TSTP Solution File: SEU209+2 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SEU209+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 08:47:39 EDT 2022
% Result : Theorem 29.09s 7.72s
% Output : Proof 57.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU209+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 19 01:41:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ____ _
% 0.19/0.59 ___ / __ \_____(_)___ ________ __________
% 0.19/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic
% 0.19/0.59 (ePrincess v.1.0)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2015
% 0.19/0.59 (c) Peter Backeman, 2014-2015
% 0.19/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59 Bug reports to peter@backeman.se
% 0.19/0.59
% 0.19/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.49/1.14 Prover 0: Preprocessing ...
% 6.63/2.01 Prover 0: Warning: ignoring some quantifiers
% 6.63/2.06 Prover 0: Constructing countermodel ...
% 21.57/5.95 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.31/6.10 Prover 1: Preprocessing ...
% 24.10/6.51 Prover 1: Warning: ignoring some quantifiers
% 24.10/6.52 Prover 1: Constructing countermodel ...
% 29.09/7.71 Prover 1: proved (1759ms)
% 29.09/7.72 Prover 0: stopped
% 29.09/7.72
% 29.09/7.72 No countermodel exists, formula is valid
% 29.09/7.72 % SZS status Theorem for theBenchmark
% 29.09/7.72
% 29.09/7.72 Generating proof ... Warning: ignoring some quantifiers
% 55.42/18.24 found it (size 80)
% 55.42/18.24
% 55.42/18.24 % SZS output start Proof for theBenchmark
% 55.42/18.24 Assumed formulas after preprocessing and simplification:
% 55.42/18.24 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v5 = 0) & relation_rng(empty_set) = empty_set & relation_dom(v2) = v4 & relation_dom(empty_set) = empty_set & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_inverse_image(v2, v1) = v3 & subset(v3, v4) = v5 & empty(v11) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(v6) = v7 & empty(empty_set) = 0 & relation(v11) = 0 & relation(v8) = 0 & relation(v2) = 0 & relation(empty_set) = 0 & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v18 = 0 | ~ (relation_composition(v12, v13) = v14) | ~ (ordered_pair(v15, v19) = v20) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ~ (relation(v12) = 0) | ~ (in(v20, v12) = 0) | ~ (in(v17, v14) = v18) | ? [v21] : ? [v22] : (( ~ (v22 = 0) & ordered_pair(v19, v16) = v21 & in(v21, v13) = v22) | ( ~ (v21 = 0) & relation(v13) = v21))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (relation_composition(v17, v15) = v18) | ~ (identity_relation(v14) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ (in(v16, v18) = v19) | ? [v20] : ? [v21] : ? [v22] : (relation(v15) = v20 & in(v16, v15) = v22 & in(v12, v14) = v21 & ( ~ (v20 = 0) | (( ~ (v22 = 0) | ~ (v21 = 0) | v19 = 0) & ( ~ (v19 = 0) | (v22 = 0 & v21 = 0)))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (relation_rng(v14) = v17) | ~ (relation_dom(v14) = v15) | ~ (in(v13, v17) = v18) | ~ (in(v12, v15) = v16) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v12, v13) = v20 & relation(v14) = v19 & in(v20, v14) = v21 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (cartesian_product2(v14, v15) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ (in(v16, v17) = v18) | ? [v19] : ? [v20] : (in(v13, v15) = v20 & in(v12, v14) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v18 = 0 | ~ (cartesian_product2(v13, v15) = v17) | ~ (cartesian_product2(v12, v14) = v16) | ~ (subset(v16, v17) = v18) | ? [v19] : ? [v20] : (subset(v14, v15) = v20 & subset(v12, v13) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (relation_rng(v14) = v17) | ~ (relation_dom(v14) = v15) | ~ (in(v13, v17) = v18) | ~ (in(v12, v15) = v16) | ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v12, v13) = v20 & relation(v14) = v19 & in(v20, v14) = v21 & ( ~ (v21 = 0) | ~ (v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (cartesian_product2(v12, v13) = v14) | ~ (ordered_pair(v17, v18) = v15) | ~ (in(v15, v14) = v16) | ? [v19] : ? [v20] : (in(v18, v13) = v20 & in(v17, v12) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (relation_inverse_image(v12, v13) = v14) | ~ (ordered_pair(v15, v17) = v18) | ~ (relation(v12) = 0) | ~ (in(v18, v12) = 0) | ~ (in(v15, v14) = v16) | ? [v19] : ( ~ (v19 = 0) & in(v17, v13) = v19)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v16 = 0 | ~ (relation_image(v12, v13) = v14) | ~ (ordered_pair(v17, v15) = v18) | ~ (relation(v12) = 0) | ~ (in(v18, v12) = 0) | ~ (in(v15, v14) = v16) | ? [v19] : ( ~ (v19 = 0) & in(v17, v13) = v19)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ~ (in(v17, v13) = v18) | ? [v19] : ? [v20] : (( ~ (v19 = 0) & relation(v13) = v19) | (in(v17, v14) = v19 & in(v16, v12) = v20 & ( ~ (v19 = 0) | (v20 = 0 & v18 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ~ (relation(v12) = 0) | ~ (in(v17, v12) = v18) | ? [v19] : ? [v20] : (in(v17, v14) = v19 & in(v15, v13) = v20 & ( ~ (v19 = 0) | (v20 = 0 & v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset_difference(v12, v13, v14) = v16) | ~ (element(v16, v15) = v17) | ~ (powerset(v12) = v15) | ? [v18] : ? [v19] : (element(v14, v15) = v19 & element(v13, v15) = v18 & ( ~ (v19 = 0) | ~ (v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (complements_of_subsets(v12, v13) = v16) | ~ (element(v16, v15) = v17) | ~ (powerset(v14) = v15) | ~ (powerset(v12) = v14) | ? [v18] : ( ~ (v18 = 0) & element(v13, v15) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_composition(v12, v14) = v15) | ~ (relation_dom(v15) = v16) | ~ (relation_dom(v12) = v13) | ~ (subset(v16, v13) = v17) | ? [v18] : (( ~ (v18 = 0) & relation(v14) = v18) | ( ~ (v18 = 0) & relation(v12) = v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_composition(v12, v13) = v14) | ~ (relation_rng(v14) = v15) | ~ (relation_rng(v13) = v16) | ~ (subset(v15, v16) = v17) | ~ (relation(v12) = 0) | ? [v18] : ( ~ (v18 = 0) & relation(v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_inverse(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ (relation(v13) = 0) | ~ (in(v16, v13) = v17) | ? [v18] : ? [v19] : (( ~ (v19 = 0) & ordered_pair(v15, v14) = v18 & in(v18, v12) = v19) | ( ~ (v18 = 0) & relation(v12) = v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_field(v14) = v15) | ~ (in(v13, v15) = v17) | ~ (in(v12, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v12, v13) = v19 & relation(v14) = v18 & in(v19, v14) = v20 & ( ~ (v20 = 0) | ~ (v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_rng(v14) = v15) | ~ (relation_rng(v13) = v16) | ~ (relation_rng_restriction(v12, v13) = v14) | ~ (subset(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & relation(v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (relation_rng(v14) = v15) | ~ (relation_rng(v13) = v16) | ~ (relation_dom_restriction(v13, v12) = v14) | ~ (subset(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & relation(v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_difference(v13, v15) = v16) | ~ (singleton(v14) = v15) | ~ (subset(v12, v16) = v17) | ? [v18] : ? [v19] : (subset(v12, v13) = v18 & in(v14, v12) = v19 & ( ~ (v18 = 0) | v19 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (set_difference(v13, v14) = v16) | ~ (set_difference(v12, v14) = v15) | ~ (subset(v15, v16) = v17) | ? [v18] : ( ~ (v18 = 0) & subset(v12, v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (subset(v15, v16) = v17) | ~ (set_intersection2(v13, v14) = v16) | ~ (set_intersection2(v12, v14) = v15) | ? [v18] : ( ~ (v18 = 0) & subset(v12, v13) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v16 = 0 | ~ (relation_field(v14) = v15) | ~ (in(v13, v15) = v17) | ~ (in(v12, v15) = v16) | ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v12, v13) = v19 & relation(v14) = v18 & in(v19, v14) = v20 & ( ~ (v20 = 0) | ~ (v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (relation_rng(v12) = v13) | ~ (ordered_pair(v16, v14) = v17) | ~ (in(v17, v12) = 0) | ~ (in(v14, v13) = v15) | ? [v18] : ( ~ (v18 = 0) & relation(v12) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v15 = 0 | ~ (relation_dom(v12) = v13) | ~ (ordered_pair(v14, v16) = v17) | ~ (in(v17, v12) = 0) | ~ (in(v14, v13) = v15) | ? [v18] : ( ~ (v18 = 0) & relation(v12) = v18)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_composition(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ~ (relation(v12) = 0) | ~ (in(v17, v14) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = 0 & v20 = 0 & ordered_pair(v18, v16) = v21 & ordered_pair(v15, v18) = v19 & in(v21, v13) = 0 & in(v19, v12) = 0) | ( ~ (v18 = 0) & relation(v13) = v18))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (subset_complement(v12, v15) = v16) | ~ (element(v13, v14) = 0) | ~ (powerset(v12) = v14) | ~ (subset(v13, v16) = v17) | ? [v18] : ? [v19] : (disjoint(v13, v15) = v19 & element(v15, v14) = v18 & ( ~ (v18 = 0) | (( ~ (v19 = 0) | v17 = 0) & ( ~ (v17 = 0) | v19 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng(v15) = v16) | ~ (relation_rng_restriction(v13, v14) = v15) | ~ (in(v12, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_rng(v14) = v20 & relation(v14) = v18 & in(v12, v20) = v21 & in(v12, v13) = v19 & ( ~ (v18 = 0) | (( ~ (v21 = 0) | ~ (v19 = 0) | v17 = 0) & ( ~ (v17 = 0) | (v21 = 0 & v19 = 0)))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom(v15) = v16) | ~ (relation_dom_restriction(v14, v13) = v15) | ~ (in(v12, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (relation_dom(v14) = v20 & relation(v14) = v18 & in(v12, v20) = v21 & in(v12, v13) = v19 & ( ~ (v18 = 0) | (( ~ (v21 = 0) | ~ (v19 = 0) | v17 = 0) & ( ~ (v17 = 0) | (v21 = 0 & v19 = 0)))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v14, v15) = v17) | ~ (ordered_pair(v12, v13) = v16) | ~ (in(v16, v17) = 0) | (in(v13, v15) = 0 & in(v12, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (cartesian_product2(v13, v14) = v16) | ~ (cartesian_product2(v12, v14) = v15) | ~ (subset(v15, v16) = v17) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (cartesian_product2(v14, v13) = v20 & cartesian_product2(v14, v12) = v19 & subset(v19, v20) = v21 & subset(v12, v13) = v18 & ( ~ (v18 = 0) | (v21 = 0 & v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ~ (in(v17, v13) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & relation(v13) = v18) | (in(v17, v14) = v19 & in(v16, v12) = v18 & ( ~ (v18 = 0) | v19 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ~ (ordered_pair(v15, v16) = v17) | ~ (relation(v14) = 0) | ~ (relation(v12) = 0) | ~ (in(v17, v12) = 0) | ? [v18] : ? [v19] : (in(v17, v14) = v19 & in(v15, v13) = v18 & ( ~ (v18 = 0) | v19 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | v12 = empty_set | ~ (set_meet(v12) = v13) | ~ (in(v14, v15) = v16) | ~ (in(v14, v13) = 0) | ? [v17] : ( ~ (v17 = 0) & in(v15, v12) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (meet_of_subsets(v12, v13) = v15) | ~ (element(v15, v14) = v16) | ~ (powerset(v12) = v14) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & element(v13, v17) = v18 & powerset(v14) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (union_of_subsets(v12, v13) = v15) | ~ (element(v15, v14) = v16) | ~ (powerset(v12) = v14) | ? [v17] : ? [v18] : ( ~ (v18 = 0) & element(v13, v17) = v18 & powerset(v14) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset_complement(v12, v13) = v15) | ~ (element(v15, v14) = v16) | ~ (powerset(v12) = v14) | ? [v17] : ( ~ (v17 = 0) & element(v13, v14) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relation_rng(v14) = v15) | ~ (relation_rng_restriction(v12, v13) = v14) | ~ (subset(v15, v12) = v16) | ? [v17] : ( ~ (v17 = 0) & relation(v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relation_rng(v13) = v15) | ~ (relation_image(v13, v12) = v14) | ~ (subset(v14, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & relation(v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (relation_rng(v12) = v14) | ~ (relation_dom(v12) = v13) | ~ (cartesian_product2(v13, v14) = v15) | ~ (subset(v12, v15) = v16) | ? [v17] : ( ~ (v17 = 0) & relation(v12) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v13, v15) = 0) | ~ (element(v12, v14) = v16) | ~ (powerset(v14) = v15) | ? [v17] : ( ~ (v17 = 0) & in(v12, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (element(v13, v14) = 0) | ~ (powerset(v12) = v14) | ~ (in(v15, v12) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v15, v13) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v15, v14) = v16) | ~ (unordered_pair(v12, v13) = v15) | ? [v17] : ? [v18] : (in(v13, v14) = v18 & in(v12, v14) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v15, v13) = v16) | ~ (set_union2(v12, v14) = v15) | ? [v17] : ? [v18] : (subset(v14, v13) = v18 & subset(v12, v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (subset(v12, v15) = v16) | ~ (set_intersection2(v13, v14) = v15) | ? [v17] : ? [v18] : (subset(v12, v14) = v18 & subset(v12, v13) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (identity_relation(v12) = v13) | ~ (ordered_pair(v14, v14) = v15) | ~ (relation(v13) = 0) | ~ (in(v15, v13) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v12) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (set_union2(v12, v13) = v14) | ~ (in(v15, v12) = v16) | ? [v17] : ? [v18] : (in(v15, v14) = v17 & in(v15, v13) = v18 & ( ~ (v17 = 0) | v18 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v14 | ~ (identity_relation(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ (relation(v13) = 0) | ~ (in(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v13 | ~ (ordered_pair(v14, v15) = v16) | ~ (ordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = v12 | v14 = v12 | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v15 = 0 | ~ (union(v12) = v13) | ~ (in(v14, v16) = 0) | ~ (in(v14, v13) = v15) | ? [v17] : ( ~ (v17 = 0) & in(v16, v12) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v14 = v12 | ~ (ordered_pair(v14, v15) = v16) | ~ (ordered_pair(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = v12 | ~ (subset_difference(v16, v15, v14) = v13) | ~ (subset_difference(v16, v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = empty_set | ~ (subset_difference(v12, v14, v15) = v16) | ~ (meet_of_subsets(v12, v13) = v15) | ~ (cast_to_subset(v12) = v14) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (union_of_subsets(v12, v20) = v21 & complements_of_subsets(v12, v13) = v20 & element(v13, v18) = v19 & powerset(v17) = v18 & powerset(v12) = v17 & ( ~ (v19 = 0) | v21 = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = empty_set | ~ (subset_difference(v12, v14, v15) = v16) | ~ (union_of_subsets(v12, v13) = v15) | ~ (cast_to_subset(v12) = v14) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (meet_of_subsets(v12, v20) = v21 & complements_of_subsets(v12, v13) = v20 & element(v13, v18) = v19 & powerset(v17) = v18 & powerset(v12) = v17 & ( ~ (v19 = 0) | v21 = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ (relation(v13) = 0) | ~ (in(v16, v13) = 0) | ? [v17] : ? [v18] : ((v18 = 0 & ordered_pair(v15, v14) = v17 & in(v17, v12) = 0) | ( ~ (v17 = 0) & relation(v12) = v17))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_difference(v12, v13) = v14) | ~ (in(v15, v12) = v16) | ? [v17] : ? [v18] : (in(v15, v14) = v17 & in(v15, v13) = v18 & ( ~ (v17 = 0) | (v16 = 0 & ~ (v18 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_dom(v13) = v14) | ~ (relation_image(v13, v15) = v16) | ~ (set_intersection2(v14, v12) = v15) | ? [v17] : ? [v18] : (relation_image(v13, v12) = v18 & relation(v13) = v17 & ( ~ (v17 = 0) | v18 = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (singleton(v12) = v15) | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_inverse_image(v14, v13) = v15) | ~ (in(v12, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_rng(v14) = v18 & relation(v14) = v17 & ( ~ (v17 = 0) | (( ~ (v16 = 0) | (v23 = 0 & v22 = 0 & v20 = 0 & ordered_pair(v12, v19) = v21 & in(v21, v14) = 0 & in(v19, v18) = 0 & in(v19, v13) = 0)) & (v16 = 0 | ! [v24] : ( ~ (in(v24, v18) = 0) | ? [v25] : ? [v26] : ? [v27] : (ordered_pair(v12, v24) = v25 & in(v25, v14) = v26 & in(v24, v13) = v27 & ( ~ (v27 = 0) | ~ (v26 = 0))))))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_image(v14, v13) = v15) | ~ (in(v12, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : (relation_dom(v14) = v18 & relation(v14) = v17 & ( ~ (v17 = 0) | (( ~ (v16 = 0) | (v23 = 0 & v22 = 0 & v20 = 0 & ordered_pair(v19, v12) = v21 & in(v21, v14) = 0 & in(v19, v18) = 0 & in(v19, v13) = 0)) & (v16 = 0 | ! [v24] : ( ~ (in(v24, v18) = 0) | ? [v25] : ? [v26] : ? [v27] : (ordered_pair(v24, v12) = v25 & in(v25, v14) = v26 & in(v24, v13) = v27 & ( ~ (v27 = 0) | ~ (v26 = 0))))))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (relation_rng_restriction(v12, v15) = v16) | ~ (relation_dom_restriction(v14, v13) = v15) | ? [v17] : ? [v18] : ? [v19] : (relation_rng_restriction(v12, v14) = v18 & relation_dom_restriction(v18, v13) = v19 & relation(v14) = v17 & ( ~ (v17 = 0) | v19 = v16))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (subset(v12, v13) = 0) | ~ (ordered_pair(v14, v15) = v16) | ~ (relation(v12) = 0) | ~ (in(v16, v12) = 0) | ? [v17] : ((v17 = 0 & in(v16, v13) = 0) | ( ~ (v17 = 0) & relation(v13) = v17))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (identity_relation(v12) = v13) | ~ (ordered_pair(v14, v15) = v16) | ~ (relation(v13) = 0) | ~ (in(v16, v13) = 0) | in(v14, v12) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_intersection2(v12, v13) = v14) | ~ (in(v15, v12) = v16) | ? [v17] : ? [v18] : (in(v15, v14) = v17 & in(v15, v13) = v18 & ( ~ (v17 = 0) | (v18 = 0 & v16 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (set_union2(v12, v13) = v14) | ~ (in(v15, v12) = v16) | ? [v17] : ? [v18] : (in(v15, v14) = v18 & in(v15, v13) = v17 & (v18 = 0 | ( ~ (v17 = 0) & ~ (v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_composition(v12, v13) = v14) | ~ (relation(v15) = 0) | ~ (relation(v12) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : (( ~ (v16 = 0) & relation(v13) = v16) | (ordered_pair(v16, v17) = v18 & in(v18, v15) = v19 & ( ~ (v19 = 0) | ! [v25] : ! [v26] : ( ~ (ordered_pair(v16, v25) = v26) | ~ (in(v26, v12) = 0) | ? [v27] : ? [v28] : ( ~ (v28 = 0) & ordered_pair(v25, v17) = v27 & in(v27, v13) = v28))) & (v19 = 0 | (v24 = 0 & v22 = 0 & ordered_pair(v20, v17) = v23 & ordered_pair(v16, v20) = v21 & in(v23, v13) = 0 & in(v21, v12) = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_rng_restriction(v12, v13) = v14) | ~ (relation(v15) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (( ~ (v16 = 0) & relation(v13) = v16) | (ordered_pair(v16, v17) = v18 & in(v18, v15) = v19 & in(v18, v13) = v21 & in(v17, v12) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0)) & (v19 = 0 | (v21 = 0 & v20 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v14 | ~ (relation_dom_restriction(v12, v13) = v15) | ~ (relation(v14) = 0) | ~ (relation(v12) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (ordered_pair(v16, v17) = v18 & in(v18, v14) = v19 & in(v18, v12) = v21 & in(v16, v13) = v20 & ( ~ (v21 = 0) | ~ (v20 = 0) | ~ (v19 = 0)) & (v19 = 0 | (v21 = 0 & v20 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | v15 = v12 | ~ (unordered_pair(v12, v13) = v14) | ~ (in(v15, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (subset_complement(v12, v14) = v15) | ~ (subset_complement(v12, v13) = v14) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & element(v13, v16) = v17 & powerset(v12) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (set_difference(v13, v12) = v14) | ~ (set_union2(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (singleton(v12) = v14) | ~ (set_union2(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_difference(v12, v14) = v15) | ~ (singleton(v13) = v14) | in(v13, v12) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | v12 = empty_set | ~ (set_meet(v12) = v13) | ~ (in(v14, v13) = v15) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & in(v16, v12) = 0 & in(v14, v16) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (disjoint(v14, v13) = v15) | ~ (singleton(v12) = v14) | in(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (disjoint(v13, v14) = 0) | ~ (disjoint(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (set_difference(v12, v13) = v14) | ~ (subset(v14, v12) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (union(v13) = v14) | ~ (subset(v12, v14) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (cast_to_subset(v12) = v13) | ~ (element(v13, v14) = v15) | ~ (powerset(v12) = v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v12, v14) = v15) | ~ (powerset(v13) = v14) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & in(v16, v13) = v17 & in(v16, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (element(v12, v14) = v15) | ~ (powerset(v13) = v14) | ? [v16] : ( ~ (v16 = 0) & subset(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (powerset(v12) = v13) | ~ (subset(v14, v12) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v14, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (singleton(v12) = v14) | ~ (subset(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & in(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (relation_rng_restriction(v12, v13) = v14) | ~ (subset(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & relation(v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (relation_dom_restriction(v13, v12) = v14) | ~ (subset(v14, v13) = v15) | ? [v16] : ( ~ (v16 = 0) & relation(v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v14, v12) = v15) | ~ (set_intersection2(v12, v13) = v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v12, v14) = v15) | ~ (subset(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & subset(v13, v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (subset(v12, v14) = v15) | ~ (set_union2(v12, v13) = v14)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (unordered_pair(v12, v13) = v14) | ~ (in(v13, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (unordered_pair(v12, v13) = v14) | ~ (in(v12, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v14 = v13 | ~ (singleton(v12) = v15) | ~ (unordered_pair(v13, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (are_equipotent(v15, v14) = v13) | ~ (are_equipotent(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (meet_of_subsets(v15, v14) = v13) | ~ (meet_of_subsets(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (union_of_subsets(v15, v14) = v13) | ~ (union_of_subsets(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (complements_of_subsets(v15, v14) = v13) | ~ (complements_of_subsets(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_composition(v15, v14) = v13) | ~ (relation_composition(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (disjoint(v15, v14) = v13) | ~ (disjoint(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset_complement(v15, v14) = v13) | ~ (subset_complement(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_difference(v15, v14) = v13) | ~ (set_difference(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (cartesian_product2(v15, v14) = v13) | ~ (cartesian_product2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (element(v15, v14) = v13) | ~ (element(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (singleton(v13) = v15) | ~ (singleton(v12) = v14) | ~ (subset(v14, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (singleton(v12) = v15) | ~ (unordered_pair(v13, v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_inverse_image(v15, v14) = v13) | ~ (relation_inverse_image(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_image(v15, v14) = v13) | ~ (relation_image(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_rng_restriction(v15, v14) = v13) | ~ (relation_rng_restriction(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (relation_dom_restriction(v15, v14) = v13) | ~ (relation_dom_restriction(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (subset(v15, v14) = v13) | ~ (subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (ordered_pair(v15, v14) = v13) | ~ (ordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_intersection2(v15, v14) = v13) | ~ (set_intersection2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (set_union2(v15, v14) = v13) | ~ (set_union2(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (unordered_pair(v15, v14) = v13) | ~ (unordered_pair(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (proper_subset(v15, v14) = v13) | ~ (proper_subset(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = v12 | ~ (in(v15, v14) = v13) | ~ (in(v15, v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v13 = empty_set | ~ (element(v13, v15) = 0) | ~ (powerset(v14) = v15) | ~ (powerset(v12) = v14) | ? [v16] : ( ~ (v16 = empty_set) & complements_of_subsets(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_composition(v14, v13) = v15) | ~ (identity_relation(v12) = v14) | ? [v16] : ? [v17] : (relation_dom_restriction(v13, v12) = v17 & relation(v13) = v16 & ( ~ (v16 = 0) | v17 = v15))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v13) = v14) | ~ (set_intersection2(v14, v12) = v15) | ? [v16] : ? [v17] : ? [v18] : (relation_rng(v17) = v18 & relation_rng_restriction(v12, v13) = v17 & relation(v13) = v16 & ( ~ (v16 = 0) | v18 = v15))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v12) = v14) | ~ (relation_dom(v12) = v13) | ~ (set_union2(v13, v14) = v15) | ? [v16] : ? [v17] : (relation_field(v12) = v17 & relation(v12) = v16 & ( ~ (v16 = 0) | v17 = v15))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_rng(v12) = v13) | ~ (relation_image(v14, v13) = v15) | ? [v16] : ? [v17] : ? [v18] : (( ~ (v16 = 0) & relation(v12) = v16) | (relation_composition(v12, v14) = v17 & relation_rng(v17) = v18 & relation(v14) = v16 & ( ~ (v16 = 0) | v18 = v15)))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v14, v13) = v15) | ~ (set_union2(v12, v13) = v14) | set_difference(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v13, v12) = v14) | ~ (set_union2(v12, v14) = v15) | set_union2(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v14) = v15) | ~ (set_difference(v12, v13) = v14) | set_intersection2(v12, v13) = v15) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_difference(v12, v13) = v14) | ~ (in(v15, v12) = 0) | ? [v16] : ? [v17] : (in(v15, v14) = v17 & in(v15, v13) = v16 & (v17 = 0 | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_dom(v13) = v14) | ~ (set_intersection2(v14, v12) = v15) | ? [v16] : ? [v17] : ? [v18] : (relation_dom(v17) = v18 & relation_dom_restriction(v13, v12) = v17 & relation(v13) = v16 & ( ~ (v16 = 0) | v18 = v15))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cartesian_product2(v12, v13) = v14) | ~ (in(v15, v14) = 0) | ? [v16] : ? [v17] : (ordered_pair(v16, v17) = v15 & in(v17, v13) = 0 & in(v16, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ~ (element(v13, v15) = 0) | ~ (powerset(v12) = v15) | ? [v16] : (subset_difference(v12, v13, v14) = v16 & set_difference(v13, v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v14, v15) = 0) | ~ (powerset(v12) = v15) | ~ (in(v13, v14) = 0) | ? [v16] : ? [v17] : ( ~ (v17 = 0) & subset_complement(v12, v14) = v16 & in(v13, v16) = v17)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v13, v15) = 0) | ~ (powerset(v14) = v15) | ~ (powerset(v12) = v14) | ? [v16] : (meet_of_subsets(v12, v13) = v16 & set_meet(v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v13, v15) = 0) | ~ (powerset(v14) = v15) | ~ (powerset(v12) = v14) | ? [v16] : (union_of_subsets(v12, v13) = v16 & union(v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v13, v15) = 0) | ~ (powerset(v14) = v15) | ~ (powerset(v12) = v14) | ? [v16] : (complements_of_subsets(v12, v16) = v13 & complements_of_subsets(v12, v13) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v13, v15) = 0) | ~ (powerset(v14) = v15) | ~ (powerset(v12) = v14) | ? [v16] : (complements_of_subsets(v12, v13) = v16 & ! [v17] : (v17 = v16 | ~ (element(v17, v15) = 0) | ? [v18] : ? [v19] : ? [v20] : ? [v21] : (subset_complement(v12, v18) = v20 & element(v18, v14) = 0 & in(v20, v13) = v21 & in(v18, v17) = v19 & ( ~ (v21 = 0) | ~ (v19 = 0)) & (v21 = 0 | v19 = 0))) & ! [v17] : ( ~ (element(v17, v14) = 0) | ~ (element(v16, v15) = 0) | ? [v18] : ? [v19] : ? [v20] : (subset_complement(v12, v17) = v19 & in(v19, v13) = v20 & in(v17, v16) = v18 & ( ~ (v20 = 0) | v18 = 0) & ( ~ (v18 = 0) | v20 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (element(v13, v15) = 0) | ~ (powerset(v14) = v15) | ~ (in(v12, v13) = 0) | ? [v16] : ( ~ (v16 = 0) & empty(v14) = v16)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_inverse_image(v12, v13) = v14) | ~ (relation(v12) = 0) | ~ (in(v15, v14) = 0) | ? [v16] : ? [v17] : (ordered_pair(v15, v16) = v17 & in(v17, v12) = 0 & in(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (relation_image(v12, v13) = v14) | ~ (relation(v12) = 0) | ~ (in(v15, v14) = 0) | ? [v16] : ? [v17] : (ordered_pair(v16, v15) = v17 & in(v17, v12) = 0 & in(v16, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (subset(v15, v14) = 0) | ~ (unordered_pair(v12, v13) = v15) | (in(v13, v14) = 0 & in(v12, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (set_intersection2(v12, v13) = v14) | ~ (in(v15, v12) = 0) | ? [v16] : ? [v17] : (in(v15, v14) = v17 & in(v15, v13) = v16 & ( ~ (v16 = 0) | v17 = 0))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_difference(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (in(v16, v14) = v19 & in(v16, v13) = v18 & in(v16, v12) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0) | v19 = 0) & (v17 = 0 | (v18 = 0 & ~ (v19 = 0))))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (cartesian_product2(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : (in(v16, v12) = v17 & ( ~ (v17 = 0) | ! [v23] : ! [v24] : ( ~ (ordered_pair(v23, v24) = v16) | ? [v25] : ? [v26] : (in(v24, v14) = v26 & in(v23, v13) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0))))) & (v17 = 0 | (v22 = v16 & v21 = 0 & v20 = 0 & ordered_pair(v18, v19) = v16 & in(v19, v14) = 0 & in(v18, v13) = 0)))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (relation_inverse_image(v13, v14) = v15) | ~ (relation(v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (in(v16, v12) = v17 & ( ~ (v17 = 0) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v16, v22) = v23) | ~ (in(v23, v13) = 0) | ? [v24] : ( ~ (v24 = 0) & in(v22, v14) = v24))) & (v17 = 0 | (v21 = 0 & v20 = 0 & ordered_pair(v16, v18) = v19 & in(v19, v13) = 0 & in(v18, v14) = 0)))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (relation_image(v13, v14) = v15) | ~ (relation(v13) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : (in(v16, v12) = v17 & ( ~ (v17 = 0) | ! [v22] : ! [v23] : ( ~ (ordered_pair(v22, v16) = v23) | ~ (in(v23, v13) = 0) | ? [v24] : ( ~ (v24 = 0) & in(v22, v14) = v24))) & (v17 = 0 | (v21 = 0 & v20 = 0 & ordered_pair(v18, v16) = v19 & in(v19, v13) = 0 & in(v18, v14) = 0)))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_intersection2(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (in(v16, v14) = v19 & in(v16, v13) = v18 & in(v16, v12) = v17 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v17 = 0)) & (v17 = 0 | (v19 = 0 & v18 = 0)))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (set_union2(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (in(v16, v14) = v19 & in(v16, v13) = v18 & in(v16, v12) = v17 & ( ~ (v17 = 0) | ( ~ (v19 = 0) & ~ (v18 = 0))) & (v19 = 0 | v18 = 0 | v17 = 0))) & ? [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v12 | ~ (unordered_pair(v13, v14) = v15) | ? [v16] : ? [v17] : (in(v16, v12) = v17 & ( ~ (v17 = 0) | ( ~ (v16 = v14) & ~ (v16 = v13))) & (v17 = 0 | v16 = v14 | v16 = v13))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (relation_inverse(v12) = v13) | ~ (relation(v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : (( ~ (v15 = 0) & relation(v12) = v15) | (ordered_pair(v16, v15) = v19 & ordered_pair(v15, v16) = v17 & in(v19, v12) = v20 & in(v17, v14) = v18 & ( ~ (v20 = 0) | ~ (v18 = 0)) & (v20 = 0 | v18 = 0)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (identity_relation(v12) = v14) | ~ (relation(v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (ordered_pair(v15, v16) = v17 & in(v17, v13) = v18 & in(v15, v12) = v19 & ( ~ (v19 = 0) | ~ (v18 = 0) | ~ (v16 = v15)) & (v18 = 0 | (v19 = 0 & v16 = v15)))) & ! [v12] : ! [v13] : ! [v14] : (v14 = v13 | ~ (set_union2(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | v12 = empty_set | ~ (singleton(v13) = v14) | ~ (subset(v12, v14) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v12) = v13) | ~ (in(v14, v13) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (set_intersection2(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = empty_set | ~ (set_difference(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | v13 = v12 | ~ (proper_subset(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = v14) | ? [v15] : ? [v16] : (set_intersection2(v12, v13) = v15 & in(v16, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = v14) | ? [v15] : ( ~ (v15 = v12) & set_difference(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = v14) | ? [v15] : ( ~ (v15 = empty_set) & set_intersection2(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (disjoint(v12, v13) = v14) | ? [v15] : (in(v15, v13) = 0 & in(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (element(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (singleton(v13) = v12) | ~ (subset(v12, v12) = v14)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (singleton(v12) = v13) | ~ (subset(empty_set, v13) = v14)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (singleton(v12) = v13) | ~ (in(v12, v13) = v14)) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ~ (relation(v12) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v18 = 0 & ~ (v19 = 0) & ordered_pair(v15, v16) = v17 & in(v17, v13) = v19 & in(v17, v12) = 0) | ( ~ (v15 = 0) & relation(v13) = v15))) & ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (subset(v12, v13) = v14) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & in(v15, v13) = v16 & in(v15, v12) = 0)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_inverse(v14) = v13) | ~ (relation_inverse(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_field(v14) = v13) | ~ (relation_field(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_rng(v14) = v13) | ~ (relation_rng(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (union(v14) = v13) | ~ (union(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (cast_to_subset(v14) = v13) | ~ (cast_to_subset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation_dom(v14) = v13) | ~ (relation_dom(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (powerset(v14) = v13) | ~ (powerset(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (singleton(v14) = v13) | ~ (singleton(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (set_meet(v14) = v13) | ~ (set_meet(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (identity_relation(v14) = v13) | ~ (identity_relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (empty(v14) = v13) | ~ (empty(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v13 = v12 | ~ (relation(v14) = v13) | ~ (relation(v14) = v12)) & ! [v12] : ! [v13] : ! [v14] : (v12 = empty_set | ~ (element(v14, v13) = 0) | ~ (powerset(v12) = v13) | ? [v15] : (subset_complement(v12, v14) = v15 & ! [v16] : ! [v17] : (v17 = 0 | ~ (in(v16, v15) = v17) | ? [v18] : ? [v19] : (element(v16, v12) = v18 & in(v16, v14) = v19 & ( ~ (v18 = 0) | v19 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v13, v12) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (empty(v14) = v17 & empty(v12) = v15 & relation(v14) = v18 & relation(v13) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | (v18 = 0 & v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (empty(v14) = v17 & empty(v12) = v15 & relation(v14) = v18 & relation(v13) = v16 & ( ~ (v16 = 0) | ~ (v15 = 0) | (v18 = 0 & v17 = 0)))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_composition(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v14) = v17 & relation(v13) = v16 & relation(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (disjoint(v14, v13) = 0) | ~ (singleton(v12) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (disjoint(v12, v13) = 0) | ~ (in(v14, v12) = 0) | ? [v15] : ( ~ (v15 = 0) & in(v14, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng(v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & ordered_pair(v15, v14) = v16 & in(v16, v12) = 0) | ( ~ (v15 = 0) & relation(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_difference(v12, v14) = v12) | ~ (singleton(v13) = v14) | ? [v15] : ( ~ (v15 = 0) & in(v13, v12) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (union(v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : (in(v15, v12) = 0 & in(v14, v15) = 0)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ (relation_image(v12, v13) = v14) | ? [v15] : ? [v16] : (relation_rng(v12) = v16 & relation(v12) = v15 & ( ~ (v15 = 0) | v16 = v14))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom(v12) = v13) | ~ (in(v14, v13) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & ordered_pair(v14, v15) = v16 & in(v16, v12) = 0) | ( ~ (v15 = 0) & relation(v12) = v15))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (cartesian_product2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (empty(v14) = v17 & empty(v13) = v16 & empty(v12) = v15 & ( ~ (v17 = 0) | v16 = 0 | v15 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v13, v14) = 0) | ~ (powerset(v12) = v14) | ? [v15] : (subset_complement(v12, v13) = v15 & set_difference(v12, v13) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v13, v12) = v14) | ? [v15] : ? [v16] : (empty(v12) = v15 & in(v13, v12) = v16 & (v15 = 0 | (( ~ (v16 = 0) | v14 = 0) & ( ~ (v14 = 0) | v16 = 0))))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (element(v12, v14) = 0) | ~ (powerset(v13) = v14) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (powerset(v12) = v13) | ~ (subset(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v12) = v14) | ~ (subset(v14, v13) = 0) | in(v12, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_rng_restriction(v12, v13) = v14) | ? [v15] : ? [v16] : (relation(v14) = v16 & relation(v13) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (relation_dom_restriction(v12, v13) = v14) | ? [v15] : ? [v16] : (relation(v14) = v16 & relation(v12) = v15 & ( ~ (v15 = 0) | v16 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (subset(v12, v13) = 0) | ~ (in(v14, v12) = 0) | in(v14, v13) = 0) & ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | set_intersection2(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_intersection2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v14) = v17 & relation(v13) = v16 & relation(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v13, v12) = v14) | ? [v15] : ? [v16] : (empty(v14) = v16 & empty(v12) = v15 & ( ~ (v16 = 0) | v15 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | set_union2(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (relation(v14) = v17 & relation(v13) = v16 & relation(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v17 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (set_union2(v12, v13) = v14) | ? [v15] : ? [v16] : (empty(v14) = v16 & empty(v12) = v15 & ( ~ (v16 = 0) | v15 = 0))) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | unordered_pair(v13, v12) = v14) & ! [v12] : ! [v13] : ! [v14] : ( ~ (unordered_pair(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & empty(v14) = v15)) & ! [v12] : ! [v13] : ! [v14] : ( ~ (empty(v13) = v14) | ~ (empty(v12) = 0) | ? [v15] : (element(v13, v12) = v15 & ( ~ (v15 = 0) | v14 = 0) & ( ~ (v14 = 0) | v15 = 0))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | v13 = empty_set | ~ (set_meet(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (in(v15, v12) = v16 & ( ~ (v16 = 0) | (v18 = 0 & ~ (v19 = 0) & in(v17, v13) = 0 & in(v15, v17) = v19)) & (v16 = 0 | ! [v20] : ! [v21] : (v21 = 0 | ~ (in(v15, v20) = v21) | ? [v22] : ( ~ (v22 = 0) & in(v20, v13) = v22))))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_rng(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ~ (v15 = 0) & relation(v13) = v15) | (in(v15, v12) = v16 & ( ~ (v16 = 0) | ! [v20] : ! [v21] : ( ~ (ordered_pair(v20, v15) = v21) | ~ (in(v21, v13) = 0))) & (v16 = 0 | (v19 = 0 & ordered_pair(v17, v15) = v18 & in(v18, v13) = 0))))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (union(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (in(v15, v12) = v16 & ( ~ (v16 = 0) | ! [v20] : ( ~ (in(v15, v20) = 0) | ? [v21] : ( ~ (v21 = 0) & in(v20, v13) = v21))) & (v16 = 0 | (v19 = 0 & v18 = 0 & in(v17, v13) = 0 & in(v15, v17) = 0)))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (relation_dom(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (( ~ (v15 = 0) & relation(v13) = v15) | (in(v15, v12) = v16 & ( ~ (v16 = 0) | ! [v20] : ! [v21] : ( ~ (ordered_pair(v15, v20) = v21) | ~ (in(v21, v13) = 0))) & (v16 = 0 | (v19 = 0 & ordered_pair(v15, v17) = v18 & in(v18, v13) = 0))))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (powerset(v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (subset(v15, v13) = v17 & in(v15, v12) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)) & (v17 = 0 | v16 = 0))) & ? [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (singleton(v13) = v14) | ? [v15] : ? [v16] : (in(v15, v12) = v16 & ( ~ (v16 = 0) | ~ (v15 = v13)) & (v16 = 0 | v15 = v13))) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_difference(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (cast_to_subset(v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (subset(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & subset(v13, v12) = v14)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_intersection2(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (set_union2(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (empty(v13) = 0) | ~ (empty(v12) = 0)) & ! [v12] : ! [v13] : (v13 = v12 | ~ (relation(v13) = 0) | ~ (relation(v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v14, v15) = v16 & in(v16, v13) = v18 & in(v16, v12) = v17 & ( ~ (v18 = 0) | ~ (v17 = 0)) & (v18 = 0 | v17 = 0))) & ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_difference(empty_set, v12) = v13)) & ! [v12] : ! [v13] : (v13 = empty_set | ~ (set_intersection2(v12, empty_set) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(v12, v12) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (subset(empty_set, v12) = v13)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (empty(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ( ~ (v16 = 0) & element(v15, v14) = 0 & powerset(v12) = v14 & empty(v15) = v16)) & ! [v12] : ! [v13] : (v13 = 0 | ~ (relation(v12) = v13) | ? [v14] : (in(v14, v12) = 0 & ! [v15] : ! [v16] : ~ (ordered_pair(v15, v16) = v14))) & ! [v12] : ! [v13] : (v12 = empty_set | ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : (relation_rng(v12) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | ( ~ (v15 = empty_set) & ~ (v13 = empty_set))))) & ! [v12] : ! [v13] : ( ~ (disjoint(v12, v13) = 0) | disjoint(v13, v12) = 0) & ! [v12] : ! [v13] : ( ~ (disjoint(v12, v13) = 0) | set_difference(v12, v13) = v12) & ! [v12] : ! [v13] : ( ~ (disjoint(v12, v13) = 0) | set_intersection2(v12, v13) = empty_set) & ! [v12] : ! [v13] : ( ~ (disjoint(v12, v13) = 0) | ? [v14] : (set_intersection2(v12, v13) = v14 & ! [v15] : ~ (in(v15, v14) = 0))) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : (relation_rng(v13) = v18 & relation_rng(v12) = v15 & relation_dom(v13) = v16 & relation_dom(v12) = v17 & relation(v12) = v14 & ( ~ (v14 = 0) | (v18 = v17 & v16 = v15)))) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ? [v14] : ? [v15] : (relation_inverse(v13) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | v15 = v12))) & ! [v12] : ! [v13] : ( ~ (relation_inverse(v12) = v13) | ? [v14] : ? [v15] : (relation(v13) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v16 & empty(v12) = v14 & relation(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v14 = 0))) & ! [v12] : ! [v13] : ( ~ (relation_rng(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v15 & empty(v12) = v14 & relation(v13) = v16 & ( ~ (v14 = 0) | (v16 = 0 & v15 = 0)))) & ! [v12] : ! [v13] : ( ~ (set_difference(v12, v13) = empty_set) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v16 & empty(v12) = v14 & relation(v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0) | v14 = 0))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (empty(v13) = v15 & empty(v12) = v14 & relation(v13) = v16 & ( ~ (v14 = 0) | (v16 = 0 & v15 = 0)))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : (relation_rng(v12) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | ! [v16] : ! [v17] : ! [v18] : ( ~ (relation_dom(v16) = v17) | ~ (subset(v13, v17) = v18) | ? [v19] : ? [v20] : ? [v21] : ? [v22] : (relation_rng(v16) = v21 & subset(v15, v21) = v22 & subset(v12, v16) = v20 & relation(v16) = v19 & ( ~ (v20 = 0) | ~ (v19 = 0) | (v22 = 0 & v18 = 0))))))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : (relation_rng(v12) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | ! [v16] : ! [v17] : ( ~ (relation_rng(v16) = v17) | ~ (subset(v13, v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_composition(v16, v12) = v19 & relation_rng(v19) = v20 & relation(v16) = v18 & ( ~ (v18 = 0) | v20 = v15)))))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : (relation_rng(v12) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | ! [v16] : ! [v17] : ( ~ (relation_dom(v16) = v17) | ~ (subset(v15, v17) = 0) | ? [v18] : ? [v19] : ? [v20] : (relation_composition(v12, v16) = v19 & relation_dom(v19) = v20 & relation(v16) = v18 & ( ~ (v18 = 0) | v20 = v13)))))) & ! [v12] : ! [v13] : ( ~ (relation_dom(v12) = v13) | ? [v14] : ? [v15] : (relation_rng(v12) = v15 & relation(v12) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = empty_set) | v13 = empty_set) & ( ~ (v13 = empty_set) | v15 = empty_set))))) & ! [v12] : ! [v13] : ( ~ (element(v12, v13) = 0) | ? [v14] : ? [v15] : (empty(v13) = v14 & in(v12, v13) = v15 & (v15 = 0 | v14 = 0))) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | union(v13) = v12) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (powerset(v12) = v13) | ? [v14] : (element(v14, v13) = 0 & empty(v14) = 0)) & ! [v12] : ! [v13] : ( ~ (singleton(v12) = v13) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation_rng(v13) = v12) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation_dom(v13) = v12) & ! [v12] : ! [v13] : ( ~ (identity_relation(v12) = v13) | relation(v13) = 0) & ! [v12] : ! [v13] : ( ~ (unordered_pair(v12, v12) = v13) | singleton(v12) = v13) & ! [v12] : ! [v13] : ( ~ (relation(v12) = 0) | ~ (in(v13, v12) = 0) | ? [v14] : ? [v15] : ordered_pair(v14, v15) = v13) & ! [v12] : ! [v13] : ( ~ (proper_subset(v13, v12) = 0) | ? [v14] : ( ~ (v14 = 0) & subset(v12, v13) = v14)) & ! [v12] : ! [v13] : ( ~ (proper_subset(v12, v13) = 0) | subset(v12, v13) = 0) & ! [v12] : ! [v13] : ( ~ (proper_subset(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & proper_subset(v13, v12) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) & ! [v12] : ! [v13] : ( ~ (in(v12, v13) = 0) | ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) & ! [v12] : (v12 = empty_set | ~ (set_meet(empty_set) = v12)) & ! [v12] : (v12 = empty_set | ~ (subset(v12, empty_set) = 0)) & ! [v12] : (v12 = empty_set | ~ (empty(v12) = 0)) & ! [v12] : (v12 = empty_set | ~ (relation(v12) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v13, v14) = v15 & in(v15, v12) = 0)) & ! [v12] : ~ (singleton(v12) = empty_set) & ! [v12] : ( ~ (empty(v12) = 0) | relation(v12) = 0) & ! [v12] : ~ (proper_subset(v12, v12) = 0) & ! [v12] : ~ (in(v12, empty_set) = 0) & ? [v12] : ? [v13] : (v13 = v12 | ? [v14] : ? [v15] : ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0)) & (v16 = 0 | v15 = 0))) & ? [v12] : ? [v13] : element(v13, v12) = 0 & ? [v12] : ? [v13] : (in(v12, v13) = 0 & ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (powerset(v14) = v15) | ~ (in(v15, v13) = v16) | ? [v17] : ( ~ (v17 = 0) & in(v14, v13) = v17)) & ! [v14] : ! [v15] : (v15 = 0 | ~ (are_equipotent(v14, v13) = v15) | ? [v16] : ? [v17] : (subset(v14, v13) = v16 & in(v14, v13) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v14] : ! [v15] : ( ~ (subset(v15, v14) = 0) | ? [v16] : ? [v17] : (in(v15, v13) = v17 & in(v14, v13) = v16 & ( ~ (v16 = 0) | v17 = 0)))) & ? [v12] : ? [v13] : (in(v12, v13) = 0 & ! [v14] : ! [v15] : (v15 = 0 | ~ (are_equipotent(v14, v13) = v15) | ? [v16] : ? [v17] : (subset(v14, v13) = v16 & in(v14, v13) = v17 & ( ~ (v16 = 0) | v17 = 0))) & ! [v14] : ! [v15] : ( ~ (subset(v15, v14) = 0) | ? [v16] : ? [v17] : (in(v15, v13) = v17 & in(v14, v13) = v16 & ( ~ (v16 = 0) | v17 = 0))) & ! [v14] : ( ~ (in(v14, v13) = 0) | ? [v15] : (in(v15, v13) = 0 & ! [v16] : ( ~ (subset(v16, v14) = 0) | in(v16, v15) = 0)))) & ? [v12] : (v12 = empty_set | ? [v13] : in(v13, v12) = 0))
% 56.01/18.41 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11 yields:
% 56.01/18.41 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & relation_rng(empty_set) = empty_set & relation_dom(all_0_9_9) = all_0_7_7 & relation_dom(empty_set) = empty_set & powerset(empty_set) = all_0_11_11 & singleton(empty_set) = all_0_11_11 & relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8 & subset(all_0_8_8, all_0_7_7) = all_0_6_6 & empty(all_0_0_0) = 0 & empty(all_0_1_1) = 0 & empty(all_0_3_3) = all_0_2_2 & empty(all_0_5_5) = all_0_4_4 & empty(empty_set) = 0 & relation(all_0_0_0) = 0 & relation(all_0_3_3) = 0 & relation(all_0_9_9) = 0 & relation(empty_set) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (relation(v3) = v8 & in(v4, v3) = v10 & in(v0, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v10 = 0 & v9 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v0, v1) = v8 & relation(v2) = v7 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v0, v1) = v8 & relation(v2) = v7 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (in(v5, v1) = v6) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & relation(v1) = v7) | (in(v5, v2) = v7 & in(v4, v0) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ? [v7] : ? [v8] : (in(v5, v2) = v7 & in(v3, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset_difference(v0, v1, v2) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v0) = v3) | ? [v6] : ? [v7] : (element(v2, v3) = v7 & element(v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (complements_of_subsets(v0, v1) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v3) = v4) | ~ (relation_dom(v0) = v1) | ~ (subset(v4, v1) = v5) | ? [v6] : (( ~ (v6 = 0) & relation(v2) = v6) | ( ~ (v6 = 0) & relation(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (subset(v3, v4) = v5) | ~ (relation(v0) = 0) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ordered_pair(v3, v2) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & relation(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v0, v1) = v7 & relation(v2) = v6 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v0, v1) = v7 & relation(v2) = v6 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (subset(v1, v4) = v5) | ? [v6] : ? [v7] : (disjoint(v1, v3) = v7 & element(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (in(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v7 & in(v4, v0) = v6 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ? [v6] : ? [v7] : (in(v5, v2) = v7 & in(v3, v1) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (meet_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset_complement(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v1) = v3) | ~ (relation_image(v1, v0) = v2) | ~ (subset(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ~ (powerset(v2) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v1) = 0) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0)) & ! [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] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [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] : ? [v9] : (union_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4))) & ! [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] : ? [v9] : (meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | ( ~ (v5 = 0) & relation(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ? [v5] : ? [v6] : (relation_image(v1, v0) = v6 & relation(v1) = v5 & ( ~ (v5 = 0) | v6 = v4))) & ! [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) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v0, v7) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0))))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v7, v0) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0))))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v0, v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ~ (in(v4, v0) = 0) | ? [v5] : ((v5 = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & relation(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0) | in(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v3) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ordered_pair(v13, v5) = v15 & in(v15, v1) = v16))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & in(v6, v1) = v9 & in(v5, v0) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & in(v6, v2) = v7 & in(v6, v0) = v9 & in(v4, v1) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [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 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) & ! [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 | ~ (subset(v3, v2) = v1) | ~ (subset(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 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ? [v5] : (relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v5) = v6 & relation_rng_restriction(v0, v1) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = 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, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v5) = v6 & relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (powerset(v0) = v3) | ? [v4] : (subset_difference(v0, v1, v2) = v4 & set_difference(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (powerset(v0) = v3) | ~ (in(v1, v2) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v3, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = v3)) & (v6 = 0 | (v7 = 0 & v4 = v3)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0) | ( ~ (v3 = 0) & relation(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [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] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (element(v2, v1) = 0) | ~ (powerset(v0) = v1) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v2) = v5 & empty(v0) = v3 & relation(v2) = v6 & relation(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v2) = v5 & empty(v0) = v3 & relation(v2) = v6 & relation(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ? [v3] : ? [v4] : (relation_rng(v0) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | (v6 = 0 & ~ (v7 = 0) & in(v5, v1) = 0 & in(v3, v5) = v7)) & (v4 = 0 | ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v1) = v10))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) & ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) & ! [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 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v4 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0))) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & powerset(v0) = v2 & empty(v3) = v4)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set))))) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) & ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v1) = v6 & relation_rng(v0) = v3 & relation_dom(v1) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v3)))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0))) & ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom(v4) = v5) | ~ (subset(v1, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & relation(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = 0))))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v1, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v3)))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ~ (subset(v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v1)))))) & ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set))))) & ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [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) = 0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) & ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ~ (proper_subset(v0, v0) = 0) & ! [v0] : ~ (in(v0, empty_set) = 0) & ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) & ? [v0] : ? [v1] : element(v1, v0) = 0 & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))) & ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0)))) & ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 56.47/18.48 |
% 56.47/18.48 | Applying alpha-rule on (1) yields:
% 56.47/18.48 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 56.47/18.48 | (3) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 56.47/18.48 | (4) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 56.47/18.48 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v0, v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ~ (in(v4, v0) = 0) | ? [v5] : ((v5 = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & relation(v1) = v5)))
