v15, v17)) & ! [v15] : ! [v16] : ! [v17] : ( ~ subset(v15, v16) | ~ in(v17, v15) | in(v17, v16)) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | v16 = empty_set | ~ (set_meet(v16) = v17) | ? [v18] : ? [v19] : (( ~ in(v18, v15) | (in(v19, v16) & ~ in(v18, v19))) & (in(v18, v15) | ! [v20] : ( ~ in(v20, v16) | in(v18, v20))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ in(v18, v15) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v21, v18) = v22) | ~ in(v22, v16))) & (in(v18, v15) | (ordered_pair(v19, v18) = v20 & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (union(v16) = v17) | ? [v18] : ? [v19] : (( ~ in(v18, v15) | ! [v20] : ( ~ in(v20, v16) | ~ in(v18, v20))) & (in(v18, v15) | (in(v19, v16) & in(v18, v19))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (( ~ in(v18, v15) | ! [v21] : ! [v22] : ( ~ (ordered_pair(v18, v21) = v22) | ~ in(v22, v16))) & (in(v18, v15) | (ordered_pair(v18, v19) = v20 & in(v20, v16))))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (powerset(v16) = v17) | ? [v18] : (( ~ subset(v18, v16) | ~ in(v18, v15)) & (subset(v18, v16) | in(v18, v15)))) & ? [v15] : ! [v16] : ! [v17] : (v17 = v15 | ~ (singleton(v16) = v17) | ? [v18] : (( ~ (v18 = v16) | ~ in(v16, v15)) & (v18 = v16 | in(v18, v15)))) & ? [v15] : ! [v16] : ! [v17] : (v16 = empty_set | ~ (set_meet(v16) = v17) | in(v15, v17) | ? [v18] : (in(v18, v16) & ~ in(v15, v18))) & ? [v15] : ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | element(v15, v17) | ? [v18] : (in(v18, v15) & ~ in(v18, v16))) & ? [v15] : ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | disjoint(v17, v15) | in(v16, v15)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_difference(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (cast_to_subset(v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_intersection2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, v15) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ (set_union2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v16, v15) | ~ subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ subset(v15, v16) | proper_subset(v15, v16)) & ! [v15] : ! [v16] : (v16 = v15 | ~ relation(v16) | ~ relation(v15) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & ( ~ in(v19, v16) | ~ in(v19, v15)) & (in(v19, v16) | in(v19, v15)))) & ! [v15] : ! [v16] : (v16 = v15 | ~ empty(v16) | ~ empty(v15)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (complements_of_subsets(v15, v16) = empty_set) | ? [v17] : ? [v18] : (powerset(v17) = v18 & powerset(v15) = v17 & ~ element(v16, v18))) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_difference(empty_set, v15) = v16)) & ! [v15] : ! [v16] : (v16 = empty_set | ~ (set_intersection2(v15, empty_set) = v16)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & relation_dom(v15) = v17)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : ( ~ (v17 = empty_set) & relation_rng(v15) = v17)) & ! [v15] : ! [v16] : (v15 = empty_set | ~ (relation_inverse_image(v16, v15) = empty_set) | ~ relation(v16) | ? [v17] : (relation_rng(v16) = v17 & ~ subset(v15, v17))) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | relation_inverse(v15) = v16) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | one_to_one(v16)) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & relation_dom(v16) = v17 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (relation_rng(v15) = v17 & relation_dom(v15) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v16) | ~ function(v16) | ~ in(v21, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v16) | ~ function(v16) | ~ in(v20, v17)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v16) | ~ function(v16) | ~ in(v21, v18) | in(v20, v17)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v16) = v19) | ~ (apply(v16, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v16) | ~ function(v16) | ~ in(v20, v17) | in(v21, v18)) & ! [v19] : (v19 = v17 | ~ (relation_dom(v16) = v19) | ~ relation(v16) | ~ function(v16)) & ! [v19] : (v19 = v16 | ~ (relation_dom(v19) = v17) | ~ relation(v19) | ~ function(v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (apply(v19, v20) = v22 & apply(v15, v21) = v23 & ((v23 = v20 & in(v21, v18) & ( ~ (v22 = v21) | ~ in(v20, v17))) | (v22 = v21 & in(v20, v17) & ( ~ (v23 = v20) | ~ in(v21, v18)))))))) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ relation(v15) | ~ function(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (function_inverse(v15) = v16) | ~ relation(v15) | ~ function(v15) | function(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | function_inverse(v15) = v16) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | function(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | relation_inverse(v16) = v15) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v16) = v18 & relation_rng(v15) = v17 & relation_dom(v16) = v17 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_inverse(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (relation_field(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_rng(v15) = v18 & relation_dom(v15) = v17 & set_union2(v17, v18) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v17 & relation_rng(v17) = v18 & relation_dom(v17) = v16 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v17 & relation_dom(v15) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v16)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18) | in(v20, v16)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v16) | in(v21, v18)) & ! [v19] : (v19 = v17 | ~ (relation_dom(v19) = v16) | ~ relation(v19) | ~ function(v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (apply(v19, v20) = v22 & apply(v15, v21) = v23 & ((v23 = v20 & in(v21, v18) & ( ~ (v22 = v21) | ~ in(v20, v16))) | (v22 = v21 & in(v20, v16) & ( ~ (v23 = v20) | ~ in(v21, v18)))))) & ! [v19] : (v19 = v16 | ~ (relation_dom(v17) = v19) | ~ relation(v17) | ~ function(v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_inverse(v15) = v17 & relation_rng(v17) = v18 & relation_dom(v17) = v16 & relation_dom(v15) = v18)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & relation_image(v15, v17) = v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v15) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v21 & relation_rng(v18) = v20 & (v21 = v16 | ~ subset(v17, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v17, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v18, v15) = v20 & relation_rng(v20) = v16)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v15, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v21 & relation_dom(v18) = v20 & (v21 = v17 | ~ subset(v16, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v16, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v15, v18) = v20 & relation_dom(v20) = v17)))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v16, v19)) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v17, v20))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v17, v19)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v16, v20))))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_dom(v15) = v17 & ( ~ (v17 = empty_set) | v16 = empty_set) & ( ~ (v16 = empty_set) | v17 = empty_set))) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_rng(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (set_difference(v15, v16) = v15) | disjoint(v15, v16)) & ! [v15] : ! [v16] : ( ~ (set_difference(v15, v16) = empty_set) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ (cast_to_subset(v15) = v16) | ? [v17] : (powerset(v15) = v17 & element(v16, v17))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v18 & relation_rng(v18) = v16 & relation_rng(v15) = v17 & relation_dom(v18) = v17)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ one_to_one(v15) | ~ relation(v15) | ~ function(v15) | ? [v17] : ? [v18] : (function_inverse(v15) = v17 & relation_rng(v15) = v18 & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v16)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v22) | ~ (apply(v15, v21) = v20) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v16) | in(v20, v18)) & ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v17) = v19) | ~ (apply(v17, v20) = v21) | ~ (apply(v15, v21) = v22) | ~ relation(v17) | ~ function(v17) | ~ in(v20, v18) | in(v21, v16)) & ! [v19] : (v19 = v18 | ~ (relation_dom(v17) = v19) | ~ relation(v17) | ~ function(v17)) & ! [v19] : (v19 = v17 | ~ (relation_dom(v19) = v18) | ~ relation(v19) | ~ function(v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (apply(v19, v20) = v22 & apply(v15, v21) = v23 & ((v23 = v20 & in(v21, v16) & ( ~ (v22 = v21) | ~ in(v20, v18))) | (v22 = v21 & in(v20, v18) & ( ~ (v23 = v20) | ~ in(v21, v16)))))))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ function(v15) | one_to_one(v15) | ? [v17] : ? [v18] : ? [v19] : ( ~ (v18 = v17) & apply(v15, v18) = v19 & apply(v15, v17) = v19 & in(v18, v16) & in(v17, v16))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ~ empty(v16) | empty(v15)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : ? [v18] : (relation_inverse(v15) = v18 & relation_rng(v18) = v16 & relation_rng(v15) = v17 & relation_dom(v18) = v17)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v15) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v21 & relation_rng(v18) = v20 & (v21 = v17 | ~ subset(v16, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v16, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v18, v15) = v20 & relation_rng(v20) = v17)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_composition(v15, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v21 & relation_dom(v18) = v20 & (v21 = v16 | ~ subset(v17, v20)))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v17, v19) | ~ relation(v18) | ? [v20] : (relation_composition(v15, v18) = v20 & relation_dom(v20) = v16)))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v17, v19)) & ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v16, v20))) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | subset(v16, v19)) & ! [v18] : ! [v19] : ( ~ (relation_dom(v18) = v19) | ~ subset(v15, v18) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v17, v20))))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ relation(v15) | ? [v17] : (relation_rng(v15) = v17 & ( ~ (v17 = empty_set) | v16 = empty_set) & ( ~ (v16 = empty_set) | v17 = empty_set))) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (relation_dom(v15) = v16) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | union(v16) = v15) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | empty(v15) | ? [v17] : (element(v17, v16) & ~ empty(v17))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (cast_to_subset(v15) = v17 & element(v17, v16))) & ! [v15] : ! [v16] : ( ~ (powerset(v15) = v16) | ? [v17] : (element(v17, v16) & empty(v17))) & ! [v15] : ! [v16] : ( ~ (singleton(v16) = v15) | subset(v15, v15)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | ~ empty(v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | unordered_pair(v15, v15) = v16) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | subset(empty_set, v16)) & ! [v15] : ! [v16] : ( ~ (singleton(v15) = v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation_rng(v16) = v15) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation_dom(v16) = v15) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | relation(v16)) & ! [v15] : ! [v16] : ( ~ (identity_relation(v15) = v16) | function(v16)) & ! [v15] : ! [v16] : ( ~ (set_intersection2(v15, v16) = empty_set) | disjoint(v15, v16)) & ! [v15] : ! [v16] : ( ~ (unordered_pair(v15, v15) = v16) | singleton(v15) = v16) & ! [v15] : ! [v16] : ( ~ disjoint(v15, v16) | disjoint(v16, v15)) & ! [v15] : ! [v16] : ( ~ element(v16, v15) | ~ empty(v15) | empty(v16)) & ! [v15] : ! [v16] : ( ~ element(v16, v15) | empty(v15) | in(v16, v15)) & ! [v15] : ! [v16] : ( ~ element(v15, v16) | empty(v16) | in(v15, v16)) & ! [v15] : ! [v16] : ( ~ subset(v15, v16) | ~ proper_subset(v16, v15)) & ! [v15] : ! [v16] : ( ~ relation(v16) | ~ relation(v15) | subset(v15, v16) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v15) & ~ in(v19, v16))) & ! [v15] : ! [v16] : ( ~ relation(v15) | ~ in(v16, v15) | ? [v17] : ? [v18] : ordered_pair(v17, v18) = v16) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ empty(v15) | element(v16, v15)) & ! [v15] : ! [v16] : ( ~ empty(v16) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v16, v15) | ~ proper_subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ proper_subset(v15, v16) | subset(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | ~ in(v15, v16)) & ! [v15] : ! [v16] : ( ~ in(v16, v15) | element(v16, v15) | empty(v15)) & ! [v15] : ! [v16] : ( ~ in(v15, v16) | element(v15, v16)) & ! [v15] : (v15 = empty_set | ~ (relation_rng(v15) = empty_set) | ~ relation(v15)) & ! [v15] : (v15 = empty_set | ~ (relation_dom(v15) = empty_set) | ~ relation(v15)) & ! [v15] : (v15 = empty_set | ~ (set_meet(empty_set) = v15)) & ! [v15] : (v15 = empty_set | ~ subset(v15, empty_set)) & ! [v15] : (v15 = empty_set | ~ relation(v15) | ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v16, v17) = v18 & in(v18, v15))) & ! [v15] : (v15 = empty_set | ~ empty(v15)) & ! [v15] : ~ (singleton(v15) = empty_set) & ! [v15] : ( ~ relation(v15) | ~ function(v15) | ~ empty(v15) | one_to_one(v15)) & ! [v15] : ( ~ empty(v15) | relation(v15)) & ! [v15] : ( ~ empty(v15) | function(v15)) & ! [v15] : ~ proper_subset(v15, v15) & ! [v15] : ~ in(v15, empty_set) & ? [v15] : ? [v16] : (v16 = v15 | ? [v17] : (( ~ in(v17, v16) | ~ in(v17, v15)) & (in(v17, v16) | in(v17, v15)))) & ? [v15] : ? [v16] : (disjoint(v15, v16) | ? [v17] : (in(v17, v16) & in(v17, v15))) & ? [v15] : ? [v16] : element(v16, v15) & ? [v15] : ? [v16] : (subset(v15, v16) | ? [v17] : (in(v17, v15) & ~ in(v17, v16))) & ? [v15] : ? [v16] : (in(v15, v16) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ! [v18] : ( ~ subset(v18, v17) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ( ~ subset(v17, v16) | are_equipotent(v17, v16) | in(v17, v16))) & ? [v15] : ? [v16] : (in(v15, v16) & ! [v17] : ! [v18] : ( ~ subset(v18, v17) | ~ in(v17, v16) | in(v18, v16)) & ! [v17] : ( ~ subset(v17, v16) | are_equipotent(v17, v16) | in(v17, v16)) & ! [v17] : ( ~ in(v17, v16) | ? [v18] : (in(v18, v16) & ! [v19] : ( ~ subset(v19, v17) | in(v19, v18))))) & ? [v15] : (v15 = empty_set | ? [v16] : in(v16, v15)) & ? [v15] : subset(v15, v15) & ? [v15] : subset(empty_set, v15) & ? [v15] : (relation(v15) | ? [v16] : (in(v16, v15) & ! [v17] : ! [v18] : ~ (ordered_pair(v17, v18) = v16))))
% 29.57/7.44 | 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, all_0_12_12, all_0_13_13, all_0_14_14 yields:
% 29.57/7.44 | (1) ~ (all_0_8_8 = all_0_9_9) & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & apply(all_0_10_10, all_0_12_12) = all_0_9_9 & apply(all_0_11_11, all_0_12_12) = all_0_8_8 & powerset(empty_set) = all_0_14_14 & singleton(empty_set) = all_0_14_14 & relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10 & relation_empty_yielding(all_0_7_7) & 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_11_11) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_11_11) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & in(all_0_12_12, all_0_13_13) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [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] : ( ~ (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] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (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 = 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] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(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) | ~ (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) | ? [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] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (meet_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & union_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (union_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (subset_difference(v0, v6, v7) = v8 & meet_of_subsets(v0, v1) = v7 & cast_to_subset(v0) = v6 & powerset(v4) = v5 & powerset(v0) = v4 & (v8 = v3 | ~ element(v1, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (set_difference(v1, v2) = v5 & powerset(v0) = v4 & (v5 = v3 | ~ element(v2, v4) | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_rng(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_rng(v3) = v4 & relation_image(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_dom(v3) = v4 & subset(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_rng(v4) = v3 & relation_rng_restriction(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : (relation_composition(v0, v2) = v4 & relation_rng(v4) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | ? [v4] : (relation_dom(v4) = v3 & relation_dom_restriction(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ (set_meet(v1) = v3) | ? [v4] : ? [v5] : (meet_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | ~ in(v3, v2) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) & in(v4, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v1) | ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) & ~ in(v4, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ in(v4, v0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v9) = v4) | ~ in(v9, v2) | ~ in(v8, v1))) & (in(v4, v0) | (v7 = v4 & ordered_pair(v5, v6) = v4 & in(v6, v2) & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v4, v7) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v4, v5) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (( ~ in(v4, v0) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v4) = v8) | ~ in(v8, v1) | ~ in(v7, v2))) & (in(v4, v0) | (ordered_pair(v5, v4) = v6 & in(v6, v1) & in(v5, v2))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v2) | ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) & ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v4 & apply(v3, v0) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v5 | ~ in(v0, v4)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v0, v5) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v0, v7) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v2, v1) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v4 & ( ~ in(v0, v3) | (ordered_pair(v5, v0) = v6 & in(v6, v2) & in(v5, v4) & in(v5, v1))) & (in(v0, v3) | ! [v7] : ! [v8] : ( ~ (ordered_pair(v7, v0) = v8) | ~ in(v8, v2) | ~ in(v7, v4) | ~ in(v7, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng_restriction(v1, v2) = v3) | ~ relation(v2) | ? [v4] : ? [v5] : (relation_rng(v3) = v4 & relation_rng(v2) = v5 & ( ~ in(v0, v5) | ~ in(v0, v1) | in(v0, v4)) & ( ~ in(v0, v4) | (in(v0, v5) & in(v0, v1))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ~ 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 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (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 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (powerset(v3) = v4 & powerset(v0) = v3 & set_meet(v1) = v5 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (union(v1) = v5 & powerset(v3) = v4 & powerset(v0) = v3 & (v5 = v2 | ~ element(v1, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | ( ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v6, v1) | in(v5, v2)) & ! [v5] : ! [v6] : ( ~ (subset_complement(v0, v5) = v6) | ~ element(v5, v3) | ~ element(v2, v4) | ~ in(v5, v2) | in(v6, v1)) & ! [v5] : (v5 = v2 | ~ element(v5, v4) | ? [v6] : ? [v7] : (subset_complement(v0, v6) = v7 & element(v6, v3) & ( ~ in(v7, v1) | ~ in(v6, v5)) & (in(v7, v1) | in(v6, v5)))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ relation(v1) | ~ relation(v0) | ? [v3] : ? [v4] : (relation_composition(v0, v1) = v3 & relation_rng(v3) = v4 & subset(v4, v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : (relation_dom(v1) = v3 & ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v1, v4) = v5) | ~ (apply(v5, v0) = v6) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | apply(v4, v2) = v6) & ! [v4] : ! [v5] : ( ~ (apply(v4, v2) = v5) | ~ relation(v4) | ~ function(v4) | ~ in(v0, v3) | ? [v6] : (relation_composition(v1, v4) = v6 & apply(v6, v0) = v5)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v1) = v3 & relation_image(v1, v4) = v2 & set_intersection2(v3, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_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] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) & ! [v0] : ! [v1] : ( ~ (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) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ 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) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) & ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ 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)))
% 30.06/7.51 |
% 30.06/7.51 | Applying alpha-rule on (1) yields:
% 30.06/7.51 | (2) ! [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))))
% 30.06/7.51 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3))
% 30.06/7.51 | (4) function(all_0_3_3)
% 30.11/7.51 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3)))
% 30.11/7.51 | (6) ! [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))
% 30.11/7.51 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 30.11/7.51 | (8) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 30.11/7.51 | (9) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 30.11/7.51 | (10) ! [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)))
% 30.11/7.51 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1))
% 30.11/7.51 | (12) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2))
% 30.11/7.51 | (13) ! [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))
% 30.11/7.51 | (14) relation_empty_yielding(all_0_7_7)
% 30.11/7.51 | (15) ! [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)))
% 30.11/7.51 | (16) ! [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))))
% 30.11/7.52 | (17) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3)))
% 30.11/7.52 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 30.11/7.52 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 30.11/7.52 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3)))
% 30.11/7.52 | (21) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 30.11/7.52 | (22) ! [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))
% 30.11/7.52 | (23) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 30.11/7.52 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 30.11/7.52 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 30.11/7.52 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 30.11/7.52 | (27) ! [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))))
% 30.11/7.52 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 30.11/7.52 | (29) ? [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)))))
% 30.11/7.52 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1))
% 30.11/7.52 | (31) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1))
% 30.11/7.52 | (32) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 30.11/7.52 | (33) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 30.11/7.52 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 30.11/7.52 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 30.11/7.52 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 30.11/7.52 | (37) ! [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))
% 30.11/7.52 | (38) ! [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))
% 30.11/7.52 | (39) ! [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)
% 30.11/7.52 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 30.11/7.52 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 30.11/7.52 | (42) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 30.11/7.52 | (43) ! [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))))
% 30.11/7.52 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 30.11/7.52 | (45) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 30.11/7.52 | (46) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2))
% 30.11/7.52 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 30.11/7.52 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 30.11/7.52 | (49) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 30.11/7.52 | (50) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 30.11/7.52 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 30.11/7.52 | (52) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 30.11/7.52 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 30.11/7.52 | (54) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 30.11/7.52 | (55) ! [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)))))
% 30.11/7.52 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 30.11/7.52 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 30.11/7.52 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 30.11/7.52 | (59) ! [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)))))
% 30.11/7.52 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 30.11/7.52 | (61) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 30.11/7.52 | (62) ! [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)))
% 30.11/7.53 | (63) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 30.11/7.53 | (64) ! [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))
% 30.11/7.53 | (65) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1))
% 30.11/7.53 | (66) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0))
% 30.11/7.53 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 30.11/7.53 | (68) ! [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))
% 30.11/7.53 | (69) ! [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)))))
% 30.11/7.53 | (70) ! [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)))
% 30.11/7.53 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 30.11/7.53 | (72) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 30.11/7.53 | (73) empty(all_0_1_1)
% 30.11/7.53 | (74) ! [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))))
% 30.11/7.53 | (75) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 30.11/7.53 | (76) ? [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)))))
% 30.11/7.53 | (77) ! [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))
% 30.11/7.53 | (78) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 30.11/7.53 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0))
% 30.11/7.53 | (80) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 30.11/7.53 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 30.11/7.53 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 30.11/7.53 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 30.11/7.53 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 30.11/7.53 | (85) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0)
% 30.11/7.53 | (86) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1)))
