TSTP Solution File: SEU220+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU220+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n020.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 08:47:48 EDT 2022
% Result : Theorem 10.77s 3.06s
% Output : Proof 22.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU220+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 00:09:48 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.56/0.61 ____ _
% 0.56/0.61 ___ / __ \_____(_)___ ________ __________
% 0.56/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.61
% 0.56/0.61 A Theorem Prover for First-Order Logic
% 0.56/0.62 (ePrincess v.1.0)
% 0.56/0.62
% 0.56/0.62 (c) Philipp Rümmer, 2009-2015
% 0.56/0.62 (c) Peter Backeman, 2014-2015
% 0.56/0.62 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.62 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.62 Bug reports to peter@backeman.se
% 0.56/0.62
% 0.56/0.62 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.62
% 0.56/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.91/1.20 Prover 0: Preprocessing ...
% 6.46/2.08 Prover 0: Warning: ignoring some quantifiers
% 7.14/2.13 Prover 0: Constructing countermodel ...
% 10.77/3.05 Prover 0: proved (2376ms)
% 10.77/3.06
% 10.77/3.06 No countermodel exists, formula is valid
% 10.77/3.06 % SZS status Theorem for theBenchmark
% 10.77/3.06
% 10.77/3.06 Generating proof ... Warning: ignoring some quantifiers
% 20.56/5.35 found it (size 317)
% 20.56/5.35
% 20.56/5.35 % SZS output start Proof for theBenchmark
% 20.56/5.35 Assumed formulas after preprocessing and simplification:
% 20.56/5.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (function_inverse(v2) = v4 & relation_composition(v4, v2) = v7 & relation_rng(v2) = v3 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & apply(v7, v1) = v8 & apply(v4, v1) = v5 & apply(v2, v5) = v6 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_empty_yielding(v9) & relation_empty_yielding(empty_set) & one_to_one(v10) & one_to_one(v2) & relation(v16) & relation(v15) & relation(v13) & relation(v12) & relation(v10) & relation(v9) & relation(v2) & relation(empty_set) & function(v16) & function(v13) & function(v10) & function(v2) & empty(v15) & empty(v14) & empty(v13) & empty(empty_set) & in(v1, v3) & ~ empty(v12) & ~ empty(v11) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_composition(v17, v18) = v19) | ~ (ordered_pair(v23, v21) = v24) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v18) | ~ relation(v17) | ~ in(v24, v18) | in(v22, v19) | ? [v25] : (ordered_pair(v20, v23) = v25 & ~ in(v25, v17))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_composition(v17, v18) = v19) | ~ (ordered_pair(v20, v23) = v24) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v18) | ~ relation(v17) | ~ in(v24, v17) | in(v22, v19) | ? [v25] : (ordered_pair(v23, v21) = v25 & ~ in(v25, v18))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v22, v20) = v23) | ~ (identity_relation(v19) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ relation(v20) | ~ in(v21, v23) | in(v21, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v22, v20) = v23) | ~ (identity_relation(v19) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ relation(v20) | ~ in(v21, v23) | in(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v22, v20) = v23) | ~ (identity_relation(v19) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ relation(v20) | ~ in(v21, v20) | ~ in(v17, v19) | in(v21, v23)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v18) | ~ relation(v17) | ~ in(v22, v19) | ? [v23] : ? [v24] : ? [v25] : (ordered_pair(v23, v21) = v25 & ordered_pair(v20, v23) = v24 & in(v25, v18) & in(v24, v17))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v19, v20) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ in(v21, v22) | in(v18, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v19, v20) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ in(v21, v22) | in(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v19, v20) = v22) | ~ (ordered_pair(v17, v18) = v21) | ~ in(v18, v20) | ~ in(v17, v19) | in(v21, v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v18, v20) = v22) | ~ (cartesian_product2(v17, v19) = v21) | ~ subset(v19, v20) | ~ subset(v17, v18) | subset(v21, v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v17, v18) = v19) | ~ (ordered_pair(v21, v22) = v20) | ~ in(v22, v18) | ~ in(v21, v17) | in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_inverse_image(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v17) | ~ in(v22, v17) | ~ in(v21, v18) | in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_image(v17, v18) = v19) | ~ (ordered_pair(v21, v20) = v22) | ~ relation(v17) | ~ in(v22, v17) | ~ in(v21, v18) | in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v18) | ~ in(v22, v19) | in(v22, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v18) | ~ in(v22, v19) | in(v21, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v18) | ~ in(v22, v18) | ~ in(v21, v17) | in(v22, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v17) | ~ in(v22, v19) | in(v22, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v17) | ~ in(v22, v19) | in(v20, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ~ (ordered_pair(v20, v21) = v22) | ~ relation(v19) | ~ relation(v17) | ~ in(v22, v17) | ~ in(v20, v18) | in(v22, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v21 = v20 | ~ (relation_dom(v18) = v19) | ~ (apply(v18, v20) = v21) | ~ (identity_relation(v17) = v18) | ~ relation(v18) | ~ function(v18) | ~ in(v20, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v19 | ~ (identity_relation(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ in(v21, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v18 | ~ (ordered_pair(v19, v20) = v21) | ~ (ordered_pair(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v20 = v17 | v19 = v17 | ~ (unordered_pair(v19, v20) = v21) | ~ (unordered_pair(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v19 = v17 | ~ (ordered_pair(v19, v20) = v21) | ~ (ordered_pair(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = v17 | ~ (subset_difference(v21, v20, v19) = v18) | ~ (subset_difference(v21, v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = empty_set | ~ (subset_difference(v17, v19, v20) = v21) | ~ (meet_of_subsets(v17, v18) = v20) | ~ (cast_to_subset(v17) = v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (union_of_subsets(v17, v24) = v25 & complements_of_subsets(v17, v18) = v24 & powerset(v22) = v23 & powerset(v17) = v22 & (v25 = v21 | ~ element(v18, v23)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v18 = empty_set | ~ (subset_difference(v17, v19, v20) = v21) | ~ (union_of_subsets(v17, v18) = v20) | ~ (cast_to_subset(v17) = v19) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (meet_of_subsets(v17, v24) = v25 & complements_of_subsets(v17, v18) = v24 & powerset(v22) = v23 & powerset(v17) = v22 & (v25 = v21 | ~ element(v18, v23)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v17 = empty_set | ~ (subset_complement(v17, v19) = v20) | ~ (powerset(v17) = v18) | ~ element(v21, v17) | ~ element(v19, v18) | in(v21, v20) | in(v21, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v19, v18) = v20) | ~ (apply(v20, v17) = v21) | ~ relation(v19) | ~ relation(v18) | ~ function(v19) | ~ function(v18) | ? [v22] : ? [v23] : ? [v24] : (relation_dom(v20) = v22 & apply(v19, v17) = v23 & apply(v18, v23) = v24 & (v24 = v21 | ~ in(v17, v22)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v20, v19) = v21) | ~ relation(v18) | ~ relation(v17) | ~ in(v21, v17) | ? [v22] : (ordered_pair(v19, v20) = v22 & in(v22, v18))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v20, v19) = v21) | ~ relation(v18) | ~ relation(v17) | in(v21, v17) | ? [v22] : (ordered_pair(v19, v20) = v22 & ~ in(v22, v18))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ in(v21, v18) | ? [v22] : (ordered_pair(v20, v19) = v22 & in(v22, v17))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | in(v21, v18) | ? [v22] : (ordered_pair(v20, v19) = v22 & ~ in(v22, v17))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_field(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ in(v20, v19) | in(v18, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_field(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ in(v20, v19) | in(v17, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_complement(v17, v20) = v21) | ~ (powerset(v17) = v19) | ~ disjoint(v18, v20) | ~ element(v20, v19) | ~ element(v18, v19) | subset(v18, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (subset_complement(v17, v20) = v21) | ~ (powerset(v17) = v19) | ~ element(v20, v19) | ~ element(v18, v19) | ~ subset(v18, v21) | disjoint(v18, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ in(v20, v19) | in(v18, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ in(v20, v19) | ? [v22] : (relation_dom(v19) = v22 & in(v17, v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng(v17) = v18) | ~ (ordered_pair(v20, v19) = v21) | ~ relation(v17) | ~ in(v21, v17) | in(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_difference(v18, v20) = v21) | ~ (singleton(v19) = v20) | ~ subset(v17, v18) | subset(v17, v21) | in(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_difference(v18, v19) = v21) | ~ (set_difference(v17, v19) = v20) | ~ subset(v17, v18) | subset(v20, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_difference(v18, v19) = v21) | ~ (powerset(v17) = v20) | ~ element(v19, v20) | ~ element(v18, v20) | subset_difference(v17, v18, v19) = v21) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ function(v19) | ? [v22] : (apply(v19, v17) = v22 & ( ~ (v22 = v18) | ~ in(v17, v21) | in(v20, v19)) & ( ~ in(v20, v19) | (v22 = v18 & in(v17, v21))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ in(v20, v19) | in(v17, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v19) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ in(v20, v19) | ? [v22] : (relation_rng(v19) = v22 & in(v18, v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v18) = v19) | ~ (apply(v20, v17) = v21) | ~ relation(v20) | ~ relation(v18) | ~ function(v20) | ~ function(v18) | ? [v22] : ? [v23] : ? [v24] : (relation_composition(v20, v18) = v22 & relation_dom(v22) = v23 & relation_dom(v20) = v24 & ( ~ in(v21, v19) | ~ in(v17, v24) | in(v17, v23)) & ( ~ in(v17, v23) | (in(v21, v19) & in(v17, v24))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v18) = v19) | ~ (relation_image(v18, v20) = v21) | ~ (set_intersection2(v19, v17) = v20) | ~ relation(v18) | relation_image(v18, v17) = v21) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v17) | ~ function(v17) | ~ in(v19, v18) | ? [v22] : (apply(v17, v19) = v22 & ( ~ (v22 = v20) | in(v21, v17)) & (v22 = v20 | ~ in(v21, v17)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v17) | ~ in(v21, v17) | in(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (apply(v19, v17) = v21) | ~ (ordered_pair(v17, v18) = v20) | ~ relation(v19) | ~ function(v19) | ? [v22] : (relation_dom(v19) = v22 & ( ~ (v21 = v18) | ~ in(v17, v22) | in(v20, v19)) & ( ~ in(v20, v19) | (v21 = v18 & in(v17, v22))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (apply(v19, v17) = v20) | ~ (apply(v18, v20) = v21) | ~ relation(v19) | ~ relation(v18) | ~ function(v19) | ~ function(v18) | ? [v22] : ? [v23] : ? [v24] : (relation_composition(v19, v18) = v22 & relation_dom(v22) = v23 & apply(v22, v17) = v24 & (v24 = v21 | ~ in(v17, v23)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v19, v18) = v21) | ~ (cartesian_product2(v19, v17) = v20) | ~ subset(v17, v18) | subset(v20, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v19, v18) = v21) | ~ (cartesian_product2(v19, v17) = v20) | ~ subset(v17, v18) | ? [v22] : ? [v23] : (cartesian_product2(v18, v19) = v23 & cartesian_product2(v17, v19) = v22 & subset(v22, v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v19, v18) = v21) | ~ (cartesian_product2(v17, v19) = v20) | ~ subset(v17, v18) | ? [v22] : ? [v23] : (cartesian_product2(v19, v17) = v23 & cartesian_product2(v18, v19) = v22 & subset(v23, v21) & subset(v20, v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v19, v17) = v21) | ~ (cartesian_product2(v18, v19) = v20) | ~ subset(v17, v18) | ? [v22] : ? [v23] : (cartesian_product2(v19, v18) = v23 & cartesian_product2(v17, v19) = v22 & subset(v22, v20) & subset(v21, v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (cartesian_product2(v17, v19) = v20) | ~ subset(v17, v18) | subset(v20, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (cartesian_product2(v17, v19) = v20) | ~ subset(v17, v18) | ? [v22] : ? [v23] : (cartesian_product2(v19, v18) = v23 & cartesian_product2(v19, v17) = v22 & subset(v22, v23))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (singleton(v17) = v20) | ~ (unordered_pair(v19, v20) = v21) | ~ (unordered_pair(v17, v18) = v19) | ordered_pair(v17, v18) = v21) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse_image(v19, v18) = v21) | ~ (relation_inverse_image(v19, v17) = v20) | ~ subset(v17, v18) | ~ relation(v19) | subset(v20, v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v17, v20) = v21) | ~ (relation_dom_restriction(v19, v18) = v20) | ~ relation(v19) | ? [v22] : (relation_rng_restriction(v17, v19) = v22 & relation_dom_restriction(v22, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v17, v19) = v20) | ~ (relation_dom_restriction(v20, v18) = v21) | ~ relation(v19) | ? [v22] : (relation_rng_restriction(v17, v22) = v21 & relation_dom_restriction(v19, v18) = v22)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (identity_relation(v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ in(v21, v18) | in(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (ordered_pair(v19, v20) = v21) | ~ subset(v17, v18) | ~ relation(v18) | ~ relation(v17) | ~ in(v21, v17) | in(v21, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (set_intersection2(v18, v19) = v21) | ~ (set_intersection2(v17, v19) = v20) | ~ subset(v17, v18) | subset(v20, v21)) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v18) = v21) | ~ (relation_dom(v18) = v19) | ~ relation(v20) | ~ relation(v18) | ~ function(v20) | ~ function(v18) | ? [v22] : ? [v23] : ? [v24] : (relation_dom(v21) = v22 & relation_dom(v20) = v23 & apply(v20, v17) = v24 & ( ~ in(v24, v19) | ~ in(v17, v23) | in(v17, v22)) & ( ~ in(v17, v22) | (in(v24, v19) & in(v17, v23))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ (relation_dom(v18) = v19) | ~ relation(v20) | ~ relation(v18) | ~ function(v20) | ~ function(v18) | ? [v22] : ? [v23] : ? [v24] : (relation_composition(v20, v18) = v22 & relation_dom(v22) = v23 & apply(v20, v17) = v24 & ( ~ in(v24, v19) | ~ in(v17, v21) | in(v17, v23)) & ( ~ in(v17, v23) | (in(v24, v19) & in(v17, v21))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_composition(v17, v18) = v19) | ~ relation(v20) | ~ relation(v18) | ~ relation(v17) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (ordered_pair(v21, v22) = v23 & ( ~ in(v23, v20) | ( ! [v27] : ! [v28] : ( ~ (ordered_pair(v27, v22) = v28) | ~ in(v28, v18) | ? [v29] : (ordered_pair(v21, v27) = v29 & ~ in(v29, v17))) & ! [v27] : ! [v28] : ( ~ (ordered_pair(v21, v27) = v28) | ~ in(v28, v17) | ? [v29] : (ordered_pair(v27, v22) = v29 & ~ in(v29, v18))))) & (in(v23, v20) | (ordered_pair(v24, v22) = v26 & ordered_pair(v21, v24) = v25 & in(v26, v18) & in(v25, v17))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v20) | ~ relation(v18) | ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v22) = v23 & ( ~ in(v23, v20) | ~ in(v23, v18) | ~ in(v22, v17)) & (in(v23, v20) | (in(v23, v18) & in(v22, v17))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_dom_restriction(v17, v18) = v20) | ~ relation(v19) | ~ relation(v17) | ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v22) = v23 & ( ~ in(v23, v19) | ~ in(v23, v17) | ~ in(v21, v18)) & (in(v23, v19) | (in(v23, v17) & in(v21, v18))))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | v20 = v17 | ~ (unordered_pair(v17, v18) = v19) | ~ in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (complements_of_subsets(v17, v19) = v20) | ~ (complements_of_subsets(v17, v18) = v19) | ? [v21] : ? [v22] : (powerset(v21) = v22 & powerset(v17) = v21 & ~ element(v18, v22))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (subset_complement(v17, v19) = v20) | ~ (subset_complement(v17, v18) = v19) | ? [v21] : (powerset(v17) = v21 & ~ element(v18, v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (set_difference(v18, v17) = v19) | ~ (set_union2(v17, v19) = v20) | ~ subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (apply(v19, v18) = v20) | ~ (identity_relation(v17) = v19) | ~ in(v18, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v18 | ~ (singleton(v17) = v19) | ~ (set_union2(v19, v18) = v20) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_difference(v17, v19) = v20) | ~ (singleton(v18) = v19) | in(v18, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = empty_set | ~ (relation_dom(v17) = v18) | ~ (apply(v17, v19) = v20) | ~ relation(v17) | ~ function(v17) | in(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (singleton(v17) = v20) | ~ (unordered_pair(v18, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (meet_of_subsets(v20, v19) = v18) | ~ (meet_of_subsets(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (union_of_subsets(v20, v19) = v18) | ~ (union_of_subsets(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (complements_of_subsets(v20, v19) = v18) | ~ (complements_of_subsets(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_composition(v20, v19) = v18) | ~ (relation_composition(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (subset_complement(v20, v19) = v18) | ~ (subset_complement(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_difference(v20, v19) = v18) | ~ (set_difference(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (apply(v20, v19) = v18) | ~ (apply(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (cartesian_product2(v20, v19) = v18) | ~ (cartesian_product2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (singleton(v18) = v20) | ~ (singleton(v17) = v19) | ~ subset(v19, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (singleton(v17) = v20) | ~ (unordered_pair(v18, v19) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_inverse_image(v20, v19) = v18) | ~ (relation_inverse_image(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_image(v20, v19) = v18) | ~ (relation_image(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_rng_restriction(v20, v19) = v18) | ~ (relation_rng_restriction(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (relation_dom_restriction(v20, v19) = v18) | ~ (relation_dom_restriction(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (ordered_pair(v20, v19) = v18) | ~ (ordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_intersection2(v20, v19) = v18) | ~ (set_intersection2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (set_union2(v20, v19) = v18) | ~ (set_union2(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v17 | ~ (unordered_pair(v20, v19) = v18) | ~ (unordered_pair(v20, v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = empty_set | ~ (meet_of_subsets(v17, v19) = v20) | ~ (complements_of_subsets(v17, v18) = v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (subset_difference(v17, v23, v24) = v25 & union_of_subsets(v17, v18) = v24 & cast_to_subset(v17) = v23 & powerset(v21) = v22 & powerset(v17) = v21 & (v25 = v20 | ~ element(v18, v22)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = empty_set | ~ (union_of_subsets(v17, v19) = v20) | ~ (complements_of_subsets(v17, v18) = v19) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (subset_difference(v17, v23, v24) = v25 & meet_of_subsets(v17, v18) = v24 & cast_to_subset(v17) = v23 & powerset(v21) = v22 & powerset(v17) = v21 & (v25 = v20 | ~ element(v18, v22)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = empty_set | ~ (set_meet(v17) = v18) | ~ in(v20, v17) | ~ in(v19, v18) | in(v19, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_difference(v17, v18, v19) = v20) | ? [v21] : ? [v22] : (set_difference(v18, v19) = v22 & powerset(v17) = v21 & (v22 = v20 | ~ element(v19, v21) | ~ element(v18, v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_difference(v17, v18, v19) = v20) | ? [v21] : (powerset(v17) = v21 & ( ~ element(v19, v21) | ~ element(v18, v21) | element(v20, v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v19, v18) = v20) | ~ (identity_relation(v17) = v19) | ~ relation(v18) | relation_dom_restriction(v18, v17) = v20) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ~ (relation_rng(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ? [v21] : (relation_rng(v20) = v21 & relation_image(v19, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v17, v19) = v20) | ~ (relation_dom(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ? [v21] : (relation_dom(v20) = v21 & subset(v21, v18))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_complement(v17, v19) = v20) | ~ in(v18, v20) | ~ in(v18, v19) | ? [v21] : (powerset(v17) = v21 & ~ element(v19, v21))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v18) = v19) | ~ (set_intersection2(v19, v17) = v20) | ~ relation(v18) | ? [v21] : (relation_rng(v21) = v20 & relation_rng_restriction(v17, v18) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v17) = v19) | ~ (relation_dom(v17) = v18) | ~ (cartesian_product2(v18, v19) = v20) | ~ relation(v17) | subset(v17, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v17) = v19) | ~ (relation_dom(v17) = v18) | ~ (set_union2(v18, v19) = v20) | ~ relation(v17) | relation_field(v17) = v20) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v17) = v18) | ~ (relation_image(v19, v18) = v20) | ~ relation(v19) | ~ relation(v17) | ? [v21] : (relation_composition(v17, v19) = v21 & relation_rng(v21) = v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v19, v18) = v20) | ~ (set_union2(v17, v18) = v19) | set_difference(v17, v18) = v20) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v18, v17) = v19) | ~ (set_union2(v17, v19) = v20) | set_union2(v17, v18) = v20) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v19) = v20) | ~ (set_difference(v17, v18) = v19) | set_intersection2(v17, v18) = v20) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v19) | ~ in(v20, v19) | ~ in(v20, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v19) | ~ in(v20, v19) | in(v20, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v19) | ~ in(v20, v17) | in(v20, v19) | in(v20, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (union(v18) = v20) | ~ (powerset(v17) = v19) | ? [v21] : ? [v22] : (union_of_subsets(v17, v18) = v22 & powerset(v19) = v21 & (v22 = v20 | ~ element(v18, v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (union(v17) = v18) | ~ in(v20, v17) | ~ in(v19, v20) | in(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v19) | ~ (set_intersection2(v19, v17) = v20) | ~ relation(v18) | ? [v21] : (relation_dom(v21) = v20 & relation_dom_restriction(v18, v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v19) | ~ in(v20, v19) | ? [v21] : ? [v22] : (ordered_pair(v21, v22) = v20 & in(v22, v18) & in(v21, v17))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ element(v18, v20) | ~ empty(v19) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ element(v18, v20) | ~ in(v17, v18) | element(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v17) = v19) | ~ (set_meet(v18) = v20) | ? [v21] : ? [v22] : (meet_of_subsets(v17, v18) = v22 & powerset(v19) = v21 & (v22 = v20 | ~ element(v18, v21)))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (powerset(v17) = v19) | ~ element(v18, v19) | ~ in(v20, v18) | in(v20, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v17, v18) = v19) | ~ relation(v17) | ~ in(v20, v19) | ? [v21] : ? [v22] : (ordered_pair(v20, v21) = v22 & in(v22, v17) & in(v21, v18))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v17, v18) = v19) | ~ relation(v17) | ~ in(v20, v19) | ? [v21] : ? [v22] : (ordered_pair(v21, v20) = v22 & in(v22, v17) & in(v21, v18))) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (identity_relation(v17) = v18) | ~ (ordered_pair(v19, v19) = v20) | ~ relation(v18) | ~ in(v19, v17) | in(v20, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v18, v19) = v20) | ~ subset(v17, v19) | ~ subset(v17, v18) | subset(v17, v20)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ disjoint(v17, v18) | ~ in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ in(v20, v19) | in(v20, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ in(v20, v19) | in(v20, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v19) | ~ in(v20, v18) | ~ in(v20, v17) | in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v19) = v20) | ~ subset(v19, v18) | ~ subset(v17, v18) | subset(v20, v18)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v18) = v19) | ~ in(v20, v19) | in(v20, v18) | in(v20, v17)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v18) = v19) | ~ in(v20, v18) | in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_union2(v17, v18) = v19) | ~ in(v20, v17) | in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v17, v18) = v20) | ~ subset(v20, v19) | in(v18, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v17, v18) = v20) | ~ subset(v20, v19) | in(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (unordered_pair(v17, v18) = v20) | ~ in(v18, v19) | ~ in(v17, v19) | subset(v20, v19)) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_difference(v18, v19) = v20) | ? [v21] : (( ~ in(v21, v18) | ~ in(v21, v17) | in(v21, v19)) & (in(v21, v17) | (in(v21, v18) & ~ in(v21, v19))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (cartesian_product2(v18, v19) = v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (( ~ in(v21, v17) | ! [v25] : ! [v26] : ( ~ (ordered_pair(v25, v26) = v21) | ~ in(v26, v19) | ~ in(v25, v18))) & (in(v21, v17) | (v24 = v21 & ordered_pair(v22, v23) = v21 & in(v23, v19) & in(v22, v18))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (relation_inverse_image(v18, v19) = v20) | ~ relation(v18) | ? [v21] : ? [v22] : ? [v23] : (( ~ in(v21, v17) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v21, v24) = v25) | ~ in(v25, v18) | ~ in(v24, v19))) & (in(v21, v17) | (ordered_pair(v21, v22) = v23 & in(v23, v18) & in(v22, v19))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (relation_image(v18, v19) = v20) | ~ relation(v18) | ? [v21] : ? [v22] : ? [v23] : (( ~ in(v21, v17) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v24, v21) = v25) | ~ in(v25, v18) | ~ in(v24, v19))) & (in(v21, v17) | (ordered_pair(v22, v21) = v23 & in(v23, v18) & in(v22, v19))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_intersection2(v18, v19) = v20) | ? [v21] : (( ~ in(v21, v19) | ~ in(v21, v18) | ~ in(v21, v17)) & (in(v21, v17) | (in(v21, v19) & in(v21, v18))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (set_union2(v18, v19) = v20) | ? [v21] : (( ~ in(v21, v17) | ( ~ in(v21, v19) & ~ in(v21, v18))) & (in(v21, v19) | in(v21, v18) | in(v21, v17)))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v17 | ~ (unordered_pair(v18, v19) = v20) | ? [v21] : ((v21 = v19 | v21 = v18 | in(v21, v17)) & ( ~ in(v21, v17) | ( ~ (v21 = v19) & ~ (v21 = v18))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v19, v18) = v20) | ~ relation(v19) | ~ relation(v18) | ~ function(v19) | ~ function(v18) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (relation_dom(v20) = v21 & apply(v20, v17) = v22 & apply(v19, v17) = v23 & apply(v18, v23) = v24 & (v24 = v22 | ~ in(v17, v21)))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v19, v18) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : ? [v23] : (relation_rng(v19) = v21 & ( ~ in(v17, v20) | (ordered_pair(v17, v22) = v23 & in(v23, v19) & in(v22, v21) & in(v22, v18))) & (in(v17, v20) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v17, v24) = v25) | ~ in(v25, v19) | ~ in(v24, v21) | ~ in(v24, v18))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_image(v19, v18) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : ? [v23] : (relation_dom(v19) = v21 & ( ~ in(v17, v20) | (ordered_pair(v22, v17) = v23 & in(v23, v19) & in(v22, v21) & in(v22, v18))) & (in(v17, v20) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v24, v17) = v25) | ~ in(v25, v19) | ~ in(v24, v21) | ~ in(v24, v18))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v18, v19) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : (relation_rng(v20) = v21 & relation_rng(v19) = v22 & ( ~ in(v17, v22) | ~ in(v17, v18) | in(v17, v21)) & ( ~ in(v17, v21) | (in(v17, v22) & in(v17, v18))))) & ? [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom_restriction(v19, v18) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : (relation_dom(v20) = v21 & relation_dom(v19) = v22 & ( ~ in(v17, v22) | ~ in(v17, v18) | in(v17, v21)) & ( ~ in(v17, v21) | (in(v17, v22) & in(v17, v18))))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_inverse(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v20) = v23 & ordered_pair(v20, v21) = v22 & ( ~ in(v23, v17) | ~ in(v22, v19)) & (in(v23, v17) | in(v22, v19)))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom(v18) = v17) | ~ (identity_relation(v17) = v19) | ~ relation(v18) | ~ function(v18) | ? [v20] : ? [v21] : ( ~ (v21 = v20) & apply(v18, v20) = v21 & in(v20, v17))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (identity_relation(v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : ? [v22] : (ordered_pair(v20, v21) = v22 & ( ~ (v21 = v20) | ~ in(v22, v18) | ~ in(v20, v17)) & (in(v22, v18) | (v21 = v20 & in(v20, v17))))) & ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (set_union2(v17, v18) = v19) | ~ subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | v17 = empty_set | ~ (singleton(v18) = v19) | ~ subset(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (set_difference(v17, v18) = v19) | ~ disjoint(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_dom(v18) = v19) | ~ (identity_relation(v17) = v18) | ~ relation(v18) | ~ function(v18)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (singleton(v17) = v18) | ~ in(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (set_intersection2(v17, v18) = v19) | ~ subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : (v19 = empty_set | ~ (set_difference(v17, v18) = v19) | ~ subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : (v19 = empty_set | ~ (set_intersection2(v17, v18) = v19) | ~ disjoint(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (function_inverse(v19) = v18) | ~ (function_inverse(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_inverse(v19) = v18) | ~ (relation_inverse(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_field(v19) = v18) | ~ (relation_field(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_rng(v19) = v18) | ~ (relation_rng(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (union(v19) = v18) | ~ (union(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (cast_to_subset(v19) = v18) | ~ (cast_to_subset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (relation_dom(v19) = v18) | ~ (relation_dom(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (powerset(v19) = v18) | ~ (powerset(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (singleton(v19) = v18) | ~ (singleton(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (set_meet(v19) = v18) | ~ (set_meet(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (identity_relation(v19) = v18) | ~ (identity_relation(v19) = v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (meet_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (powerset(v20) = v21 & powerset(v17) = v20 & set_meet(v18) = v22 & (v22 = v19 | ~ element(v18, v21)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (meet_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : (powerset(v20) = v21 & powerset(v17) = v20 & ( ~ element(v18, v21) | element(v19, v20)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (union(v18) = v22 & powerset(v20) = v21 & powerset(v17) = v20 & (v22 = v19 | ~ element(v18, v21)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : (powerset(v20) = v21 & powerset(v17) = v20 & ( ~ element(v18, v21) | element(v19, v20)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : (powerset(v20) = v21 & powerset(v17) = v20 & ( ~ element(v18, v21) | element(v19, v21)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (complements_of_subsets(v17, v18) = v19) | ? [v20] : ? [v21] : (powerset(v20) = v21 & powerset(v17) = v20 & ( ~ element(v18, v21) | ( ! [v22] : ! [v23] : ( ~ (subset_complement(v17, v22) = v23) | ~ element(v22, v20) | ~ element(v19, v21) | ~ in(v23, v18) | in(v22, v19)) & ! [v22] : ! [v23] : ( ~ (subset_complement(v17, v22) = v23) | ~ element(v22, v20) | ~ element(v19, v21) | ~ in(v22, v19) | in(v23, v18)) & ! [v22] : (v22 = v19 | ~ element(v22, v21) | ? [v23] : ? [v24] : (subset_complement(v17, v23) = v24 & element(v23, v20) & ( ~ in(v24, v18) | ~ in(v23, v22)) & (in(v24, v18) | in(v23, v22)))))))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ~ relation(v18) | ~ empty(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ~ relation(v18) | ~ empty(v17) | empty(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | function(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | ? [v20] : ? [v21] : (relation_rng(v19) = v20 & relation_rng(v18) = v21 & subset(v20, v21))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ empty(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v18) = v19) | ~ relation(v18) | ~ empty(v17) | empty(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v17, v18) = v19) | ? [v20] : ? [v21] : (set_difference(v17, v18) = v21 & powerset(v17) = v20 & (v21 = v19 | ~ element(v18, v20)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v17, v18) = v19) | ? [v20] : (powerset(v17) = v20 & ( ~ element(v18, v20) | element(v19, v20)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v18) = v19) | ~ relation(v18) | ~ relation(v17) | ? [v20] : ? [v21] : (relation_composition(v17, v18) = v20 & relation_rng(v20) = v21 & subset(v21, v19))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ~ in(v19, v18) | ? [v20] : ? [v21] : (ordered_pair(v20, v19) = v21 & in(v21, v17))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v19) = v17) | ~ (singleton(v18) = v19) | ~ in(v18, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | subset(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | ? [v20] : ? [v21] : (subset_complement(v17, v18) = v21 & powerset(v17) = v20 & (v21 = v19 | ~ element(v18, v20)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v18) = v19) | ? [v20] : (set_difference(v20, v18) = v19 & set_union2(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union(v18) = v19) | ~ in(v17, v18) | subset(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (union(v17) = v18) | ~ in(v19, v18) | ? [v20] : (in(v20, v17) & in(v19, v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v18) | ~ (relation_image(v17, v18) = v19) | ~ relation(v17) | relation_rng(v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ~ in(v19, v18) | ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & in(v21, v17))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (apply(v18, v17) = v19) | ~ relation(v18) | ~ function(v18) | ? [v20] : (relation_dom(v18) = v20 & ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v18, v21) = v22) | ~ (apply(v22, v17) = v23) | ~ relation(v21) | ~ function(v21) | ~ in(v17, v20) | apply(v21, v19) = v23) & ! [v21] : ! [v22] : ( ~ (apply(v21, v19) = v22) | ~ relation(v21) | ~ function(v21) | ~ in(v17, v20) | ? [v23] : (relation_composition(v18, v21) = v23 & apply(v23, v17) = v22)))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v17, v18) = v19) | ~ empty(v19) | empty(v18) | empty(v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | subset(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ subset(v17, v18) | element(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v17) = v18) | ~ subset(v19, v17) | in(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v17) = v18) | ~ in(v19, v18) | subset(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v17) = v19) | ~ disjoint(v19, v18) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v17) = v19) | ~ subset(v19, v18) | in(v17, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v17) = v19) | ~ in(v17, v18) | subset(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v18, v17) = v19) | ~ relation(v18) | ? [v20] : (relation_dom(v18) = v20 & subset(v19, v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v18) = v20 & relation_image(v18, v21) = v19 & set_intersection2(v20, v17) = v21)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v18, v17) = v19) | ~ relation(v18) | ? [v20] : (relation_rng(v18) = v20 & subset(v19, v20))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v18) | subset(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v18) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v20 & relation_rng(v18) = v21 & set_intersection2(v21, v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v20 & relation_rng(v18) = v21 & subset(v20, v21))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v18) | ? [v20] : (relation_rng(v19) = v20 & subset(v20, v17))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ~ relation(v18) | subset(v19, v18)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v20 & relation_rng(v18) = v21 & subset(v20, v21))) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v20 & relation_dom(v18) = v21 & set_intersection2(v21, v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ~ relation(v18) | ? [v20] : (relation_composition(v20, v18) = v19 & identity_relation(v17) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v17, v18) = v19) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ~ empty(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (ordered_pair(v17, v18) = v19) | ? [v20] : ? [v21] : (singleton(v17) = v21 & unordered_pair(v20, v21) = v19 & unordered_pair(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v18, v17) = v19) | set_intersection2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | set_intersection2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | disjoint(v17, v18) | ? [v20] : in(v20, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | subset(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ? [v20] : (set_difference(v17, v20) = v19 & set_difference(v17, v18) = v20)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v18, v17) = v19) | ~ empty(v19) | empty(v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v18, v17) = v19) | set_union2(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ~ relation(v18) | ~ relation(v17) | relation(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ~ empty(v19) | empty(v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | set_union2(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | subset(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v17, v18) = v19) | ? [v20] : (set_difference(v18, v17) = v20 & set_union2(v17, v20) = v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v18, v17) = v19) | unordered_pair(v17, v18) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | ~ empty(v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | unordered_pair(v18, v17) = v19) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | in(v18, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v17, v18) = v19) | in(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ disjoint(v18, v19) | ~ subset(v17, v18) | disjoint(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ disjoint(v17, v18) | ~ in(v19, v18) | ~ in(v19, v17)) & ! [v17] : ! [v18] : ! [v19] : ( ~ subset(v18, v19) | ~ subset(v17, v18) | subset(v17, v19)) & ! [v17] : ! [v18] : ! [v19] : ( ~ subset(v17, v18) | ~ in(v19, v17) | in(v19, v18)) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | v18 = empty_set | ~ (set_meet(v18) = v19) | ? [v20] : ? [v21] : (( ~ in(v20, v17) | (in(v21, v18) & ~ in(v20, v21))) & (in(v20, v17) | ! [v22] : ( ~ in(v22, v18) | in(v20, v22))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_rng(v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : ? [v22] : (( ~ in(v20, v17) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v20) = v24) | ~ in(v24, v18))) & (in(v20, v17) | (ordered_pair(v21, v20) = v22 & in(v22, v18))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (union(v18) = v19) | ? [v20] : ? [v21] : (( ~ in(v20, v17) | ! [v22] : ( ~ in(v22, v18) | ~ in(v20, v22))) & (in(v20, v17) | (in(v21, v18) & in(v20, v21))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (relation_dom(v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : ? [v22] : (( ~ in(v20, v17) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v20, v23) = v24) | ~ in(v24, v18))) & (in(v20, v17) | (ordered_pair(v20, v21) = v22 & in(v22, v18))))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (powerset(v18) = v19) | ? [v20] : (( ~ subset(v20, v18) | ~ in(v20, v17)) & (subset(v20, v18) | in(v20, v17)))) & ? [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (singleton(v18) = v19) | ? [v20] : (( ~ (v20 = v18) | ~ in(v18, v17)) & (v20 = v18 | in(v20, v17)))) & ? [v17] : ! [v18] : ! [v19] : (v18 = empty_set | ~ (set_meet(v18) = v19) | in(v17, v19) | ? [v20] : (in(v20, v18) & ~ in(v17, v20))) & ? [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | element(v17, v19) | ? [v20] : (in(v20, v17) & ~ in(v20, v18))) & ? [v17] : ! [v18] : ! [v19] : ( ~ (singleton(v18) = v19) | disjoint(v19, v17) | in(v18, v17)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_difference(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (cast_to_subset(v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_intersection2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v17, v17) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ subset(v18, v17) | ~ subset(v17, v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ subset(v17, v18) | proper_subset(v17, v18)) & ! [v17] : ! [v18] : (v18 = v17 | ~ relation(v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ in(v21, v18) | ~ in(v21, v17)) & (in(v21, v18) | in(v21, v17)))) & ! [v17] : ! [v18] : (v18 = v17 | ~ empty(v18) | ~ empty(v17)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (complements_of_subsets(v17, v18) = empty_set) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v17) = v19 & ~ element(v18, v20))) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_difference(empty_set, v17) = v18)) & ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_intersection2(v17, empty_set) = v18)) & ! [v17] : ! [v18] : (v17 = empty_set | ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : ( ~ (v19 = empty_set) & relation_dom(v17) = v19)) & ! [v17] : ! [v18] : (v17 = empty_set | ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : ( ~ (v19 = empty_set) & relation_rng(v17) = v19)) & ! [v17] : ! [v18] : (v17 = empty_set | ~ (relation_inverse_image(v18, v17) = empty_set) | ~ relation(v18) | ? [v19] : (relation_rng(v18) = v19 & ~ subset(v17, v19))) & ! [v17] : ! [v18] : ( ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | relation_inverse(v17) = v18) & ! [v17] : ! [v18] : ( ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v20 & relation_rng(v17) = v19 & relation_dom(v18) = v19 & relation_dom(v17) = v20)) & ! [v17] : ! [v18] : ( ~ (function_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (relation_rng(v17) = v19 & relation_dom(v17) = v20 & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v23 | ~ (relation_dom(v18) = v21) | ~ (apply(v18, v22) = v24) | ~ (apply(v17, v23) = v22) | ~ relation(v18) | ~ function(v18) | ~ in(v23, v20)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v22 | ~ (relation_dom(v18) = v21) | ~ (apply(v18, v22) = v23) | ~ (apply(v17, v23) = v24) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v19)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v18) = v21) | ~ (apply(v18, v22) = v24) | ~ (apply(v17, v23) = v22) | ~ relation(v18) | ~ function(v18) | ~ in(v23, v20) | in(v22, v19)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v18) = v21) | ~ (apply(v18, v22) = v23) | ~ (apply(v17, v23) = v24) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v19) | in(v23, v20)) & ! [v21] : (v21 = v19 | ~ (relation_dom(v18) = v21) | ~ relation(v18) | ~ function(v18)) & ! [v21] : (v21 = v18 | ~ (relation_dom(v21) = v19) | ~ relation(v21) | ~ function(v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v21, v22) = v24 & apply(v17, v23) = v25 & ((v25 = v22 & in(v23, v20) & ( ~ (v24 = v23) | ~ in(v22, v19))) | (v24 = v23 & in(v22, v19) & ( ~ (v25 = v22) | ~ in(v23, v20)))))))) & ! [v17] : ! [v18] : ( ~ (function_inverse(v17) = v18) | ~ relation(v17) | ~ function(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (function_inverse(v17) = v18) | ~ relation(v17) | ~ function(v17) | function(v18)) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | function_inverse(v17) = v18) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | function(v18)) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ relation(v17) | relation_inverse(v18) = v17) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ relation(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v20 & relation_rng(v17) = v19 & relation_dom(v18) = v19 & relation_dom(v17) = v20)) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ empty(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_inverse(v17) = v18) | ~ empty(v17) | empty(v18)) & ! [v17] : ! [v18] : ( ~ (relation_field(v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v17) = v20 & relation_dom(v17) = v19 & set_union2(v19, v20) = v18)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (function_inverse(v17) = v19 & relation_rng(v19) = v20 & relation_dom(v19) = v18 & relation_dom(v17) = v20)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (function_inverse(v17) = v19 & relation_dom(v17) = v20 & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v23 | ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v24) | ~ (apply(v17, v23) = v22) | ~ relation(v19) | ~ function(v19) | ~ in(v23, v20)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v22 | ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v23) | ~ (apply(v17, v23) = v24) | ~ relation(v19) | ~ function(v19) | ~ in(v22, v18)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v24) | ~ (apply(v17, v23) = v22) | ~ relation(v19) | ~ function(v19) | ~ in(v23, v20) | in(v22, v18)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v23) | ~ (apply(v17, v23) = v24) | ~ relation(v19) | ~ function(v19) | ~ in(v22, v18) | in(v23, v20)) & ! [v21] : (v21 = v19 | ~ (relation_dom(v21) = v18) | ~ relation(v21) | ~ function(v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v21, v22) = v24 & apply(v17, v23) = v25 & ((v25 = v22 & in(v23, v20) & ( ~ (v24 = v23) | ~ in(v22, v18))) | (v24 = v23 & in(v22, v18) & ( ~ (v25 = v22) | ~ in(v23, v20)))))) & ! [v21] : (v21 = v18 | ~ (relation_dom(v19) = v21) | ~ relation(v19) | ~ function(v19)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ~ empty(v18) | empty(v17)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_inverse(v17) = v19 & relation_rng(v19) = v20 & relation_dom(v19) = v18 & relation_dom(v17) = v20)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & relation_image(v17, v19) = v18)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v17) = v21) | ~ relation(v20) | ? [v22] : ? [v23] : (relation_rng(v21) = v23 & relation_rng(v20) = v22 & (v23 = v18 | ~ subset(v19, v22)))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ~ subset(v19, v21) | ~ relation(v20) | ? [v22] : (relation_composition(v20, v17) = v22 & relation_rng(v22) = v18)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v17, v20) = v21) | ~ relation(v20) | ? [v22] : ? [v23] : (relation_dom(v21) = v23 & relation_dom(v20) = v22 & (v23 = v19 | ~ subset(v18, v22)))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v18, v21) | ~ relation(v20) | ? [v22] : (relation_composition(v17, v20) = v22 & relation_dom(v22) = v19)))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | subset(v18, v21)) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | ? [v22] : (relation_dom(v20) = v22 & subset(v19, v22))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | subset(v19, v21)) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | ? [v22] : (relation_rng(v20) = v22 & subset(v18, v22))))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & ( ~ (v19 = empty_set) | v18 = empty_set) & ( ~ (v18 = empty_set) | v19 = empty_set))) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ empty(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ empty(v17) | empty(v18)) & ! [v17] : ! [v18] : ( ~ (set_difference(v17, v18) = v17) | disjoint(v17, v18)) & ! [v17] : ! [v18] : ( ~ (set_difference(v17, v18) = empty_set) | subset(v17, v18)) & ! [v17] : ! [v18] : ( ~ (cast_to_subset(v17) = v18) | ? [v19] : (powerset(v17) = v19 & element(v18, v19))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (function_inverse(v17) = v20 & relation_rng(v20) = v18 & relation_rng(v17) = v19 & relation_dom(v20) = v19)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : (function_inverse(v17) = v19 & relation_rng(v17) = v20 & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v23 | ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v24) | ~ (apply(v17, v23) = v22) | ~ relation(v19) | ~ function(v19) | ~ in(v23, v18)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = v22 | ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v23) | ~ (apply(v17, v23) = v24) | ~ relation(v19) | ~ function(v19) | ~ in(v22, v20)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v24) | ~ (apply(v17, v23) = v22) | ~ relation(v19) | ~ function(v19) | ~ in(v23, v18) | in(v22, v20)) & ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v19) = v21) | ~ (apply(v19, v22) = v23) | ~ (apply(v17, v23) = v24) | ~ relation(v19) | ~ function(v19) | ~ in(v22, v20) | in(v23, v18)) & ! [v21] : (v21 = v20 | ~ (relation_dom(v19) = v21) | ~ relation(v19) | ~ function(v19)) & ! [v21] : (v21 = v19 | ~ (relation_dom(v21) = v20) | ~ relation(v21) | ~ function(v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (apply(v21, v22) = v24 & apply(v17, v23) = v25 & ((v25 = v22 & in(v23, v18) & ( ~ (v24 = v23) | ~ in(v22, v20))) | (v24 = v23 & in(v22, v20) & ( ~ (v25 = v22) | ~ in(v23, v18)))))))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ~ empty(v18) | empty(v17)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_inverse(v17) = v20 & relation_rng(v20) = v18 & relation_rng(v17) = v19 & relation_dom(v20) = v19)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v20, v17) = v21) | ~ relation(v20) | ? [v22] : ? [v23] : (relation_rng(v21) = v23 & relation_rng(v20) = v22 & (v23 = v19 | ~ subset(v18, v22)))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ~ subset(v18, v21) | ~ relation(v20) | ? [v22] : (relation_composition(v20, v17) = v22 & relation_rng(v22) = v19)))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_composition(v17, v20) = v21) | ~ relation(v20) | ? [v22] : ? [v23] : (relation_dom(v21) = v23 & relation_dom(v20) = v22 & (v23 = v18 | ~ subset(v19, v22)))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v19, v21) | ~ relation(v20) | ? [v22] : (relation_composition(v17, v20) = v22 & relation_dom(v22) = v18)))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v17) = v19 & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | subset(v19, v21)) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | ? [v22] : (relation_dom(v20) = v22 & subset(v18, v22))) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | subset(v18, v21)) & ! [v20] : ! [v21] : ( ~ (relation_dom(v20) = v21) | ~ subset(v17, v20) | ~ relation(v20) | ? [v22] : (relation_rng(v20) = v22 & subset(v19, v22))))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v17) = v19 & ( ~ (v19 = empty_set) | v18 = empty_set) & ( ~ (v18 = empty_set) | v19 = empty_set))) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ empty(v17) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (relation_dom(v17) = v18) | ~ empty(v17) | empty(v18)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ empty(v18)) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | union(v18) = v17) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | empty(v17) | ? [v19] : (element(v19, v18) & ~ empty(v19))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (cast_to_subset(v17) = v19 & element(v19, v18))) & ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ? [v19] : (element(v19, v18) & empty(v19))) & ! [v17] : ! [v18] : ( ~ (singleton(v18) = v17) | subset(v17, v17)) & ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | ~ empty(v18)) & ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | unordered_pair(v17, v17) = v18) & ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | subset(empty_set, v18)) & ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | in(v17, v18)) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | relation_rng(v18) = v17) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | relation_dom(v18) = v17) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | relation(v18)) & ! [v17] : ! [v18] : ( ~ (identity_relation(v17) = v18) | function(v18)) & ! [v17] : ! [v18] : ( ~ (set_intersection2(v17, v18) = empty_set) | disjoint(v17, v18)) & ! [v17] : ! [v18] : ( ~ (unordered_pair(v17, v17) = v18) | singleton(v17) = v18) & ! [v17] : ! [v18] : ( ~ disjoint(v17, v18) | disjoint(v18, v17)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | ~ empty(v17) | empty(v18)) & ! [v17] : ! [v18] : ( ~ element(v18, v17) | empty(v17) | in(v18, v17)) & ! [v17] : ! [v18] : ( ~ element(v17, v18) | empty(v18) | in(v17, v18)) & ! [v17] : ! [v18] : ( ~ subset(v17, v18) | ~ proper_subset(v18, v17)) & ! [v17] : ! [v18] : ( ~ relation(v18) | ~ relation(v17) | subset(v17, v18) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & in(v21, v17) & ~ in(v21, v18))) & ! [v17] : ! [v18] : ( ~ relation(v17) | ~ in(v18, v17) | ? [v19] : ? [v20] : ordered_pair(v19, v20) = v18) & ! [v17] : ! [v18] : ( ~ empty(v18) | ~ empty(v17) | element(v18, v17)) & ! [v17] : ! [v18] : ( ~ empty(v18) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ( ~ proper_subset(v18, v17) | ~ proper_subset(v17, v18)) & ! [v17] : ! [v18] : ( ~ proper_subset(v17, v18) | subset(v17, v18)) & ! [v17] : ! [v18] : ( ~ in(v18, v17) | ~ in(v17, v18)) & ! [v17] : ! [v18] : ( ~ in(v18, v17) | element(v18, v17) | empty(v17)) & ! [v17] : ! [v18] : ( ~ in(v17, v18) | element(v17, v18)) & ! [v17] : (v17 = empty_set | ~ (relation_rng(v17) = empty_set) | ~ relation(v17)) & ! [v17] : (v17 = empty_set | ~ (relation_dom(v17) = empty_set) | ~ relation(v17)) & ! [v17] : (v17 = empty_set | ~ (set_meet(empty_set) = v17)) & ! [v17] : (v17 = empty_set | ~ subset(v17, empty_set)) & ! [v17] : (v17 = empty_set | ~ relation(v17) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v17))) & ! [v17] : (v17 = empty_set | ~ empty(v17)) & ! [v17] : ~ (singleton(v17) = empty_set) & ! [v17] : ( ~ relation(v17) | ~ function(v17) | ~ empty(v17) | one_to_one(v17)) & ! [v17] : ( ~ empty(v17) | relation(v17)) & ! [v17] : ( ~ empty(v17) | function(v17)) & ! [v17] : ~ proper_subset(v17, v17) & ! [v17] : ~ in(v17, empty_set) & ? [v17] : ? [v18] : (v18 = v17 | ? [v19] : (( ~ in(v19, v18) | ~ in(v19, v17)) & (in(v19, v18) | in(v19, v17)))) & ? [v17] : ? [v18] : (disjoint(v17, v18) | ? [v19] : (in(v19, v18) & in(v19, v17))) & ? [v17] : ? [v18] : element(v18, v17) & ? [v17] : ? [v18] : (subset(v17, v18) | ? [v19] : (in(v19, v17) & ~ in(v19, v18))) & ? [v17] : ? [v18] : (in(v17, v18) & ! [v19] : ! [v20] : ( ~ (powerset(v19) = v20) | ~ in(v19, v18) | in(v20, v18)) & ! [v19] : ! [v20] : ( ~ subset(v20, v19) | ~ in(v19, v18) | in(v20, v18)) & ! [v19] : ( ~ subset(v19, v18) | are_equipotent(v19, v18) | in(v19, v18))) & ? [v17] : ? [v18] : (in(v17, v18) & ! [v19] : ! [v20] : ( ~ subset(v20, v19) | ~ in(v19, v18) | in(v20, v18)) & ! [v19] : ( ~ subset(v19, v18) | are_equipotent(v19, v18) | in(v19, v18)) & ! [v19] : ( ~ in(v19, v18) | ? [v20] : (in(v20, v18) & ! [v21] : ( ~ subset(v21, v19) | in(v21, v20))))) & ? [v17] : (v17 = empty_set | ? [v18] : in(v18, v17)) & ? [v17] : subset(v17, v17) & ? [v17] : subset(empty_set, v17) & ? [v17] : (relation(v17) | ? [v18] : (in(v18, v17) & ! [v19] : ! [v20] : ~ (ordered_pair(v19, v20) = v18))) & ( ~ (v8 = v1) | ~ (v6 = v1)))
% 20.96/5.48 | 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, all_0_15_15, all_0_16_16 yields:
% 20.96/5.48 | (1) function_inverse(all_0_14_14) = all_0_12_12 & relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9 & relation_rng(all_0_14_14) = all_0_13_13 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & apply(all_0_9_9, all_0_15_15) = all_0_8_8 & apply(all_0_12_12, all_0_15_15) = all_0_11_11 & apply(all_0_14_14, all_0_11_11) = all_0_10_10 & powerset(empty_set) = all_0_16_16 & singleton(empty_set) = all_0_16_16 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & one_to_one(all_0_14_14) & 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_14_14) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_14_14) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & in(all_0_15_15, 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] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ element(v3, v2) | ~ element(v1, v2) | ~ subset(v1, v4) | disjoint(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (relation_dom(v2) = v5 & ( ~ (v4 = v1) | ~ in(v0, v5) | in(v3, v2)) & ( ~ in(v3, v2) | (v4 = v1 & in(v0, v5))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v5 & relation_dom(v5) = v6 & apply(v5, v0) = v7 & (v7 = v4 | ~ in(v0, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v1, v2) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v0) = v6 & cartesian_product2(v1, v2) = v5 & subset(v6, v4) & subset(v3, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v0) = v4) | ~ (cartesian_product2(v1, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v0, v2) = v5 & subset(v5, v3) & subset(v4, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | ? [v5] : ? [v6] : (cartesian_product2(v2, v1) = v6 & cartesian_product2(v2, v0) = v5 & subset(v5, v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ subset(v0, v1) | ~ relation(v2) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v2) = v5 & relation_dom_restriction(v5, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v2) = v3) | ~ (relation_dom_restriction(v3, v1) = v4) | ~ relation(v2) | ? [v5] : (relation_rng_restriction(v0, v5) = v4 & relation_dom_restriction(v2, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v1) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v4) = v5 & relation_dom(v3) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v6) | in(v0, v5)) & ( ~ in(v0, v5) | (in(v7, v2) & in(v0, v6))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & apply(v3, v0) = v7 & ( ~ in(v7, v2) | ~ in(v0, v4) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v7, v2) & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ( ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v5) = v11) | ~ in(v11, v1) | ? [v12] : (ordered_pair(v4, v10) = v12 & ~ in(v12, v0))) & ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ in(v11, v0) | ? [v12] : (ordered_pair(v10, v5) = v12 & ~ in(v12, v1))))) & (in(v6, v3) | (ordered_pair(v7, v5) = v9 & ordered_pair(v4, v7) = v8 & in(v9, v1) & in(v8, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v3) | ~ relation(v1) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v3) | ~ in(v6, v1) | ~ in(v5, v0)) & (in(v6, v3) | (in(v6, v1) & in(v5, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ relation(v2) | ~ relation(v0) | ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v4, v5) = v6 & ( ~ in(v6, v2) | ~ in(v6, v0) | ~ in(v4, v1)) & (in(v6, v2) | (in(v6, v0) & in(v4, v1))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (complements_of_subsets(v0, v2) = v3) | ~ (complements_of_subsets(v0, v1) = v2) | ? [v4] : ? [v5] : (powerset(v4) = v5 & powerset(v0) = v4 & ~ element(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (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) | ? [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(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) | ? [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) | ~ 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))) & ( ~ (all_0_8_8 = all_0_15_15) | ~ (all_0_10_10 = all_0_15_15))
% 21.62/5.55 |
% 21.62/5.55 | Applying alpha-rule on (1) yields:
% 21.62/5.55 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 21.62/5.55 | (3) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0)))
% 21.62/5.55 | (4) relation_empty_yielding(empty_set)
% 21.62/5.55 | (5) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 21.62/5.55 | (6) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0)
% 21.62/5.55 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0))
% 21.62/5.55 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 21.62/5.55 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 21.62/5.55 | (10) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 21.62/5.55 | (11) ! [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))
% 21.62/5.55 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 21.62/5.55 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 21.62/5.55 | (14) ! [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))
% 21.62/5.55 | (15) ! [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))
% 21.62/5.55 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 21.62/5.55 | (17) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 21.62/5.55 | (18) ! [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)))
% 21.62/5.55 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 21.62/5.55 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 21.62/5.55 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 21.62/5.55 | (22) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 21.62/5.55 | (23) ! [v0] : ~ (singleton(v0) = empty_set)
% 21.62/5.55 | (24) ? [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)))))
% 21.62/5.55 | (25) ! [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))))
% 21.62/5.56 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 21.62/5.56 | (27) ! [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))
% 21.62/5.56 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 21.62/5.56 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 21.62/5.56 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 21.62/5.56 | (31) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 21.62/5.56 | (32) ! [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))
% 21.62/5.56 | (33) ! [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)))
% 21.62/5.56 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 21.62/5.56 | (35) ! [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)))))
% 21.62/5.56 | (36) ! [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))
% 21.62/5.56 | (37) ! [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))
% 21.62/5.56 | (38) ! [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))))))))
% 21.62/5.56 | (39) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 21.62/5.56 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4))))
% 21.62/5.56 | (41) ! [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))
% 21.62/5.56 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2)
% 21.62/5.56 | (43) ? [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)))))
% 21.62/5.56 | (44) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 21.62/5.56 | (45) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 21.62/5.56 | (46) ~ (all_0_8_8 = all_0_15_15) | ~ (all_0_10_10 = all_0_15_15)
% 21.62/5.56 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 21.62/5.56 | (48) function(all_0_14_14)
% 21.62/5.56 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 21.62/5.56 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 21.62/5.56 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 21.62/5.56 | (52) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 21.62/5.56 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 21.62/5.56 | (54) ! [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)))
% 21.62/5.56 | (55) ! [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)))
