TSTP Solution File: SEU223+2 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU223+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n008.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 08:47:50 EDT 2022
% Result : Theorem 10.39s 2.99s
% Output : Proof 19.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU223+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 19 07:41:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.60 ____ _
% 0.60/0.60 ___ / __ \_____(_)___ ________ __________
% 0.60/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.60
% 0.60/0.60 A Theorem Prover for First-Order Logic
% 0.60/0.60 (ePrincess v.1.0)
% 0.60/0.60
% 0.60/0.60 (c) Philipp Rümmer, 2009-2015
% 0.60/0.60 (c) Peter Backeman, 2014-2015
% 0.60/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.60 Bug reports to peter@backeman.se
% 0.60/0.60
% 0.60/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.60
% 0.60/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.90/1.24 Prover 0: Preprocessing ...
% 6.91/2.13 Prover 0: Warning: ignoring some quantifiers
% 6.91/2.18 Prover 0: Constructing countermodel ...
% 10.39/2.98 Prover 0: proved (2300ms)
% 10.39/2.98
% 10.39/2.99 No countermodel exists, formula is valid
% 10.39/2.99 % SZS status Theorem for theBenchmark
% 10.39/2.99
% 10.39/2.99 Generating proof ... Warning: ignoring some quantifiers
% 17.76/4.64 found it (size 23)
% 17.76/4.64
% 17.76/4.64 % SZS output start Proof for theBenchmark
% 17.76/4.64 Assumed formulas after preprocessing and simplification:
% 17.76/4.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v7 = v6) & relation_rng(empty_set) = empty_set & relation_dom(v4) = v5 & relation_dom(empty_set) = empty_set & apply(v4, v2) = v6 & apply(v3, v2) = v7 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_dom_restriction(v3, v1) = v4 & relation_empty_yielding(v8) & relation_empty_yielding(empty_set) & one_to_one(v9) & relation(v15) & relation(v14) & relation(v12) & relation(v11) & relation(v9) & relation(v8) & relation(v3) & relation(empty_set) & function(v15) & function(v12) & function(v9) & function(v3) & empty(v14) & empty(v13) & empty(v12) & empty(empty_set) & in(v2, v5) & ~ empty(v11) & ~ empty(v10) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v16, v17) = v18) | ~ (ordered_pair(v22, v20) = v23) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ relation(v16) | ~ in(v23, v17) | in(v21, v18) | ? [v24] : (ordered_pair(v19, v22) = v24 & ~ in(v24, v16))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v16, v17) = v18) | ~ (ordered_pair(v19, v22) = v23) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ relation(v16) | ~ in(v23, v16) | in(v21, v18) | ? [v24] : (ordered_pair(v22, v20) = v24 & ~ in(v24, v17))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v21, v19) = v22) | ~ (identity_relation(v18) = v21) | ~ (ordered_pair(v16, v17) = v20) | ~ relation(v19) | ~ in(v20, v22) | in(v20, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v21, v19) = v22) | ~ (identity_relation(v18) = v21) | ~ (ordered_pair(v16, v17) = v20) | ~ relation(v19) | ~ in(v20, v22) | in(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v21, v19) = v22) | ~ (identity_relation(v18) = v21) | ~ (ordered_pair(v16, v17) = v20) | ~ relation(v19) | ~ in(v20, v19) | ~ in(v16, v18) | in(v20, v22)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_composition(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ relation(v16) | ~ in(v21, v18) | ? [v22] : ? [v23] : ? [v24] : (ordered_pair(v22, v20) = v24 & ordered_pair(v19, v22) = v23 & in(v24, v17) & in(v23, v16))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom(v19) = v20) | ~ (relation_dom(v17) = v18) | ~ (set_intersection2(v20, v16) = v21) | ~ relation(v19) | ~ relation(v17) | ~ function(v19) | ~ function(v17) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_dom_restriction(v19, v16) = v22 & ( ~ (v22 = v17) | (v21 = v18 & ! [v26] : ! [v27] : ( ~ (apply(v19, v26) = v27) | ~ in(v26, v18) | apply(v17, v26) = v27) & ! [v26] : ! [v27] : ( ~ (apply(v17, v26) = v27) | ~ in(v26, v18) | apply(v19, v26) = v27))) & ( ~ (v21 = v18) | v22 = v17 | ( ~ (v25 = v24) & apply(v19, v23) = v25 & apply(v17, v23) = v24 & in(v23, v18))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (ordered_pair(v16, v17) = v20) | ~ in(v20, v21) | in(v17, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (ordered_pair(v16, v17) = v20) | ~ in(v20, v21) | in(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v18, v19) = v21) | ~ (ordered_pair(v16, v17) = v20) | ~ in(v17, v19) | ~ in(v16, v18) | in(v20, v21)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v17, v19) = v21) | ~ (cartesian_product2(v16, v18) = v20) | ~ subset(v18, v19) | ~ subset(v16, v17) | subset(v20, v21)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (cartesian_product2(v16, v17) = v18) | ~ (ordered_pair(v20, v21) = v19) | ~ in(v21, v17) | ~ in(v20, v16) | in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_inverse_image(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v16) | ~ in(v21, v16) | ~ in(v20, v17) | in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_image(v16, v17) = v18) | ~ (ordered_pair(v20, v19) = v21) | ~ relation(v16) | ~ in(v21, v16) | ~ in(v20, v17) | in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ in(v21, v18) | in(v21, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ in(v21, v18) | in(v20, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v17) | ~ in(v21, v17) | ~ in(v20, v16) | in(v21, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v16) | ~ in(v21, v18) | in(v21, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v16) | ~ in(v21, v18) | in(v19, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ (ordered_pair(v19, v20) = v21) | ~ relation(v18) | ~ relation(v16) | ~ in(v21, v16) | ~ in(v19, v17) | in(v21, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v20 = v19 | ~ (relation_dom(v17) = v18) | ~ (apply(v17, v19) = v20) | ~ (identity_relation(v16) = v17) | ~ relation(v17) | ~ function(v17) | ~ in(v19, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (relation_dom(v16) = v17) | ~ (apply(v16, v19) = v20) | ~ (apply(v16, v18) = v20) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ~ in(v19, v17) | ~ in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v18 | ~ (identity_relation(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ in(v20, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v17 | ~ (ordered_pair(v18, v19) = v20) | ~ (ordered_pair(v16, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v19 = v16 | v18 = v16 | ~ (unordered_pair(v18, v19) = v20) | ~ (unordered_pair(v16, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = v16 | ~ (ordered_pair(v18, v19) = v20) | ~ (ordered_pair(v16, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = v16 | ~ (subset_difference(v20, v19, v18) = v17) | ~ (subset_difference(v20, v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = empty_set | ~ (subset_difference(v16, v18, v19) = v20) | ~ (meet_of_subsets(v16, v17) = v19) | ~ (cast_to_subset(v16) = v18) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (union_of_subsets(v16, v23) = v24 & complements_of_subsets(v16, v17) = v23 & powerset(v21) = v22 & powerset(v16) = v21 & (v24 = v20 | ~ element(v17, v22)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v17 = empty_set | ~ (subset_difference(v16, v18, v19) = v20) | ~ (union_of_subsets(v16, v17) = v19) | ~ (cast_to_subset(v16) = v18) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (meet_of_subsets(v16, v23) = v24 & complements_of_subsets(v16, v17) = v23 & powerset(v21) = v22 & powerset(v16) = v21 & (v24 = v20 | ~ element(v17, v22)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v16 = empty_set | ~ (subset_complement(v16, v18) = v19) | ~ (powerset(v16) = v17) | ~ element(v20, v16) | ~ element(v18, v17) | in(v20, v19) | in(v20, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (function_inverse(v17) = v18) | ~ (relation_composition(v18, v17) = v19) | ~ (apply(v19, v16) = v20) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_rng(v17) = v21 & apply(v18, v16) = v22 & apply(v17, v22) = v23 & ( ~ in(v16, v21) | (v23 = v16 & v20 = v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (function_inverse(v17) = v18) | ~ (apply(v18, v16) = v19) | ~ (apply(v17, v19) = v20) | ~ one_to_one(v17) | ~ relation(v17) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_composition(v18, v17) = v22 & relation_rng(v17) = v21 & apply(v22, v16) = v23 & ( ~ in(v16, v21) | (v23 = v16 & v20 = v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v18, v17) = v19) | ~ (apply(v19, v16) = v20) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_dom(v19) = v21 & apply(v18, v16) = v22 & apply(v17, v22) = v23 & (v23 = v20 | ~ in(v16, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse(v16) = v17) | ~ (ordered_pair(v19, v18) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v16) | ? [v21] : (ordered_pair(v18, v19) = v21 & in(v21, v17))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse(v16) = v17) | ~ (ordered_pair(v19, v18) = v20) | ~ relation(v17) | ~ relation(v16) | in(v20, v16) | ? [v21] : (ordered_pair(v18, v19) = v21 & ~ in(v21, v17))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v17) | ? [v21] : (ordered_pair(v19, v18) = v21 & in(v21, v16))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ relation(v16) | in(v20, v17) | ? [v21] : (ordered_pair(v19, v18) = v21 & ~ in(v21, v16))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_field(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ in(v19, v18) | in(v17, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_field(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ in(v19, v18) | in(v16, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_complement(v16, v19) = v20) | ~ (powerset(v16) = v18) | ~ disjoint(v17, v19) | ~ element(v19, v18) | ~ element(v17, v18) | subset(v17, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (subset_complement(v16, v19) = v20) | ~ (powerset(v16) = v18) | ~ element(v19, v18) | ~ element(v17, v18) | ~ subset(v17, v20) | disjoint(v17, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ in(v19, v18) | in(v17, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ in(v19, v18) | ? [v21] : (relation_dom(v18) = v21 & in(v16, v21))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng(v16) = v17) | ~ (ordered_pair(v19, v18) = v20) | ~ relation(v16) | ~ in(v20, v16) | in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v19) = v20) | ~ (singleton(v18) = v19) | ~ subset(v16, v17) | subset(v16, v20) | in(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v20) | ~ (set_difference(v16, v18) = v19) | ~ subset(v16, v17) | subset(v19, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_difference(v17, v18) = v20) | ~ (powerset(v16) = v19) | ~ element(v18, v19) | ~ element(v17, v19) | subset_difference(v16, v17, v18) = v20) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ function(v18) | ? [v21] : (apply(v18, v16) = v21 & ( ~ (v21 = v17) | ~ in(v16, v20) | in(v19, v18)) & ( ~ in(v19, v18) | (v21 = v17 & in(v16, v20))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ in(v19, v18) | in(v16, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v18) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ in(v19, v18) | ? [v21] : (relation_rng(v18) = v21 & in(v17, v21))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v17) = v18) | ~ (apply(v19, v16) = v20) | ~ relation(v19) | ~ relation(v17) | ~ function(v19) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_composition(v19, v17) = v21 & relation_dom(v21) = v22 & relation_dom(v19) = v23 & ( ~ in(v20, v18) | ~ in(v16, v23) | in(v16, v22)) & ( ~ in(v16, v22) | (in(v20, v18) & in(v16, v23))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v17) = v18) | ~ (relation_image(v17, v19) = v20) | ~ (set_intersection2(v18, v16) = v19) | ~ relation(v17) | relation_image(v17, v16) = v20) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v17) = v18) | ~ (relation_dom_restriction(v19, v16) = v20) | ~ relation(v19) | ~ relation(v17) | ~ function(v19) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_dom(v19) = v21 & set_intersection2(v21, v16) = v22 & ( ~ (v22 = v18) | v20 = v17 | ( ~ (v25 = v24) & apply(v19, v23) = v25 & apply(v17, v23) = v24 & in(v23, v18))) & ( ~ (v20 = v17) | (v22 = v18 & ! [v26] : ! [v27] : ( ~ (apply(v19, v26) = v27) | ~ in(v26, v18) | apply(v17, v26) = v27) & ! [v26] : ! [v27] : ( ~ (apply(v17, v26) = v27) | ~ in(v26, v18) | apply(v19, v26) = v27))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v16) | ~ function(v16) | ~ in(v18, v17) | ? [v21] : (apply(v16, v18) = v21 & ( ~ (v21 = v19) | in(v20, v16)) & (v21 = v19 | ~ in(v20, v16)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v16) | ~ in(v20, v16) | in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (apply(v18, v16) = v20) | ~ (ordered_pair(v16, v17) = v19) | ~ relation(v18) | ~ function(v18) | ? [v21] : (relation_dom(v18) = v21 & ( ~ (v20 = v17) | ~ in(v16, v21) | in(v19, v18)) & ( ~ in(v19, v18) | (v20 = v17 & in(v16, v21))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (apply(v18, v16) = v19) | ~ (apply(v17, v19) = v20) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_composition(v18, v17) = v21 & relation_dom(v21) = v22 & apply(v21, v16) = v23 & (v23 = v20 | ~ in(v16, v22)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v17) = v20) | ~ (cartesian_product2(v18, v16) = v19) | ~ subset(v16, v17) | subset(v19, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v17) = v20) | ~ (cartesian_product2(v18, v16) = v19) | ~ subset(v16, v17) | ? [v21] : ? [v22] : (cartesian_product2(v17, v18) = v22 & cartesian_product2(v16, v18) = v21 & subset(v21, v22))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v17) = v20) | ~ (cartesian_product2(v16, v18) = v19) | ~ subset(v16, v17) | ? [v21] : ? [v22] : (cartesian_product2(v18, v16) = v22 & cartesian_product2(v17, v18) = v21 & subset(v22, v20) & subset(v19, v21))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v18, v16) = v20) | ~ (cartesian_product2(v17, v18) = v19) | ~ subset(v16, v17) | ? [v21] : ? [v22] : (cartesian_product2(v18, v17) = v22 & cartesian_product2(v16, v18) = v21 & subset(v21, v19) & subset(v20, v22))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (cartesian_product2(v16, v18) = v19) | ~ subset(v16, v17) | subset(v19, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (cartesian_product2(v17, v18) = v20) | ~ (cartesian_product2(v16, v18) = v19) | ~ subset(v16, v17) | ? [v21] : ? [v22] : (cartesian_product2(v18, v17) = v22 & cartesian_product2(v18, v16) = v21 & subset(v21, v22))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (singleton(v16) = v19) | ~ (unordered_pair(v18, v19) = v20) | ~ (unordered_pair(v16, v17) = v18) | ordered_pair(v16, v17) = v20) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_inverse_image(v18, v17) = v20) | ~ (relation_inverse_image(v18, v16) = v19) | ~ subset(v16, v17) | ~ relation(v18) | subset(v19, v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v16, v19) = v20) | ~ (relation_dom_restriction(v18, v17) = v19) | ~ relation(v18) | ? [v21] : (relation_rng_restriction(v16, v18) = v21 & relation_dom_restriction(v21, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_rng_restriction(v16, v18) = v19) | ~ (relation_dom_restriction(v19, v17) = v20) | ~ relation(v18) | ? [v21] : (relation_rng_restriction(v16, v21) = v20 & relation_dom_restriction(v18, v17) = v21)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (identity_relation(v16) = v17) | ~ (ordered_pair(v18, v19) = v20) | ~ relation(v17) | ~ in(v20, v17) | in(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (ordered_pair(v18, v19) = v20) | ~ subset(v16, v17) | ~ relation(v17) | ~ relation(v16) | ~ in(v20, v16) | in(v20, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (set_intersection2(v17, v18) = v20) | ~ (set_intersection2(v16, v18) = v19) | ~ subset(v16, v17) | subset(v19, v20)) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_composition(v19, v17) = v20) | ~ (relation_dom(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ function(v19) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_dom(v20) = v21 & relation_dom(v19) = v22 & apply(v19, v16) = v23 & ( ~ in(v23, v18) | ~ in(v16, v22) | in(v16, v21)) & ( ~ in(v16, v21) | (in(v23, v18) & in(v16, v22))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ (relation_dom(v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ function(v19) | ~ function(v17) | ? [v21] : ? [v22] : ? [v23] : (relation_composition(v19, v17) = v21 & relation_dom(v21) = v22 & apply(v19, v16) = v23 & ( ~ in(v23, v18) | ~ in(v16, v20) | in(v16, v22)) & ( ~ in(v16, v22) | (in(v23, v18) & in(v16, v20))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_composition(v16, v17) = v18) | ~ relation(v19) | ~ relation(v17) | ~ relation(v16) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (ordered_pair(v20, v21) = v22 & ( ~ in(v22, v19) | ( ! [v26] : ! [v27] : ( ~ (ordered_pair(v26, v21) = v27) | ~ in(v27, v17) | ? [v28] : (ordered_pair(v20, v26) = v28 & ~ in(v28, v16))) & ! [v26] : ! [v27] : ( ~ (ordered_pair(v20, v26) = v27) | ~ in(v27, v16) | ? [v28] : (ordered_pair(v26, v21) = v28 & ~ in(v28, v17))))) & (in(v22, v19) | (ordered_pair(v23, v21) = v25 & ordered_pair(v20, v23) = v24 & in(v25, v17) & in(v24, v16))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v19) | ~ relation(v17) | ? [v20] : ? [v21] : ? [v22] : (ordered_pair(v20, v21) = v22 & ( ~ in(v22, v19) | ~ in(v22, v17) | ~ in(v21, v16)) & (in(v22, v19) | (in(v22, v17) & in(v21, v16))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v18 | ~ (relation_dom_restriction(v16, v17) = v19) | ~ relation(v18) | ~ relation(v16) | ? [v20] : ? [v21] : ? [v22] : (ordered_pair(v20, v21) = v22 & ( ~ in(v22, v18) | ~ in(v22, v16) | ~ in(v20, v17)) & (in(v22, v18) | (in(v22, v16) & in(v20, v17))))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | v19 = v16 | ~ (unordered_pair(v16, v17) = v18) | ~ in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (complements_of_subsets(v16, v18) = v19) | ~ (complements_of_subsets(v16, v17) = v18) | ? [v20] : ? [v21] : (powerset(v20) = v21 & powerset(v16) = v20 & ~ element(v17, v21))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (subset_complement(v16, v18) = v19) | ~ (subset_complement(v16, v17) = v18) | ? [v20] : (powerset(v16) = v20 & ~ element(v17, v20))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (set_difference(v17, v16) = v18) | ~ (set_union2(v16, v18) = v19) | ~ subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (apply(v18, v17) = v19) | ~ (identity_relation(v16) = v18) | ~ in(v17, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v17 | ~ (singleton(v16) = v18) | ~ (set_union2(v18, v17) = v19) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (set_difference(v16, v18) = v19) | ~ (singleton(v17) = v18) | in(v17, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = empty_set | ~ (relation_dom(v16) = v17) | ~ (apply(v16, v18) = v19) | ~ relation(v16) | ~ function(v16) | in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v18 = v17 | ~ (singleton(v16) = v19) | ~ (unordered_pair(v17, v18) = v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (meet_of_subsets(v19, v18) = v17) | ~ (meet_of_subsets(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (union_of_subsets(v19, v18) = v17) | ~ (union_of_subsets(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (complements_of_subsets(v19, v18) = v17) | ~ (complements_of_subsets(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_composition(v19, v18) = v17) | ~ (relation_composition(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (subset_complement(v19, v18) = v17) | ~ (subset_complement(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_difference(v19, v18) = v17) | ~ (set_difference(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (apply(v19, v18) = v17) | ~ (apply(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (cartesian_product2(v19, v18) = v17) | ~ (cartesian_product2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (singleton(v17) = v19) | ~ (singleton(v16) = v18) | ~ subset(v18, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (singleton(v16) = v19) | ~ (unordered_pair(v17, v18) = v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_inverse_image(v19, v18) = v17) | ~ (relation_inverse_image(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_image(v19, v18) = v17) | ~ (relation_image(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_rng_restriction(v19, v18) = v17) | ~ (relation_rng_restriction(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (relation_dom_restriction(v19, v18) = v17) | ~ (relation_dom_restriction(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (ordered_pair(v19, v18) = v17) | ~ (ordered_pair(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_intersection2(v19, v18) = v17) | ~ (set_intersection2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (set_union2(v19, v18) = v17) | ~ (set_union2(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = v16 | ~ (unordered_pair(v19, v18) = v17) | ~ (unordered_pair(v19, v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = empty_set | ~ (meet_of_subsets(v16, v18) = v19) | ~ (complements_of_subsets(v16, v17) = v18) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset_difference(v16, v22, v23) = v24 & union_of_subsets(v16, v17) = v23 & cast_to_subset(v16) = v22 & powerset(v20) = v21 & powerset(v16) = v20 & (v24 = v19 | ~ element(v17, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v17 = empty_set | ~ (union_of_subsets(v16, v18) = v19) | ~ (complements_of_subsets(v16, v17) = v18) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (subset_difference(v16, v22, v23) = v24 & meet_of_subsets(v16, v17) = v23 & cast_to_subset(v16) = v22 & powerset(v20) = v21 & powerset(v16) = v20 & (v24 = v19 | ~ element(v17, v21)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v16 = empty_set | ~ (set_meet(v16) = v17) | ~ in(v19, v16) | ~ in(v18, v17) | in(v18, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_difference(v16, v17, v18) = v19) | ? [v20] : ? [v21] : (set_difference(v17, v18) = v21 & powerset(v16) = v20 & (v21 = v19 | ~ element(v18, v20) | ~ element(v17, v20)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_difference(v16, v17, v18) = v19) | ? [v20] : (powerset(v16) = v20 & ( ~ element(v18, v20) | ~ element(v17, v20) | element(v19, v20)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ~ (identity_relation(v16) = v18) | ~ relation(v17) | relation_dom_restriction(v17, v16) = v19) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v16, v18) = v19) | ~ (relation_rng(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ? [v20] : (relation_rng(v19) = v20 & relation_image(v18, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v16, v18) = v19) | ~ (relation_dom(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ? [v20] : (relation_dom(v19) = v20 & subset(v20, v17))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (subset_complement(v16, v18) = v19) | ~ in(v17, v19) | ~ in(v17, v18) | ? [v20] : (powerset(v16) = v20 & ~ element(v18, v20))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v17) = v18) | ~ (set_intersection2(v18, v16) = v19) | ~ relation(v17) | ? [v20] : (relation_rng(v20) = v19 & relation_rng_restriction(v16, v17) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v16) = v18) | ~ (relation_dom(v16) = v17) | ~ (cartesian_product2(v17, v18) = v19) | ~ relation(v16) | subset(v16, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v16) = v18) | ~ (relation_dom(v16) = v17) | ~ (set_union2(v17, v18) = v19) | ~ relation(v16) | relation_field(v16) = v19) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng(v16) = v17) | ~ (relation_image(v18, v17) = v19) | ~ relation(v18) | ~ relation(v16) | ? [v20] : (relation_composition(v16, v18) = v20 & relation_rng(v20) = v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v18, v17) = v19) | ~ (set_union2(v16, v17) = v18) | set_difference(v16, v17) = v19) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v17, v16) = v18) | ~ (set_union2(v16, v18) = v19) | set_union2(v16, v17) = v19) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v18) = v19) | ~ (set_difference(v16, v17) = v18) | set_intersection2(v16, v17) = v19) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v18) | ~ in(v19, v18) | ~ in(v19, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v18) | ~ in(v19, v18) | in(v19, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_difference(v16, v17) = v18) | ~ in(v19, v16) | in(v19, v18) | in(v19, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (union(v17) = v19) | ~ (powerset(v16) = v18) | ? [v20] : ? [v21] : (union_of_subsets(v16, v17) = v21 & powerset(v18) = v20 & (v21 = v19 | ~ element(v17, v20)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (union(v16) = v17) | ~ in(v19, v16) | ~ in(v18, v19) | in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom(v17) = v18) | ~ (set_intersection2(v18, v16) = v19) | ~ relation(v17) | ? [v20] : (relation_dom(v20) = v19 & relation_dom_restriction(v17, v16) = v20)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (cartesian_product2(v16, v17) = v18) | ~ in(v19, v18) | ? [v20] : ? [v21] : (ordered_pair(v20, v21) = v19 & in(v21, v17) & in(v20, v16))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ empty(v18) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ element(v17, v19) | ~ in(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v16) = v18) | ~ (set_meet(v17) = v19) | ? [v20] : ? [v21] : (meet_of_subsets(v16, v17) = v21 & powerset(v18) = v20 & (v21 = v19 | ~ element(v17, v20)))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (powerset(v16) = v18) | ~ element(v17, v18) | ~ in(v19, v17) | in(v19, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v16, v17) = v18) | ~ relation(v16) | ~ in(v19, v18) | ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & in(v21, v16) & in(v20, v17))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | ~ in(v19, v18) | ? [v20] : ? [v21] : (ordered_pair(v20, v19) = v21 & in(v21, v16) & in(v20, v17))) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (identity_relation(v16) = v17) | ~ (ordered_pair(v18, v18) = v19) | ~ relation(v17) | ~ in(v18, v16) | in(v19, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v17, v18) = v19) | ~ subset(v16, v18) | ~ subset(v16, v17) | subset(v16, v19)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v18) | ~ disjoint(v16, v17) | ~ in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v18) | ~ in(v19, v18) | in(v19, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v18) | ~ in(v19, v18) | in(v19, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_intersection2(v16, v17) = v18) | ~ in(v19, v17) | ~ in(v19, v16) | in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v16, v18) = v19) | ~ subset(v18, v17) | ~ subset(v16, v17) | subset(v19, v17)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v16, v17) = v18) | ~ in(v19, v18) | in(v19, v17) | in(v19, v16)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v16, v17) = v18) | ~ in(v19, v17) | in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (set_union2(v16, v17) = v18) | ~ in(v19, v16) | in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v16, v17) = v19) | ~ subset(v19, v18) | in(v17, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v16, v17) = v19) | ~ subset(v19, v18) | in(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (unordered_pair(v16, v17) = v19) | ~ in(v17, v18) | ~ in(v16, v18) | subset(v19, v18)) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (set_difference(v17, v18) = v19) | ? [v20] : (( ~ in(v20, v17) | ~ in(v20, v16) | in(v20, v18)) & (in(v20, v16) | (in(v20, v17) & ~ in(v20, v18))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (cartesian_product2(v17, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (( ~ in(v20, v16) | ! [v24] : ! [v25] : ( ~ (ordered_pair(v24, v25) = v20) | ~ in(v25, v18) | ~ in(v24, v17))) & (in(v20, v16) | (v23 = v20 & ordered_pair(v21, v22) = v20 & in(v22, v18) & in(v21, v17))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (relation_inverse_image(v17, v18) = v19) | ~ relation(v17) | ? [v20] : ? [v21] : ? [v22] : (( ~ in(v20, v16) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v20, v23) = v24) | ~ in(v24, v17) | ~ in(v23, v18))) & (in(v20, v16) | (ordered_pair(v20, v21) = v22 & in(v22, v17) & in(v21, v18))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (relation_image(v17, v18) = v19) | ~ relation(v17) | ? [v20] : ? [v21] : ? [v22] : (( ~ in(v20, v16) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v20) = v24) | ~ in(v24, v17) | ~ in(v23, v18))) & (in(v20, v16) | (ordered_pair(v21, v20) = v22 & in(v22, v17) & in(v21, v18))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (set_intersection2(v17, v18) = v19) | ? [v20] : (( ~ in(v20, v18) | ~ in(v20, v17) | ~ in(v20, v16)) & (in(v20, v16) | (in(v20, v18) & in(v20, v17))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (set_union2(v17, v18) = v19) | ? [v20] : (( ~ in(v20, v16) | ( ~ in(v20, v18) & ~ in(v20, v17))) & (in(v20, v18) | in(v20, v17) | in(v20, v16)))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : (v19 = v16 | ~ (unordered_pair(v17, v18) = v19) | ? [v20] : ((v20 = v18 | v20 = v17 | in(v20, v16)) & ( ~ in(v20, v16) | ( ~ (v20 = v18) & ~ (v20 = v17))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v18, v17) = v19) | ~ relation(v18) | ~ relation(v17) | ~ function(v18) | ~ function(v17) | ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v19) = v20 & apply(v19, v16) = v21 & apply(v18, v16) = v22 & apply(v17, v22) = v23 & (v23 = v21 | ~ in(v16, v20)))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_inverse_image(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : ? [v22] : (relation_rng(v18) = v20 & ( ~ in(v16, v19) | (ordered_pair(v16, v21) = v22 & in(v22, v18) & in(v21, v20) & in(v21, v17))) & (in(v16, v19) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v16, v23) = v24) | ~ in(v24, v18) | ~ in(v23, v20) | ~ in(v23, v17))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_image(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : ? [v22] : (relation_dom(v18) = v20 & ( ~ in(v16, v19) | (ordered_pair(v21, v16) = v22 & in(v22, v18) & in(v21, v20) & in(v21, v17))) & (in(v16, v19) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v16) = v24) | ~ in(v24, v18) | ~ in(v23, v20) | ~ in(v23, v17))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_rng_restriction(v17, v18) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_rng(v19) = v20 & relation_rng(v18) = v21 & ( ~ in(v16, v21) | ~ in(v16, v17) | in(v16, v20)) & ( ~ in(v16, v20) | (in(v16, v21) & in(v16, v17))))) & ? [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_dom_restriction(v18, v17) = v19) | ~ relation(v18) | ? [v20] : ? [v21] : (relation_dom(v19) = v20 & relation_dom(v18) = v21 & ( ~ in(v16, v21) | ~ in(v16, v17) | in(v16, v20)) & ( ~ in(v16, v20) | (in(v16, v21) & in(v16, v17))))) & ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_inverse(v16) = v17) | ~ relation(v18) | ~ relation(v16) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (ordered_pair(v20, v19) = v22 & ordered_pair(v19, v20) = v21 & ( ~ in(v22, v16) | ~ in(v21, v18)) & (in(v22, v16) | in(v21, v18)))) & ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (relation_dom(v17) = v16) | ~ (identity_relation(v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v19] : ? [v20] : ( ~ (v20 = v19) & apply(v17, v19) = v20 & in(v19, v16))) & ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (identity_relation(v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v19, v20) = v21 & ( ~ (v20 = v19) | ~ in(v21, v17) | ~ in(v19, v16)) & (in(v21, v17) | (v20 = v19 & in(v19, v16))))) & ! [v16] : ! [v17] : ! [v18] : (v18 = v17 | ~ (set_union2(v16, v17) = v18) | ~ subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | v16 = empty_set | ~ (singleton(v17) = v18) | ~ subset(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (set_difference(v16, v17) = v18) | ~ disjoint(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_dom(v17) = v18) | ~ (identity_relation(v16) = v17) | ~ relation(v17) | ~ function(v17)) & ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (singleton(v16) = v17) | ~ in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (set_intersection2(v16, v17) = v18) | ~ subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_difference(v16, v17) = v18) | ~ subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : (v18 = empty_set | ~ (set_intersection2(v16, v17) = v18) | ~ disjoint(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (function_inverse(v18) = v17) | ~ (function_inverse(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_inverse(v18) = v17) | ~ (relation_inverse(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_field(v18) = v17) | ~ (relation_field(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_rng(v18) = v17) | ~ (relation_rng(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (union(v18) = v17) | ~ (union(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (cast_to_subset(v18) = v17) | ~ (cast_to_subset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (relation_dom(v18) = v17) | ~ (relation_dom(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (powerset(v18) = v17) | ~ (powerset(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (singleton(v18) = v17) | ~ (singleton(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (set_meet(v18) = v17) | ~ (set_meet(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : (v17 = v16 | ~ (identity_relation(v18) = v17) | ~ (identity_relation(v18) = v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (meet_of_subsets(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (powerset(v19) = v20 & powerset(v16) = v19 & set_meet(v17) = v21 & (v21 = v18 | ~ element(v17, v20)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (meet_of_subsets(v16, v17) = v18) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v16) = v19 & ( ~ element(v17, v20) | element(v18, v19)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (union_of_subsets(v16, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : (union(v17) = v21 & powerset(v19) = v20 & powerset(v16) = v19 & (v21 = v18 | ~ element(v17, v20)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (union_of_subsets(v16, v17) = v18) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v16) = v19 & ( ~ element(v17, v20) | element(v18, v19)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (complements_of_subsets(v16, v17) = v18) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v16) = v19 & ( ~ element(v17, v20) | element(v18, v20)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (complements_of_subsets(v16, v17) = v18) | ? [v19] : ? [v20] : (powerset(v19) = v20 & powerset(v16) = v19 & ( ~ element(v17, v20) | ( ! [v21] : ! [v22] : ( ~ (subset_complement(v16, v21) = v22) | ~ element(v21, v19) | ~ element(v18, v20) | ~ in(v22, v17) | in(v21, v18)) & ! [v21] : ! [v22] : ( ~ (subset_complement(v16, v21) = v22) | ~ element(v21, v19) | ~ element(v18, v20) | ~ in(v21, v18) | in(v22, v17)) & ! [v21] : (v21 = v18 | ~ element(v21, v20) | ? [v22] : ? [v23] : (subset_complement(v16, v22) = v23 & element(v22, v19) & ( ~ in(v23, v17) | ~ in(v22, v21)) & (in(v23, v17) | in(v22, v21)))))))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ empty(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v17, v16) = v18) | ~ relation(v17) | ~ empty(v16) | empty(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ~ function(v17) | ~ function(v16) | function(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & subset(v19, v20))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ empty(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_composition(v16, v17) = v18) | ~ relation(v17) | ~ empty(v16) | empty(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v16, v17) = v18) | ? [v19] : ? [v20] : (set_difference(v16, v17) = v20 & powerset(v16) = v19 & (v20 = v18 | ~ element(v17, v19)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (subset_complement(v16, v17) = v18) | ? [v19] : (powerset(v16) = v19 & ( ~ element(v17, v19) | element(v18, v19)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v17) = v18) | ~ relation(v17) | ~ relation(v16) | ? [v19] : ? [v20] : (relation_composition(v16, v17) = v19 & relation_rng(v19) = v20 & subset(v20, v18))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v19, v18) = v20 & in(v20, v16))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v18) = v16) | ~ (singleton(v17) = v18) | ~ in(v17, v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v17) = v18) | subset(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v17) = v18) | ? [v19] : ? [v20] : (subset_complement(v16, v17) = v20 & powerset(v16) = v19 & (v20 = v18 | ~ element(v17, v19)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_difference(v16, v17) = v18) | ? [v19] : (set_difference(v19, v17) = v18 & set_union2(v16, v17) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v17) = v18) | ~ in(v16, v17) | subset(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (union(v16) = v17) | ~ in(v18, v17) | ? [v19] : (in(v19, v16) & in(v18, v19))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ (relation_image(v16, v17) = v18) | ~ relation(v16) | relation_rng(v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ~ in(v18, v17) | ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v16))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (apply(v17, v16) = v18) | ~ relation(v17) | ~ function(v17) | ? [v19] : (relation_dom(v17) = v19 & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v17, v20) = v21) | ~ (apply(v21, v16) = v22) | ~ relation(v20) | ~ function(v20) | ~ in(v16, v19) | apply(v20, v18) = v22) & ! [v20] : ! [v21] : ( ~ (apply(v20, v18) = v21) | ~ relation(v20) | ~ function(v20) | ~ in(v16, v19) | ? [v22] : (relation_composition(v17, v20) = v22 & apply(v22, v16) = v21)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (cartesian_product2(v16, v17) = v18) | ~ empty(v18) | empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ element(v16, v18) | subset(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | ~ subset(v16, v17) | element(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v16) = v17) | ~ subset(v18, v16) | in(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v16) = v17) | ~ in(v18, v17) | subset(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (singleton(v16) = v18) | ~ disjoint(v18, v17) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (singleton(v16) = v18) | ~ subset(v18, v17) | in(v16, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (singleton(v16) = v18) | ~ in(v16, v17) | subset(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_inverse_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : (relation_dom(v17) = v19 & subset(v18, v19))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_dom(v17) = v19 & relation_image(v17, v20) = v18 & set_intersection2(v19, v16) = v20)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_image(v17, v16) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v17) = v19 & subset(v18, v19))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | subset(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & set_intersection2(v20, v16) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & subset(v19, v20))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v16, v17) = v18) | ~ relation(v17) | ? [v19] : (relation_rng(v18) = v19 & subset(v19, v16))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | subset(v18, v17)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_rng(v18) = v19 & relation_rng(v17) = v20 & subset(v19, v20))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : (relation_dom(v18) = v19 & relation_dom(v17) = v20 & set_intersection2(v20, v16) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v17, v16) = v18) | ~ relation(v17) | ? [v19] : (relation_composition(v19, v17) = v18 & identity_relation(v16) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ relation_empty_yielding(v16) | ~ relation(v16) | relation_empty_yielding(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ relation_empty_yielding(v16) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ relation(v16) | ~ function(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ relation(v16) | ~ function(v16) | function(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v16, v17) = v18) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (ordered_pair(v16, v17) = v18) | ~ empty(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (ordered_pair(v16, v17) = v18) | ? [v19] : ? [v20] : (singleton(v16) = v20 & unordered_pair(v19, v20) = v18 & unordered_pair(v16, v17) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v17, v16) = v18) | set_intersection2(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | set_intersection2(v17, v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | disjoint(v16, v17) | ? [v19] : in(v19, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | subset(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_intersection2(v16, v17) = v18) | ? [v19] : (set_difference(v16, v19) = v18 & set_difference(v16, v17) = v19)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v17, v16) = v18) | set_union2(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ~ relation(v17) | ~ relation(v16) | relation(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ~ empty(v18) | empty(v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | set_union2(v17, v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | subset(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (set_union2(v16, v17) = v18) | ? [v19] : (set_difference(v17, v16) = v19 & set_union2(v16, v19) = v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v17, v16) = v18) | unordered_pair(v16, v17) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | ~ empty(v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | unordered_pair(v17, v16) = v18) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | in(v17, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ (unordered_pair(v16, v17) = v18) | in(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ disjoint(v17, v18) | ~ subset(v16, v17) | disjoint(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ disjoint(v16, v17) | ~ in(v18, v17) | ~ in(v18, v16)) & ! [v16] : ! [v17] : ! [v18] : ( ~ subset(v17, v18) | ~ subset(v16, v17) | subset(v16, v18)) & ! [v16] : ! [v17] : ! [v18] : ( ~ subset(v16, v17) | ~ in(v18, v16) | in(v18, v17)) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | v17 = empty_set | ~ (set_meet(v17) = v18) | ? [v19] : ? [v20] : (( ~ in(v19, v16) | (in(v20, v17) & ~ in(v19, v20))) & (in(v19, v16) | ! [v21] : ( ~ in(v21, v17) | in(v19, v21))))) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_rng(v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v16) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v19) = v23) | ~ in(v23, v17))) & (in(v19, v16) | (ordered_pair(v20, v19) = v21 & in(v21, v17))))) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (union(v17) = v18) | ? [v19] : ? [v20] : (( ~ in(v19, v16) | ! [v21] : ( ~ in(v21, v17) | ~ in(v19, v21))) & (in(v19, v16) | (in(v20, v17) & in(v19, v20))))) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (relation_dom(v17) = v18) | ~ relation(v17) | ? [v19] : ? [v20] : ? [v21] : (( ~ in(v19, v16) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v19, v22) = v23) | ~ in(v23, v17))) & (in(v19, v16) | (ordered_pair(v19, v20) = v21 & in(v21, v17))))) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (powerset(v17) = v18) | ? [v19] : (( ~ subset(v19, v17) | ~ in(v19, v16)) & (subset(v19, v17) | in(v19, v16)))) & ? [v16] : ! [v17] : ! [v18] : (v18 = v16 | ~ (singleton(v17) = v18) | ? [v19] : (( ~ (v19 = v17) | ~ in(v17, v16)) & (v19 = v17 | in(v19, v16)))) & ? [v16] : ! [v17] : ! [v18] : (v17 = empty_set | ~ (set_meet(v17) = v18) | in(v16, v18) | ? [v19] : (in(v19, v17) & ~ in(v16, v19))) & ? [v16] : ! [v17] : ! [v18] : ( ~ (powerset(v17) = v18) | element(v16, v18) | ? [v19] : (in(v19, v16) & ~ in(v19, v17))) & ? [v16] : ! [v17] : ! [v18] : ( ~ (singleton(v17) = v18) | disjoint(v18, v16) | in(v17, v16)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_difference(v16, empty_set) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (cast_to_subset(v16) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_intersection2(v16, v16) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, v16) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ (set_union2(v16, empty_set) = v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ subset(v17, v16) | ~ subset(v16, v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ subset(v16, v17) | proper_subset(v16, v17)) & ! [v16] : ! [v17] : (v17 = v16 | ~ relation(v17) | ~ relation(v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & ( ~ in(v20, v17) | ~ in(v20, v16)) & (in(v20, v17) | in(v20, v16)))) & ! [v16] : ! [v17] : (v17 = v16 | ~ empty(v17) | ~ empty(v16)) & ! [v16] : ! [v17] : (v17 = empty_set | ~ (complements_of_subsets(v16, v17) = empty_set) | ? [v18] : ? [v19] : (powerset(v18) = v19 & powerset(v16) = v18 & ~ element(v17, v19))) & ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_difference(empty_set, v16) = v17)) & ! [v16] : ! [v17] : (v17 = empty_set | ~ (set_intersection2(v16, empty_set) = v17)) & ! [v16] : ! [v17] : (v16 = empty_set | ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : ( ~ (v18 = empty_set) & relation_dom(v16) = v18)) & ! [v16] : ! [v17] : (v16 = empty_set | ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : ( ~ (v18 = empty_set) & relation_rng(v16) = v18)) & ! [v16] : ! [v17] : (v16 = empty_set | ~ (relation_inverse_image(v17, v16) = empty_set) | ~ relation(v17) | ? [v18] : (relation_rng(v17) = v18 & ~ subset(v16, v18))) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | relation_inverse(v16) = v17) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | one_to_one(v17)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_rng(v16) = v18 & relation_dom(v17) = v18 & relation_dom(v16) = v19)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (relation_rng(v16) = v18 & relation_dom(v16) = v19 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (relation_dom(v17) = v20) | ~ (apply(v17, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ relation(v17) | ~ function(v17) | ~ in(v22, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (relation_dom(v17) = v20) | ~ (apply(v17, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v17) = v20) | ~ (apply(v17, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ relation(v17) | ~ function(v17) | ~ in(v22, v19) | in(v21, v18)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v17) = v20) | ~ (apply(v17, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ relation(v17) | ~ function(v17) | ~ in(v21, v18) | in(v22, v19)) & ! [v20] : (v20 = v18 | ~ (relation_dom(v17) = v20) | ~ relation(v17) | ~ function(v17)) & ! [v20] : (v20 = v17 | ~ (relation_dom(v20) = v18) | ~ relation(v20) | ~ function(v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v20, v21) = v23 & apply(v16, v22) = v24 & ((v24 = v21 & in(v22, v19) & ( ~ (v23 = v22) | ~ in(v21, v18))) | (v23 = v22 & in(v21, v18) & ( ~ (v24 = v21) | ~ in(v22, v19)))))))) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ relation(v16) | ~ function(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (function_inverse(v16) = v17) | ~ relation(v16) | ~ function(v16) | function(v17)) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | function_inverse(v16) = v17) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | function(v17)) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ relation(v16) | relation_inverse(v17) = v16) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ relation(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v17) = v19 & relation_rng(v16) = v18 & relation_dom(v17) = v18 & relation_dom(v16) = v19)) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_inverse(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (relation_field(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_rng(v16) = v19 & relation_dom(v16) = v18 & set_union2(v18, v19) = v17)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (function_inverse(v16) = v18 & relation_rng(v18) = v19 & relation_dom(v18) = v17 & relation_dom(v16) = v19)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (function_inverse(v16) = v18 & relation_dom(v16) = v19 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v17)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v19) | in(v21, v17)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v17) | in(v22, v19)) & ! [v20] : (v20 = v18 | ~ (relation_dom(v20) = v17) | ~ relation(v20) | ~ function(v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v20, v21) = v23 & apply(v16, v22) = v24 & ((v24 = v21 & in(v22, v19) & ( ~ (v23 = v22) | ~ in(v21, v17))) | (v23 = v22 & in(v21, v17) & ( ~ (v24 = v21) | ~ in(v22, v19)))))) & ! [v20] : (v20 = v17 | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18)))) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ~ empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_inverse(v16) = v18 & relation_rng(v18) = v19 & relation_dom(v18) = v17 & relation_dom(v16) = v19)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & relation_image(v16, v18) = v17)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & ! [v19] : ! [v20] : ( ~ (relation_composition(v19, v16) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : (relation_rng(v20) = v22 & relation_rng(v19) = v21 & (v22 = v17 | ~ subset(v18, v21)))) & ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ subset(v18, v20) | ~ relation(v19) | ? [v21] : (relation_composition(v19, v16) = v21 & relation_rng(v21) = v17)))) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & ! [v19] : ! [v20] : ( ~ (relation_composition(v16, v19) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : (relation_dom(v20) = v22 & relation_dom(v19) = v21 & (v22 = v18 | ~ subset(v17, v21)))) & ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ subset(v17, v20) | ~ relation(v19) | ? [v21] : (relation_composition(v16, v19) = v21 & relation_dom(v21) = v18)))) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | subset(v17, v20)) & ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | ? [v21] : (relation_dom(v19) = v21 & subset(v18, v21))) & ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | subset(v18, v20)) & ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | ? [v21] : (relation_rng(v19) = v21 & subset(v17, v21))))) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_dom(v16) = v18 & ( ~ (v18 = empty_set) | v17 = empty_set) & ( ~ (v17 = empty_set) | v18 = empty_set))) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (set_difference(v16, v17) = v16) | disjoint(v16, v17)) & ! [v16] : ! [v17] : ( ~ (set_difference(v16, v17) = empty_set) | subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ (cast_to_subset(v16) = v17) | ? [v18] : (powerset(v16) = v18 & element(v17, v18))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (function_inverse(v16) = v19 & relation_rng(v19) = v17 & relation_rng(v16) = v18 & relation_dom(v19) = v18)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ one_to_one(v16) | ~ relation(v16) | ~ function(v16) | ? [v18] : ? [v19] : (function_inverse(v16) = v18 & relation_rng(v16) = v19 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v17)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v23) | ~ (apply(v16, v22) = v21) | ~ relation(v18) | ~ function(v18) | ~ in(v22, v17) | in(v21, v19)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v18) = v20) | ~ (apply(v18, v21) = v22) | ~ (apply(v16, v22) = v23) | ~ relation(v18) | ~ function(v18) | ~ in(v21, v19) | in(v22, v17)) & ! [v20] : (v20 = v19 | ~ (relation_dom(v18) = v20) | ~ relation(v18) | ~ function(v18)) & ! [v20] : (v20 = v18 | ~ (relation_dom(v20) = v19) | ~ relation(v20) | ~ function(v20) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : (apply(v20, v21) = v23 & apply(v16, v22) = v24 & ((v24 = v21 & in(v22, v17) & ( ~ (v23 = v22) | ~ in(v21, v19))) | (v23 = v22 & in(v21, v19) & ( ~ (v24 = v21) | ~ in(v22, v17)))))))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ~ function(v16) | one_to_one(v16) | ? [v18] : ? [v19] : ? [v20] : ( ~ (v19 = v18) & apply(v16, v19) = v20 & apply(v16, v18) = v20 & in(v19, v17) & in(v18, v17))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ~ empty(v17) | empty(v16)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : ? [v19] : (relation_inverse(v16) = v19 & relation_rng(v19) = v17 & relation_rng(v16) = v18 & relation_dom(v19) = v18)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & ! [v19] : ! [v20] : ( ~ (relation_composition(v19, v16) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : (relation_rng(v20) = v22 & relation_rng(v19) = v21 & (v22 = v18 | ~ subset(v17, v21)))) & ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ subset(v17, v20) | ~ relation(v19) | ? [v21] : (relation_composition(v19, v16) = v21 & relation_rng(v21) = v18)))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & ! [v19] : ! [v20] : ( ~ (relation_composition(v16, v19) = v20) | ~ relation(v19) | ? [v21] : ? [v22] : (relation_dom(v20) = v22 & relation_dom(v19) = v21 & (v22 = v17 | ~ subset(v18, v21)))) & ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ subset(v18, v20) | ~ relation(v19) | ? [v21] : (relation_composition(v16, v19) = v21 & relation_dom(v21) = v17)))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | subset(v18, v20)) & ! [v19] : ! [v20] : ( ~ (relation_rng(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | ? [v21] : (relation_dom(v19) = v21 & subset(v17, v21))) & ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | subset(v17, v20)) & ! [v19] : ! [v20] : ( ~ (relation_dom(v19) = v20) | ~ subset(v16, v19) | ~ relation(v19) | ? [v21] : (relation_rng(v19) = v21 & subset(v18, v21))))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ relation(v16) | ? [v18] : (relation_rng(v16) = v18 & ( ~ (v18 = empty_set) | v17 = empty_set) & ( ~ (v17 = empty_set) | v18 = empty_set))) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ empty(v16) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ~ empty(v17)) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | union(v17) = v16) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | empty(v16) | ? [v18] : (element(v18, v17) & ~ empty(v18))) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : (cast_to_subset(v16) = v18 & element(v18, v17))) & ! [v16] : ! [v17] : ( ~ (powerset(v16) = v17) | ? [v18] : (element(v18, v17) & empty(v18))) & ! [v16] : ! [v17] : ( ~ (singleton(v17) = v16) | subset(v16, v16)) & ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | ~ empty(v17)) & ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | unordered_pair(v16, v16) = v17) & ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | subset(empty_set, v17)) & ! [v16] : ! [v17] : ( ~ (singleton(v16) = v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ (identity_relation(v16) = v17) | relation_rng(v17) = v16) & ! [v16] : ! [v17] : ( ~ (identity_relation(v16) = v17) | relation_dom(v17) = v16) & ! [v16] : ! [v17] : ( ~ (identity_relation(v16) = v17) | relation(v17)) & ! [v16] : ! [v17] : ( ~ (identity_relation(v16) = v17) | function(v17)) & ! [v16] : ! [v17] : ( ~ (set_intersection2(v16, v17) = empty_set) | disjoint(v16, v17)) & ! [v16] : ! [v17] : ( ~ (unordered_pair(v16, v16) = v17) | singleton(v16) = v17) & ! [v16] : ! [v17] : ( ~ disjoint(v16, v17) | disjoint(v17, v16)) & ! [v16] : ! [v17] : ( ~ element(v17, v16) | ~ empty(v16) | empty(v17)) & ! [v16] : ! [v17] : ( ~ element(v17, v16) | empty(v16) | in(v17, v16)) & ! [v16] : ! [v17] : ( ~ element(v16, v17) | empty(v17) | in(v16, v17)) & ! [v16] : ! [v17] : ( ~ subset(v16, v17) | ~ proper_subset(v17, v16)) & ! [v16] : ! [v17] : ( ~ relation(v17) | ~ relation(v16) | subset(v16, v17) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v19) = v20 & in(v20, v16) & ~ in(v20, v17))) & ! [v16] : ! [v17] : ( ~ relation(v16) | ~ in(v17, v16) | ? [v18] : ? [v19] : ordered_pair(v18, v19) = v17) & ! [v16] : ! [v17] : ( ~ empty(v17) | ~ empty(v16) | element(v17, v16)) & ! [v16] : ! [v17] : ( ~ empty(v17) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ proper_subset(v17, v16) | ~ proper_subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ proper_subset(v16, v17) | subset(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v17, v16) | ~ in(v16, v17)) & ! [v16] : ! [v17] : ( ~ in(v17, v16) | element(v17, v16) | empty(v16)) & ! [v16] : ! [v17] : ( ~ in(v16, v17) | element(v16, v17)) & ! [v16] : (v16 = empty_set | ~ (relation_rng(v16) = empty_set) | ~ relation(v16)) & ! [v16] : (v16 = empty_set | ~ (relation_dom(v16) = empty_set) | ~ relation(v16)) & ! [v16] : (v16 = empty_set | ~ (set_meet(empty_set) = v16)) & ! [v16] : (v16 = empty_set | ~ subset(v16, empty_set)) & ! [v16] : (v16 = empty_set | ~ relation(v16) | ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v17, v18) = v19 & in(v19, v16))) & ! [v16] : (v16 = empty_set | ~ empty(v16)) & ! [v16] : ~ (singleton(v16) = empty_set) & ! [v16] : ( ~ relation(v16) | ~ function(v16) | ~ empty(v16) | one_to_one(v16)) & ! [v16] : ( ~ empty(v16) | relation(v16)) & ! [v16] : ( ~ empty(v16) | function(v16)) & ! [v16] : ~ proper_subset(v16, v16) & ! [v16] : ~ in(v16, empty_set) & ? [v16] : ? [v17] : (v17 = v16 | ? [v18] : (( ~ in(v18, v17) | ~ in(v18, v16)) & (in(v18, v17) | in(v18, v16)))) & ? [v16] : ? [v17] : (disjoint(v16, v17) | ? [v18] : (in(v18, v17) & in(v18, v16))) & ? [v16] : ? [v17] : element(v17, v16) & ? [v16] : ? [v17] : (subset(v16, v17) | ? [v18] : (in(v18, v16) & ~ in(v18, v17))) & ? [v16] : ? [v17] : (in(v16, v17) & ! [v18] : ! [v19] : ( ~ (powerset(v18) = v19) | ~ in(v18, v17) | in(v19, v17)) & ! [v18] : ! [v19] : ( ~ subset(v19, v18) | ~ in(v18, v17) | in(v19, v17)) & ! [v18] : ( ~ subset(v18, v17) | are_equipotent(v18, v17) | in(v18, v17))) & ? [v16] : ? [v17] : (in(v16, v17) & ! [v18] : ! [v19] : ( ~ subset(v19, v18) | ~ in(v18, v17) | in(v19, v17)) & ! [v18] : ( ~ subset(v18, v17) | are_equipotent(v18, v17) | in(v18, v17)) & ! [v18] : ( ~ in(v18, v17) | ? [v19] : (in(v19, v17) & ! [v20] : ( ~ subset(v20, v18) | in(v20, v19))))) & ? [v16] : (v16 = empty_set | ? [v17] : in(v17, v16)) & ? [v16] : subset(v16, v16) & ? [v16] : subset(empty_set, v16) & ? [v16] : (relation(v16) | ? [v17] : (in(v17, v16) & ! [v18] : ! [v19] : ~ (ordered_pair(v18, v19) = v17))))
% 18.22/4.77 | 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 yields:
% 18.22/4.77 | (1) ~ (all_0_8_8 = all_0_9_9) & relation_rng(empty_set) = empty_set & relation_dom(all_0_11_11) = all_0_10_10 & relation_dom(empty_set) = empty_set & apply(all_0_11_11, all_0_13_13) = all_0_9_9 & apply(all_0_12_12, all_0_13_13) = all_0_8_8 & powerset(empty_set) = all_0_15_15 & singleton(empty_set) = all_0_15_15 & relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11 & relation_empty_yielding(all_0_7_7) & relation_empty_yielding(empty_set) & one_to_one(all_0_6_6) & relation(all_0_0_0) & relation(all_0_1_1) & relation(all_0_3_3) & relation(all_0_4_4) & relation(all_0_6_6) & relation(all_0_7_7) & relation(all_0_12_12) & relation(empty_set) & function(all_0_0_0) & function(all_0_3_3) & function(all_0_6_6) & function(all_0_12_12) & empty(all_0_1_1) & empty(all_0_2_2) & empty(all_0_3_3) & empty(empty_set) & in(all_0_13_13, all_0_10_10) & ~ empty(all_0_4_4) & ~ empty(all_0_5_5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v6, v4) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v1) | in(v5, v2) | ? [v8] : (ordered_pair(v3, v6) = v8 & ~ in(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v6) = v7) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v7, v0) | in(v5, v2) | ? [v8] : (ordered_pair(v6, v4) = v8 & ~ in(v8, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v4, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v6) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ relation(v3) | ~ in(v4, v3) | ~ in(v0, v2) | in(v4, v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ relation(v0) | ~ in(v5, v2) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v6, v4) = v8 & ordered_pair(v3, v6) = v7 & in(v8, v1) & in(v7, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v1, v3) | ~ in(v0, v2) | in(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ subset(v2, v3) | ~ subset(v0, v1) | subset(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v4, v5) = v3) | ~ in(v5, v1) | ~ in(v4, v0) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v4, v3) = v5) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v4, v1) | in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v2) | in(v4, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v1) | ~ in(v5, v1) | ~ in(v4, v0) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v5, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v2) | in(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ relation(v2) | ~ relation(v0) | ~ in(v5, v0) | ~ in(v3, v1) | in(v5, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v3 | ~ (relation_dom(v1) = v2) | ~ (apply(v1, v3) = v4) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1) | ~ in(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (meet_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (union_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = empty_set | ~ (subset_difference(v0, v2, v3) = v4) | ~ (union_of_subsets(v0, v1) = v3) | ~ (cast_to_subset(v0) = v2) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (meet_of_subsets(v0, v7) = v8 & complements_of_subsets(v0, v1) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & (v8 = v4 | ~ element(v1, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v0 = empty_set | ~ (subset_complement(v0, v2) = v3) | ~ (powerset(v0) = v1) | ~ element(v4, v0) | ~ element(v2, v1) | in(v4, v3) | in(v4, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v6 & relation_rng(v1) = v5 & apply(v6, v0) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ relation(v2) | ~ relation(v1) | ~ function(v2) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_dom(v3) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & (v7 = v4 | ~ in(v0, v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v0) | ? [v5] : (ordered_pair(v2, v3) = v5 & ~ in(v5, v1))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ relation(v0) | in(v4, v1) | ? [v5] : (ordered_pair(v3, v2) = v5 & ~ in(v5, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ disjoint(v1, v3) | ~ element(v3, v2) | ~ element(v1, v2) | subset(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset_complement(v0, v3) = v4) | ~ (powerset(v0) = v2) | ~ element(v3, v2) | ~ element(v1, v2) | ~ subset(v1, v4) | disjoint(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_dom(v2) = v5 & in(v0, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (powerset(v0) = v3) | ~ element(v2, v3) | ~ element(v1, v3) | subset_difference(v0, v1, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ function(v2) | ? [v5] : (apply(v2, v0) = v5 & ( ~ (v5 = v1) | ~ in(v0, v4) | in(v3, v2)) & ( ~ in(v3, v2) | (v5 = v1 & in(v0, v4))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | ? [v5] : (relation_rng(v2) = v5 & in(v1, v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (apply(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v3, v1) = v5 & relation_dom(v5) = v6 & relation_dom(v3) = v7 & ( ~ in(v4, v2) | ~ in(v0, v7) | in(v0, v6)) & ( ~ in(v0, v6) | (in(v4, v2) & in(v0, v7))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ~ relation(v1) | relation_image(v1, v0) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ function(v0) | ~ in(v2, v1) | ? [v5] : (apply(v0, v2) = v5 & ( ~ (v5 = v3) | in(v4, v0)) & (v5 = v3 | ~ in(v4, v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (apply(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_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1)) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | (in(v4, v1) & ~ in(v3, v4))) & (in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | in(v3, v5))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v6, v3) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v4, v3) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : (( ~ in(v3, v0) | ! [v5] : ( ~ in(v5, v1) | ~ in(v3, v5))) & (in(v3, v0) | (in(v4, v1) & in(v3, v4))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : ? [v5] : (( ~ in(v3, v0) | ! [v6] : ! [v7] : ( ~ (ordered_pair(v3, v6) = v7) | ~ in(v7, v1))) & (in(v3, v0) | (ordered_pair(v3, v4) = v5 & in(v5, v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) & ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1))) & ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ relation(v1) | ~ relation(v0) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & ( ~ in(v4, v1) | ~ in(v4, v0)) & (in(v4, v1) | in(v4, v0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2)) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v1) | ~ function(v1) | ~ in(v6, v3) | in(v5, v2)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v1) = v4) | ~ (apply(v1, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v1) | ~ function(v1) | ~ in(v5, v2) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v1) = v4) | ~ relation(v1) | ~ function(v1)) & ! [v4] : (v4 = v1 | ~ (relation_dom(v4) = v2) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v2))) | (v7 = v6 & in(v5, v2) & ( ~ (v8 = v5) | ~ in(v6, v3)))))))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v1) = v3 & relation_rng(v0) = v2 & relation_dom(v1) = v2 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_dom(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v3) | in(v5, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v1) | in(v6, v3)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v1) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v3) & ( ~ (v7 = v6) | ~ in(v5, v1))) | (v7 = v6 & in(v5, v1) & ( ~ (v8 = v5) | ~ in(v6, v3)))))) & ! [v4] : (v4 = v1 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v2 & relation_rng(v2) = v3 & relation_dom(v2) = v1 & relation_dom(v0) = v3)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v2, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v1, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ? [v2] : ? [v3] : (function_inverse(v0) = v2 & relation_rng(v0) = v3 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v6 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v5 | ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v7) | ~ (apply(v0, v6) = v5) | ~ relation(v2) | ~ function(v2) | ~ in(v6, v1) | in(v5, v3)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_dom(v2) = v4) | ~ (apply(v2, v5) = v6) | ~ (apply(v0, v6) = v7) | ~ relation(v2) | ~ function(v2) | ~ in(v5, v3) | in(v6, v1)) & ! [v4] : (v4 = v3 | ~ (relation_dom(v2) = v4) | ~ relation(v2) | ~ function(v2)) & ! [v4] : (v4 = v2 | ~ (relation_dom(v4) = v3) | ~ relation(v4) | ~ function(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v4, v5) = v7 & apply(v0, v6) = v8 & ((v8 = v5 & in(v6, v1) & ( ~ (v7 = v6) | ~ in(v5, v3))) | (v7 = v6 & in(v5, v3) & ( ~ (v8 = v5) | ~ in(v6, v1)))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & in(v3, v1) & in(v2, v1))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_inverse(v0) = v3 & relation_rng(v3) = v1 & relation_rng(v0) = v2 & relation_dom(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v3, v0) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_rng(v4) = v6 & relation_rng(v3) = v5 & (v6 = v2 | ~ subset(v1, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v1, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v3, v0) = v5 & relation_rng(v5) = v2)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_composition(v0, v3) = v4) | ~ relation(v3) | ? [v5] : ? [v6] : (relation_dom(v4) = v6 & relation_dom(v3) = v5 & (v6 = v1 | ~ subset(v2, v5)))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v2, v4) | ~ relation(v3) | ? [v5] : (relation_composition(v0, v3) = v5 & relation_dom(v5) = v1)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v2, v4)) & ! [v3] : ! [v4] : ( ~ (relation_rng(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_dom(v3) = v5 & subset(v1, v5))) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | subset(v1, v4)) & ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ subset(v0, v3) | ~ relation(v3) | ? [v5] : (relation_rng(v3) = v5 & subset(v2, v5))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_rng(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2))) & ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1)) & ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1)) & ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1)) & ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0)) & ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1)) & ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0)) & ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1))) & ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0)) & ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1)) & ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0)) & ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1)) & ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set)) & ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0))) & ! [v0] : (v0 = empty_set | ~ empty(v0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0)) & ! [v0] : ( ~ empty(v0) | relation(v0)) & ! [v0] : ( ~ empty(v0) | function(v0)) & ! [v0] : ~ proper_subset(v0, v0) & ! [v0] : ~ in(v0, empty_set) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0))) & ? [v0] : ? [v1] : element(v1, v0) & ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1))) & ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1))) & ? [v0] : ? [v1] : (in(v0, v1) & ! [v2] : ! [v3] : ( ~ subset(v3, v2) | ~ in(v2, v1) | in(v3, v1)) & ! [v2] : ( ~ subset(v2, v1) | are_equipotent(v2, v1) | in(v2, v1)) & ! [v2] : ( ~ in(v2, v1) | ? [v3] : (in(v3, v1) & ! [v4] : ( ~ subset(v4, v2) | in(v4, v3))))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0)) & ? [v0] : subset(v0, v0) & ? [v0] : subset(empty_set, v0) & ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 18.53/4.83 |