% 56.47/18.48 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (powerset(v0) = v3) | ? [v4] : (subset_difference(v0, v1, v2) = v4 & set_difference(v1, v2) = v4))
% 56.47/18.48 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0))
% 56.47/18.48 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 56.47/18.48 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 56.47/18.48 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0))
% 56.47/18.48 | (11) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (powerset(v2) = v3) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))
% 56.47/18.48 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 56.47/18.48 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v0, v1) = v8 & relation(v2) = v7 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0))))
% 56.47/18.48 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3))
% 56.47/18.48 | (15) singleton(empty_set) = all_0_11_11
% 56.47/18.49 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0))
% 56.47/18.49 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4))
% 56.47/18.49 | (18) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 56.47/18.49 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6))
% 56.47/18.49 | (20) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 56.47/18.49 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0)
% 56.47/18.49 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (subset(v3, v4) = v5) | ~ (relation(v0) = 0) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6))
% 56.47/18.49 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0) | in(v2, v0) = 0)
% 56.47/18.49 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 56.47/18.49 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 56.47/18.49 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4))
% 56.47/18.49 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v0) = v5))
% 56.47/18.49 | (28) ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0))
% 56.47/18.49 | (29) ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1)
% 56.47/18.49 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 56.47/18.49 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 56.84/18.49 | (32) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (union(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ( ~ (in(v3, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 56.84/18.49 | (33) relation(all_0_3_3) = 0
% 56.84/18.49 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 56.84/18.49 | (35) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1)))
% 56.84/18.49 | (36) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 56.84/18.49 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1))
% 56.84/18.49 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 56.84/18.49 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 56.84/18.49 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3))
% 56.84/18.49 | (41) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0)))))
% 56.84/18.49 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1))
% 56.84/18.49 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1))
% 56.84/18.49 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 56.84/18.49 | (45) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0))
% 56.84/18.49 | (46) empty(empty_set) = 0
% 56.84/18.49 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7))
% 56.84/18.49 | (48) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 56.84/18.49 | (49) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 56.84/18.49 | (50) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 56.84/18.49 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ? [v7] : ? [v8] : (in(v5, v2) = v7 & in(v3, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0))))
% 56.84/18.49 | (52) subset(all_0_8_8, all_0_7_7) = all_0_6_6
% 56.84/18.49 | (53) ~ (all_0_6_6 = 0)
% 56.84/18.49 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0))
% 56.84/18.49 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0))
% 56.84/18.49 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 56.84/18.50 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 56.84/18.50 | (58) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0))
% 56.84/18.50 | (59) ! [v0] : ~ (in(v0, empty_set) = 0)
% 56.84/18.50 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 56.84/18.50 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v0, v1) = v8 & relation(v2) = v7 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0))))
% 56.84/18.50 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 56.84/18.50 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 56.84/18.50 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 56.84/18.50 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0))
% 56.84/18.50 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (complements_of_subsets(v0, v1) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6))
% 56.84/18.50 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 56.84/18.50 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 56.84/18.50 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 56.84/18.50 | (70) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0))
% 56.84/18.50 | (71) ! [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] : ? [v9] : (union_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4)))
% 56.84/18.50 | (72) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1))
% 56.84/18.50 | (73) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2))
% 56.84/18.50 | (74) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom(v4) = v5) | ~ (subset(v1, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_rng(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & relation(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = 0)))))))
% 56.84/18.50 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4))
% 56.84/18.50 | (76) powerset(empty_set) = all_0_11_11
% 56.84/18.50 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2))
% 56.84/18.50 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 56.84/18.50 | (79) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 56.84/18.50 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 56.84/18.50 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 56.84/18.50 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v7, v0) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))))))))
% 56.84/18.51 | (83) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0)
% 56.84/18.51 | (84) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | v1 = empty_set | ~ (set_meet(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | (v6 = 0 & ~ (v7 = 0) & in(v5, v1) = 0 & in(v3, v5) = v7)) & (v4 = 0 | ! [v8] : ! [v9] : (v9 = 0 | ~ (in(v3, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v1) = v10)))))
% 56.84/18.51 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4)))
% 56.84/18.51 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 56.84/18.51 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (meet_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5))
% 56.84/18.51 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | ( ~ (v5 = 0) & relation(v0) = v5)))
% 56.84/18.51 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2))
% 56.84/18.51 | (90) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1))
% 56.84/18.51 | (91) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 56.84/18.51 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0))
% 56.84/18.51 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 56.84/18.51 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 56.84/18.51 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 56.84/18.51 | (96) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0)
% 56.84/18.51 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0))
% 56.84/18.51 | (98) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v3, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = v3)) & (v6 = 0 | (v7 = 0 & v4 = v3))))
% 56.84/18.51 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset_difference(v0, v1, v2) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v0) = v3) | ? [v6] : ? [v7] : (element(v2, v3) = v7 & element(v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 56.84/18.51 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0))
% 56.84/18.52 | (101) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_dom(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v3, v8) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v3, v5) = v6 & in(v6, v1) = 0)))))
% 56.84/18.52 | (102) ! [v0] : ~ (proper_subset(v0, v0) = 0)
% 56.84/18.52 | (103) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 56.84/18.52 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v2) = v5 & empty(v0) = v3 & relation(v2) = v6 & relation(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 56.84/18.52 | (105) relation(all_0_0_0) = 0
% 56.84/18.52 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v3) = 0) | ~ (element(v0, v2) = v4) | ~ (powerset(v2) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 56.84/18.52 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 56.84/18.52 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ? [v6] : ? [v7] : (in(v5, v2) = v7 & in(v3, v1) = v6 & ( ~ (v6 = 0) | v7 = 0)))
% 56.84/18.52 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4))
% 56.84/18.52 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3))
% 56.84/18.52 | (111) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & powerset(v0) = v2 & empty(v3) = v4))
% 56.84/18.52 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0))
% 56.84/18.52 | (113) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 56.84/18.52 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3)))
% 56.84/18.52 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ordered_pair(v3, v2) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & relation(v0) = v6)))
% 56.84/18.52 | (116) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0))
% 56.84/18.52 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 56.84/18.52 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 56.84/18.52 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0))
% 56.84/18.52 | (120) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0)))
% 56.84/18.52 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0)))))
% 56.84/18.52 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0))
% 56.84/18.52 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 56.84/18.52 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v0, v3) = v4) | ~ (set_intersection2(v1, v2) = v3) | ? [v5] : ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 56.84/18.52 | (125) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 56.84/18.52 | (126) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 56.84/18.52 | (127) ~ (all_0_4_4 = 0)
% 56.84/18.52 | (128) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 56.84/18.52 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset_complement(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5))
% 56.84/18.52 | (130) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 56.84/18.52 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 56.84/18.52 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0))))))