% 30.11/7.53 | (87) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 30.11/7.53 | (88) ! [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))))
% 30.11/7.53 | (89) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 30.11/7.53 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 30.11/7.53 | (91) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 30.11/7.53 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 30.11/7.53 | (93) ! [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))
% 30.11/7.53 | (94) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 30.11/7.53 | (95) ! [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))
% 30.11/7.53 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 30.11/7.53 | (97) ! [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)))
% 30.11/7.53 | (98) ? [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)))))
% 30.11/7.53 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2))
% 30.11/7.53 | (100) ? [v0] : subset(v0, v0)
% 30.11/7.53 | (101) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 30.11/7.53 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1))
% 30.11/7.53 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 30.11/7.53 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2))
% 30.11/7.53 | (105) ? [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)))))
% 30.11/7.53 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 30.11/7.53 | (107) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0))
% 30.11/7.54 | (108) ? [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)))))
% 30.11/7.54 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 30.11/7.54 | (110) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1)
% 30.11/7.54 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2))
% 30.11/7.54 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 30.11/7.54 | (113) ! [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))
% 30.11/7.54 | (114) ! [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)))
% 30.11/7.54 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 30.11/7.54 | (116) ! [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)))
% 30.11/7.54 | (117) ! [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))
% 30.11/7.54 | (118) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 30.11/7.54 | (119) ! [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)))
% 30.11/7.54 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0))
% 30.11/7.54 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 30.11/7.54 | (122) ! [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)))
% 30.11/7.54 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3)))
% 30.11/7.54 | (124) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 30.11/7.54 | (125) ! [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))
% 30.11/7.54 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 30.11/7.54 | (127) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 30.11/7.54 | (128) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 30.11/7.54 | (129) singleton(empty_set) = all_0_14_14
% 30.11/7.54 | (130) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1))
% 30.11/7.54 | (131) ! [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)))
% 30.11/7.54 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 30.11/7.54 | (133) ! [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))
% 30.11/7.54 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 30.11/7.54 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 30.11/7.54 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3))
% 30.11/7.54 | (137) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1))
% 30.11/7.54 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 30.11/7.54 | (139) ! [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)))))
% 30.11/7.54 | (140) ? [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)))))
% 30.11/7.54 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 30.11/7.54 | (142) ! [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))
% 30.11/7.54 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4)))
% 30.11/7.54 | (144) relation(all_0_7_7)
% 30.11/7.54 | (145) ? [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)))))
% 30.11/7.54 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4)))
% 30.11/7.54 | (147) ! [v0] : ~ proper_subset(v0, v0)
% 30.11/7.54 | (148) ! [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))
% 30.11/7.54 | (149) ? [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)))))
% 30.11/7.54 | (150) ! [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))
% 30.11/7.54 | (151) ! [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))
% 30.11/7.54 | (152) ! [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))))
% 30.11/7.54 | (153) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 30.11/7.54 | (154) ! [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))))
% 30.11/7.55 | (155) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1))
% 30.11/7.55 | (156) ! [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))))
% 30.11/7.55 | (157) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 30.11/7.55 | (158) ! [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))))
% 30.11/7.55 | (159) ! [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))))
% 30.11/7.55 | (160) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 30.11/7.55 | (161) ! [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))
% 30.11/7.55 | (162) ! [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))))))))
% 30.11/7.55 | (163) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 30.11/7.55 | (164) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 30.11/7.55 | (165) ? [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)))))
% 30.11/7.55 | (166) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 30.11/7.55 | (167) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 30.11/7.55 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 30.11/7.55 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 30.11/7.55 | (170) relation_dom(empty_set) = empty_set
% 30.11/7.55 | (171) relation(all_0_1_1)
% 30.11/7.55 | (172) ? [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))))
% 30.11/7.55 | (173) ! [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)))
% 30.11/7.55 | (174) powerset(empty_set) = all_0_14_14
% 30.11/7.55 | (175) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 30.11/7.55 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 30.11/7.55 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 30.11/7.55 | (178) ! [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)))
% 30.11/7.55 | (179) function(all_0_11_11)
% 30.11/7.55 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2)
% 30.11/7.55 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0)))))
% 30.11/7.55 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 30.11/7.55 | (183) function(all_0_6_6)
% 30.11/7.55 | (184) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 30.11/7.55 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 30.11/7.55 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 30.11/7.55 | (187) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 30.11/7.55 | (188) relation(all_0_11_11)
% 30.11/7.55 | (189) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 30.11/7.55 | (190) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 30.11/7.55 | (191) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 30.11/7.55 | (192) ! [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)))
% 30.11/7.55 | (193) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 30.11/7.55 | (194) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 30.11/7.55 | (195) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 30.11/7.55 | (196) ! [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))))
% 30.11/7.55 | (197) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 30.11/7.55 | (198) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 30.11/7.55 | (199) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2)))
% 30.11/7.55 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 30.11/7.55 | (201) relation_rng(empty_set) = empty_set
% 30.11/7.55 | (202) ! [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))
% 30.11/7.55 | (203) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 30.11/7.56 | (204) ! [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))))
% 30.11/7.56 | (205) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1))
% 30.11/7.56 | (206) ! [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)))
% 30.11/7.56 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 30.11/7.56 | (208) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 30.11/7.56 | (209) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 30.11/7.56 | (210) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 30.11/7.56 | (211) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 30.11/7.56 | (212) ! [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))