% 21.62/5.56 | (56) ! [v0] : ~ proper_subset(v0, v0)
% 21.62/5.56 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 21.62/5.56 | (58) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 21.62/5.56 | (59) ! [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))
% 21.62/5.56 | (60) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 21.62/5.56 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 21.62/5.56 | (62) ! [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))
% 21.62/5.56 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 21.62/5.56 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 21.62/5.56 | (65) function(all_0_3_3)
% 21.62/5.57 | (66) ! [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))
% 21.62/5.57 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 21.62/5.57 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 21.62/5.57 | (69) ! [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)))
% 21.62/5.57 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 21.62/5.57 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 21.62/5.57 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 21.62/5.57 | (73) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 21.62/5.57 | (74) ! [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)))
% 21.62/5.57 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 21.62/5.57 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 21.62/5.57 | (77) ? [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))))
% 21.62/5.57 | (78) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 21.62/5.57 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 21.62/5.57 | (80) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 21.62/5.57 | (81) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1)))
% 21.62/5.57 | (82) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 21.62/5.57 | (83) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 21.62/5.57 | (84) ! [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))
% 21.62/5.57 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 21.62/5.57 | (86) ? [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)))))
% 21.62/5.57 | (87) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1)
% 21.62/5.57 | (88) relation(all_0_3_3)
% 21.62/5.57 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 21.62/5.57 | (90) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 21.62/5.57 | (91) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0))
% 21.62/5.57 | (92) ? [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)))))
% 21.62/5.57 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 21.62/5.57 | (94) ? [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)))))
% 21.62/5.57 | (95) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 21.62/5.57 | (96) ? [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))))
% 21.62/5.57 | (97) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 21.62/5.57 | (98) apply(all_0_12_12, all_0_15_15) = all_0_11_11
% 21.62/5.57 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 21.62/5.57 | (100) relation(all_0_6_6)
% 21.62/5.57 | (101) ! [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))))
% 21.62/5.57 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1))
% 21.62/5.57 | (103) relation(all_0_14_14)
% 21.62/5.57 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 21.62/5.57 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2))
% 21.62/5.57 | (106) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 21.62/5.57 | (107) relation(all_0_1_1)
% 21.62/5.57 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 21.62/5.57 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 21.62/5.57 | (110) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 21.62/5.57 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4)))
% 21.62/5.57 | (112) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 21.62/5.57 | (113) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 21.62/5.57 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 21.62/5.57 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 21.62/5.57 | (116) empty(empty_set)
% 21.62/5.57 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 21.62/5.57 | (118) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 21.62/5.57 | (119) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2)))
% 21.62/5.58 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 21.62/5.58 | (121) ! [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))))))))
% 21.62/5.58 | (122) ! [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)))
% 21.62/5.58 | (123) in(all_0_15_15, all_0_13_13)
% 21.62/5.58 | (124) ! [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)))
% 21.62/5.58 | (125) ~ empty(all_0_5_5)
% 21.62/5.58 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 21.62/5.58 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 21.62/5.58 | (128) ! [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)))
% 21.62/5.58 | (129) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 21.62/5.58 | (130) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0))
% 21.62/5.58 | (131) ! [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)))
% 21.62/5.58 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 21.62/5.58 | (133) ! [v0] : ( ~ empty(v0) | function(v0))
% 21.62/5.58 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 21.62/5.58 | (135) ! [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))))
% 21.62/5.58 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 21.62/5.58 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 21.62/5.58 | (138) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1)))
% 21.62/5.58 | (139) ! [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))
% 21.62/5.58 | (140) ! [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)
% 21.62/5.58 | (141) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 21.62/5.58 | (142) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 21.62/5.58 | (143) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 21.62/5.58 | (144) ! [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))
% 21.62/5.58 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 21.62/5.58 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 21.62/5.58 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3))
% 21.62/5.58 | (148) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2)))
% 21.62/5.58 | (149) ! [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))))
% 21.62/5.58 | (150) ! [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))
% 21.62/5.58 | (151) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 21.62/5.58 | (152) ! [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))))
% 21.62/5.58 | (153) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1))
% 21.62/5.58 | (154) ! [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)))
% 21.62/5.58 | (155) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 21.62/5.58 | (156) relation_dom(empty_set) = empty_set
% 21.62/5.58 | (157) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 21.62/5.58 | (158) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 21.62/5.58 | (159) empty(all_0_1_1)
% 21.62/5.58 | (160) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1))
% 21.62/5.58 | (161) ! [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))))))))
% 21.62/5.59 | (162) ! [v0] : ( ~ empty(v0) | relation(v0))
% 21.62/5.59 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 21.62/5.59 | (164) one_to_one(all_0_6_6)
% 21.62/5.59 | (165) ! [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)))))
% 21.62/5.59 | (166) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 21.62/5.59 | (167) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 21.62/5.59 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 21.62/5.59 | (169) ? [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)))))
% 21.62/5.59 | (170) ! [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))))
% 21.62/5.59 | (171) ? [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)))))
% 21.62/5.59 | (172) ! [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))))
% 21.62/5.59 | (173) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 21.62/5.59 | (174) ! [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))))
% 21.62/5.59 | (175) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 21.62/5.59 | (176) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 21.62/5.59 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 21.62/5.59 | (178) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1))
% 21.62/5.59 | (179) ! [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))
% 21.62/5.59 | (180) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 21.62/5.59 | (181) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 21.62/5.59 | (182) ! [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))))
% 21.62/5.59 | (183) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2))
% 21.62/5.59 | (184) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 21.62/5.59 | (185) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1))
% 21.62/5.59 | (186) ! [v0] : ~ in(v0, empty_set)
% 21.62/5.59 | (187) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 21.62/5.59 | (188) ! [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))))
% 21.62/5.59 | (189) ? [v0] : subset(v0, v0)
% 21.62/5.59 | (190) relation(empty_set)
% 21.62/5.59 | (191) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1))
% 21.62/5.59 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3)
% 21.62/5.59 | (193) relation(all_0_4_4)
% 21.62/5.59 | (194) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 21.62/5.59 | (195) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 21.62/5.59 | (196) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 21.62/5.59 | (197) ! [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)))
% 21.62/5.59 | (198) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 21.62/5.59 | (199) relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9
% 21.62/5.59 | (200) ! [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))
% 21.62/5.59 | (201) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 21.62/5.59 | (202) empty(all_0_2_2)
% 21.62/5.59 | (203) relation_rng(all_0_14_14) = all_0_13_13
% 21.62/5.59 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 21.62/5.59 | (205) ! [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))))
% 21.62/5.59 | (206) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 21.62/5.59 | (207) ! [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))))
% 21.62/5.59 | (208) ! [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))
% 21.62/5.59 | (209) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 21.62/5.59 | (210) ! [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))
% 21.62/5.59 | (211) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3))))
% 21.62/5.59 | (212) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 21.62/5.59 | (213) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 21.62/5.59 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 21.62/5.59 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 21.62/5.60 | (216) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 21.62/5.60 | (217) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 21.62/5.60 | (218) ! [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))))
% 21.62/5.60 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1))
% 21.62/5.60 | (220) ! [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)))
% 21.62/5.60 | (221) ! [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))))
% 21.62/5.60 | (222) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 21.62/5.60 | (223) ! [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))
% 21.62/5.60 | (224) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 21.62/5.60 | (225) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 21.62/5.60 | (226) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1))
% 21.62/5.60 | (227) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 21.62/5.60 | (228) apply(all_0_9_9, all_0_15_15) = all_0_8_8
% 21.62/5.60 | (229) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 21.62/5.60 | (230) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 21.62/5.60 | (231) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 21.62/5.60 | (232) ? [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)))))
% 21.62/5.60 | (233) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 21.62/5.60 | (234) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 21.62/5.60 | (235) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 21.62/5.60 | (236) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 21.62/5.60 | (237) ? [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)))))
% 21.62/5.60 | (238) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 21.62/5.60 | (239) function(all_0_6_6)
% 21.62/5.60 | (240) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 21.62/5.60 | (241) ! [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)))))
% 21.62/5.60 | (242) ? [v0] : subset(empty_set, v0)
% 21.62/5.60 | (243) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1))
% 21.62/5.60 | (244) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1))
% 21.62/5.60 | (245) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 21.62/5.60 | (246) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 21.62/5.60 | (247) ! [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)))
% 21.62/5.60 | (248) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 21.62/5.60 | (249) ! [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))
% 21.62/5.60 | (250) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1))
% 21.62/5.60 | (251) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 21.62/5.60 | (252) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1))
% 21.62/5.60 | (253) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3)))
% 21.62/5.60 | (254) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 21.62/5.60 | (255) ! [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)))))
% 21.62/5.60 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0))
% 21.62/5.60 | (257) relation_empty_yielding(all_0_7_7)
% 21.62/5.60 | (258) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 21.62/5.60 | (259) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 21.62/5.60 | (260) ? [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)))))
% 21.62/5.60 | (261) ? [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)))))
% 21.62/5.60 | (262) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0))
% 21.62/5.60 | (263) function(all_0_0_0)
% 21.62/5.60 | (264) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 21.62/5.60 | (265) ! [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)))
% 21.62/5.60 | (266) ! [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))
% 21.62/5.60 | (267) ! [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))
% 21.62/5.60 | (268) ! [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))))
% 21.62/5.60 | (269) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 21.62/5.60 | (270) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 21.62/5.60 | (271) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 21.62/5.60 | (272) ! [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))))
% 21.62/5.60 | (273) ! [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)))))
% 21.62/5.60 | (274) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 21.62/5.60 | (275) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 21.62/5.60 | (276) ! [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)))))
% 21.62/5.60 | (277) ? [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)))))
% 21.62/5.60 | (278) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 21.62/5.60 | (279) ! [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))))
% 21.62/5.60 | (280) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 21.62/5.60 | (281) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3))
% 21.62/5.60 | (282) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 21.62/5.60 | (283) ? [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)))))
% 21.62/5.60 | (284) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 21.62/5.60 | (285) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 21.62/5.60 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 21.62/5.60 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 21.62/5.60 | (288) ! [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)))
% 21.62/5.61 | (289) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 21.62/5.61 | (290) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 21.62/5.61 | (291) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 21.62/5.61 | (292) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 21.62/5.61 | (293) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 21.62/5.61 | (294) ! [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))))
% 21.62/5.61 | (295) ! [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))
% 21.62/5.61 | (296) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 21.62/5.61 | (297) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 21.62/5.61 | (298) singleton(empty_set) = all_0_16_16
% 21.62/5.61 | (299) powerset(empty_set) = all_0_16_16
% 21.62/5.61 | (300) ! [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)))
% 21.62/5.61 | (301) ! [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))
% 21.62/5.61 | (302) ! [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))
% 21.62/5.61 | (303) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0))
% 21.62/5.61 | (304) ! [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)))
% 21.62/5.61 | (305) ! [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))
% 21.62/5.61 | (306) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 21.62/5.61 | (307) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 21.62/5.61 | (308) ! [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))
% 21.62/5.61 | (309) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 21.62/5.61 | (310) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 21.62/5.61 | (311) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 21.62/5.61 | (312) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 21.62/5.61 | (313) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 21.62/5.61 | (314) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0)))
% 21.62/5.61 | (315) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 21.62/5.61 | (316) ! [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)))))
% 21.62/5.61 | (317) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 21.62/5.61 | (318) one_to_one(all_0_14_14)
% 21.62/5.61 | (319) relation(all_0_7_7)
% 21.62/5.61 | (320) relation_rng(empty_set) = empty_set
% 21.62/5.61 | (321) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0))
% 21.62/5.61 | (322) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 21.62/5.61 | (323) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 21.62/5.61 | (324) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3)))
% 21.62/5.61 | (325) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2))
% 21.62/5.61 | (326) ! [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))
% 21.62/5.61 | (327) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3))
% 21.62/5.61 | (328) function_inverse(all_0_14_14) = all_0_12_12
% 21.62/5.61 | (329) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 21.62/5.61 | (330) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 21.62/5.61 | (331) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 21.62/5.61 | (332) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 21.62/5.61 | (333) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 21.62/5.61 | (334) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3)))
% 21.62/5.61 | (335) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 21.62/5.61 | (336) ! [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))
% 21.62/5.61 | (337) ! [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)))
% 21.62/5.61 | (338) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 21.62/5.61 | (339) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 21.62/5.61 | (340) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1))
% 21.62/5.61 | (341) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 21.62/5.61 | (342) ! [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))
% 21.62/5.61 | (343) ! [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))
% 21.62/5.61 | (344) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 21.62/5.61 | (345) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 21.62/5.61 | (346) ! [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)))
% 21.62/5.61 | (347) ! [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)))))
% 21.62/5.61 | (348) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 21.62/5.61 | (349) ~ empty(all_0_4_4)
% 21.62/5.61 | (350) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 21.62/5.61 | (351) ? [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)))
% 21.62/5.61 | (352) relation(all_0_0_0)
% 21.62/5.61 | (353) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3)))
% 21.62/5.61 | (354) apply(all_0_14_14, all_0_11_11) = all_0_10_10
% 21.62/5.61 | (355) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v1) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ? [v5] : (union_of_subsets(v0, v1) = v5 & powerset(v2) = v4 & (v5 = v3 | ~ element(v1, v4))))