% 18.53/4.83 | Applying alpha-rule on (1) yields:
% 18.53/4.83 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 18.53/4.83 | (3) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function(v1))
% 18.53/4.83 | (4) ! [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))))
% 18.53/4.83 | (5) ! [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)))
% 18.53/4.83 | (6) ! [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))))
% 18.53/4.83 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_rng(v1) = v5 & apply(v2, v0) = v6 & apply(v1, v6) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 18.53/4.83 | (8) ? [v0] : (relation(v0) | ? [v1] : (in(v1, v0) & ! [v2] : ! [v3] : ~ (ordered_pair(v2, v3) = v1)))
% 18.53/4.83 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v2) = v3 & subset(v3, v0)))
% 18.53/4.83 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v0, v2))
% 18.53/4.83 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v1) | ~ in(v3, v0) | in(v3, v2))
% 18.53/4.83 | (12) ? [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)))))
% 18.53/4.83 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 18.53/4.83 | (14) empty(all_0_2_2)
% 18.53/4.83 | (15) ! [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))
% 18.53/4.83 | (16) relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11
% 18.53/4.83 | (17) ! [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))))
% 18.53/4.83 | (18) ! [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))
% 18.53/4.83 | (19) ! [v0] : ! [v1] : ( ~ (relation_field(v0) = v1) | ~ relation(v0) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation_dom(v0) = v2 & set_union2(v2, v3) = v1))
% 18.53/4.83 | (20) relation(all_0_0_0)
% 18.53/4.83 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ relation(v1) | relation_dom_restriction(v1, v0) = v3)
% 18.53/4.83 | (22) relation(all_0_3_3)
% 18.53/4.83 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 18.53/4.83 | (24) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v0, v1) | proper_subset(v0, v1))
% 18.53/4.83 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 18.53/4.83 | (26) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1))
% 18.53/4.83 | (27) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 18.53/4.83 | (28) ! [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)))))
% 18.53/4.83 | (29) ! [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)))
% 18.53/4.83 | (30) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) & empty(v2)))
% 18.53/4.83 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 18.53/4.83 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ empty(v2))
% 18.53/4.83 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (meet_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 18.53/4.83 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ relation(v0) | subset(v0, v3))
% 18.53/4.83 | (35) relation_dom(all_0_11_11) = all_0_10_10
% 18.53/4.84 | (36) ! [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)))))
% 18.53/4.84 | (37) ! [v0] : ~ (singleton(v0) = empty_set)
% 18.53/4.84 | (38) ? [v0] : ? [v1] : (subset(v0, v1) | ? [v2] : (in(v2, v0) & ~ in(v2, v1)))
% 18.53/4.84 | (39) ! [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)))
% 18.53/4.84 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 18.53/4.84 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 18.53/4.84 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 18.53/4.84 | (43) ! [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))))
% 18.53/4.84 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ in(v2, v1))
% 18.53/4.84 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 18.53/4.84 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 18.53/4.84 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) | ~ subset(v0, v2) | ~ subset(v0, v1) | subset(v0, v3))
% 18.53/4.84 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 18.53/4.84 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (union_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v3))))
% 18.53/4.84 | (50) ! [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)))
% 18.53/4.84 | (51) ! [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))))
% 18.53/4.84 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 18.53/4.84 | (53) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | empty(v0) | ? [v2] : (element(v2, v1) & ~ empty(v2)))
% 18.53/4.84 | (54) ! [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))))
% 18.53/4.84 | (55) ! [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))
% 18.53/4.84 | (56) ! [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)))
% 18.53/4.84 | (57) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation_inverse(v0) = v1)
% 18.53/4.84 | (58) ! [v0] : ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 18.53/4.84 | (59) ! [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)
% 18.53/4.84 | (60) ! [v0] : ! [v1] : ( ~ proper_subset(v1, v0) | ~ proper_subset(v0, v1))
% 18.53/4.84 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | relation(v2))
% 18.53/4.84 | (62) ! [v0] : ! [v1] : ( ~ element(v1, v0) | empty(v0) | in(v1, v0))
% 18.53/4.84 | (63) ! [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))
% 18.53/4.84 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1) | ~ in(v3, v2))
% 18.53/4.84 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ in(v2, v1) | subset(v2, v0))
% 18.53/4.84 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ subset(v2, v0) | in(v2, v1))
% 18.53/4.84 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2))
% 18.53/4.84 | (68) ! [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))))
% 18.53/4.84 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 18.53/4.84 | (70) ! [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)))
% 18.53/4.84 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) | ? [v3] : in(v3, v2))
% 18.53/4.84 | (72) relation(all_0_1_1)
% 18.53/4.84 | (73) relation_empty_yielding(all_0_7_7)
% 18.53/4.84 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 18.53/4.84 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 18.53/4.84 | (76) ! [v0] : ( ~ relation(v0) | ~ function(v0) | ~ empty(v0) | one_to_one(v0))
% 18.53/4.84 | (77) ! [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))
% 18.53/4.84 | (78) function(all_0_6_6)
% 18.53/4.84 | (79) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 18.53/4.84 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ in(v0, v1) | element(v0, v2))
% 18.53/4.84 | (81) ! [v0] : ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 18.53/4.84 | (82) ! [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)))))
% 18.53/4.84 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v1, v2))
% 18.53/4.84 | (84) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 18.53/4.84 | (85) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (in(v2, v1) & in(v2, v0)))
% 18.53/4.84 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 18.53/4.85 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 18.53/4.85 | (88) ! [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))
% 18.53/4.85 | (89) ? [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)))))
% 18.53/4.85 | (90) ! [v0] : ! [v1] : (v1 = v0 | ~ subset(v1, v0) | ~ subset(v0, v1))
% 18.53/4.85 | (91) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & ( ~ (v2 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v2 = empty_set)))
% 18.53/4.85 | (92) ! [v0] : (v0 = empty_set | ~ relation(v0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0)))
% 18.53/4.85 | (93) empty(all_0_1_1)
% 18.53/4.85 | (94) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | one_to_one(v1))
% 18.53/4.85 | (95) ! [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)))
% 18.53/4.85 | (96) ! [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))
% 18.53/4.85 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0)))
% 18.53/4.85 | (98) ! [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))))
% 18.53/4.85 | (99) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 18.53/4.85 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 18.53/4.85 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 18.53/4.85 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ~ in(v1, v0))
% 18.53/4.85 | (103) ? [v0] : subset(v0, v0)
% 18.53/4.85 | (104) ! [v0] : ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 18.53/4.85 | (105) ! [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))))
% 18.53/4.85 | (106) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 18.53/4.85 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 18.53/4.85 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_inverse_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_dom(v1) = v3 & subset(v2, v3)))
% 18.53/4.85 | (109) ! [v0] : ! [v1] : ( ~ relation(v0) | ~ in(v1, v0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 18.53/4.85 | (110) ! [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))))
% 18.53/4.85 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 18.53/4.85 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 18.53/4.85 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 18.53/4.85 | (114) ? [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)))))
% 18.53/4.85 | (115) ! [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)))
% 18.53/4.85 | (116) ? [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)))))
% 18.53/4.85 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1) | in(v2, v0))
% 18.53/4.85 | (118) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ~ empty(v1))
% 18.53/4.85 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 18.53/4.85 | (120) ? [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)))))
% 18.53/4.85 | (121) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ disjoint(v2, v1) | ~ in(v0, v1))
% 18.53/4.85 | (122) singleton(empty_set) = all_0_15_15
% 18.53/4.85 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_difference(v0, v1, v2) = v3) | ? [v4] : (powerset(v0) = v4 & ( ~ element(v2, v4) | ~ element(v1, v4) | element(v3, v4))))
% 18.53/4.85 | (124) ? [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)))))
% 18.53/4.85 | (125) ? [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)))))
% 18.53/4.85 | (126) ! [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)))
% 18.53/4.85 | (127) ! [v0] : ! [v1] : ( ~ in(v1, v0) | ~ in(v0, v1))
% 18.53/4.85 | (128) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : (( ~ in(v2, v1) | ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 18.53/4.85 | (129) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_difference(v0, v1) = v2) | ~ disjoint(v0, v1))
% 18.53/4.85 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v1) | ~ in(v4, v1))
% 18.53/4.85 | (131) ? [v0] : ! [v1] : ! [v2] : (v1 = empty_set | ~ (set_meet(v1) = v2) | in(v0, v2) | ? [v3] : (in(v3, v1) & ~ in(v0, v3)))
% 18.53/4.85 | (132) ! [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))
% 18.53/4.86 | (133) relation(empty_set)
% 18.53/4.86 | (134) ! [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))
% 18.53/4.86 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ relation(v1) | ~ in(v2, v0) | in(v3, v1))
% 18.53/4.86 | (136) ? [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)))))
% 18.53/4.86 | (137) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_rng(v0) = v2))
% 18.53/4.86 | (138) ~ (all_0_8_8 = all_0_9_9)
% 18.53/4.86 | (139) ! [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))
% 18.53/4.86 | (140) ? [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))))
% 18.53/4.86 | (141) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 18.53/4.86 | (142) ! [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))
% 18.53/4.86 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : ? [v4] : (set_difference(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 18.53/4.86 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ~ subset(v0, v1))
% 18.53/4.86 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 18.53/4.86 | (146) ! [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))))))))
% 18.53/4.86 | (147) ! [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))))
% 18.53/4.86 | (148) ? [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)))))
% 18.53/4.86 | (149) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | empty(v1))
% 18.53/4.86 | (150) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 18.53/4.86 | (151) ! [v0] : ~ proper_subset(v0, v0)
% 18.53/4.86 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 18.53/4.86 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v4, v0) = v5) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v3, v0) = v6 & ( ~ (v6 = v1) | (v5 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11))) & ( ~ (v5 = v2) | v6 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2)))))
% 18.53/4.86 | (154) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ~ subset(v0, v1))
% 18.53/4.86 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 18.53/4.86 | (156) ? [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)))))
% 18.53/4.86 | (157) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | relation(v1))
% 18.53/4.86 | (158) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 18.53/4.86 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1))
% 18.53/4.86 | (160) apply(all_0_11_11, all_0_13_13) = all_0_9_9
% 18.53/4.86 | (161) ! [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)))
% 18.53/4.86 | (162) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | function(v2))
% 18.53/4.86 | (163) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | subset(v2, v1))
% 18.53/4.86 | (164) ! [v0] : ! [v1] : ( ~ element(v1, v0) | ~ empty(v0) | empty(v1))
% 18.53/4.86 | (165) one_to_one(all_0_6_6)
% 18.53/4.86 | (166) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1))
% 18.53/4.86 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cartesian_product2(v2, v1) = v4) | ~ (cartesian_product2(v2, v0) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 18.53/4.86 | (168) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | empty(v1))