% 30.11/7.56 | (213) function(all_0_0_0)
% 30.11/7.56 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 30.11/7.56 | (215) ! [v0] : ~ in(v0, empty_set)
% 30.11/7.56 | (216) ! [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)))
% 30.11/7.56 | (217) ! [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))
% 30.11/7.56 | (218) ! [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))
% 30.11/7.56 | (219) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 30.11/7.56 | (220) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 30.11/7.56 | (221) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 30.11/7.56 | (222) ! [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))))
% 30.11/7.56 | (223) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 30.11/7.56 | (224) ! [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))))
% 30.11/7.56 | (225) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1)))
% 30.11/7.56 | (226) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 30.11/7.56 | (227) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 30.11/7.56 | (228) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 30.11/7.56 | (229) ? [v0] : ? [v1] : element(v1, v0)
% 30.11/7.56 | (230) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3)
% 30.11/7.56 | (231) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 30.11/7.56 | (232) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 30.11/7.56 | (233) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 30.11/7.56 | (234) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 30.11/7.56 | (235) ! [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))
% 30.11/7.56 | (236) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 30.11/7.56 | (237) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 30.11/7.56 | (238) ! [v0] : ~ (singleton(v0) = empty_set)
% 30.11/7.56 | (239) ? [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)))))
% 30.11/7.56 | (240) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1)))
% 30.11/7.56 | (241) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 30.11/7.56 | (242) ! [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)
% 30.11/7.56 | (243) ! [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)))))
% 30.11/7.56 | (244) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0))
% 30.11/7.56 | (245) ! [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)))
% 30.11/7.56 | (246) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1))
% 30.11/7.56 | (247) relation(all_0_3_3)
% 30.11/7.56 | (248) ? [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)))))
% 30.11/7.56 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 30.11/7.56 | (250) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1))
% 30.11/7.56 | (251) relation(all_0_4_4)
% 30.11/7.56 | (252) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 30.11/7.56 | (253) in(all_0_12_12, all_0_13_13)
% 30.11/7.56 | (254) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 30.11/7.56 | (255) ! [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))))
% 30.11/7.56 | (256) empty(all_0_2_2)
% 30.11/7.56 | (257) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 30.11/7.57 | (258) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 30.11/7.57 | (259) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3))
% 30.11/7.57 | (260) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 30.11/7.57 | (261) ~ empty(all_0_4_4)
% 30.11/7.57 | (262) ? [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)))))
% 30.11/7.57 | (263) ! [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)))))
% 30.11/7.57 | (264) ? [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)))))
% 30.11/7.57 | (265) ? [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)))
% 30.11/7.57 | (266) ! [v0] : ( ~ empty(v0) | function(v0))
% 30.11/7.57 | (267) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 30.11/7.57 | (268) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 30.11/7.57 | (269) ? [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)))))
% 30.11/7.57 | (270) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 30.11/7.57 | (271) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0))
% 30.11/7.57 | (272) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 30.11/7.57 | (273) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 30.11/7.57 | (274) ! [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))
% 30.11/7.57 | (275) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 30.11/7.57 | (276) ! [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))))
% 30.11/7.57 | (277) relation(all_0_0_0)
% 30.11/7.57 | (278) ! [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))))))))
% 30.11/7.57 | (279) empty(empty_set)
% 30.11/7.57 | (280) ! [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)))
% 30.11/7.57 | (281) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2))
% 30.11/7.57 | (282) ! [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)))))
% 30.11/7.57 | (283) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 30.11/7.57 | (284) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3)
% 30.11/7.57 | (285) ? [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))))
% 30.11/7.57 | (286) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 30.11/7.57 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 30.11/7.57 | (288) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 30.11/7.57 | (289) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 30.11/7.57 | (290) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 30.11/7.57 | (291) ! [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)))
% 30.11/7.57 | (292) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 30.11/7.57 | (293) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 30.11/7.57 | (294) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 30.11/7.57 | (295) ! [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)))
% 30.11/7.57 | (296) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 30.11/7.57 | (297) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3))))
% 30.11/7.57 | (298) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 30.11/7.58 | (299) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 30.11/7.58 | (300) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 30.11/7.58 | (301) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 30.11/7.58 | (302) ! [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))))
% 30.11/7.58 | (303) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 30.11/7.58 | (304) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 30.11/7.58 | (305) ? [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)))))
% 30.11/7.58 | (306) ! [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)))
% 30.11/7.58 | (307) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 30.11/7.58 | (308) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0)))
% 30.11/7.58 | (309) ! [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)))
% 30.11/7.58 | (310) relation_empty_yielding(empty_set)
% 30.11/7.58 | (311) ~ empty(all_0_5_5)
% 30.11/7.58 | (312) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 30.11/7.58 | (313) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 30.11/7.58 | (314) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2)))
% 30.11/7.58 | (315) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 30.11/7.58 | (316) ! [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)))))
% 30.11/7.58 | (317) ! [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)))
% 30.11/7.58 | (318) ! [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))))
% 30.11/7.58 | (319) ? [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)))))
% 30.11/7.58 | (320) ! [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))
% 30.11/7.58 | (321) relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10
% 30.11/7.58 | (322) ? [v0] : subset(empty_set, v0)
% 30.11/7.58 | (323) ! [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)))
% 30.11/7.58 | (324) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0))
% 30.11/7.58 | (325) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 30.11/7.58 | (326) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 30.11/7.58 | (327) ! [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)))))
% 30.11/7.58 | (328) ! [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))))
% 30.11/7.58 | (329) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 30.11/7.58 | (330) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2))
% 30.11/7.58 | (331) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1))
% 30.11/7.58 | (332) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1)
% 30.11/7.58 | (333) ~ (all_0_8_8 = all_0_9_9)
% 30.11/7.58 | (334) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0))
% 30.11/7.58 | (335) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 30.11/7.58 | (336) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2))