% 21.62/5.61 | (356) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1)
% 21.62/5.61 | (357) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0))
% 21.62/5.61 | (358) ! [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)))
% 21.62/5.61 | (359) ! [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)))))
% 21.62/5.61 | (360) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 21.62/5.61 | (361) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2))
% 21.62/5.61 | (362) ! [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)))
% 21.62/5.61 | (363) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 21.62/5.61 | (364) ? [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)))))
% 21.62/5.61 | (365) ! [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))
% 21.62/5.61 | (366) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 21.62/5.61 | (367) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3)
% 21.62/5.61 | (368) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3)))
% 21.62/5.61 | (369) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0))
% 21.62/5.61 | (370) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0))
% 21.62/5.61 | (371) ? [v0] : ? [v1] : element(v1, v0)
% 21.62/5.61 | (372) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 21.62/5.61 | (373) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 21.62/5.62 | (374) ? [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)))))
% 21.62/5.62 | (375) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 21.62/5.62 | (376) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0))
% 21.62/5.62 | (377) ! [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)
% 21.62/5.62 | (378) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 21.62/5.62 | (379) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1))
% 21.62/5.62 | (380) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 21.62/5.62 | (381) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 21.62/5.62 | (382) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 21.62/5.62 | (383) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 21.62/5.62 | (384) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 21.62/5.62 | (385) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1)))
% 21.62/5.62 | (386) empty(all_0_3_3)
% 21.62/5.62 | (387) ! [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)))
% 21.62/5.62 | (388) ? [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)))))
% 21.62/5.62 | (389) ! [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))))
% 21.62/5.62 | (390) ? [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)))))
% 21.62/5.62 | (391) ! [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))
% 21.62/5.62 | (392) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 21.62/5.62 | (393) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 21.62/5.62 | (394) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4)))
% 21.62/5.62 |
% 21.62/5.62 | Instantiating (77) with all_28_0_36 yields:
% 21.62/5.62 | (395) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_dom(v2) = v3 & apply(v2, all_28_0_36) = v4 & apply(v1, all_28_0_36) = v5 & apply(v0, v5) = v6 & (v6 = v4 | ~ in(all_28_0_36, v3))))
% 21.62/5.62 |
% 21.62/5.62 | Instantiating (261) with all_56_0_51 yields:
% 21.62/5.62 | (396) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v0) = v3) | ~ (relation_dom(v0) = v1) | ~ relation(v2) | ~ relation(v0) | ~ function(v2) | ~ function(v0) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v3) = v4 & relation_dom(v2) = v5 & apply(v2, all_56_0_51) = v6 & ( ~ in(v6, v1) | ~ in(all_56_0_51, v5) | in(all_56_0_51, v4)) & ( ~ in(all_56_0_51, v4) | (in(v6, v1) & in(all_56_0_51, v5)))))
% 21.62/5.62 |
% 21.62/5.62 | Instantiating formula (264) with all_0_2_2, all_0_1_1 and discharging atoms empty(all_0_1_1), empty(all_0_2_2), yields:
% 21.62/5.62 | (397) all_0_1_1 = all_0_2_2
% 21.62/5.62 |
% 21.62/5.62 | Instantiating formula (264) with all_0_3_3, all_0_1_1 and discharging atoms empty(all_0_1_1), empty(all_0_3_3), yields:
% 21.62/5.62 | (398) all_0_1_1 = all_0_3_3
% 21.62/5.62 |
% 21.62/5.62 | Instantiating formula (264) with empty_set, all_0_2_2 and discharging atoms empty(all_0_2_2), empty(empty_set), yields:
% 21.62/5.62 | (399) all_0_2_2 = empty_set
% 21.62/5.62 |
% 22.00/5.62 | Combining equations (397,398) yields a new equation:
% 22.00/5.62 | (400) all_0_2_2 = all_0_3_3
% 22.00/5.62 |
% 22.00/5.62 | Simplifying 400 yields:
% 22.00/5.62 | (401) all_0_2_2 = all_0_3_3
% 22.00/5.62 |
% 22.00/5.62 | Combining equations (401,399) yields a new equation:
% 22.00/5.62 | (402) all_0_3_3 = empty_set
% 22.00/5.62 |
% 22.00/5.62 | Simplifying 402 yields:
% 22.00/5.62 | (403) all_0_3_3 = empty_set
% 22.00/5.62 |
% 22.00/5.62 | From (403) and (88) follows:
% 22.00/5.62 | (190) relation(empty_set)
% 22.00/5.62 |
% 22.00/5.62 | From (403) and (65) follows:
% 22.00/5.62 | (405) function(empty_set)
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (150) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, relation(all_0_14_14), yields:
% 22.00/5.62 | (406) ? [v0] : ? [v1] : (relation_inverse(all_0_14_14) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = all_0_13_13 & relation_dom(all_0_14_14) = v1)
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (178) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, relation(all_0_14_14), yields:
% 22.00/5.62 | (407) ? [v0] : (relation_dom(all_0_14_14) = v0 & relation_image(all_0_14_14, v0) = all_0_13_13)
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (182) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, relation(all_0_14_14), yields:
% 22.00/5.62 | (408) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, all_0_14_14) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = all_0_13_13 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, all_0_14_14) = v3 & relation_rng(v3) = all_0_13_13)))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (268) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, relation(all_0_14_14), yields:
% 22.00/5.62 | (409) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_14_14, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_0_13_13, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_13_13, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_14_14, v1) = v3 & relation_dom(v3) = v0)))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (273) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, relation(all_0_14_14), yields:
% 22.00/5.62 | (410) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | subset(all_0_13_13, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(all_0_13_13, v3))))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (122) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, relation(all_0_14_14), yields:
% 22.00/5.62 | (411) ? [v0] : (relation_dom(all_0_14_14) = v0 & ( ~ (v0 = empty_set) | all_0_13_13 = empty_set) & ( ~ (all_0_13_13 = empty_set) | v0 = empty_set))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (138) with all_0_14_14, all_0_14_14 and discharging atoms relation(all_0_14_14), yields:
% 22.00/5.62 | (412) subset(all_0_14_14, all_0_14_14)
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (362) with empty_set, empty_set, all_0_14_14 and discharging atoms relation_rng(empty_set) = empty_set, relation(all_0_14_14), relation(empty_set), yields:
% 22.00/5.62 | (413) ? [v0] : ? [v1] : (relation_composition(all_0_14_14, empty_set) = v0 & relation_rng(v0) = v1 & subset(v1, empty_set))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (150) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields:
% 22.00/5.62 | (414) ? [v0] : ? [v1] : (relation_inverse(empty_set) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = empty_set & relation_dom(empty_set) = v1)
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (178) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields:
% 22.00/5.62 | (415) ? [v0] : (relation_dom(empty_set) = v0 & relation_image(empty_set, v0) = empty_set)
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (182) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields:
% 22.00/5.62 | (416) ? [v0] : (relation_dom(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, empty_set) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = empty_set | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, empty_set) = v3 & relation_rng(v3) = empty_set)))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (268) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields:
% 22.00/5.62 | (417) ? [v0] : (relation_dom(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(empty_set, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(empty_set, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v2) | ~ relation(v1) | ? [v3] : (relation_composition(empty_set, v1) = v3 & relation_dom(v3) = v0)))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (273) with empty_set, empty_set and discharging atoms relation_rng(empty_set) = empty_set, relation(empty_set), yields:
% 22.00/5.62 | (418) ? [v0] : (relation_dom(empty_set) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | subset(empty_set, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(empty_set, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(empty_set, v3))))
% 22.00/5.62 |
% 22.00/5.62 | Instantiating formula (218) with all_0_10_10, all_0_14_14, all_0_11_11 and discharging atoms apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.62 | (419) ? [v0] : (relation_dom(all_0_14_14) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_14_14, v1) = v2) | ~ (apply(v2, all_0_11_11) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_11_11, v0) | apply(v1, all_0_10_10) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_10_10) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_11_11, v0) | ? [v3] : (relation_composition(all_0_14_14, v1) = v3 & apply(v3, all_0_11_11) = v2)))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (84) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, one_to_one(all_0_14_14), relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.63 | (420) ? [v0] : ? [v1] : (relation_rng(all_0_12_12) = v1 & relation_rng(all_0_14_14) = v0 & relation_dom(all_0_12_12) = v0 & relation_dom(all_0_14_14) = v1)
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (38) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, one_to_one(all_0_14_14), relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.63 | (421) ? [v0] : ? [v1] : (relation_rng(all_0_14_14) = v0 & relation_dom(all_0_14_14) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (relation_dom(all_0_12_12) = v2) | ~ (apply(all_0_12_12, v3) = v5) | ~ (apply(all_0_14_14, v4) = v3) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v4, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_dom(all_0_12_12) = v2) | ~ (apply(all_0_12_12, v3) = v4) | ~ (apply(all_0_14_14, v4) = v5) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v3, v0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(all_0_12_12) = v2) | ~ (apply(all_0_12_12, v3) = v5) | ~ (apply(all_0_14_14, v4) = v3) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v4, v1) | in(v3, v0)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(all_0_12_12) = v2) | ~ (apply(all_0_12_12, v3) = v4) | ~ (apply(all_0_14_14, v4) = v5) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v3, v0) | in(v4, v1)) & ! [v2] : (v2 = v0 | ~ (relation_dom(all_0_12_12) = v2) | ~ relation(all_0_12_12) | ~ function(all_0_12_12)) & ! [v2] : (v2 = all_0_12_12 | ~ (relation_dom(v2) = v0) | ~ relation(v2) | ~ function(v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (apply(v2, v3) = v5 & apply(all_0_14_14, v4) = v6 & ((v6 = v3 & in(v4, v1) & ( ~ (v5 = v4) | ~ in(v3, v0))) | (v5 = v4 & in(v3, v0) & ( ~ (v6 = v3) | ~ in(v4, v1)))))))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (80) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.63 | (422) relation(all_0_12_12)
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (333) with all_0_12_12, all_0_14_14 and discharging atoms function_inverse(all_0_14_14) = all_0_12_12, relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.63 | (423) function(all_0_12_12)
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (295) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, one_to_one(all_0_14_14), relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.63 | (424) ? [v0] : ? [v1] : (function_inverse(all_0_14_14) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = all_0_13_13 & relation_dom(all_0_14_14) = v1)
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (152) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, one_to_one(all_0_14_14), relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.63 | (425) ? [v0] : ? [v1] : (function_inverse(all_0_14_14) = v0 & relation_dom(all_0_14_14) = v1 & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v4 | ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v5) | ~ (apply(all_0_14_14, v4) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v1)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = v3 | ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v4) | ~ (apply(all_0_14_14, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v3, all_0_13_13)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v5) | ~ (apply(all_0_14_14, v4) = v3) | ~ relation(v0) | ~ function(v0) | ~ in(v4, v1) | in(v3, all_0_13_13)) & ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v0) = v2) | ~ (apply(v0, v3) = v4) | ~ (apply(all_0_14_14, v4) = v5) | ~ relation(v0) | ~ function(v0) | ~ in(v3, all_0_13_13) | in(v4, v1)) & ! [v2] : (v2 = v0 | ~ (relation_dom(v2) = all_0_13_13) | ~ relation(v2) | ~ function(v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (apply(v2, v3) = v5 & apply(all_0_14_14, v4) = v6 & ((v6 = v3 & in(v4, v1) & ( ~ (v5 = v4) | ~ in(v3, all_0_13_13))) | (v5 = v4 & in(v3, all_0_13_13) & ( ~ (v6 = v3) | ~ in(v4, v1)))))) & ! [v2] : (v2 = all_0_13_13 | ~ (relation_dom(v0) = v2) | ~ relation(v0) | ~ function(v0)))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating formula (241) with all_0_10_10, all_0_14_14, empty_set, empty_set, all_0_11_11 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation(all_0_14_14), relation(empty_set), function(all_0_14_14), function(empty_set), yields:
% 22.00/5.63 | (426) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_14_14, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_14_14) = v2 & ( ~ in(all_0_10_10, empty_set) | ~ in(all_0_11_11, v2) | in(all_0_11_11, v1)) & ( ~ in(all_0_11_11, v1) | (in(all_0_10_10, empty_set) & in(all_0_11_11, v2))))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (419) with all_86_0_62 yields:
% 22.00/5.63 | (427) relation_dom(all_0_14_14) = all_86_0_62 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ~ (apply(v1, all_0_11_11) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_86_0_62) | apply(v0, all_0_10_10) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_10_10) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_86_0_62) | ? [v2] : (relation_composition(all_0_14_14, v0) = v2 & apply(v2, all_0_11_11) = v1))
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (427) yields:
% 22.00/5.63 | (428) relation_dom(all_0_14_14) = all_86_0_62
% 22.00/5.63 | (429) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ~ (apply(v1, all_0_11_11) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_86_0_62) | apply(v0, all_0_10_10) = v2)
% 22.00/5.63 | (430) ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_10_10) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_11_11, all_86_0_62) | ? [v2] : (relation_composition(all_0_14_14, v0) = v2 & apply(v2, all_0_11_11) = v1))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (411) with all_91_0_64 yields:
% 22.00/5.63 | (431) relation_dom(all_0_14_14) = all_91_0_64 & ( ~ (all_91_0_64 = empty_set) | all_0_13_13 = empty_set) & ( ~ (all_0_13_13 = empty_set) | all_91_0_64 = empty_set)
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (431) yields:
% 22.00/5.63 | (432) relation_dom(all_0_14_14) = all_91_0_64
% 22.00/5.63 | (433) ~ (all_91_0_64 = empty_set) | all_0_13_13 = empty_set
% 22.00/5.63 | (434) ~ (all_0_13_13 = empty_set) | all_91_0_64 = empty_set
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (409) with all_93_0_65 yields:
% 22.00/5.63 | (435) relation_dom(all_0_14_14) = all_93_0_65 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_93_0_65 | ~ subset(all_0_13_13, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_13_13, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_14_14, v0) = v2 & relation_dom(v2) = all_93_0_65))
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (435) yields:
% 22.00/5.63 | (436) relation_dom(all_0_14_14) = all_93_0_65
% 22.00/5.63 | (437) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_14_14, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_93_0_65 | ~ subset(all_0_13_13, v2))))
% 22.00/5.63 | (438) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_13_13, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_14_14, v0) = v2 & relation_dom(v2) = all_93_0_65))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (407) with all_96_0_66 yields:
% 22.00/5.63 | (439) relation_dom(all_0_14_14) = all_96_0_66 & relation_image(all_0_14_14, all_96_0_66) = all_0_13_13
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (439) yields:
% 22.00/5.63 | (440) relation_dom(all_0_14_14) = all_96_0_66
% 22.00/5.63 | (441) relation_image(all_0_14_14, all_96_0_66) = all_0_13_13
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (406) with all_100_0_68, all_100_1_69 yields:
% 22.00/5.63 | (442) relation_inverse(all_0_14_14) = all_100_1_69 & relation_rng(all_100_1_69) = all_100_0_68 & relation_dom(all_100_1_69) = all_0_13_13 & relation_dom(all_0_14_14) = all_100_0_68
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (442) yields:
% 22.00/5.63 | (443) relation_inverse(all_0_14_14) = all_100_1_69
% 22.00/5.63 | (444) relation_rng(all_100_1_69) = all_100_0_68
% 22.00/5.63 | (445) relation_dom(all_100_1_69) = all_0_13_13
% 22.00/5.63 | (446) relation_dom(all_0_14_14) = all_100_0_68
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (408) with all_102_0_70 yields:
% 22.00/5.63 | (447) relation_dom(all_0_14_14) = all_102_0_70 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_14_14) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_0_13_13 | ~ subset(all_102_0_70, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_102_0_70, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_14_14) = v2 & relation_rng(v2) = all_0_13_13))
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (447) yields:
% 22.00/5.63 | (448) relation_dom(all_0_14_14) = all_102_0_70
% 22.00/5.63 | (449) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_14_14) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_0_13_13 | ~ subset(all_102_0_70, v2))))
% 22.00/5.63 | (450) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_102_0_70, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_14_14) = v2 & relation_rng(v2) = all_0_13_13))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (410) with all_105_0_71 yields:
% 22.00/5.63 | (451) relation_dom(all_0_14_14) = all_105_0_71 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_0_13_13, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_105_0_71, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_105_0_71, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_13_13, v2)))
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (451) yields:
% 22.00/5.63 | (452) relation_dom(all_0_14_14) = all_105_0_71
% 22.00/5.63 | (453) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_0_13_13, v2)))
% 22.00/5.63 | (454) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_105_0_71, v2)))
% 22.00/5.63 | (455) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_105_0_71, v1))
% 22.00/5.63 | (456) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_0_13_13, v1))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (418) with all_110_0_74 yields:
% 22.00/5.63 | (457) relation_dom(empty_set) = all_110_0_74 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_110_0_74, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_110_0_74, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(empty_set, v2)))
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (457) yields:
% 22.00/5.63 | (458) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(empty_set, v1))
% 22.00/5.63 | (459) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | subset(all_110_0_74, v1))
% 22.00/5.63 | (460) relation_dom(empty_set) = all_110_0_74
% 22.00/5.63 | (461) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_110_0_74, v2)))
% 22.00/5.63 | (462) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(empty_set, v2)))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (417) with all_113_0_75 yields:
% 22.00/5.63 | (463) relation_dom(empty_set) = all_113_0_75 & ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_113_0_75 | ~ subset(empty_set, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = all_113_0_75))
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (463) yields:
% 22.00/5.63 | (464) relation_dom(empty_set) = all_113_0_75
% 22.00/5.63 | (465) ! [v0] : ! [v1] : ( ~ (relation_composition(empty_set, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_113_0_75 | ~ subset(empty_set, v2))))