% 18.53/4.86 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v1) | in(v3, v2))
% 18.53/4.86 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ~ in(v0, v1))
% 18.53/4.86 | (171) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 18.53/4.86 | (172) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 18.53/4.86 | (173) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 18.53/4.86 | (174) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ empty(v2) | empty(v1) | empty(v0))
% 18.53/4.86 | (175) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 18.53/4.86 | (176) ! [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))
% 18.53/4.86 | (177) in(all_0_13_13, all_0_10_10)
% 18.53/4.86 | (178) ! [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)))))
% 18.53/4.87 | (179) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ empty(v0) | empty(v2))
% 18.53/4.87 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ~ relation(v0) | relation_rng(v0) = v2)
% 18.53/4.87 | (181) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ in(v2, v1) | ? [v3] : ? [v4] : (ordered_pair(v3, v2) = v4 & in(v4, v0)))
% 18.53/4.87 | (182) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 18.53/4.87 | (183) ! [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)))
% 18.53/4.87 | (184) ! [v0] : ! [v1] : ( ~ relation(v1) | ~ relation(v0) | subset(v0, v1) | ? [v2] : ? [v3] : ? [v4] : (ordered_pair(v2, v3) = v4 & in(v4, v0) & ~ in(v4, v1)))
% 18.53/4.87 | (185) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0))
% 18.53/4.87 | (186) ! [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))))
% 18.53/4.87 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v2) = v3) | ~ element(v1, v3) | ~ empty(v2) | ~ in(v0, v1))
% 18.53/4.87 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 18.53/4.87 | (189) ! [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))
% 18.53/4.87 | (190) ! [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)))
% 18.53/4.87 | (191) ! [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))
% 18.53/4.87 | (192) ! [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))
% 18.53/4.87 | (193) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 18.53/4.87 | (194) ? [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)))
% 18.53/4.87 | (195) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = empty_set | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v2) = v3) | ~ relation(v0) | ~ function(v0) | in(v2, v1))
% 18.53/4.87 | (196) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_composition(v3, v1) = v2 & identity_relation(v0) = v3))
% 18.53/4.87 | (197) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 18.53/4.87 | (198) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_rng(v2) = v3 & relation_rng(v1) = v4 & subset(v3, v4)))
% 18.53/4.87 | (199) ! [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)
% 18.53/4.87 | (200) ~ empty(all_0_5_5)
% 18.53/4.87 | (201) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation(v2))
% 18.53/4.87 | (202) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_image(v1, v0) = v2) | ~ relation(v1) | ? [v3] : (relation_rng(v1) = v3 & subset(v2, v3)))
% 18.53/4.87 | (203) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_inverse_image(v1, v0) = empty_set) | ~ relation(v1) | ? [v2] : (relation_rng(v1) = v2 & ~ subset(v0, v2)))
% 18.53/4.87 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ subset(v0, v1) | subset(v3, v4))
% 18.53/4.87 | (205) ! [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)))
% 18.53/4.87 | (206) ! [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))
% 18.53/4.87 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 18.53/4.87 | (208) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 18.53/4.87 | (209) ! [v0] : ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 18.53/4.87 | (210) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 18.53/4.87 | (211) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ~ relation(v0) | relation_field(v0) = v3)
% 18.53/4.87 | (212) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : (( ~ (v3 = v1) | ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 18.53/4.87 | (213) function(all_0_0_0)
% 18.53/4.87 | (214) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ~ empty(v1))
% 18.53/4.87 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 18.53/4.87 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = empty_set | ~ (set_meet(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v1) | in(v2, v3))
% 18.53/4.87 | (217) ! [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)))))
% 18.53/4.87 | (218) ! [v0] : (v0 = empty_set | ~ empty(v0))
% 18.53/4.87 | (219) ! [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))
% 18.53/4.87 | (220) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ empty(v2))
% 18.53/4.87 | (221) ? [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)))))
% 18.53/4.87 | (222) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | relation(v1))
% 18.53/4.87 | (223) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | subset(v2, v1))
% 18.53/4.87 | (224) ! [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))
% 18.53/4.87 | (225) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ in(v0, v1))
% 18.53/4.88 | (226) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v0) | in(v3, v2))
% 18.53/4.88 | (227) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v1, v4))
% 18.53/4.88 | (228) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 18.53/4.88 | (229) ? [v0] : ? [v1] : element(v1, v0)
% 18.53/4.88 | (230) ! [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))
% 18.53/4.88 | (231) ! [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))
% 18.53/4.88 | (232) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0) = v1) | ~ in(v3, v0) | ~ in(v2, v3) | in(v2, v1))
% 18.53/4.88 | (233) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 18.53/4.88 | (234) relation_rng(empty_set) = empty_set
% 18.53/4.88 | (235) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | relation(v2))
% 18.53/4.88 | (236) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 18.53/4.88 | (237) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ in(v2, v1) | ~ in(v2, v0))
% 18.53/4.88 | (238) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ in(v2, v1) | ? [v3] : (in(v3, v0) & in(v2, v3)))
% 18.53/4.88 | (239) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 18.53/4.88 | (240) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ~ empty(v2) | empty(v0))
% 18.53/4.88 | (241) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation(v1))
% 18.53/4.88 | (242) ! [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))))))))
% 18.53/4.88 | (243) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 18.53/4.88 | (244) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 18.53/4.88 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_field(v2) = v4) | ~ (ordered_pair(v0, v1) = v3) | ~ relation(v2) | ~ in(v3, v2) | in(v0, v4))
% 18.88/4.88 | (246) ? [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | element(v0, v2) | ? [v3] : (in(v3, v0) & ~ in(v3, v1)))
% 18.88/4.88 | (247) ! [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))))
% 18.88/4.88 | (248) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & set_intersection2(v4, v0) = v3))
% 18.88/4.88 | (249) ! [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))
% 18.88/4.88 | (250) function(all_0_3_3)
% 18.88/4.88 | (251) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_union2(v0, v2) = v3) | ~ subset(v2, v1) | ~ subset(v0, v1) | subset(v3, v1))
% 18.88/4.88 | (252) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 18.88/4.88 | (253) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 18.88/4.88 | (254) function(all_0_12_12)
% 18.88/4.88 | (255) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 18.88/4.88 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 18.88/4.88 | (257) ! [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)))
% 18.88/4.88 | (258) ? [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)))))
% 18.88/4.88 | (259) ! [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))))
% 18.88/4.88 | (260) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v1, v2) | ~ subset(v0, v1) | disjoint(v0, v2))
% 18.88/4.88 | (261) ! [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))
% 18.88/4.88 | (262) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | relation(v2))
% 18.88/4.88 | (263) ! [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))
% 18.88/4.88 | (264) ? [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)))))
% 18.88/4.88 | (265) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_dom_restriction(v3, v0) = v4) | ~ relation(v3) | ~ relation(v1) | ~ function(v3) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v3) = v5 & set_intersection2(v5, v0) = v6 & ( ~ (v6 = v2) | v4 = v1 | ( ~ (v9 = v8) & apply(v3, v7) = v9 & apply(v1, v7) = v8 & in(v7, v2))) & ( ~ (v4 = v1) | (v6 = v2 & ! [v10] : ! [v11] : ( ~ (apply(v3, v10) = v11) | ~ in(v10, v2) | apply(v1, v10) = v11) & ! [v10] : ! [v11] : ( ~ (apply(v1, v10) = v11) | ~ in(v10, v2) | apply(v3, v10) = v11)))))
% 18.88/4.88 | (266) ! [v0] : ( ~ empty(v0) | function(v0))
% 18.88/4.88 | (267) ! [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))
% 18.88/4.88 | (268) ! [v0] : ! [v1] : (v1 = empty_set | ~ (complements_of_subsets(v0, v1) = empty_set) | ? [v2] : ? [v3] : (powerset(v2) = v3 & powerset(v0) = v2 & ~ element(v1, v3)))
% 18.88/4.88 | (269) ? [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)))))
% 18.88/4.89 | (270) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset_complement(v0, v1) = v2) | ? [v3] : (powerset(v0) = v3 & ( ~ element(v1, v3) | element(v2, v3))))
% 18.92/4.89 | (271) ! [v0] : ! [v1] : ! [v2] : ( ~ subset(v0, v1) | ~ in(v2, v0) | in(v2, v1))
% 18.92/4.89 | (272) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ empty(v0) | relation(v1))
% 18.92/4.89 | (273) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (powerset(v0) = v2) | ~ element(v1, v2) | ~ in(v3, v1) | in(v3, v0))
% 18.92/4.89 | (274) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 18.92/4.89 | (275) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3))
% 18.92/4.89 | (276) ! [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))
% 18.92/4.89 | (277) ! [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)))))
% 18.92/4.89 | (278) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ subset(v2, v3))
% 18.92/4.89 | (279) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation_empty_yielding(v0) | ~ relation(v0) | relation_empty_yielding(v2))
% 18.92/4.89 | (280) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0))
% 18.92/4.89 | (281) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 18.92/4.89 | (282) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (apply(v2, v0) = v3) | ~ (apply(v1, v3) = v4) | ~ one_to_one(v1) | ~ relation(v1) | ~ function(v1) | ? [v5] : ? [v6] : ? [v7] : (relation_composition(v2, v1) = v6 & relation_rng(v1) = v5 & apply(v6, v0) = v7 & ( ~ in(v0, v5) | (v7 = v0 & v4 = v0))))
% 18.92/4.89 | (283) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ in(v4, v5) | in(v1, v3))
% 18.92/4.89 | (284) apply(all_0_12_12, all_0_13_13) = all_0_8_8
% 18.92/4.89 | (285) ! [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)))
% 18.92/4.89 | (286) relation(all_0_4_4)
% 18.92/4.89 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ in(v3, v2) | in(v3, v0))
% 18.92/4.89 | (288) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 18.92/4.89 | (289) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v1, v4)))
% 18.92/4.89 | (290) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ relation(v0) | relation_inverse(v1) = v0)
% 18.92/4.89 | (291) ! [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))))
% 18.92/4.89 | (292) ? [v0] : subset(empty_set, v0)
% 18.92/4.89 | (293) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ function(v0) | one_to_one(v0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v3 = v2) & apply(v0, v3) = v4 & apply(v0, v2) = v4 & in(v3, v1) & in(v2, v1)))
% 18.92/4.89 | (294) powerset(empty_set) = all_0_15_15
% 18.92/4.89 | (295) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 18.92/4.89 | (296) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 18.92/4.89 | (297) ! [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)))
% 18.92/4.89 | (298) ! [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))
% 18.92/4.89 | (299) ! [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)))
% 18.92/4.89 | (300) ! [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)))))
% 18.92/4.89 | (301) ! [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))
% 18.92/4.89 | (302) empty(all_0_3_3)
% 18.92/4.89 | (303) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ in(v0, v1) | subset(v2, v1))
% 18.92/4.89 | (304) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ subset(v2, v1) | in(v0, v1))
% 18.92/4.89 | (305) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v1) = v2) | ~ in(v0, v1) | subset(v0, v2))
% 18.92/4.89 | (306) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ~ relation(v0) | ~ function(v0) | function(v1))
% 18.92/4.89 | (307) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 18.92/4.89 | (308) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ~ in(v1, v0))
% 18.92/4.89 | (309) ! [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))
% 18.92/4.89 | (310) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset_complement(v0, v2) = v3) | ~ in(v1, v3) | ~ in(v1, v2) | ? [v4] : (powerset(v0) = v4 & ~ element(v2, v4)))
% 18.92/4.89 | (311) ! [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)))
% 18.92/4.89 | (312) ! [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)))))
% 18.92/4.89 | (313) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ in(v3, v2) | ~ in(v3, v1))
% 18.92/4.89 | (314) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ~ relation(v1) | ~ relation(v0) | ~ function(v1) | ~ function(v0) | function(v2))