% 56.84/18.53 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 56.84/18.53 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 56.84/18.53 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (relation(v3) = v8 & in(v4, v3) = v10 & in(v0, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v10 = 0 & v9 = 0))))))
% 56.84/18.53 | (136) relation(empty_set) = 0
% 56.84/18.53 | (137) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0))
% 56.84/18.53 | (138) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0))
% 56.84/18.53 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v1) = v4) | ~ (set_union2(v0, v2) = v3) | ? [v5] : ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 56.84/18.53 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2))
% 56.84/18.53 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v2) = v3) | ~ (relation(v1) = 0) | ~ (in(v3, v1) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v2, v0) = v5))
% 56.84/18.53 | (142) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 56.84/18.53 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v0, v1) = v7 & relation(v2) = v6 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 56.84/18.53 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5))
% 56.84/18.53 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0))
% 56.84/18.53 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6))
% 56.84/18.53 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (in(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v7 & in(v4, v0) = v6 & ( ~ (v6 = 0) | v7 = 0))))
% 56.84/18.53 | (148) relation_dom(empty_set) = empty_set
% 56.84/18.53 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (powerset(v0) = v3) | ~ (in(v1, v2) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5))
% 56.84/18.53 | (150) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0) | ( ~ (v3 = 0) & relation(v1) = v3)))
% 56.84/18.53 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v0, v7) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0)))))))))
% 56.84/18.53 | (152) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0))))
% 56.84/18.53 | (153) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1))
% 56.84/18.53 | (154) relation(all_0_9_9) = 0
% 56.84/18.53 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 56.84/18.53 | (156) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1))
% 56.84/18.53 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 56.84/18.53 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ (in(v2, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 56.84/18.53 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0))
% 56.84/18.53 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 56.84/18.53 | (161) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 56.84/18.53 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 56.84/18.53 | (163) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0))
% 56.84/18.53 | (164) ~ (all_0_2_2 = 0)
% 56.84/18.53 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4))
% 56.84/18.53 | (166) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 56.84/18.53 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 56.84/18.53 | (168) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 56.84/18.53 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 56.84/18.53 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ? [v5] : ? [v6] : (relation_image(v1, v0) = v6 & relation(v1) = v5 & ( ~ (v5 = 0) | v6 = v4)))
% 56.84/18.53 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4))
% 56.84/18.54 | (172) ! [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] : ? [v9] : (meet_of_subsets(v0, v8) = v9 & complements_of_subsets(v0, v1) = v8 & element(v1, v6) = v7 & powerset(v5) = v6 & powerset(v0) = v5 & ( ~ (v7 = 0) | v9 = v4)))
% 56.84/18.54 | (173) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0)
% 56.84/18.54 | (174) ! [v0] : ~ (singleton(v0) = empty_set)
% 56.84/18.54 | (175) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v1, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v3))))))
% 56.84/18.54 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5))
% 56.84/18.54 | (177) relation_dom(all_0_9_9) = all_0_7_7
% 56.84/18.54 | (178) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v5) = v6 & relation_rng_restriction(v0, v1) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3)))
% 56.84/18.54 | (179) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0)
% 56.84/18.54 | (180) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 56.84/18.54 | (181) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v3) = v4) | ~ (relation_dom(v0) = v1) | ~ (subset(v4, v1) = v5) | ? [v6] : (( ~ (v6 = 0) & relation(v2) = v6) | ( ~ (v6 = 0) & relation(v0) = v6)))
% 56.84/18.54 | (182) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 56.84/18.54 | (183) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0))
% 56.84/18.54 | (184) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 56.84/18.54 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7))
% 56.84/18.54 | (186) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0))
% 56.84/18.54 | (187) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 56.84/18.54 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0))
% 56.84/18.54 | (189) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (in(v5, v1) = v6) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & relation(v1) = v7) | (in(v5, v2) = v7 & in(v4, v0) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))))
% 56.84/18.54 | (190) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (relation(v3) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & in(v6, v1) = v9 & in(v5, v0) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0)))))
% 56.84/18.54 | (191) ? [v0] : ? [v1] : element(v1, v0) = 0
% 56.84/18.54 | (192) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0)))
% 56.84/18.54 | (193) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v1) = v6 & relation_rng(v0) = v3 & relation_dom(v1) = v4 & relation_dom(v0) = v5 & relation(v0) = v2 & ( ~ (v2 = 0) | (v6 = v5 & v4 = v3))))
% 56.84/18.54 | (194) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0))
% 56.84/18.54 | (195) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (relation_rng(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (( ~ (v3 = 0) & relation(v1) = v3) | (in(v3, v0) = v4 & ( ~ (v4 = 0) | ! [v8] : ! [v9] : ( ~ (ordered_pair(v8, v3) = v9) | ~ (in(v9, v1) = 0))) & (v4 = 0 | (v7 = 0 & ordered_pair(v5, v3) = v6 & in(v6, v1) = 0)))))
% 56.84/18.54 | (196) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 56.84/18.54 | (197) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 56.84/18.54 | (198) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0)
% 56.84/18.54 | (199) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 56.84/18.54 | (200) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0))
% 56.84/18.54 | (201) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 56.84/18.54 | (202) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0))
% 56.84/18.54 | (203) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2))
% 56.84/18.54 | (204) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 56.84/18.54 | (205) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_composition(v0, v1) = v2) | ~ (relation(v3) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (( ~ (v4 = 0) & relation(v1) = v4) | (ordered_pair(v4, v5) = v6 & in(v6, v3) = v7 & ( ~ (v7 = 0) | ! [v13] : ! [v14] : ( ~ (ordered_pair(v4, v13) = v14) | ~ (in(v14, v0) = 0) | ? [v15] : ? [v16] : ( ~ (v16 = 0) & ordered_pair(v13, v5) = v15 & in(v15, v1) = v16))) & (v7 = 0 | (v12 = 0 & v10 = 0 & ordered_pair(v8, v5) = v11 & ordered_pair(v4, v8) = v9 & in(v11, v1) = 0 & in(v9, v0) = 0)))))
% 56.84/18.54 | (206) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 56.84/18.54 | (207) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 56.84/18.54 | (208) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 56.84/18.55 | (209) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 56.84/18.55 | (210) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 56.84/18.55 | (211) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0))
% 56.84/18.55 | (212) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0))
% 56.84/18.55 | (213) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 56.84/18.55 | (214) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 56.84/18.55 | (215) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 56.84/18.55 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (subset(v1, v4) = v5) | ? [v6] : ? [v7] : (disjoint(v1, v3) = v7 & element(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0)))))
% 56.84/18.55 | (217) empty(all_0_3_3) = all_0_2_2
% 56.84/18.55 | (218) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1))
% 56.84/18.55 | (219) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 56.84/18.55 | (220) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6)))
% 56.84/18.55 | (221) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0))
% 56.84/18.55 | (222) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 56.84/18.55 | (223) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 56.84/18.55 | (224) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5))
% 56.84/18.55 | (225) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v0, v1) = v7 & relation(v2) = v6 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0))))
% 56.84/18.55 | (226) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 56.84/18.55 | (227) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 56.84/18.55 | (228) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0))
% 56.84/18.55 | (229) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6))
% 56.84/18.55 | (230) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0))
% 56.84/18.55 | (231) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9)))
% 56.84/18.55 | (232) ! [v0] : ! [v1] : (v1 = v0 | ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (ordered_pair(v2, v3) = v4 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)) & (v6 = 0 | v5 = 0)))
% 56.84/18.55 | (233) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0))))))
% 56.84/18.55 | (234) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0)))
% 56.84/18.55 | (235) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 56.84/18.55 | (236) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1))
% 56.84/18.55 | (237) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ? [v3] : ? [v4] : (relation_rng(v0) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = v2)))
% 56.84/18.55 | (238) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5))
% 56.84/18.55 | (239) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 56.84/18.55 | (240) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2)))
% 56.84/18.55 | (241) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0))
% 56.84/18.55 | (242) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (powerset(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 56.84/18.55 | (243) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 56.84/18.55 | (244) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set)))))
% 56.84/18.55 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v2 | ~ (relation_dom_restriction(v0, v1) = v3) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v4, v5) = v6 & in(v6, v2) = v7 & in(v6, v0) = v9 & in(v4, v1) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)) & (v7 = 0 | (v9 = 0 & v8 = 0))))