% 22.00/5.63 | (466) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(empty_set, v1) | ~ relation(v0) | ? [v2] : (relation_composition(empty_set, v0) = v2 & relation_dom(v2) = all_113_0_75))
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (415) with all_119_0_77 yields:
% 22.00/5.63 | (467) relation_dom(empty_set) = all_119_0_77 & relation_image(empty_set, all_119_0_77) = empty_set
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (467) yields:
% 22.00/5.63 | (468) relation_dom(empty_set) = all_119_0_77
% 22.00/5.63 | (469) relation_image(empty_set, all_119_0_77) = empty_set
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (414) with all_121_0_78, all_121_1_79 yields:
% 22.00/5.63 | (470) relation_inverse(empty_set) = all_121_1_79 & relation_rng(all_121_1_79) = all_121_0_78 & relation_dom(all_121_1_79) = empty_set & relation_dom(empty_set) = all_121_0_78
% 22.00/5.63 |
% 22.00/5.63 | Applying alpha-rule on (470) yields:
% 22.00/5.63 | (471) relation_inverse(empty_set) = all_121_1_79
% 22.00/5.63 | (472) relation_rng(all_121_1_79) = all_121_0_78
% 22.00/5.63 | (473) relation_dom(all_121_1_79) = empty_set
% 22.00/5.63 | (474) relation_dom(empty_set) = all_121_0_78
% 22.00/5.63 |
% 22.00/5.63 | Instantiating (425) with all_123_0_80, all_123_1_81 yields:
% 22.00/5.63 | (475) function_inverse(all_0_14_14) = all_123_1_81 & relation_dom(all_0_14_14) = all_123_0_80 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v2, all_123_0_80)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v1, all_0_13_13)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v2, all_123_0_80) | in(v1, all_0_13_13)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v1, all_0_13_13) | in(v2, all_123_0_80)) & ! [v0] : (v0 = all_123_1_81 | ~ (relation_dom(v0) = all_0_13_13) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_14_14, v2) = v4 & ((v4 = v1 & in(v2, all_123_0_80) & ( ~ (v3 = v2) | ~ in(v1, all_0_13_13))) | (v3 = v2 & in(v1, all_0_13_13) & ( ~ (v4 = v1) | ~ in(v2, all_123_0_80)))))) & ! [v0] : (v0 = all_0_13_13 | ~ (relation_dom(all_123_1_81) = v0) | ~ relation(all_123_1_81) | ~ function(all_123_1_81))
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (475) yields:
% 22.00/5.64 | (476) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v2, all_123_0_80) | in(v1, all_0_13_13))
% 22.00/5.64 | (477) function_inverse(all_0_14_14) = all_123_1_81
% 22.00/5.64 | (478) ! [v0] : (v0 = all_0_13_13 | ~ (relation_dom(all_123_1_81) = v0) | ~ relation(all_123_1_81) | ~ function(all_123_1_81))
% 22.00/5.64 | (479) ! [v0] : (v0 = all_123_1_81 | ~ (relation_dom(v0) = all_0_13_13) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_14_14, v2) = v4 & ((v4 = v1 & in(v2, all_123_0_80) & ( ~ (v3 = v2) | ~ in(v1, all_0_13_13))) | (v3 = v2 & in(v1, all_0_13_13) & ( ~ (v4 = v1) | ~ in(v2, all_123_0_80))))))
% 22.00/5.64 | (480) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v2, all_123_0_80))
% 22.00/5.64 | (481) relation_dom(all_0_14_14) = all_123_0_80
% 22.00/5.64 | (482) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v1, all_0_13_13))
% 22.00/5.64 | (483) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_123_1_81) = v0) | ~ (apply(all_123_1_81, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | ~ in(v1, all_0_13_13) | in(v2, all_123_0_80))
% 22.00/5.64 |
% 22.00/5.64 | Instantiating (424) with all_130_0_86, all_130_1_87 yields:
% 22.00/5.64 | (484) function_inverse(all_0_14_14) = all_130_1_87 & relation_rng(all_130_1_87) = all_130_0_86 & relation_dom(all_130_1_87) = all_0_13_13 & relation_dom(all_0_14_14) = all_130_0_86
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (484) yields:
% 22.00/5.64 | (485) function_inverse(all_0_14_14) = all_130_1_87
% 22.00/5.64 | (486) relation_rng(all_130_1_87) = all_130_0_86
% 22.00/5.64 | (487) relation_dom(all_130_1_87) = all_0_13_13
% 22.00/5.64 | (488) relation_dom(all_0_14_14) = all_130_0_86
% 22.00/5.64 |
% 22.00/5.64 | Instantiating (413) with all_132_0_88, all_132_1_89 yields:
% 22.00/5.64 | (489) relation_composition(all_0_14_14, empty_set) = all_132_1_89 & relation_rng(all_132_1_89) = all_132_0_88 & subset(all_132_0_88, empty_set)
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (489) yields:
% 22.00/5.64 | (490) relation_composition(all_0_14_14, empty_set) = all_132_1_89
% 22.00/5.64 | (491) relation_rng(all_132_1_89) = all_132_0_88
% 22.00/5.64 | (492) subset(all_132_0_88, empty_set)
% 22.00/5.64 |
% 22.00/5.64 | Instantiating (416) with all_136_0_92 yields:
% 22.00/5.64 | (493) relation_dom(empty_set) = all_136_0_92 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = empty_set | ~ subset(all_136_0_92, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_136_0_92, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = empty_set))
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (493) yields:
% 22.00/5.64 | (494) relation_dom(empty_set) = all_136_0_92
% 22.00/5.64 | (495) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, empty_set) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = empty_set | ~ subset(all_136_0_92, v2))))
% 22.00/5.64 | (496) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_136_0_92, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, empty_set) = v2 & relation_rng(v2) = empty_set))
% 22.00/5.64 |
% 22.00/5.64 | Instantiating (421) with all_149_0_103, all_149_1_104 yields:
% 22.00/5.64 | (497) relation_rng(all_0_14_14) = all_149_1_104 & relation_dom(all_0_14_14) = all_149_0_103 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_149_0_103)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_149_1_104)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_149_0_103) | in(v1, all_149_1_104)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_149_1_104) | in(v2, all_149_0_103)) & ! [v0] : (v0 = all_149_1_104 | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12)) & ! [v0] : (v0 = all_0_12_12 | ~ (relation_dom(v0) = all_149_1_104) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_14_14, v2) = v4 & ((v4 = v1 & in(v2, all_149_0_103) & ( ~ (v3 = v2) | ~ in(v1, all_149_1_104))) | (v3 = v2 & in(v1, all_149_1_104) & ( ~ (v4 = v1) | ~ in(v2, all_149_0_103))))))
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (497) yields:
% 22.00/5.64 | (498) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_149_1_104) | in(v2, all_149_0_103))
% 22.00/5.64 | (499) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_149_0_103) | in(v1, all_149_1_104))
% 22.00/5.64 | (500) relation_dom(all_0_14_14) = all_149_0_103
% 22.00/5.64 | (501) ! [v0] : (v0 = all_0_12_12 | ~ (relation_dom(v0) = all_149_1_104) | ~ relation(v0) | ~ function(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (apply(v0, v1) = v3 & apply(all_0_14_14, v2) = v4 & ((v4 = v1 & in(v2, all_149_0_103) & ( ~ (v3 = v2) | ~ in(v1, all_149_1_104))) | (v3 = v2 & in(v1, all_149_1_104) & ( ~ (v4 = v1) | ~ in(v2, all_149_0_103))))))
% 22.00/5.64 | (502) relation_rng(all_0_14_14) = all_149_1_104
% 22.00/5.64 | (503) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v3) | ~ (apply(all_0_14_14, v2) = v1) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v2, all_149_0_103))
% 22.00/5.64 | (504) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (relation_dom(all_0_12_12) = v0) | ~ (apply(all_0_12_12, v1) = v2) | ~ (apply(all_0_14_14, v2) = v3) | ~ relation(all_0_12_12) | ~ function(all_0_12_12) | ~ in(v1, all_149_1_104))
% 22.00/5.64 | (505) ! [v0] : (v0 = all_149_1_104 | ~ (relation_dom(all_0_12_12) = v0) | ~ relation(all_0_12_12) | ~ function(all_0_12_12))
% 22.00/5.64 |
% 22.00/5.64 | Instantiating (420) with all_152_0_105, all_152_1_106 yields:
% 22.00/5.64 | (506) relation_rng(all_0_12_12) = all_152_0_105 & relation_rng(all_0_14_14) = all_152_1_106 & relation_dom(all_0_12_12) = all_152_1_106 & relation_dom(all_0_14_14) = all_152_0_105
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (506) yields:
% 22.00/5.64 | (507) relation_rng(all_0_12_12) = all_152_0_105
% 22.00/5.64 | (508) relation_rng(all_0_14_14) = all_152_1_106
% 22.00/5.64 | (509) relation_dom(all_0_12_12) = all_152_1_106
% 22.00/5.64 | (510) relation_dom(all_0_14_14) = all_152_0_105
% 22.00/5.64 |
% 22.00/5.64 | Instantiating (426) with all_159_0_110, all_159_1_111, all_159_2_112 yields:
% 22.00/5.64 | (511) relation_composition(all_0_14_14, empty_set) = all_159_2_112 & relation_dom(all_159_2_112) = all_159_1_111 & relation_dom(all_0_14_14) = all_159_0_110 & ( ~ in(all_0_10_10, empty_set) | ~ in(all_0_11_11, all_159_0_110) | in(all_0_11_11, all_159_1_111)) & ( ~ in(all_0_11_11, all_159_1_111) | (in(all_0_10_10, empty_set) & in(all_0_11_11, all_159_0_110)))
% 22.00/5.64 |
% 22.00/5.64 | Applying alpha-rule on (511) yields:
% 22.00/5.64 | (512) relation_dom(all_159_2_112) = all_159_1_111
% 22.00/5.64 | (513) ~ in(all_0_11_11, all_159_1_111) | (in(all_0_10_10, empty_set) & in(all_0_11_11, all_159_0_110))
% 22.00/5.64 | (514) relation_composition(all_0_14_14, empty_set) = all_159_2_112
% 22.00/5.64 | (515) relation_dom(all_0_14_14) = all_159_0_110
% 22.00/5.64 | (516) ~ in(all_0_10_10, empty_set) | ~ in(all_0_11_11, all_159_0_110) | in(all_0_11_11, all_159_1_111)
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (238) with all_0_14_14, all_130_1_87, all_0_12_12 and discharging atoms function_inverse(all_0_14_14) = all_130_1_87, function_inverse(all_0_14_14) = all_0_12_12, yields:
% 22.00/5.64 | (517) all_130_1_87 = all_0_12_12
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (238) with all_0_14_14, all_123_1_81, all_130_1_87 and discharging atoms function_inverse(all_0_14_14) = all_130_1_87, function_inverse(all_0_14_14) = all_123_1_81, yields:
% 22.00/5.64 | (518) all_130_1_87 = all_123_1_81
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (115) with all_0_14_14, empty_set, all_132_1_89, all_159_2_112 and discharging atoms relation_composition(all_0_14_14, empty_set) = all_159_2_112, relation_composition(all_0_14_14, empty_set) = all_132_1_89, yields:
% 22.00/5.64 | (519) all_159_2_112 = all_132_1_89
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (136) with all_0_14_14, all_152_1_106, all_0_13_13 and discharging atoms relation_rng(all_0_14_14) = all_152_1_106, relation_rng(all_0_14_14) = all_0_13_13, yields:
% 22.00/5.64 | (520) all_152_1_106 = all_0_13_13
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_123_0_80, all_159_0_110 and discharging atoms relation_dom(all_0_14_14) = all_159_0_110, relation_dom(all_0_14_14) = all_123_0_80, yields:
% 22.00/5.64 | (521) all_159_0_110 = all_123_0_80
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_105_0_71, all_152_0_105 and discharging atoms relation_dom(all_0_14_14) = all_152_0_105, relation_dom(all_0_14_14) = all_105_0_71, yields:
% 22.00/5.64 | (522) all_152_0_105 = all_105_0_71
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_105_0_71, all_130_0_86 and discharging atoms relation_dom(all_0_14_14) = all_130_0_86, relation_dom(all_0_14_14) = all_105_0_71, yields:
% 22.00/5.64 | (523) all_130_0_86 = all_105_0_71
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_102_0_70, all_159_0_110 and discharging atoms relation_dom(all_0_14_14) = all_159_0_110, relation_dom(all_0_14_14) = all_102_0_70, yields:
% 22.00/5.64 | (524) all_159_0_110 = all_102_0_70
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_102_0_70, all_149_0_103 and discharging atoms relation_dom(all_0_14_14) = all_149_0_103, relation_dom(all_0_14_14) = all_102_0_70, yields:
% 22.00/5.64 | (525) all_149_0_103 = all_102_0_70
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_100_0_68, all_149_0_103 and discharging atoms relation_dom(all_0_14_14) = all_149_0_103, relation_dom(all_0_14_14) = all_100_0_68, yields:
% 22.00/5.64 | (526) all_149_0_103 = all_100_0_68
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_96_0_66, all_105_0_71 and discharging atoms relation_dom(all_0_14_14) = all_105_0_71, relation_dom(all_0_14_14) = all_96_0_66, yields:
% 22.00/5.64 | (527) all_105_0_71 = all_96_0_66
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_96_0_66, all_102_0_70 and discharging atoms relation_dom(all_0_14_14) = all_102_0_70, relation_dom(all_0_14_14) = all_96_0_66, yields:
% 22.00/5.64 | (528) all_102_0_70 = all_96_0_66
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_93_0_65, all_152_0_105 and discharging atoms relation_dom(all_0_14_14) = all_152_0_105, relation_dom(all_0_14_14) = all_93_0_65, yields:
% 22.00/5.64 | (529) all_152_0_105 = all_93_0_65
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_91_0_64, all_159_0_110 and discharging atoms relation_dom(all_0_14_14) = all_159_0_110, relation_dom(all_0_14_14) = all_91_0_64, yields:
% 22.00/5.64 | (530) all_159_0_110 = all_91_0_64
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with all_0_14_14, all_86_0_62, all_130_0_86 and discharging atoms relation_dom(all_0_14_14) = all_130_0_86, relation_dom(all_0_14_14) = all_86_0_62, yields:
% 22.00/5.64 | (531) all_130_0_86 = all_86_0_62
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with empty_set, all_121_0_78, empty_set and discharging atoms relation_dom(empty_set) = all_121_0_78, relation_dom(empty_set) = empty_set, yields:
% 22.00/5.64 | (532) all_121_0_78 = empty_set
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with empty_set, all_121_0_78, all_136_0_92 and discharging atoms relation_dom(empty_set) = all_136_0_92, relation_dom(empty_set) = all_121_0_78, yields:
% 22.00/5.64 | (533) all_136_0_92 = all_121_0_78
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with empty_set, all_119_0_77, all_121_0_78 and discharging atoms relation_dom(empty_set) = all_121_0_78, relation_dom(empty_set) = all_119_0_77, yields:
% 22.00/5.64 | (534) all_121_0_78 = all_119_0_77
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with empty_set, all_113_0_75, all_136_0_92 and discharging atoms relation_dom(empty_set) = all_136_0_92, relation_dom(empty_set) = all_113_0_75, yields:
% 22.00/5.64 | (535) all_136_0_92 = all_113_0_75
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (143) with empty_set, all_110_0_74, all_136_0_92 and discharging atoms relation_dom(empty_set) = all_136_0_92, relation_dom(empty_set) = all_110_0_74, yields:
% 22.00/5.64 | (536) all_136_0_92 = all_110_0_74
% 22.00/5.64 |
% 22.00/5.64 | Instantiating formula (505) with all_152_1_106 and discharging atoms relation_dom(all_0_12_12) = all_152_1_106, relation(all_0_12_12), function(all_0_12_12), yields:
% 22.00/5.64 | (537) all_152_1_106 = all_149_1_104
% 22.00/5.64 |
% 22.00/5.64 | Combining equations (530,521) yields a new equation:
% 22.00/5.64 | (538) all_123_0_80 = all_91_0_64
% 22.00/5.64 |
% 22.00/5.64 | Combining equations (524,521) yields a new equation:
% 22.00/5.64 | (539) all_123_0_80 = all_102_0_70
% 22.00/5.64 |
% 22.00/5.64 | Combining equations (522,529) yields a new equation:
% 22.00/5.64 | (540) all_105_0_71 = all_93_0_65
% 22.00/5.64 |
% 22.00/5.64 | Simplifying 540 yields:
% 22.00/5.64 | (541) all_105_0_71 = all_93_0_65
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (537,520) yields a new equation:
% 22.00/5.65 | (542) all_149_1_104 = all_0_13_13
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 542 yields:
% 22.00/5.65 | (543) all_149_1_104 = all_0_13_13
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (525,526) yields a new equation:
% 22.00/5.65 | (544) all_102_0_70 = all_100_0_68
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 544 yields:
% 22.00/5.65 | (545) all_102_0_70 = all_100_0_68
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (536,535) yields a new equation:
% 22.00/5.65 | (546) all_113_0_75 = all_110_0_74
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (533,535) yields a new equation:
% 22.00/5.65 | (547) all_121_0_78 = all_113_0_75
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 547 yields:
% 22.00/5.65 | (548) all_121_0_78 = all_113_0_75
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (523,531) yields a new equation:
% 22.00/5.65 | (549) all_105_0_71 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 549 yields:
% 22.00/5.65 | (550) all_105_0_71 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (518,517) yields a new equation:
% 22.00/5.65 | (551) all_123_1_81 = all_0_12_12
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 551 yields:
% 22.00/5.65 | (552) all_123_1_81 = all_0_12_12
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (539,538) yields a new equation:
% 22.00/5.65 | (553) all_102_0_70 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 553 yields:
% 22.00/5.65 | (554) all_102_0_70 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (548,534) yields a new equation:
% 22.00/5.65 | (555) all_119_0_77 = all_113_0_75
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (532,534) yields a new equation:
% 22.00/5.65 | (556) all_119_0_77 = empty_set
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (555,556) yields a new equation:
% 22.00/5.65 | (557) all_113_0_75 = empty_set
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 557 yields:
% 22.00/5.65 | (558) all_113_0_75 = empty_set
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (546,558) yields a new equation:
% 22.00/5.65 | (559) all_110_0_74 = empty_set
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 559 yields:
% 22.00/5.65 | (560) all_110_0_74 = empty_set
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (550,541) yields a new equation:
% 22.00/5.65 | (561) all_93_0_65 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (527,541) yields a new equation:
% 22.00/5.65 | (562) all_96_0_66 = all_93_0_65
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 562 yields:
% 22.00/5.65 | (563) all_96_0_66 = all_93_0_65
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (528,545) yields a new equation:
% 22.00/5.65 | (564) all_100_0_68 = all_96_0_66
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (554,545) yields a new equation:
% 22.00/5.65 | (565) all_100_0_68 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (564,565) yields a new equation:
% 22.00/5.65 | (566) all_96_0_66 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 566 yields:
% 22.00/5.65 | (567) all_96_0_66 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (563,567) yields a new equation:
% 22.00/5.65 | (568) all_93_0_65 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Simplifying 568 yields:
% 22.00/5.65 | (569) all_93_0_65 = all_91_0_64
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (561,569) yields a new equation:
% 22.00/5.65 | (570) all_91_0_64 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (570,569) yields a new equation:
% 22.00/5.65 | (561) all_93_0_65 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (561,541) yields a new equation:
% 22.00/5.65 | (550) all_105_0_71 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (570,538) yields a new equation:
% 22.00/5.65 | (573) all_123_0_80 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | Combining equations (561,529) yields a new equation:
% 22.00/5.65 | (574) all_152_0_105 = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | From (519) and (514) follows:
% 22.00/5.65 | (490) relation_composition(all_0_14_14, empty_set) = all_132_1_89
% 22.00/5.65 |
% 22.00/5.65 | From (574) and (507) follows:
% 22.00/5.65 | (576) relation_rng(all_0_12_12) = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | From (543) and (502) follows:
% 22.00/5.65 | (203) relation_rng(all_0_14_14) = all_0_13_13
% 22.00/5.65 |
% 22.00/5.65 | From (520) and (509) follows:
% 22.00/5.65 | (578) relation_dom(all_0_12_12) = all_0_13_13
% 22.00/5.65 |
% 22.00/5.65 | From (570) and (432) follows:
% 22.00/5.65 | (428) relation_dom(all_0_14_14) = all_86_0_62
% 22.00/5.65 |
% 22.00/5.65 | From (560) and (460) follows:
% 22.00/5.65 | (156) relation_dom(empty_set) = empty_set
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (504) with all_0_10_10, all_0_11_11, all_0_15_15, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_0_13_13, apply(all_0_12_12, all_0_15_15) = all_0_11_11, apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation(all_0_12_12), function(all_0_12_12), yields:
% 22.00/5.65 | (581) all_0_10_10 = all_0_15_15 | ~ in(all_0_15_15, all_149_1_104)
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (396) with all_132_1_89, all_0_14_14, empty_set, empty_set and discharging atoms relation_composition(all_0_14_14, empty_set) = all_132_1_89, relation_dom(empty_set) = empty_set, relation(all_0_14_14), relation(empty_set), function(all_0_14_14), function(empty_set), yields:
% 22.00/5.65 | (582) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_132_1_89) = v0 & relation_dom(all_0_14_14) = v1 & apply(all_0_14_14, all_56_0_51) = v2 & ( ~ in(v2, empty_set) | ~ in(all_56_0_51, v1) | in(all_56_0_51, v0)) & ( ~ in(all_56_0_51, v0) | (in(v2, empty_set) & in(all_56_0_51, v1))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (286) with all_0_10_10, all_0_11_11, all_86_0_62, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_86_0_62, apply(all_0_14_14, all_0_11_11) = all_0_10_10, relation(all_0_14_14), function(all_0_14_14), yields:
% 22.00/5.65 | (583) all_0_10_10 = empty_set | in(all_0_11_11, all_86_0_62)
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (165) with all_86_0_62, all_0_14_14 and discharging atoms relation_dom(all_0_14_14) = all_86_0_62, relation(all_0_14_14), yields:
% 22.00/5.65 | (584) ? [v0] : (relation_rng(all_0_14_14) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(all_86_0_62, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | subset(all_86_0_62, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_14_14, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v0, v3))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (454) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, subset(all_0_14_14, all_0_14_14), relation(all_0_14_14), yields:
% 22.00/5.65 | (585) ? [v0] : (relation_dom(all_0_14_14) = v0 & subset(all_105_0_71, v0))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (131) with all_0_9_9, all_0_14_14, all_0_13_13, all_0_12_12 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation_dom(all_0_12_12) = all_0_13_13, relation(all_0_12_12), relation(all_0_14_14), yields:
% 22.00/5.65 | (586) ? [v0] : (relation_dom(all_0_9_9) = v0 & subset(v0, all_0_13_13))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (150) with all_86_0_62, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_86_0_62, relation(all_0_12_12), yields:
% 22.00/5.65 | (587) ? [v0] : ? [v1] : (relation_inverse(all_0_12_12) = v0 & relation_rng(v0) = v1 & relation_dom(v0) = all_86_0_62 & relation_dom(all_0_12_12) = v1)
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (178) with all_86_0_62, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_86_0_62, relation(all_0_12_12), yields:
% 22.00/5.65 | (588) ? [v0] : (relation_dom(all_0_12_12) = v0 & relation_image(all_0_12_12, v0) = all_86_0_62)
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (182) with all_86_0_62, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_86_0_62, relation(all_0_12_12), yields:
% 22.00/5.65 | (589) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(v1, all_0_12_12) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v4 & relation_rng(v1) = v3 & (v4 = all_86_0_62 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(v1, all_0_12_12) = v3 & relation_rng(v3) = all_86_0_62)))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (268) with all_86_0_62, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_86_0_62, relation(all_0_12_12), yields:
% 22.00/5.65 | (590) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_12_12, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = v0 | ~ subset(all_86_0_62, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_86_0_62, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_12_12, v1) = v3 & relation_dom(v3) = v0)))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (273) with all_86_0_62, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_86_0_62, relation(all_0_12_12), yields:
% 22.00/5.65 | (591) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | subset(all_86_0_62, v2)) & ! [v1] : ! [v2] : ( ~ (relation_rng(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v0, v3))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | subset(v0, v2)) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(all_0_12_12, v1) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(all_86_0_62, v3))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (122) with all_86_0_62, all_0_12_12 and discharging atoms relation_rng(all_0_12_12) = all_86_0_62, relation(all_0_12_12), yields:
% 22.00/5.65 | (592) ? [v0] : (relation_dom(all_0_12_12) = v0 & ( ~ (v0 = empty_set) | all_86_0_62 = empty_set) & ( ~ (all_86_0_62 = empty_set) | v0 = empty_set))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (174) with all_0_13_13, all_0_12_12 and discharging atoms relation_dom(all_0_12_12) = all_0_13_13, relation(all_0_12_12), yields:
% 22.00/5.65 | (593) ? [v0] : (relation_rng(all_0_12_12) = v0 & ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_12_12, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v4 & relation_dom(v1) = v3 & (v4 = all_0_13_13 | ~ subset(v0, v3)))) & ! [v1] : ! [v2] : ( ~ (relation_dom(v1) = v2) | ~ subset(v0, v2) | ~ relation(v1) | ? [v3] : (relation_composition(all_0_12_12, v1) = v3 & relation_dom(v3) = all_0_13_13)))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (149) with all_0_8_8, all_0_9_9, all_0_12_12, all_0_14_14, all_0_15_15 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, apply(all_0_9_9, all_0_15_15) = all_0_8_8, relation(all_0_12_12), relation(all_0_14_14), function(all_0_12_12), function(all_0_14_14), yields:
% 22.00/5.65 | (594) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_9_9) = v0 & apply(all_0_12_12, all_0_15_15) = v1 & apply(all_0_14_14, v1) = v2 & (v2 = all_0_8_8 | ~ in(all_0_15_15, v0)))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (396) with all_0_9_9, all_0_12_12, all_86_0_62, all_0_14_14 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation_dom(all_0_14_14) = all_86_0_62, relation(all_0_12_12), relation(all_0_14_14), function(all_0_12_12), function(all_0_14_14), yields:
% 22.00/5.65 | (595) ? [v0] : ? [v1] : ? [v2] : (relation_dom(all_0_9_9) = v0 & relation_dom(all_0_12_12) = v1 & apply(all_0_12_12, all_56_0_51) = v2 & ( ~ in(v2, all_86_0_62) | ~ in(all_56_0_51, v1) | in(all_56_0_51, v0)) & ( ~ in(all_56_0_51, v0) | (in(v2, all_86_0_62) & in(all_56_0_51, v1))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (395) with all_0_9_9, all_0_12_12, all_0_14_14 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_12_12), relation(all_0_14_14), function(all_0_12_12), function(all_0_14_14), yields:
% 22.00/5.65 | (596) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_9_9) = v0 & apply(all_0_9_9, all_28_0_36) = v1 & apply(all_0_12_12, all_28_0_36) = v2 & apply(all_0_14_14, v2) = v3 & (v3 = v1 | ~ in(all_28_0_36, v0)))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (241) with all_0_11_11, all_0_12_12, empty_set, empty_set, all_0_15_15 and discharging atoms relation_dom(empty_set) = empty_set, apply(all_0_12_12, all_0_15_15) = all_0_11_11, relation(all_0_12_12), relation(empty_set), function(all_0_12_12), function(empty_set), yields:
% 22.00/5.65 | (597) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, empty_set) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_11_11, empty_set) | ~ in(all_0_15_15, v2) | in(all_0_15_15, v1)) & ( ~ in(all_0_15_15, v1) | (in(all_0_11_11, empty_set) & in(all_0_15_15, v2))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (241) with all_0_11_11, all_0_12_12, all_0_13_13, all_0_12_12, all_0_15_15 and discharging atoms relation_dom(all_0_12_12) = all_0_13_13, apply(all_0_12_12, all_0_15_15) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 22.00/5.65 | (598) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_12_12) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_11_11, all_0_13_13) | ~ in(all_0_15_15, v2) | in(all_0_15_15, v1)) & ( ~ in(all_0_15_15, v1) | (in(all_0_11_11, all_0_13_13) & in(all_0_15_15, v2))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (241) with all_0_11_11, all_0_12_12, all_86_0_62, all_0_14_14, all_0_15_15 and discharging atoms relation_dom(all_0_14_14) = all_86_0_62, apply(all_0_12_12, all_0_15_15) = all_0_11_11, relation(all_0_12_12), relation(all_0_14_14), function(all_0_12_12), function(all_0_14_14), yields:
% 22.00/5.65 | (599) ? [v0] : ? [v1] : ? [v2] : (relation_composition(all_0_12_12, all_0_14_14) = v0 & relation_dom(v0) = v1 & relation_dom(all_0_12_12) = v2 & ( ~ in(all_0_11_11, all_86_0_62) | ~ in(all_0_15_15, v2) | in(all_0_15_15, v1)) & ( ~ in(all_0_15_15, v1) | (in(all_0_11_11, all_86_0_62) & in(all_0_15_15, v2))))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (218) with all_0_11_11, all_0_12_12, all_0_15_15 and discharging atoms apply(all_0_12_12, all_0_15_15) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 22.00/5.65 | (600) ? [v0] : (relation_dom(all_0_12_12) = v0 & ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(all_0_12_12, v1) = v2) | ~ (apply(v2, all_0_15_15) = v3) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_15_15, v0) | apply(v1, all_0_11_11) = v3) & ! [v1] : ! [v2] : ( ~ (apply(v1, all_0_11_11) = v2) | ~ relation(v1) | ~ function(v1) | ~ in(all_0_15_15, v0) | ? [v3] : (relation_composition(all_0_12_12, v1) = v3 & apply(v3, all_0_15_15) = v2)))
% 22.00/5.65 |
% 22.00/5.65 | Instantiating formula (483) with all_0_10_10, all_0_11_11, all_0_15_15, all_0_13_13 and discharging atoms apply(all_0_14_14, all_0_11_11) = all_0_10_10, in(all_0_15_15, all_0_13_13), yields:
% 22.00/5.65 | (601) ~ (relation_dom(all_123_1_81) = all_0_13_13) | ~ (apply(all_123_1_81, all_0_15_15) = all_0_11_11) | ~ relation(all_123_1_81) | ~ function(all_123_1_81) | in(all_0_11_11, all_123_0_80)
% 22.00/5.65 |
% 22.00/5.65 | Instantiating (593) with all_182_0_126 yields:
% 22.00/5.65 | (602) relation_rng(all_0_12_12) = all_182_0_126 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_0_13_13 | ~ subset(all_182_0_126, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_182_0_126, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_0_13_13))
% 22.00/5.65 |
% 22.00/5.65 | Applying alpha-rule on (602) yields:
% 22.00/5.65 | (603) relation_rng(all_0_12_12) = all_182_0_126
% 22.00/5.65 | (604) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_0_13_13 | ~ subset(all_182_0_126, v2))))
% 22.00/5.65 | (605) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_182_0_126, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_0_13_13))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating formula (604) with all_0_9_9, all_0_14_14 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_14_14), yields:
% 22.00/5.66 | (606) ? [v0] : ? [v1] : (relation_dom(all_0_9_9) = v1 & relation_dom(all_0_14_14) = v0 & (v1 = all_0_13_13 | ~ subset(all_182_0_126, v0)))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (592) with all_194_0_133 yields:
% 22.00/5.66 | (607) relation_dom(all_0_12_12) = all_194_0_133 & ( ~ (all_194_0_133 = empty_set) | all_86_0_62 = empty_set) & ( ~ (all_86_0_62 = empty_set) | all_194_0_133 = empty_set)
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (607) yields:
% 22.00/5.66 | (608) relation_dom(all_0_12_12) = all_194_0_133
% 22.00/5.66 | (609) ~ (all_194_0_133 = empty_set) | all_86_0_62 = empty_set
% 22.00/5.66 | (610) ~ (all_86_0_62 = empty_set) | all_194_0_133 = empty_set
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (591) with all_196_0_134 yields:
% 22.00/5.66 | (611) relation_dom(all_0_12_12) = all_196_0_134 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_86_0_62, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_196_0_134, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_196_0_134, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_86_0_62, v2)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (611) yields:
% 22.00/5.66 | (612) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_196_0_134, v2)))
% 22.00/5.66 | (613) relation_dom(all_0_12_12) = all_196_0_134
% 22.00/5.66 | (614) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_196_0_134, v1))
% 22.00/5.66 | (615) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | subset(all_86_0_62, v1))
% 22.00/5.66 | (616) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_12_12, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_86_0_62, v2)))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (597) with all_209_0_149, all_209_1_150, all_209_2_151 yields:
% 22.00/5.66 | (617) relation_composition(all_0_12_12, empty_set) = all_209_2_151 & relation_dom(all_209_2_151) = all_209_1_150 & relation_dom(all_0_12_12) = all_209_0_149 & ( ~ in(all_0_11_11, empty_set) | ~ in(all_0_15_15, all_209_0_149) | in(all_0_15_15, all_209_1_150)) & ( ~ in(all_0_15_15, all_209_1_150) | (in(all_0_11_11, empty_set) & in(all_0_15_15, all_209_0_149)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (617) yields:
% 22.00/5.66 | (618) relation_dom(all_0_12_12) = all_209_0_149
% 22.00/5.66 | (619) relation_dom(all_209_2_151) = all_209_1_150
% 22.00/5.66 | (620) ~ in(all_0_11_11, empty_set) | ~ in(all_0_15_15, all_209_0_149) | in(all_0_15_15, all_209_1_150)
% 22.00/5.66 | (621) ~ in(all_0_15_15, all_209_1_150) | (in(all_0_11_11, empty_set) & in(all_0_15_15, all_209_0_149))
% 22.00/5.66 | (622) relation_composition(all_0_12_12, empty_set) = all_209_2_151
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (584) with all_256_0_194 yields:
% 22.00/5.66 | (623) relation_rng(all_0_14_14) = all_256_0_194 & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_256_0_194, v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_86_0_62, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_86_0_62, v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_256_0_194, v2)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (623) yields:
% 22.00/5.66 | (624) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & subset(all_86_0_62, v2)))
% 22.00/5.66 | (625) relation_rng(all_0_14_14) = all_256_0_194
% 22.00/5.66 | (626) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_86_0_62, v1))
% 22.00/5.66 | (627) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & subset(all_256_0_194, v2)))
% 22.00/5.66 | (628) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_0_14_14, v0) | ~ relation(v0) | subset(all_256_0_194, v1))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating formula (624) with all_0_13_13, all_0_14_14 and discharging atoms relation_rng(all_0_14_14) = all_0_13_13, subset(all_0_14_14, all_0_14_14), relation(all_0_14_14), yields:
% 22.00/5.66 | (629) ? [v0] : (relation_dom(all_0_14_14) = v0 & subset(all_86_0_62, v0))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (598) with all_279_0_218, all_279_1_219, all_279_2_220 yields:
% 22.00/5.66 | (630) relation_composition(all_0_12_12, all_0_12_12) = all_279_2_220 & relation_dom(all_279_2_220) = all_279_1_219 & relation_dom(all_0_12_12) = all_279_0_218 & ( ~ in(all_0_11_11, all_0_13_13) | ~ in(all_0_15_15, all_279_0_218) | in(all_0_15_15, all_279_1_219)) & ( ~ in(all_0_15_15, all_279_1_219) | (in(all_0_11_11, all_0_13_13) & in(all_0_15_15, all_279_0_218)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (630) yields:
% 22.00/5.66 | (631) ~ in(all_0_11_11, all_0_13_13) | ~ in(all_0_15_15, all_279_0_218) | in(all_0_15_15, all_279_1_219)
% 22.00/5.66 | (632) relation_dom(all_0_12_12) = all_279_0_218
% 22.00/5.66 | (633) relation_dom(all_279_2_220) = all_279_1_219
% 22.00/5.66 | (634) relation_composition(all_0_12_12, all_0_12_12) = all_279_2_220
% 22.00/5.66 | (635) ~ in(all_0_15_15, all_279_1_219) | (in(all_0_11_11, all_0_13_13) & in(all_0_15_15, all_279_0_218))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (595) with all_281_0_221, all_281_1_222, all_281_2_223 yields:
% 22.00/5.66 | (636) relation_dom(all_0_9_9) = all_281_2_223 & relation_dom(all_0_12_12) = all_281_1_222 & apply(all_0_12_12, all_56_0_51) = all_281_0_221 & ( ~ in(all_281_0_221, all_86_0_62) | ~ in(all_56_0_51, all_281_1_222) | in(all_56_0_51, all_281_2_223)) & ( ~ in(all_56_0_51, all_281_2_223) | (in(all_281_0_221, all_86_0_62) & in(all_56_0_51, all_281_1_222)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (636) yields:
% 22.00/5.66 | (637) relation_dom(all_0_12_12) = all_281_1_222
% 22.00/5.66 | (638) ~ in(all_56_0_51, all_281_2_223) | (in(all_281_0_221, all_86_0_62) & in(all_56_0_51, all_281_1_222))
% 22.00/5.66 | (639) relation_dom(all_0_9_9) = all_281_2_223
% 22.00/5.66 | (640) apply(all_0_12_12, all_56_0_51) = all_281_0_221
% 22.00/5.66 | (641) ~ in(all_281_0_221, all_86_0_62) | ~ in(all_56_0_51, all_281_1_222) | in(all_56_0_51, all_281_2_223)
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (594) with all_283_0_224, all_283_1_225, all_283_2_226 yields:
% 22.00/5.66 | (642) relation_dom(all_0_9_9) = all_283_2_226 & apply(all_0_12_12, all_0_15_15) = all_283_1_225 & apply(all_0_14_14, all_283_1_225) = all_283_0_224 & (all_283_0_224 = all_0_8_8 | ~ in(all_0_15_15, all_283_2_226))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (642) yields:
% 22.00/5.66 | (643) relation_dom(all_0_9_9) = all_283_2_226
% 22.00/5.66 | (644) apply(all_0_12_12, all_0_15_15) = all_283_1_225
% 22.00/5.66 | (645) apply(all_0_14_14, all_283_1_225) = all_283_0_224
% 22.00/5.66 | (646) all_283_0_224 = all_0_8_8 | ~ in(all_0_15_15, all_283_2_226)
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (596) with all_310_0_249, all_310_1_250, all_310_2_251, all_310_3_252 yields:
% 22.00/5.66 | (647) relation_dom(all_0_9_9) = all_310_3_252 & apply(all_0_9_9, all_28_0_36) = all_310_2_251 & apply(all_0_12_12, all_28_0_36) = all_310_1_250 & apply(all_0_14_14, all_310_1_250) = all_310_0_249 & (all_310_0_249 = all_310_2_251 | ~ in(all_28_0_36, all_310_3_252))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (647) yields:
% 22.00/5.66 | (648) apply(all_0_12_12, all_28_0_36) = all_310_1_250
% 22.00/5.66 | (649) apply(all_0_9_9, all_28_0_36) = all_310_2_251
% 22.00/5.66 | (650) all_310_0_249 = all_310_2_251 | ~ in(all_28_0_36, all_310_3_252)
% 22.00/5.66 | (651) apply(all_0_14_14, all_310_1_250) = all_310_0_249
% 22.00/5.66 | (652) relation_dom(all_0_9_9) = all_310_3_252
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (586) with all_333_0_273 yields:
% 22.00/5.66 | (653) relation_dom(all_0_9_9) = all_333_0_273 & subset(all_333_0_273, all_0_13_13)
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (653) yields:
% 22.00/5.66 | (654) relation_dom(all_0_9_9) = all_333_0_273
% 22.00/5.66 | (655) subset(all_333_0_273, all_0_13_13)
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (590) with all_335_0_274 yields:
% 22.00/5.66 | (656) relation_dom(all_0_12_12) = all_335_0_274 & ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_335_0_274 | ~ subset(all_86_0_62, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_86_0_62, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_335_0_274))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (656) yields:
% 22.00/5.66 | (657) relation_dom(all_0_12_12) = all_335_0_274
% 22.00/5.66 | (658) ! [v0] : ! [v1] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation_dom(v0) = v2 & (v3 = all_335_0_274 | ~ subset(all_86_0_62, v2))))
% 22.00/5.66 | (659) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ subset(all_86_0_62, v1) | ~ relation(v0) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & relation_dom(v2) = all_335_0_274))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating formula (658) with all_0_9_9, all_0_14_14 and discharging atoms relation_composition(all_0_12_12, all_0_14_14) = all_0_9_9, relation(all_0_14_14), yields:
% 22.00/5.66 | (660) ? [v0] : ? [v1] : (relation_dom(all_0_9_9) = v1 & relation_dom(all_0_14_14) = v0 & (v1 = all_335_0_274 | ~ subset(all_86_0_62, v0)))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (589) with all_338_0_275 yields:
% 22.00/5.66 | (661) relation_dom(all_0_12_12) = all_338_0_275 & ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_12_12) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_86_0_62 | ~ subset(all_338_0_275, v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_338_0_275, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_12_12) = v2 & relation_rng(v2) = all_86_0_62))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (661) yields:
% 22.00/5.66 | (662) relation_dom(all_0_12_12) = all_338_0_275
% 22.00/5.66 | (663) ! [v0] : ! [v1] : ( ~ (relation_composition(v0, all_0_12_12) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & (v3 = all_86_0_62 | ~ subset(all_338_0_275, v2))))
% 22.00/5.66 | (664) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ subset(all_338_0_275, v1) | ~ relation(v0) | ? [v2] : (relation_composition(v0, all_0_12_12) = v2 & relation_rng(v2) = all_86_0_62))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (588) with all_343_0_278 yields:
% 22.00/5.66 | (665) relation_dom(all_0_12_12) = all_343_0_278 & relation_image(all_0_12_12, all_343_0_278) = all_86_0_62
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (665) yields:
% 22.00/5.66 | (666) relation_dom(all_0_12_12) = all_343_0_278
% 22.00/5.66 | (667) relation_image(all_0_12_12, all_343_0_278) = all_86_0_62
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (587) with all_345_0_279, all_345_1_280 yields:
% 22.00/5.66 | (668) relation_inverse(all_0_12_12) = all_345_1_280 & relation_rng(all_345_1_280) = all_345_0_279 & relation_dom(all_345_1_280) = all_86_0_62 & relation_dom(all_0_12_12) = all_345_0_279
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (668) yields:
% 22.00/5.66 | (669) relation_inverse(all_0_12_12) = all_345_1_280
% 22.00/5.66 | (670) relation_rng(all_345_1_280) = all_345_0_279
% 22.00/5.66 | (671) relation_dom(all_345_1_280) = all_86_0_62
% 22.00/5.66 | (672) relation_dom(all_0_12_12) = all_345_0_279
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (585) with all_372_0_308 yields:
% 22.00/5.66 | (673) relation_dom(all_0_14_14) = all_372_0_308 & subset(all_105_0_71, all_372_0_308)
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (673) yields:
% 22.00/5.66 | (674) relation_dom(all_0_14_14) = all_372_0_308
% 22.00/5.66 | (675) subset(all_105_0_71, all_372_0_308)
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (600) with all_404_0_338 yields:
% 22.00/5.66 | (676) relation_dom(all_0_12_12) = all_404_0_338 & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ (apply(v1, all_0_15_15) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_404_0_338) | apply(v0, all_0_11_11) = v2) & ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_11_11) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_404_0_338) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & apply(v2, all_0_15_15) = v1))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (676) yields:
% 22.00/5.66 | (677) relation_dom(all_0_12_12) = all_404_0_338