% 18.92/4.89 | (315) relation(all_0_6_6)
% 18.92/4.89 | (316) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | relation(v2))
% 18.92/4.89 | (317) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ relation(v1) | relation(v2))
% 18.92/4.89 | (318) relation(all_0_12_12)
% 18.92/4.89 | (319) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | function_inverse(v0) = v1)
% 18.92/4.90 | (320) ! [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))
% 18.92/4.90 | (321) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ relation(v0) | ~ empty(v1) | empty(v0))
% 18.92/4.90 | (322) ? [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v1) = v2) | disjoint(v2, v0) | in(v1, v0))
% 18.92/4.90 | (323) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 18.92/4.90 | (324) empty(empty_set)
% 18.92/4.90 | (325) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v1) = v2) | ? [v3] : ? [v4] : (subset_complement(v0, v1) = v4 & powerset(v0) = v3 & (v4 = v2 | ~ element(v1, v3))))
% 18.92/4.90 | (326) ! [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))
% 18.92/4.90 | (327) ! [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)))
% 18.92/4.90 | (328) ! [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))
% 18.92/4.90 | (329) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : ( ~ (v2 = empty_set) & relation_dom(v0) = v2))
% 18.92/4.90 | (330) ! [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)))
% 18.92/4.90 | (331) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : (( ~ subset(v3, v1) | ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 18.92/4.90 | (332) ~ empty(all_0_4_4)
% 18.92/4.90 | (333) ! [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)))))
% 18.92/4.90 | (334) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 18.92/4.90 | (335) ! [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)))
% 18.92/4.90 | (336) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 18.92/4.90 | (337) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ in(v3, v2))
% 18.92/4.90 | (338) ! [v0] : ! [v1] : ( ~ in(v1, v0) | element(v1, v0) | empty(v0))
% 18.92/4.90 | (339) ! [v0] : ! [v1] : ( ~ in(v0, v1) | element(v0, v1))
% 18.92/4.90 | (340) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ subset(v0, v2))
% 18.92/4.90 | (341) ? [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)))))
% 18.92/4.90 | (342) ! [v0] : ! [v1] : ( ~ subset(v0, v1) | ~ proper_subset(v1, v0))
% 18.92/4.90 | (343) ! [v0] : ! [v1] : ! [v2] : ( ~ (complements_of_subsets(v0, v1) = v2) | ? [v3] : ? [v4] : (powerset(v3) = v4 & powerset(v0) = v3 & ( ~ element(v1, v4) | element(v2, v4))))
% 18.92/4.90 | (344) ? [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)))))
% 18.92/4.90 | (345) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ~ empty(v0) | relation(v1))
% 18.92/4.90 | (346) ! [v0] : (v0 = empty_set | ~ (relation_dom(v0) = empty_set) | ~ relation(v0))
% 18.92/4.90 | (347) ! [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)))
% 18.92/4.90 | (348) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 18.92/4.90 | (349) relation_dom(empty_set) = empty_set
% 18.92/4.90 | (350) ? [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))))
% 18.92/4.90 | (351) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 18.92/4.90 | (352) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ empty(v0) | empty(v1))
% 18.92/4.90 | (353) ! [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))
% 18.92/4.90 | (354) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ relation(v0) | ? [v2] : (relation_dom(v0) = v2 & relation_image(v0, v2) = v1))
% 18.92/4.90 | (355) ! [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))))
% 18.92/4.90 | (356) ! [v0] : ! [v1] : (v1 = v0 | ~ empty(v1) | ~ empty(v0))
% 18.92/4.90 | (357) relation_empty_yielding(empty_set)
% 18.92/4.90 | (358) ! [v0] : (v0 = empty_set | ~ (relation_rng(v0) = empty_set) | ~ relation(v0))
% 18.92/4.90 | (359) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 18.92/4.90 | (360) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 18.92/4.90 | (361) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 18.92/4.90 | (362) ? [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)))))
% 18.92/4.90 | (363) ! [v0] : ~ in(v0, empty_set)
% 18.92/4.90 | (364) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 18.92/4.90 | (365) relation(all_0_7_7)
% 18.92/4.90 | (366) ! [v0] : (v0 = empty_set | ~ subset(v0, empty_set))
% 18.92/4.90 | (367) ! [v0] : ( ~ empty(v0) | relation(v0))
% 18.92/4.90 | (368) ! [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))))
% 18.92/4.90 | (369) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (relation_dom(v0) = v1) | ~ (apply(v0, v3) = v4) | ~ (apply(v0, v2) = v4) | ~ one_to_one(v0) | ~ relation(v0) | ~ function(v0) | ~ in(v3, v1) | ~ in(v2, v1))
% 18.92/4.90 | (370) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ~ subset(v0, v1))
% 18.92/4.91 | (371) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 18.92/4.91 | (372) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ relation(v0) | ~ function(v0) | relation(v2))
% 18.92/4.91 | (373) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v2, v3) = v4) | ~ subset(v0, v1) | ~ relation(v1) | ~ relation(v0) | ~ in(v4, v0) | in(v4, v1))
% 18.92/4.91 | (374) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 18.92/4.91 | (375) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ~ subset(v0, v1))
% 18.92/4.91 | (376) ! [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))))
% 18.92/4.91 | (377) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 18.92/4.91 | (378) ! [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))))))))
% 18.92/4.91 | (379) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 18.92/4.91 | (380) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ~ (identity_relation(v0) = v1) | ~ relation(v1) | ~ function(v1))
% 18.92/4.91 | (381) ! [v0] : ! [v1] : ( ~ element(v0, v1) | empty(v1) | in(v0, v1))
% 18.92/4.91 | (382) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 18.92/4.91 | (383) ! [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))))
% 18.92/4.91 | (384) ! [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))))
% 18.92/4.91 | (385) ! [v0] : ! [v1] : ( ~ empty(v1) | ~ empty(v0) | element(v1, v0))
% 18.92/4.91 | (386) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 18.92/4.91 | (387) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0))
% 18.92/4.91 | (388) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ~ empty(v2) | empty(v0))
% 18.92/4.91 | (389) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_intersection2(v0, v1) = v2) | ~ disjoint(v0, v1))
% 18.92/4.91 | (390) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 18.92/4.91 | (391) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 18.92/4.91 | (392) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 18.92/4.91 | (393) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ subset(v3, v2) | in(v0, v2))
% 18.92/4.91 | (394) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 18.92/4.91 | (395) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v0, v1) = v3) | ~ in(v1, v2) | ~ in(v0, v2) | subset(v3, v2))
% 18.92/4.91 | (396) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v3, v2) = v4) | ~ relation(v0) | ~ in(v4, v0) | in(v2, v1))
% 18.92/4.91 | (397) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 18.92/4.91 | (398) ! [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))
% 18.92/4.91 | (399) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ subset(v0, v1) | element(v0, v2))
% 18.92/4.91 | (400) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v1) = v2) | ~ element(v0, v2) | subset(v0, v1))
% 18.92/4.91 | (401) ! [v0] : ! [v1] : ( ~ (cast_to_subset(v0) = v1) | ? [v2] : (powerset(v0) = v2 & element(v1, v2)))
% 18.92/4.91 | (402) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (cast_to_subset(v0) = v2 & element(v2, v1)))
% 18.92/4.91 |
% 18.92/4.91 | Instantiating (89) with all_23_0_32 yields:
% 18.92/4.91 | (403) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v1, v0) = v2) | ~ relation(v1) | ? [v3] : ? [v4] : (relation_dom(v2) = v3 & relation_dom(v1) = v4 & ( ~ in(all_23_0_32, v4) | ~ in(all_23_0_32, v0) | in(all_23_0_32, v3)) & ( ~ in(all_23_0_32, v3) | (in(all_23_0_32, v4) & in(all_23_0_32, v0)))))
% 18.92/4.91 |
% 18.92/4.91 | Instantiating formula (248) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, relation(all_0_12_12), yields:
% 18.92/4.91 | (404) ? [v0] : ? [v1] : (relation_dom(all_0_11_11) = v0 & relation_dom(all_0_12_12) = v1 & set_intersection2(v1, all_0_14_14) = v0)
% 18.92/4.91 |
% 18.92/4.91 | Instantiating formula (403) with all_0_11_11, all_0_12_12, all_0_14_14 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, relation(all_0_12_12), yields:
% 18.92/4.91 | (405) ? [v0] : ? [v1] : (relation_dom(all_0_11_11) = v0 & relation_dom(all_0_12_12) = v1 & ( ~ in(all_23_0_32, v1) | ~ in(all_23_0_32, all_0_14_14) | in(all_23_0_32, v0)) & ( ~ in(all_23_0_32, v0) | (in(all_23_0_32, v1) & in(all_23_0_32, all_0_14_14))))
% 18.92/4.91 |
% 18.92/4.91 | Instantiating formula (372) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 18.92/4.91 | (406) relation(all_0_11_11)
% 18.92/4.91 |
% 18.92/4.91 | Instantiating formula (162) with all_0_11_11, all_0_14_14, all_0_12_12 and discharging atoms relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, relation(all_0_12_12), function(all_0_12_12), yields:
% 18.92/4.91 | (407) function(all_0_11_11)
% 18.92/4.91 |
% 18.92/4.91 | Instantiating (405) with all_96_0_66, all_96_1_67 yields:
% 18.92/4.91 | (408) relation_dom(all_0_11_11) = all_96_1_67 & relation_dom(all_0_12_12) = all_96_0_66 & ( ~ in(all_23_0_32, all_96_0_66) | ~ in(all_23_0_32, all_0_14_14) | in(all_23_0_32, all_96_1_67)) & ( ~ in(all_23_0_32, all_96_1_67) | (in(all_23_0_32, all_96_0_66) & in(all_23_0_32, all_0_14_14)))
% 18.92/4.91 |
% 18.92/4.91 | Applying alpha-rule on (408) yields:
% 18.92/4.91 | (409) relation_dom(all_0_11_11) = all_96_1_67
% 18.92/4.91 | (410) relation_dom(all_0_12_12) = all_96_0_66
% 18.92/4.91 | (411) ~ in(all_23_0_32, all_96_0_66) | ~ in(all_23_0_32, all_0_14_14) | in(all_23_0_32, all_96_1_67)
% 18.92/4.91 | (412) ~ in(all_23_0_32, all_96_1_67) | (in(all_23_0_32, all_96_0_66) & in(all_23_0_32, all_0_14_14))
% 18.92/4.91 |
% 18.92/4.91 | Instantiating (404) with all_98_0_68, all_98_1_69 yields:
% 18.92/4.91 | (413) relation_dom(all_0_11_11) = all_98_1_69 & relation_dom(all_0_12_12) = all_98_0_68 & set_intersection2(all_98_0_68, all_0_14_14) = all_98_1_69
% 18.92/4.91 |
% 18.92/4.91 | Applying alpha-rule on (413) yields:
% 18.92/4.91 | (414) relation_dom(all_0_11_11) = all_98_1_69
% 18.92/4.91 | (415) relation_dom(all_0_12_12) = all_98_0_68
% 18.92/4.91 | (416) set_intersection2(all_98_0_68, all_0_14_14) = all_98_1_69
% 18.92/4.91 |
% 18.92/4.91 | Instantiating formula (348) with all_0_11_11, all_98_1_69, all_0_10_10 and discharging atoms relation_dom(all_0_11_11) = all_98_1_69, relation_dom(all_0_11_11) = all_0_10_10, yields:
% 18.92/4.91 | (417) all_98_1_69 = all_0_10_10
% 18.92/4.91 |
% 18.92/4.91 | Instantiating formula (348) with all_0_11_11, all_96_1_67, all_98_1_69 and discharging atoms relation_dom(all_0_11_11) = all_98_1_69, relation_dom(all_0_11_11) = all_96_1_67, yields:
% 18.92/4.91 | (418) all_98_1_69 = all_96_1_67
% 18.92/4.92 |
% 18.92/4.92 | Combining equations (418,417) yields a new equation:
% 18.92/4.92 | (419) all_96_1_67 = all_0_10_10
% 18.92/4.92 |
% 18.92/4.92 | Simplifying 419 yields:
% 18.92/4.92 | (420) all_96_1_67 = all_0_10_10
% 18.92/4.92 |
% 18.92/4.92 | From (420) and (409) follows:
% 18.92/4.92 | (35) relation_dom(all_0_11_11) = all_0_10_10
% 18.92/4.92 |
% 18.92/4.92 | Instantiating formula (265) with all_0_11_11, all_0_12_12, all_0_10_10, all_0_11_11, all_0_14_14 and discharging atoms relation_dom(all_0_11_11) = all_0_10_10, relation_dom_restriction(all_0_12_12, all_0_14_14) = all_0_11_11, relation(all_0_11_11), relation(all_0_12_12), function(all_0_11_11), function(all_0_12_12), yields:
% 18.92/4.92 | (422) ? [v0] : (relation_dom(all_0_12_12) = v0 & set_intersection2(v0, all_0_14_14) = all_0_10_10 & ! [v1] : ! [v2] : ( ~ (apply(all_0_11_11, v1) = v2) | ~ in(v1, all_0_10_10) | apply(all_0_12_12, v1) = v2) & ! [v1] : ! [v2] : ( ~ (apply(all_0_12_12, v1) = v2) | ~ in(v1, all_0_10_10) | apply(all_0_11_11, v1) = v2))
% 18.92/4.92 |
% 18.92/4.92 | Instantiating (422) with all_195_0_152 yields:
% 18.92/4.92 | (423) relation_dom(all_0_12_12) = all_195_0_152 & set_intersection2(all_195_0_152, all_0_14_14) = all_0_10_10 & ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1) & ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1)
% 18.92/4.92 |
% 18.92/4.92 | Applying alpha-rule on (423) yields:
% 18.92/4.92 | (424) relation_dom(all_0_12_12) = all_195_0_152
% 18.92/4.92 | (425) set_intersection2(all_195_0_152, all_0_14_14) = all_0_10_10
% 18.92/4.92 | (426) ! [v0] : ! [v1] : ( ~ (apply(all_0_11_11, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_12_12, v0) = v1)
% 18.92/4.92 | (427) ! [v0] : ! [v1] : ( ~ (apply(all_0_12_12, v0) = v1) | ~ in(v0, all_0_10_10) | apply(all_0_11_11, v0) = v1)
% 18.92/4.92 |
% 18.92/4.92 | Instantiating formula (426) with all_0_9_9, all_0_13_13 and discharging atoms apply(all_0_11_11, all_0_13_13) = all_0_9_9, in(all_0_13_13, all_0_10_10), yields:
% 18.92/4.92 | (428) apply(all_0_12_12, all_0_13_13) = all_0_9_9
% 18.92/4.92 |
% 18.92/4.92 | Instantiating formula (48) with all_0_12_12, all_0_13_13, all_0_9_9, all_0_8_8 and discharging atoms apply(all_0_12_12, all_0_13_13) = all_0_8_8, apply(all_0_12_12, all_0_13_13) = all_0_9_9, yields:
% 18.92/4.92 | (429) all_0_8_8 = all_0_9_9
% 18.92/4.92 |
% 18.92/4.92 | Equations (429) can reduce 138 to:
% 18.92/4.92 | (430) $false
% 18.92/4.92 |
% 19.07/4.92 |-The branch is then unsatisfiable
% 19.07/4.92 % SZS output end Proof for theBenchmark
% 19.07/4.92
% 19.07/4.92 4299ms
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