% 30.11/7.58 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0))
% 30.11/7.58 | (338) ! [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))
% 30.11/7.58 | (339) ! [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)))
% 30.11/7.58 | (340) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 30.11/7.58 | (341) empty(all_0_3_3)
% 30.11/7.58 | (342) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0))
% 30.11/7.58 | (343) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 30.11/7.58 | (344) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 30.11/7.58 | (345) ? [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)))))
% 30.11/7.59 | (346) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 30.11/7.59 | (347) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 30.11/7.59 | (348) ! [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))
% 30.11/7.59 | (349) apply(all_0_10_10, all_0_12_12) = all_0_9_9
% 30.11/7.59 | (350) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 30.11/7.59 | (351) relation(empty_set)
% 30.11/7.59 | (352) ! [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))))
% 30.11/7.59 | (353) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4))))
% 30.11/7.59 | (354) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 30.11/7.59 | (355) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 30.11/7.59 | (356) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 30.11/7.59 | (357) one_to_one(all_0_6_6)
% 30.11/7.59 | (358) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 30.11/7.59 | (359) ! [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))
% 30.11/7.59 | (360) ? [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)))))
% 30.11/7.59 | (361) ! [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))
% 30.11/7.59 | (362) ! [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))))))))
% 30.11/7.59 | (363) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 30.11/7.59 | (364) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 30.11/7.59 | (365) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 30.11/7.59 | (366) ! [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))
% 30.11/7.59 | (367) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 30.11/7.59 | (368) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3)))
% 30.11/7.59 | (369) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 30.11/7.59 | (370) ! [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))
% 30.11/7.59 | (371) ! [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))
% 30.11/7.59 | (372) ! [v0] : ( ~ empty(v0) | relation(v0))
% 30.11/7.59 | (373) relation(all_0_6_6)
% 30.11/7.59 | (374) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 30.11/7.59 | (375) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 30.11/7.59 | (376) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 30.11/7.59 | (377) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 30.11/7.59 | (378) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 30.11/7.59 | (379) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 30.11/7.59 | (380) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0)))
% 30.11/7.59 | (381) ! [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)))))
% 30.11/7.59 | (382) ! [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))))
% 30.11/7.60 | (383) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 30.11/7.60 | (384) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1))
% 30.11/7.60 | (385) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0))
% 30.11/7.60 | (386) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 30.11/7.60 | (387) ! [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))
% 30.11/7.60 | (388) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 30.11/7.60 | (389) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 30.11/7.60 | (390) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 30.11/7.60 | (391) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 30.11/7.60 | (392) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 30.11/7.60 | (393) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 30.11/7.60 | (394) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 30.11/7.60 | (395) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 30.11/7.60 | (396) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 30.11/7.60 | (397) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1))
% 30.11/7.60 | (398) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 30.11/7.60 | (399) ! [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))))
% 30.11/7.60 | (400) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2))
% 30.11/7.60 | (401) ! [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))))
% 30.11/7.60 | (402) apply(all_0_11_11, all_0_12_12) = all_0_8_8
% 30.11/7.60 | (403) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 30.11/7.60 | (404) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1))
% 30.11/7.60 |
% 30.11/7.60 | Instantiating (264) with all_34_0_36 yields:
% 30.11/7.60 | (405) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ~ function(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & ( ~ in(all_34_0_36, v4) | ~ in(all_34_0_36, v0) | in(all_34_0_36, v3)) & ( ~ in(all_34_0_36, v3) | (in(all_34_0_36, v4) & in(all_34_0_36, v0)))))
% 30.11/7.60 |
% 30.11/7.60 | Instantiating (105) with all_52_0_45 yields:
% 30.11/7.60 | (406) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & ( ~ in(all_52_0_45, v4) | ~ in(all_52_0_45, v0) | in(all_52_0_45, v3)) & ( ~ in(all_52_0_45, v3) | (in(all_52_0_45, v4) & in(all_52_0_45, v0)))))
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (356) with all_0_2_2, all_0_1_1 and discharging atoms empty(all_0_1_1), empty(all_0_2_2), yields:
% 30.11/7.60 | (407) all_0_1_1 = all_0_2_2
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (356) with all_0_3_3, all_0_1_1 and discharging atoms empty(all_0_1_1), empty(all_0_3_3), yields:
% 30.11/7.60 | (408) all_0_1_1 = all_0_3_3
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (356) with empty_set, all_0_2_2 and discharging atoms empty(all_0_2_2), empty(empty_set), yields:
% 30.11/7.60 | (409) all_0_2_2 = empty_set
% 30.11/7.60 |
% 30.11/7.60 | Combining equations (407,408) yields a new equation:
% 30.11/7.60 | (410) all_0_2_2 = all_0_3_3
% 30.11/7.60 |
% 30.11/7.60 | Simplifying 410 yields:
% 30.11/7.60 | (411) all_0_2_2 = all_0_3_3
% 30.11/7.60 |
% 30.11/7.60 | Combining equations (411,409) yields a new equation:
% 30.11/7.60 | (412) all_0_3_3 = empty_set
% 30.11/7.60 |
% 30.11/7.60 | Simplifying 412 yields:
% 30.11/7.60 | (413) all_0_3_3 = empty_set
% 30.11/7.60 |
% 30.11/7.60 | From (413) and (247) follows:
% 30.11/7.60 | (351) relation(empty_set)
% 30.11/7.60 |
% 30.11/7.60 | From (413) and (4) follows:
% 30.11/7.60 | (415) function(empty_set)
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (142) with all_0_10_10, all_0_11_11, all_0_13_13 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), yields:
% 30.11/7.60 | (416) ? [v0] : ? [v1] : (relation_dom(all_0_10_10) = v0 & relation_dom(all_0_11_11) = v1 & set_intersection2(v1, all_0_13_13) = v0)
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (406) with all_0_10_10, all_0_11_11, all_0_13_13 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), yields:
% 30.11/7.60 | (417) ? [v0] : ? [v1] : (relation_dom(all_0_10_10) = v0 & relation_dom(all_0_11_11) = v1 & ( ~ in(all_52_0_45, v1) | ~ in(all_52_0_45, all_0_13_13) | in(all_52_0_45, v0)) & ( ~ in(all_52_0_45, v0) | (in(all_52_0_45, v1) & in(all_52_0_45, all_0_13_13))))
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (401) with all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms apply(all_0_10_10, all_0_12_12) = all_0_9_9, relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.11/7.60 | (418) ? [v0] : ? [v1] : (relation_dom(all_0_10_10) = v0 & apply(all_0_11_11, all_0_12_12) = v1 & (v1 = all_0_9_9 | ~ in(all_0_12_12, v0)))
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (255) with all_0_8_8, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13 and discharging atoms apply(all_0_11_11, all_0_12_12) = all_0_8_8, relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.11/7.60 | (419) ? [v0] : ? [v1] : (relation_dom(all_0_10_10) = v0 & apply(all_0_10_10, all_0_12_12) = v1 & (v1 = all_0_8_8 | ~ in(all_0_12_12, v0)))
% 30.11/7.60 |
% 30.11/7.60 | Instantiating formula (399) with all_0_8_8, all_0_11_11, all_0_12_12 and discharging atoms apply(all_0_11_11, all_0_12_12) = all_0_8_8, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.11/7.60 | (420) ? [v0] : (relation_dom(all_0_11_11) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_11_11, v1) = v2) | ~ (apply(v2, all_0_12_12) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_12_12, v0) | apply(v1, all_0_8_8) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_8_8) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_12_12, v0) | ? [v3] : (relation_composition(all_0_11_11, v1) = v3 & apply(v3, all_0_12_12) = v2)))