% 22.00/5.66 | (678) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(all_0_12_12, v0) = v1) | ~ (apply(v1, all_0_15_15) = v2) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_404_0_338) | apply(v0, all_0_11_11) = v2)
% 22.00/5.66 | (679) ! [v0] : ! [v1] : ( ~ (apply(v0, all_0_11_11) = v1) | ~ relation(v0) | ~ function(v0) | ~ in(all_0_15_15, all_404_0_338) | ? [v2] : (relation_composition(all_0_12_12, v0) = v2 & apply(v2, all_0_15_15) = v1))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (599) with all_413_0_349, all_413_1_350, all_413_2_351 yields:
% 22.00/5.66 | (680) relation_composition(all_0_12_12, all_0_14_14) = all_413_2_351 & relation_dom(all_413_2_351) = all_413_1_350 & relation_dom(all_0_12_12) = all_413_0_349 & ( ~ in(all_0_11_11, all_86_0_62) | ~ in(all_0_15_15, all_413_0_349) | in(all_0_15_15, all_413_1_350)) & ( ~ in(all_0_15_15, all_413_1_350) | (in(all_0_11_11, all_86_0_62) & in(all_0_15_15, all_413_0_349)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (680) yields:
% 22.00/5.66 | (681) ~ in(all_0_15_15, all_413_1_350) | (in(all_0_11_11, all_86_0_62) & in(all_0_15_15, all_413_0_349))
% 22.00/5.66 | (682) ~ in(all_0_11_11, all_86_0_62) | ~ in(all_0_15_15, all_413_0_349) | in(all_0_15_15, all_413_1_350)
% 22.00/5.66 | (683) relation_dom(all_0_12_12) = all_413_0_349
% 22.00/5.66 | (684) relation_composition(all_0_12_12, all_0_14_14) = all_413_2_351
% 22.00/5.66 | (685) relation_dom(all_413_2_351) = all_413_1_350
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (582) with all_421_0_359, all_421_1_360, all_421_2_361 yields:
% 22.00/5.66 | (686) relation_dom(all_132_1_89) = all_421_2_361 & relation_dom(all_0_14_14) = all_421_1_360 & apply(all_0_14_14, all_56_0_51) = all_421_0_359 & ( ~ in(all_421_0_359, empty_set) | ~ in(all_56_0_51, all_421_1_360) | in(all_56_0_51, all_421_2_361)) & ( ~ in(all_56_0_51, all_421_2_361) | (in(all_421_0_359, empty_set) & in(all_56_0_51, all_421_1_360)))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (686) yields:
% 22.00/5.66 | (687) apply(all_0_14_14, all_56_0_51) = all_421_0_359
% 22.00/5.66 | (688) ~ in(all_421_0_359, empty_set) | ~ in(all_56_0_51, all_421_1_360) | in(all_56_0_51, all_421_2_361)
% 22.00/5.66 | (689) relation_dom(all_0_14_14) = all_421_1_360
% 22.00/5.66 | (690) relation_dom(all_132_1_89) = all_421_2_361
% 22.00/5.66 | (691) ~ in(all_56_0_51, all_421_2_361) | (in(all_421_0_359, empty_set) & in(all_56_0_51, all_421_1_360))
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (606) with all_425_0_365, all_425_1_366 yields:
% 22.00/5.66 | (692) relation_dom(all_0_9_9) = all_425_0_365 & relation_dom(all_0_14_14) = all_425_1_366 & (all_425_0_365 = all_0_13_13 | ~ subset(all_182_0_126, all_425_1_366))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (692) yields:
% 22.00/5.66 | (693) relation_dom(all_0_9_9) = all_425_0_365
% 22.00/5.66 | (694) relation_dom(all_0_14_14) = all_425_1_366
% 22.00/5.66 | (695) all_425_0_365 = all_0_13_13 | ~ subset(all_182_0_126, all_425_1_366)
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (629) with all_443_0_382 yields:
% 22.00/5.66 | (696) relation_dom(all_0_14_14) = all_443_0_382 & subset(all_86_0_62, all_443_0_382)
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (696) yields:
% 22.00/5.66 | (697) relation_dom(all_0_14_14) = all_443_0_382
% 22.00/5.66 | (698) subset(all_86_0_62, all_443_0_382)
% 22.00/5.66 |
% 22.00/5.66 | Instantiating (660) with all_449_0_387, all_449_1_388 yields:
% 22.00/5.66 | (699) relation_dom(all_0_9_9) = all_449_0_387 & relation_dom(all_0_14_14) = all_449_1_388 & (all_449_0_387 = all_335_0_274 | ~ subset(all_86_0_62, all_449_1_388))
% 22.00/5.66 |
% 22.00/5.66 | Applying alpha-rule on (699) yields:
% 22.00/5.66 | (700) relation_dom(all_0_9_9) = all_449_0_387
% 22.00/5.66 | (701) relation_dom(all_0_14_14) = all_449_1_388
% 22.00/5.66 | (702) all_449_0_387 = all_335_0_274 | ~ subset(all_86_0_62, all_449_1_388)
% 22.00/5.66 |
% 22.00/5.66 | From (550) and (675) follows:
% 22.00/5.67 | (703) subset(all_86_0_62, all_372_0_308)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (581), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (704) ~ in(all_0_15_15, all_149_1_104)
% 22.00/5.67 |
% 22.00/5.67 | From (543) and (704) follows:
% 22.00/5.67 | (705) ~ in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 | Using (123) and (705) yields:
% 22.00/5.67 | (706) $false
% 22.00/5.67 |
% 22.00/5.67 |-The branch is then unsatisfiable
% 22.00/5.67 |-Branch two:
% 22.00/5.67 | (707) in(all_0_15_15, all_149_1_104)
% 22.00/5.67 | (708) all_0_10_10 = all_0_15_15
% 22.00/5.67 |
% 22.00/5.67 | From (543) and (707) follows:
% 22.00/5.67 | (123) in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (46), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (710) ~ (all_0_8_8 = all_0_15_15)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (601), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (711) in(all_0_11_11, all_123_0_80)
% 22.00/5.67 |
% 22.00/5.67 | From (573) and (711) follows:
% 22.00/5.67 | (712) in(all_0_11_11, all_86_0_62)
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_9_9, all_425_0_365, all_449_0_387 and discharging atoms relation_dom(all_0_9_9) = all_449_0_387, relation_dom(all_0_9_9) = all_425_0_365, yields:
% 22.00/5.67 | (713) all_449_0_387 = all_425_0_365
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_9_9, all_333_0_273, all_425_0_365 and discharging atoms relation_dom(all_0_9_9) = all_425_0_365, relation_dom(all_0_9_9) = all_333_0_273, yields:
% 22.00/5.67 | (714) all_425_0_365 = all_333_0_273
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_9_9, all_310_3_252, all_449_0_387 and discharging atoms relation_dom(all_0_9_9) = all_449_0_387, relation_dom(all_0_9_9) = all_310_3_252, yields:
% 22.00/5.67 | (715) all_449_0_387 = all_310_3_252
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_9_9, all_283_2_226, all_333_0_273 and discharging atoms relation_dom(all_0_9_9) = all_333_0_273, relation_dom(all_0_9_9) = all_283_2_226, yields:
% 22.00/5.67 | (716) all_333_0_273 = all_283_2_226
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_9_9, all_281_2_223, all_333_0_273 and discharging atoms relation_dom(all_0_9_9) = all_333_0_273, relation_dom(all_0_9_9) = all_281_2_223, yields:
% 22.00/5.67 | (717) all_333_0_273 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_404_0_338, all_413_0_349 and discharging atoms relation_dom(all_0_12_12) = all_413_0_349, relation_dom(all_0_12_12) = all_404_0_338, yields:
% 22.00/5.67 | (718) all_413_0_349 = all_404_0_338
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_345_0_279, all_404_0_338 and discharging atoms relation_dom(all_0_12_12) = all_404_0_338, relation_dom(all_0_12_12) = all_345_0_279, yields:
% 22.00/5.67 | (719) all_404_0_338 = all_345_0_279
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_343_0_278, all_345_0_279 and discharging atoms relation_dom(all_0_12_12) = all_345_0_279, relation_dom(all_0_12_12) = all_343_0_278, yields:
% 22.00/5.67 | (720) all_345_0_279 = all_343_0_278
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_338_0_275, all_343_0_278 and discharging atoms relation_dom(all_0_12_12) = all_343_0_278, relation_dom(all_0_12_12) = all_338_0_275, yields:
% 22.00/5.67 | (721) all_343_0_278 = all_338_0_275
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_335_0_274, all_338_0_275 and discharging atoms relation_dom(all_0_12_12) = all_338_0_275, relation_dom(all_0_12_12) = all_335_0_274, yields:
% 22.00/5.67 | (722) all_338_0_275 = all_335_0_274
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_281_1_222, all_335_0_274 and discharging atoms relation_dom(all_0_12_12) = all_335_0_274, relation_dom(all_0_12_12) = all_281_1_222, yields:
% 22.00/5.67 | (723) all_335_0_274 = all_281_1_222
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_279_0_218, all_281_1_222 and discharging atoms relation_dom(all_0_12_12) = all_281_1_222, relation_dom(all_0_12_12) = all_279_0_218, yields:
% 22.00/5.67 | (724) all_281_1_222 = all_279_0_218
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_209_0_149, all_0_13_13 and discharging atoms relation_dom(all_0_12_12) = all_209_0_149, relation_dom(all_0_12_12) = all_0_13_13, yields:
% 22.00/5.67 | (725) all_209_0_149 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_209_0_149, all_279_0_218 and discharging atoms relation_dom(all_0_12_12) = all_279_0_218, relation_dom(all_0_12_12) = all_209_0_149, yields:
% 22.00/5.67 | (726) all_279_0_218 = all_209_0_149
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_12_12, all_196_0_134, all_413_0_349 and discharging atoms relation_dom(all_0_12_12) = all_413_0_349, relation_dom(all_0_12_12) = all_196_0_134, yields:
% 22.00/5.67 | (727) all_413_0_349 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_14_14, all_449_1_388, all_86_0_62 and discharging atoms relation_dom(all_0_14_14) = all_449_1_388, relation_dom(all_0_14_14) = all_86_0_62, yields:
% 22.00/5.67 | (728) all_449_1_388 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_14_14, all_443_0_382, all_449_1_388 and discharging atoms relation_dom(all_0_14_14) = all_449_1_388, relation_dom(all_0_14_14) = all_443_0_382, yields:
% 22.00/5.67 | (729) all_449_1_388 = all_443_0_382
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_14_14, all_421_1_360, all_443_0_382 and discharging atoms relation_dom(all_0_14_14) = all_443_0_382, relation_dom(all_0_14_14) = all_421_1_360, yields:
% 22.00/5.67 | (730) all_443_0_382 = all_421_1_360
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (143) with all_0_14_14, all_372_0_308, all_421_1_360 and discharging atoms relation_dom(all_0_14_14) = all_421_1_360, relation_dom(all_0_14_14) = all_372_0_308, yields:
% 22.00/5.67 | (731) all_421_1_360 = all_372_0_308
% 22.00/5.67 |
% 22.00/5.67 | Instantiating formula (504) with all_283_0_224, all_283_1_225, all_0_15_15, all_194_0_133 and discharging atoms relation_dom(all_0_12_12) = all_194_0_133, apply(all_0_12_12, all_0_15_15) = all_283_1_225, apply(all_0_14_14, all_283_1_225) = all_283_0_224, relation(all_0_12_12), function(all_0_12_12), yields:
% 22.00/5.67 | (732) all_283_0_224 = all_0_15_15 | ~ in(all_0_15_15, all_149_1_104)
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (713,715) yields a new equation:
% 22.00/5.67 | (733) all_425_0_365 = all_310_3_252
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 733 yields:
% 22.00/5.67 | (734) all_425_0_365 = all_310_3_252
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (729,728) yields a new equation:
% 22.00/5.67 | (735) all_443_0_382 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 735 yields:
% 22.00/5.67 | (736) all_443_0_382 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (730,736) yields a new equation:
% 22.00/5.67 | (737) all_421_1_360 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 737 yields:
% 22.00/5.67 | (738) all_421_1_360 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (714,734) yields a new equation:
% 22.00/5.67 | (739) all_333_0_273 = all_310_3_252
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 739 yields:
% 22.00/5.67 | (740) all_333_0_273 = all_310_3_252
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (731,738) yields a new equation:
% 22.00/5.67 | (741) all_372_0_308 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 741 yields:
% 22.00/5.67 | (742) all_372_0_308 = all_86_0_62
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (718,727) yields a new equation:
% 22.00/5.67 | (743) all_404_0_338 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 743 yields:
% 22.00/5.67 | (744) all_404_0_338 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (719,744) yields a new equation:
% 22.00/5.67 | (745) all_345_0_279 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 745 yields:
% 22.00/5.67 | (746) all_345_0_279 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (720,746) yields a new equation:
% 22.00/5.67 | (747) all_343_0_278 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 747 yields:
% 22.00/5.67 | (748) all_343_0_278 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (721,748) yields a new equation:
% 22.00/5.67 | (749) all_338_0_275 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 749 yields:
% 22.00/5.67 | (750) all_338_0_275 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (722,750) yields a new equation:
% 22.00/5.67 | (751) all_335_0_274 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 751 yields:
% 22.00/5.67 | (752) all_335_0_274 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (723,752) yields a new equation:
% 22.00/5.67 | (753) all_281_1_222 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 753 yields:
% 22.00/5.67 | (754) all_281_1_222 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (717,740) yields a new equation:
% 22.00/5.67 | (755) all_310_3_252 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (716,740) yields a new equation:
% 22.00/5.67 | (756) all_310_3_252 = all_283_2_226
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (755,756) yields a new equation:
% 22.00/5.67 | (757) all_283_2_226 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (724,754) yields a new equation:
% 22.00/5.67 | (758) all_279_0_218 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 758 yields:
% 22.00/5.67 | (759) all_279_0_218 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (726,759) yields a new equation:
% 22.00/5.67 | (760) all_209_0_149 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 760 yields:
% 22.00/5.67 | (761) all_209_0_149 = all_196_0_134
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (725,761) yields a new equation:
% 22.00/5.67 | (762) all_196_0_134 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (757,756) yields a new equation:
% 22.00/5.67 | (755) all_310_3_252 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (762,752) yields a new equation:
% 22.00/5.67 | (764) all_335_0_274 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (762,727) yields a new equation:
% 22.00/5.67 | (765) all_413_0_349 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (755,715) yields a new equation:
% 22.00/5.67 | (766) all_449_0_387 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | From (742) and (703) follows:
% 22.00/5.67 | (767) subset(all_86_0_62, all_86_0_62)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (682), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (768) ~ in(all_0_11_11, all_86_0_62)
% 22.00/5.67 |
% 22.00/5.67 | Using (712) and (768) yields:
% 22.00/5.67 | (706) $false
% 22.00/5.67 |
% 22.00/5.67 |-The branch is then unsatisfiable
% 22.00/5.67 |-Branch two:
% 22.00/5.67 | (712) in(all_0_11_11, all_86_0_62)
% 22.00/5.67 | (771) ~ in(all_0_15_15, all_413_0_349) | in(all_0_15_15, all_413_1_350)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (702), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (772) ~ subset(all_86_0_62, all_449_1_388)
% 22.00/5.67 |
% 22.00/5.67 | From (728) and (772) follows:
% 22.00/5.67 | (773) ~ subset(all_86_0_62, all_86_0_62)
% 22.00/5.67 |
% 22.00/5.67 | Using (767) and (773) yields:
% 22.00/5.67 | (706) $false
% 22.00/5.67 |
% 22.00/5.67 |-The branch is then unsatisfiable
% 22.00/5.67 |-Branch two:
% 22.00/5.67 | (775) subset(all_86_0_62, all_449_1_388)
% 22.00/5.67 | (776) all_449_0_387 = all_335_0_274
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (776,766) yields a new equation:
% 22.00/5.67 | (777) all_335_0_274 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 777 yields:
% 22.00/5.67 | (778) all_335_0_274 = all_281_2_223
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (778,764) yields a new equation:
% 22.00/5.67 | (779) all_281_2_223 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 779 yields:
% 22.00/5.67 | (780) all_281_2_223 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (780,757) yields a new equation:
% 22.00/5.67 | (781) all_283_2_226 = all_0_13_13
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (646), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (782) ~ in(all_0_15_15, all_283_2_226)
% 22.00/5.67 |
% 22.00/5.67 | From (781) and (782) follows:
% 22.00/5.67 | (705) ~ in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 | Using (123) and (705) yields:
% 22.00/5.67 | (706) $false
% 22.00/5.67 |
% 22.00/5.67 |-The branch is then unsatisfiable
% 22.00/5.67 |-Branch two:
% 22.00/5.67 | (785) in(all_0_15_15, all_283_2_226)
% 22.00/5.67 | (786) all_283_0_224 = all_0_8_8
% 22.00/5.67 |
% 22.00/5.67 | From (781) and (785) follows:
% 22.00/5.67 | (123) in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (771), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (788) ~ in(all_0_15_15, all_413_0_349)
% 22.00/5.67 |
% 22.00/5.67 | From (765) and (788) follows:
% 22.00/5.67 | (705) ~ in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 | Using (123) and (705) yields:
% 22.00/5.67 | (706) $false
% 22.00/5.67 |
% 22.00/5.67 |-The branch is then unsatisfiable
% 22.00/5.67 |-Branch two:
% 22.00/5.67 | (791) in(all_0_15_15, all_413_0_349)
% 22.00/5.67 | (792) in(all_0_15_15, all_413_1_350)
% 22.00/5.67 |
% 22.00/5.67 | From (765) and (791) follows:
% 22.00/5.67 | (123) in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 +-Applying beta-rule and splitting (732), into two cases.
% 22.00/5.67 |-Branch one:
% 22.00/5.67 | (704) ~ in(all_0_15_15, all_149_1_104)
% 22.00/5.67 |
% 22.00/5.67 | From (543) and (704) follows:
% 22.00/5.67 | (705) ~ in(all_0_15_15, all_0_13_13)
% 22.00/5.67 |
% 22.00/5.67 | Using (123) and (705) yields:
% 22.00/5.67 | (706) $false
% 22.00/5.67 |
% 22.00/5.67 |-The branch is then unsatisfiable
% 22.00/5.67 |-Branch two:
% 22.00/5.67 | (707) in(all_0_15_15, all_149_1_104)
% 22.00/5.67 | (798) all_283_0_224 = all_0_15_15
% 22.00/5.67 |
% 22.00/5.67 | Combining equations (786,798) yields a new equation:
% 22.00/5.67 | (799) all_0_8_8 = all_0_15_15
% 22.00/5.67 |
% 22.00/5.67 | Simplifying 799 yields:
% 22.00/5.67 | (800) all_0_8_8 = all_0_15_15
% 22.00/5.67 |
% 22.00/5.68 | Equations (800) can reduce 710 to:
% 22.00/5.68 | (801) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 |-Branch two:
% 22.00/5.68 | (802) ~ in(all_0_11_11, all_123_0_80)
% 22.00/5.68 | (803) ~ (relation_dom(all_123_1_81) = all_0_13_13) | ~ (apply(all_123_1_81, all_0_15_15) = all_0_11_11) | ~ relation(all_123_1_81) | ~ function(all_123_1_81)
% 22.00/5.68 |
% 22.00/5.68 | From (573) and (802) follows:
% 22.00/5.68 | (768) ~ in(all_0_11_11, all_86_0_62)
% 22.00/5.68 |
% 22.00/5.68 +-Applying beta-rule and splitting (583), into two cases.
% 22.00/5.68 |-Branch one:
% 22.00/5.68 | (712) in(all_0_11_11, all_86_0_62)
% 22.00/5.68 |
% 22.00/5.68 | Using (712) and (768) yields:
% 22.00/5.68 | (706) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 |-Branch two:
% 22.00/5.68 | (768) ~ in(all_0_11_11, all_86_0_62)
% 22.00/5.68 | (808) all_0_10_10 = empty_set
% 22.00/5.68 |
% 22.00/5.68 | Combining equations (808,708) yields a new equation:
% 22.00/5.68 | (809) all_0_15_15 = empty_set
% 22.00/5.68 |
% 22.00/5.68 | From (809) and (98) follows:
% 22.00/5.68 | (810) apply(all_0_12_12, empty_set) = all_0_11_11
% 22.00/5.68 |
% 22.00/5.68 +-Applying beta-rule and splitting (803), into two cases.
% 22.00/5.68 |-Branch one:
% 22.00/5.68 | (811) ~ relation(all_123_1_81)
% 22.00/5.68 |
% 22.00/5.68 | From (552) and (811) follows:
% 22.00/5.68 | (812) ~ relation(all_0_12_12)
% 22.00/5.68 |
% 22.00/5.68 | Using (422) and (812) yields:
% 22.00/5.68 | (706) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 |-Branch two:
% 22.00/5.68 | (814) relation(all_123_1_81)
% 22.00/5.68 | (815) ~ (relation_dom(all_123_1_81) = all_0_13_13) | ~ (apply(all_123_1_81, all_0_15_15) = all_0_11_11) | ~ function(all_123_1_81)
% 22.00/5.68 |
% 22.00/5.68 +-Applying beta-rule and splitting (815), into two cases.
% 22.00/5.68 |-Branch one:
% 22.00/5.68 | (816) ~ (relation_dom(all_123_1_81) = all_0_13_13)
% 22.00/5.68 |
% 22.00/5.68 | From (552) and (816) follows:
% 22.00/5.68 | (817) ~ (relation_dom(all_0_12_12) = all_0_13_13)
% 22.00/5.68 |
% 22.00/5.68 | Using (578) and (817) yields:
% 22.00/5.68 | (706) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 |-Branch two:
% 22.00/5.68 | (819) relation_dom(all_123_1_81) = all_0_13_13
% 22.00/5.68 | (820) ~ (apply(all_123_1_81, all_0_15_15) = all_0_11_11) | ~ function(all_123_1_81)
% 22.00/5.68 |
% 22.00/5.68 +-Applying beta-rule and splitting (820), into two cases.
% 22.00/5.68 |-Branch one:
% 22.00/5.68 | (821) ~ (apply(all_123_1_81, all_0_15_15) = all_0_11_11)
% 22.00/5.68 |
% 22.00/5.68 | From (552)(809) and (821) follows:
% 22.00/5.68 | (822) ~ (apply(all_0_12_12, empty_set) = all_0_11_11)
% 22.00/5.68 |
% 22.00/5.68 | Using (810) and (822) yields:
% 22.00/5.68 | (706) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 |-Branch two:
% 22.00/5.68 | (824) apply(all_123_1_81, all_0_15_15) = all_0_11_11
% 22.00/5.68 | (825) ~ function(all_123_1_81)
% 22.00/5.68 |
% 22.00/5.68 | From (552) and (825) follows:
% 22.00/5.68 | (826) ~ function(all_0_12_12)
% 22.00/5.68 |
% 22.00/5.68 | Using (423) and (826) yields:
% 22.00/5.68 | (706) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 |-Branch two:
% 22.00/5.68 | (800) all_0_8_8 = all_0_15_15
% 22.00/5.68 | (829) ~ (all_0_10_10 = all_0_15_15)
% 22.00/5.68 |
% 22.00/5.68 | Equations (708) can reduce 829 to:
% 22.00/5.68 | (801) $false
% 22.00/5.68 |
% 22.00/5.68 |-The branch is then unsatisfiable
% 22.00/5.68 % SZS output end Proof for theBenchmark
% 22.00/5.68
% 22.00/5.68 5046ms
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