% 30.11/7.61 |
% 30.11/7.61 | Instantiating formula (405) with all_0_10_10, all_0_11_11, all_0_13_13 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.11/7.61 | (421) ? [v0] : ? [v1] : (relation_dom(all_0_10_10) = v0 & relation_dom(all_0_11_11) = v1 & ( ~ in(all_34_0_36, v1) | ~ in(all_34_0_36, all_0_13_13) | in(all_34_0_36, v0)) & ( ~ in(all_34_0_36, v0) | (in(all_34_0_36, v1) & in(all_34_0_36, all_0_13_13))))
% 30.11/7.61 |
% 30.11/7.61 | Instantiating formula (281) with all_0_10_10, all_0_13_13, all_0_11_11 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.11/7.61 | (422) relation(all_0_10_10)
% 30.11/7.61 |
% 30.11/7.61 | Instantiating formula (330) with all_0_10_10, all_0_13_13, all_0_11_11 and discharging atoms relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.11/7.61 | (423) function(all_0_10_10)
% 30.11/7.61 |
% 30.11/7.61 | Instantiating formula (55) with all_0_8_8, all_0_11_11, empty_set, empty_set, all_0_12_12 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_11_11, all_0_12_12) = all_0_8_8, relation(all_0_11_11), relation(empty_set), function(all_0_11_11), function(empty_set), yields:
% 30.11/7.61 | (424) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_11_11, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_11_11) = v2 & ( ~ in(all_0_8_8, empty_set) | ~ in(all_0_12_12, v2) | in(all_0_12_12, v1)) & ( ~ in(all_0_12_12, v1) | (in(all_0_8_8, empty_set) & in(all_0_12_12, v2))))
% 30.11/7.61 |
% 30.11/7.61 | Instantiating formula (263) with all_0_10_10, all_0_11_11, empty_set, empty_set, all_0_13_13 and discharging atoms relation_dom(empty_set) = empty_set, relation_dom_restriction(all_0_11_11, all_0_13_13) = all_0_10_10, relation(all_0_11_11), relation(empty_set), function(all_0_11_11), function(empty_set), yields:
% 30.11/7.61 | (425) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : (relation_dom(all_0_11_11) = v0 & set_intersection2(v0, all_0_13_13) = v1 & ( ~ (v1 = empty_set) | all_0_10_10 = empty_set | ( ~ (v4 = v3) & apply(all_0_11_11, v2) = v4 & apply(empty_set, v2) = v3 & in(v2, empty_set))) & ( ~ (all_0_10_10 = empty_set) | (v1 = empty_set & ! [v5] : ! [v6] : ( ~ (apply(all_0_11_11, v5) = v6) | ~ in(v5, empty_set) | apply(empty_set, v5) = v6) & ! [v5] : ! [v6] : ( ~ (apply(empty_set, v5) = v6) | ~ in(v5, empty_set) | apply(all_0_11_11, v5) = v6))))
% 30.11/7.61 |
% 30.11/7.61 | Instantiating (419) with all_78_0_55, all_78_1_56 yields:
% 30.11/7.61 | (426) relation_dom(all_0_10_10) = all_78_1_56 & apply(all_0_10_10, all_0_12_12) = all_78_0_55 & (all_78_0_55 = all_0_8_8 | ~ in(all_0_12_12, all_78_1_56))
% 30.11/7.61 |
% 30.11/7.61 | Applying alpha-rule on (426) yields:
% 30.11/7.61 | (427) relation_dom(all_0_10_10) = all_78_1_56
% 30.51/7.61 | (428) apply(all_0_10_10, all_0_12_12) = all_78_0_55
% 30.51/7.61 | (429) all_78_0_55 = all_0_8_8 | ~ in(all_0_12_12, all_78_1_56)
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (418) with all_80_0_57, all_80_1_58 yields:
% 30.51/7.61 | (430) relation_dom(all_0_10_10) = all_80_1_58 & apply(all_0_11_11, all_0_12_12) = all_80_0_57 & (all_80_0_57 = all_0_9_9 | ~ in(all_0_12_12, all_80_1_58))
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (430) yields:
% 30.51/7.61 | (431) relation_dom(all_0_10_10) = all_80_1_58
% 30.51/7.61 | (432) apply(all_0_11_11, all_0_12_12) = all_80_0_57
% 30.51/7.61 | (433) all_80_0_57 = all_0_9_9 | ~ in(all_0_12_12, all_80_1_58)
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (417) with all_84_0_60, all_84_1_61 yields:
% 30.51/7.61 | (434) relation_dom(all_0_10_10) = all_84_1_61 & relation_dom(all_0_11_11) = all_84_0_60 & ( ~ in(all_52_0_45, all_84_0_60) | ~ in(all_52_0_45, all_0_13_13) | in(all_52_0_45, all_84_1_61)) & ( ~ in(all_52_0_45, all_84_1_61) | (in(all_52_0_45, all_84_0_60) & in(all_52_0_45, all_0_13_13)))
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (434) yields:
% 30.51/7.61 | (435) relation_dom(all_0_10_10) = all_84_1_61
% 30.51/7.61 | (436) relation_dom(all_0_11_11) = all_84_0_60
% 30.51/7.61 | (437) ~ in(all_52_0_45, all_84_0_60) | ~ in(all_52_0_45, all_0_13_13) | in(all_52_0_45, all_84_1_61)
% 30.51/7.61 | (438) ~ in(all_52_0_45, all_84_1_61) | (in(all_52_0_45, all_84_0_60) & in(all_52_0_45, all_0_13_13))
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (425) with all_86_0_62, all_86_1_63, all_86_2_64, all_86_3_65, all_86_4_66 yields:
% 30.51/7.61 | (439) relation_dom(all_0_11_11) = all_86_4_66 & set_intersection2(all_86_4_66, all_0_13_13) = all_86_3_65 & ( ~ (all_86_3_65 = empty_set) | all_0_10_10 = empty_set | ( ~ (all_86_0_62 = all_86_1_63) & apply(all_0_11_11, all_86_2_64) = all_86_0_62 & apply(empty_set, all_86_2_64) = all_86_1_63 & in(all_86_2_64, empty_set))) & ( ~ (all_0_10_10 = empty_set) | (all_86_3_65 = empty_set & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, empty_set) | apply(empty_set, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(empty_set, v0) = v1) | ~ in(v0, empty_set) | apply(all_0_11_11, v0) = v1)))
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (439) yields:
% 30.51/7.61 | (440) relation_dom(all_0_11_11) = all_86_4_66
% 30.51/7.61 | (441) set_intersection2(all_86_4_66, all_0_13_13) = all_86_3_65
% 30.51/7.61 | (442) ~ (all_86_3_65 = empty_set) | all_0_10_10 = empty_set | ( ~ (all_86_0_62 = all_86_1_63) & apply(all_0_11_11, all_86_2_64) = all_86_0_62 & apply(empty_set, all_86_2_64) = all_86_1_63 & in(all_86_2_64, empty_set))
% 30.51/7.61 | (443) ~ (all_0_10_10 = empty_set) | (all_86_3_65 = empty_set & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, empty_set) | apply(empty_set, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(empty_set, v0) = v1) | ~ in(v0, empty_set) | apply(all_0_11_11, v0) = v1))
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (424) with all_88_0_67, all_88_1_68, all_88_2_69 yields:
% 30.51/7.61 | (444) relation_composition(all_0_11_11, empty_set) = all_88_2_69 & relation_dom(all_88_2_69) = all_88_1_68 & relation_dom(all_0_11_11) = all_88_0_67 & ( ~ in(all_0_8_8, empty_set) | ~ in(all_0_12_12, all_88_0_67) | in(all_0_12_12, all_88_1_68)) & ( ~ in(all_0_12_12, all_88_1_68) | (in(all_0_8_8, empty_set) & in(all_0_12_12, all_88_0_67)))
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (444) yields:
% 30.51/7.61 | (445) relation_dom(all_0_11_11) = all_88_0_67
% 30.51/7.61 | (446) ~ in(all_0_8_8, empty_set) | ~ in(all_0_12_12, all_88_0_67) | in(all_0_12_12, all_88_1_68)
% 30.51/7.61 | (447) relation_composition(all_0_11_11, empty_set) = all_88_2_69
% 30.51/7.61 | (448) relation_dom(all_88_2_69) = all_88_1_68
% 30.51/7.61 | (449) ~ in(all_0_12_12, all_88_1_68) | (in(all_0_8_8, empty_set) & in(all_0_12_12, all_88_0_67))
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (416) with all_92_0_71, all_92_1_72 yields:
% 30.51/7.61 | (450) relation_dom(all_0_10_10) = all_92_1_72 & relation_dom(all_0_11_11) = all_92_0_71 & set_intersection2(all_92_0_71, all_0_13_13) = all_92_1_72
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (450) yields:
% 30.51/7.61 | (451) relation_dom(all_0_10_10) = all_92_1_72
% 30.51/7.61 | (452) relation_dom(all_0_11_11) = all_92_0_71
% 30.51/7.61 | (453) set_intersection2(all_92_0_71, all_0_13_13) = all_92_1_72
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (421) with all_139_0_103, all_139_1_104 yields:
% 30.51/7.61 | (454) relation_dom(all_0_10_10) = all_139_1_104 & relation_dom(all_0_11_11) = all_139_0_103 & ( ~ in(all_34_0_36, all_139_0_103) | ~ in(all_34_0_36, all_0_13_13) | in(all_34_0_36, all_139_1_104)) & ( ~ in(all_34_0_36, all_139_1_104) | (in(all_34_0_36, all_139_0_103) & in(all_34_0_36, all_0_13_13)))
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (454) yields:
% 30.51/7.61 | (455) relation_dom(all_0_10_10) = all_139_1_104
% 30.51/7.61 | (456) relation_dom(all_0_11_11) = all_139_0_103
% 30.51/7.61 | (457) ~ in(all_34_0_36, all_139_0_103) | ~ in(all_34_0_36, all_0_13_13) | in(all_34_0_36, all_139_1_104)
% 30.51/7.61 | (458) ~ in(all_34_0_36, all_139_1_104) | (in(all_34_0_36, all_139_0_103) & in(all_34_0_36, all_0_13_13))
% 30.51/7.61 |
% 30.51/7.61 | Instantiating (420) with all_141_0_105 yields:
% 30.51/7.61 | (459) relation_dom(all_0_11_11) = all_141_0_105 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_0_12_12) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_12_12, all_141_0_105) | apply(v0, all_0_8_8) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_8_8) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_12_12, all_141_0_105) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_0_12_12) = v1))
% 30.51/7.61 |
% 30.51/7.61 | Applying alpha-rule on (459) yields:
% 30.51/7.61 | (460) relation_dom(all_0_11_11) = all_141_0_105
% 30.51/7.61 | (461) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_11_11, v0) = v1) | ~ (apply(v1, all_0_12_12) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_12_12, all_141_0_105) | apply(v0, all_0_8_8) = v2)
% 30.51/7.61 | (462) ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_8_8) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_12_12, all_141_0_105) | ? [v2] : (relation_composition(all_0_11_11, v0) = v2 & apply(v2, all_0_12_12) = v1))
% 30.51/7.61 |
% 30.51/7.61 | Instantiating formula (260) with all_0_10_10, all_92_1_72, all_139_1_104 and discharging atoms relation_dom(all_0_10_10) = all_139_1_104, relation_dom(all_0_10_10) = all_92_1_72, yields:
% 30.51/7.61 | (463) all_139_1_104 = all_92_1_72
% 30.51/7.61 |
% 30.51/7.61 | Instantiating formula (260) with all_0_10_10, all_84_1_61, all_139_1_104 and discharging atoms relation_dom(all_0_10_10) = all_139_1_104, relation_dom(all_0_10_10) = all_84_1_61, yields:
% 30.51/7.61 | (464) all_139_1_104 = all_84_1_61
% 30.51/7.61 |
% 30.51/7.62 | Instantiating formula (260) with all_0_10_10, all_80_1_58, all_139_1_104 and discharging atoms relation_dom(all_0_10_10) = all_139_1_104, relation_dom(all_0_10_10) = all_80_1_58, yields:
% 30.51/7.62 | (465) all_139_1_104 = all_80_1_58
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (260) with all_0_10_10, all_78_1_56, all_139_1_104 and discharging atoms relation_dom(all_0_10_10) = all_139_1_104, relation_dom(all_0_10_10) = all_78_1_56, yields:
% 30.51/7.62 | (466) all_139_1_104 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (260) with all_0_11_11, all_139_0_103, all_141_0_105 and discharging atoms relation_dom(all_0_11_11) = all_141_0_105, relation_dom(all_0_11_11) = all_139_0_103, yields:
% 30.51/7.62 | (467) all_141_0_105 = all_139_0_103
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (260) with all_0_11_11, all_92_0_71, all_139_0_103 and discharging atoms relation_dom(all_0_11_11) = all_139_0_103, relation_dom(all_0_11_11) = all_92_0_71, yields:
% 30.51/7.62 | (468) all_139_0_103 = all_92_0_71
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (260) with all_0_11_11, all_88_0_67, all_92_0_71 and discharging atoms relation_dom(all_0_11_11) = all_92_0_71, relation_dom(all_0_11_11) = all_88_0_67, yields:
% 30.51/7.62 | (469) all_92_0_71 = all_88_0_67
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (260) with all_0_11_11, all_86_4_66, all_141_0_105 and discharging atoms relation_dom(all_0_11_11) = all_141_0_105, relation_dom(all_0_11_11) = all_86_4_66, yields:
% 30.51/7.62 | (470) all_141_0_105 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (260) with all_0_11_11, all_84_0_60, all_88_0_67 and discharging atoms relation_dom(all_0_11_11) = all_88_0_67, relation_dom(all_0_11_11) = all_84_0_60, yields:
% 30.51/7.62 | (471) all_88_0_67 = all_84_0_60
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (273) with all_0_10_10, all_0_12_12, all_78_0_55, all_0_9_9 and discharging atoms apply(all_0_10_10, all_0_12_12) = all_78_0_55, apply(all_0_10_10, all_0_12_12) = all_0_9_9, yields:
% 30.51/7.62 | (472) all_78_0_55 = all_0_9_9
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (273) with all_0_11_11, all_0_12_12, all_80_0_57, all_0_8_8 and discharging atoms apply(all_0_11_11, all_0_12_12) = all_80_0_57, apply(all_0_11_11, all_0_12_12) = all_0_8_8, yields:
% 30.51/7.62 | (473) all_80_0_57 = all_0_8_8
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (467,470) yields a new equation:
% 30.51/7.62 | (474) all_139_0_103 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Simplifying 474 yields:
% 30.51/7.62 | (475) all_139_0_103 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (468,475) yields a new equation:
% 30.51/7.62 | (476) all_92_0_71 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Simplifying 476 yields:
% 30.51/7.62 | (477) all_92_0_71 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (465,463) yields a new equation:
% 30.51/7.62 | (478) all_92_1_72 = all_80_1_58
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (464,463) yields a new equation:
% 30.51/7.62 | (479) all_92_1_72 = all_84_1_61
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (466,463) yields a new equation:
% 30.51/7.62 | (480) all_92_1_72 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (469,477) yields a new equation:
% 30.51/7.62 | (481) all_88_0_67 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Simplifying 481 yields:
% 30.51/7.62 | (482) all_88_0_67 = all_86_4_66
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (480,479) yields a new equation:
% 30.51/7.62 | (483) all_84_1_61 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (478,479) yields a new equation:
% 30.51/7.62 | (484) all_84_1_61 = all_80_1_58
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (471,482) yields a new equation:
% 30.51/7.62 | (485) all_86_4_66 = all_84_0_60
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (484,483) yields a new equation:
% 30.51/7.62 | (486) all_80_1_58 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Simplifying 486 yields:
% 30.51/7.62 | (487) all_80_1_58 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (483,479) yields a new equation:
% 30.51/7.62 | (480) all_92_1_72 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (485,477) yields a new equation:
% 30.51/7.62 | (489) all_92_0_71 = all_84_0_60
% 30.51/7.62 |
% 30.51/7.62 | From (487) and (431) follows:
% 30.51/7.62 | (427) relation_dom(all_0_10_10) = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | From (485) and (440) follows:
% 30.51/7.62 | (436) relation_dom(all_0_11_11) = all_84_0_60
% 30.51/7.62 |
% 30.51/7.62 | From (472) and (428) follows:
% 30.51/7.62 | (349) apply(all_0_10_10, all_0_12_12) = all_0_9_9
% 30.51/7.62 |
% 30.51/7.62 | From (473) and (432) follows:
% 30.51/7.62 | (402) apply(all_0_11_11, all_0_12_12) = all_0_8_8
% 30.51/7.62 |
% 30.51/7.62 | From (489)(480) and (453) follows:
% 30.51/7.62 | (494) set_intersection2(all_84_0_60, all_0_13_13) = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | From (485) and (441) follows:
% 30.51/7.62 | (495) set_intersection2(all_84_0_60, all_0_13_13) = all_86_3_65
% 30.51/7.62 |
% 30.51/7.62 +-Applying beta-rule and splitting (429), into two cases.
% 30.51/7.62 |-Branch one:
% 30.51/7.62 | (496) ~ in(all_0_12_12, all_78_1_56)
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (81) with all_84_0_60, all_0_13_13, all_78_1_56, all_86_3_65 and discharging atoms set_intersection2(all_84_0_60, all_0_13_13) = all_86_3_65, set_intersection2(all_84_0_60, all_0_13_13) = all_78_1_56, yields:
% 30.51/7.62 | (497) all_86_3_65 = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | From (497) and (495) follows:
% 30.51/7.62 | (494) set_intersection2(all_84_0_60, all_0_13_13) = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (403) with all_0_8_8, all_0_12_12, all_84_0_60, all_0_11_11 and discharging atoms relation_dom(all_0_11_11) = all_84_0_60, apply(all_0_11_11, all_0_12_12) = all_0_8_8, relation(all_0_11_11), function(all_0_11_11), yields:
% 30.51/7.62 | (499) all_0_8_8 = empty_set | in(all_0_12_12, all_84_0_60)
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (390) with all_78_1_56, all_84_0_60, all_0_13_13 and discharging atoms set_intersection2(all_84_0_60, all_0_13_13) = all_78_1_56, yields:
% 30.51/7.62 | (500) set_intersection2(all_0_13_13, all_84_0_60) = all_78_1_56
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (403) with all_0_9_9, all_0_12_12, all_78_1_56, all_0_10_10 and discharging atoms relation_dom(all_0_10_10) = all_78_1_56, apply(all_0_10_10, all_0_12_12) = all_0_9_9, relation(all_0_10_10), function(all_0_10_10), ~ in(all_0_12_12, all_78_1_56), yields:
% 30.51/7.62 | (501) all_0_9_9 = empty_set
% 30.51/7.62 |
% 30.51/7.62 | Equations (501) can reduce 333 to:
% 30.51/7.62 | (502) ~ (all_0_8_8 = empty_set)
% 30.51/7.62 |
% 30.51/7.62 +-Applying beta-rule and splitting (499), into two cases.
% 30.51/7.62 |-Branch one:
% 30.51/7.62 | (503) in(all_0_12_12, all_84_0_60)
% 30.51/7.62 |
% 30.51/7.62 | Instantiating formula (92) with all_0_12_12, all_78_1_56, all_84_0_60, all_0_13_13 and discharging atoms set_intersection2(all_0_13_13, all_84_0_60) = all_78_1_56, in(all_0_12_12, all_84_0_60), in(all_0_12_12, all_0_13_13), ~ in(all_0_12_12, all_78_1_56), yields:
% 30.51/7.62 | (504) $false
% 30.51/7.62 |
% 30.51/7.62 |-The branch is then unsatisfiable
% 30.51/7.62 |-Branch two:
% 30.51/7.62 | (505) ~ in(all_0_12_12, all_84_0_60)
% 30.51/7.62 | (506) all_0_8_8 = empty_set
% 30.51/7.62 |
% 30.51/7.62 | Equations (506) can reduce 502 to:
% 30.51/7.62 | (507) $false
% 30.51/7.62 |
% 30.51/7.62 |-The branch is then unsatisfiable
% 30.51/7.62 |-Branch two:
% 30.51/7.62 | (508) in(all_0_12_12, all_78_1_56)
% 30.51/7.62 | (509) all_78_0_55 = all_0_8_8
% 30.51/7.62 |
% 30.51/7.62 | Combining equations (472,509) yields a new equation:
% 30.51/7.62 | (510) all_0_8_8 = all_0_9_9
% 30.51/7.62 |
% 30.51/7.62 | Equations (510) can reduce 333 to:
% 30.51/7.62 | (507) $false
% 30.51/7.62 |
% 30.51/7.62 |-The branch is then unsatisfiable
% 30.51/7.62 % SZS output end Proof for theBenchmark
% 30.51/7.62
% 30.51/7.62 7033ms
%------------------------------------------------------------------------------