% 56.84/18.55 | (246) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v1) = v3) | ~ (relation_image(v1, v0) = v2) | ~ (subset(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5))
% 56.84/18.55 | (247) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 56.84/18.55 | (248) ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0)))
% 56.84/18.55 | (249) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 56.84/18.55 | (250) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))
% 56.84/18.56 | (251) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (subset_complement(v0, v2) = v3) | ~ (subset_complement(v0, v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v0) = v4))
% 56.84/18.56 | (252) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0)))))
% 56.84/18.56 | (253) relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8
% 56.84/18.56 | (254) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0))))
% 56.84/18.56 | (255) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set)))))
% 56.84/18.56 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0))
% 56.84/18.56 | (257) empty(all_0_5_5) = all_0_4_4
% 56.84/18.56 | (258) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 56.84/18.56 | (259) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0))
% 56.84/18.56 | (260) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 56.84/18.56 | (261) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3))
% 56.84/18.56 | (262) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0))
% 56.84/18.56 | (263) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 56.84/18.56 | (264) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 56.84/18.56 | (265) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4))
% 56.84/18.56 | (266) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v5) = v6 & relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3)))
% 56.84/18.56 | (267) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ? [v5] : (relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 56.84/18.56 | (268) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5))
% 56.84/18.56 | (269) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 56.84/18.56 | (270) ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (element(v2, v1) = 0) | ~ (powerset(v0) = v1) | ? [v3] : (subset_complement(v0, v2) = v3 & ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v3) = v5) | ? [v6] : ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0)))))
% 56.84/18.56 | (271) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4))
% 56.84/18.56 | (272) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : (relation_rng(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ~ (subset(v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v1))))))
% 56.84/18.56 | (273) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ? [v5] : ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 56.84/18.56 | (274) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2))
% 56.84/18.56 | (275) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0))))
% 56.84/18.56 | (276) relation_rng(empty_set) = empty_set
% 56.84/18.56 | (277) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 56.84/18.56 | (278) empty(all_0_0_0) = 0
% 56.84/18.56 | (279) empty(all_0_1_1) = 0
% 56.84/18.56 | (280) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0))
% 56.84/18.56 | (281) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 56.84/18.56 | (282) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (empty(v2) = v5 & empty(v0) = v3 & relation(v2) = v6 & relation(v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0))))
% 56.84/18.56 | (283) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 56.84/18.56 | (284) ? [v0] : ? [v1] : (in(v0, v1) = 0 & ! [v2] : ! [v3] : (v3 = 0 | ~ (are_equipotent(v2, v1) = v3) | ? [v4] : ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ? [v4] : ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v2] : ( ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v1) = 0 & ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0))))
% 56.84/18.56 | (285) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0))
% 56.84/18.56 | (286) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0))
% 56.84/18.56 | (287) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 56.84/18.56 | (288) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3))))
% 56.84/18.56 | (289) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (244) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 56.84/18.56 | (290) all_0_9_9 = empty_set | ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | ( ~ (v1 = empty_set) & ~ (all_0_7_7 = empty_set))))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (192) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 56.84/18.56 | (291) ? [v0] : ? [v1] : ? [v2] : (empty(all_0_7_7) = v2 & empty(all_0_9_9) = v0 & relation(all_0_9_9) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (74) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 56.84/18.56 | (292) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v3) | ~ (subset(all_0_7_7, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v2) = v7 & subset(v1, v7) = v8 & subset(all_0_9_9, v2) = v6 & relation(v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | (v8 = 0 & v4 = 0))))))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (175) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 56.84/18.56 | (293) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | ! [v2] : ! [v3] : ( ~ (relation_rng(v2) = v3) | ~ (subset(all_0_7_7, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (relation_composition(v2, all_0_9_9) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v1)))))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (272) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 56.84/18.56 | (294) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | ! [v2] : ! [v3] : ( ~ (relation_dom(v2) = v3) | ~ (subset(v1, v3) = 0) | ? [v4] : ? [v5] : ? [v6] : (relation_composition(all_0_9_9, v2) = v5 & relation_dom(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = all_0_7_7)))))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (255) with all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, yields:
% 56.84/18.56 | (295) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = empty_set) | all_0_7_7 = empty_set) & ( ~ (all_0_7_7 = empty_set) | v1 = empty_set))))
% 56.84/18.56 |
% 56.84/18.56 | Instantiating formula (281) with all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms subset(all_0_8_8, all_0_7_7) = all_0_6_6, yields:
% 56.84/18.56 | (296) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 56.84/18.56 |
% 56.84/18.56 | Instantiating (294) with all_63_0_36, all_63_1_37 yields:
% 56.84/18.56 | (297) relation_rng(all_0_9_9) = all_63_0_36 & relation(all_0_9_9) = all_63_1_37 & ( ~ (all_63_1_37 = 0) | ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ (subset(all_63_0_36, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_9_9, v0) = v3 & relation_dom(v3) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = all_0_7_7))))
% 56.84/18.56 |
% 56.84/18.56 | Applying alpha-rule on (297) yields:
% 56.84/18.56 | (298) relation_rng(all_0_9_9) = all_63_0_36
% 56.84/18.56 | (299) relation(all_0_9_9) = all_63_1_37
% 56.84/18.56 | (300) ~ (all_63_1_37 = 0) | ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ~ (subset(all_63_0_36, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (relation_composition(all_0_9_9, v0) = v3 & relation_dom(v3) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = all_0_7_7)))
% 56.84/18.57 |
% 56.84/18.57 | Instantiating (292) with all_65_0_38, all_65_1_39 yields:
% 56.84/18.57 | (301) relation_rng(all_0_9_9) = all_65_0_38 & relation(all_0_9_9) = all_65_1_39 & ( ~ (all_65_1_39 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (subset(all_0_7_7, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_65_0_38, v5) = v6 & subset(all_0_9_9, v0) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0)))))
% 56.84/18.57 |
% 56.84/18.57 | Applying alpha-rule on (301) yields:
% 56.84/18.57 | (302) relation_rng(all_0_9_9) = all_65_0_38
% 56.84/18.57 | (303) relation(all_0_9_9) = all_65_1_39
% 56.84/18.57 | (304) ~ (all_65_1_39 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (subset(all_0_7_7, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & subset(all_65_0_38, v5) = v6 & subset(all_0_9_9, v0) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v2 = 0))))
% 56.84/18.57 |
% 56.84/18.57 | Instantiating (295) with all_71_0_44, all_71_1_45 yields:
% 56.84/18.57 | (305) relation_rng(all_0_9_9) = all_71_0_44 & relation(all_0_9_9) = all_71_1_45 & ( ~ (all_71_1_45 = 0) | (( ~ (all_71_0_44 = empty_set) | all_0_7_7 = empty_set) & ( ~ (all_0_7_7 = empty_set) | all_71_0_44 = empty_set)))
% 56.84/18.57 |
% 56.84/18.57 | Applying alpha-rule on (305) yields:
% 56.84/18.57 | (306) relation_rng(all_0_9_9) = all_71_0_44
% 56.84/18.57 | (307) relation(all_0_9_9) = all_71_1_45
% 56.84/18.57 | (308) ~ (all_71_1_45 = 0) | (( ~ (all_71_0_44 = empty_set) | all_0_7_7 = empty_set) & ( ~ (all_0_7_7 = empty_set) | all_71_0_44 = empty_set))
% 56.84/18.57 |
% 56.84/18.57 | Instantiating (293) with all_86_0_55, all_86_1_56 yields:
% 56.84/18.57 | (309) relation_rng(all_0_9_9) = all_86_0_55 & relation(all_0_9_9) = all_86_1_56 & ( ~ (all_86_1_56 = 0) | ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ (subset(all_0_7_7, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_9_9) = v3 & relation_rng(v3) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = all_86_0_55))))
% 56.84/18.57 |
% 56.84/18.57 | Applying alpha-rule on (309) yields:
% 56.84/18.57 | (310) relation_rng(all_0_9_9) = all_86_0_55
% 56.84/18.57 | (311) relation(all_0_9_9) = all_86_1_56
% 56.84/18.57 | (312) ~ (all_86_1_56 = 0) | ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ~ (subset(all_0_7_7, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (relation_composition(v0, all_0_9_9) = v3 & relation_rng(v3) = v4 & relation(v0) = v2 & ( ~ (v2 = 0) | v4 = all_86_0_55)))
% 56.84/18.57 |
% 56.84/18.57 | Instantiating (291) with all_94_0_60, all_94_1_61, all_94_2_62 yields:
% 56.84/18.57 | (313) empty(all_0_7_7) = all_94_0_60 & empty(all_0_9_9) = all_94_2_62 & relation(all_0_9_9) = all_94_1_61 & ( ~ (all_94_0_60 = 0) | ~ (all_94_1_61 = 0) | all_94_2_62 = 0)
% 56.84/18.57 |
% 56.84/18.57 | Applying alpha-rule on (313) yields:
% 56.84/18.57 | (314) empty(all_0_7_7) = all_94_0_60
% 56.84/18.57 | (315) empty(all_0_9_9) = all_94_2_62
% 56.84/18.57 | (316) relation(all_0_9_9) = all_94_1_61
% 56.84/18.57 | (317) ~ (all_94_0_60 = 0) | ~ (all_94_1_61 = 0) | all_94_2_62 = 0
% 56.84/18.57 |
% 56.84/18.57 +-Applying beta-rule and splitting (296), into two cases.
% 56.84/18.57 |-Branch one:
% 56.84/18.57 | (318) all_0_6_6 = 0
% 56.84/18.57 |
% 56.84/18.57 | Equations (318) can reduce 53 to:
% 56.84/18.57 | (319) $false
% 56.84/18.57 |
% 56.84/18.57 |-The branch is then unsatisfiable
% 56.84/18.57 |-Branch two:
% 56.84/18.57 | (53) ~ (all_0_6_6 = 0)
% 56.84/18.57 | (321) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = v1 & in(v0, all_0_8_8) = 0)
% 56.84/18.57 |
% 56.84/18.57 | Instantiating (321) with all_111_0_65, all_111_1_66 yields:
% 56.84/18.57 | (322) ~ (all_111_0_65 = 0) & in(all_111_1_66, all_0_7_7) = all_111_0_65 & in(all_111_1_66, all_0_8_8) = 0
% 56.84/18.57 |
% 56.84/18.57 | Applying alpha-rule on (322) yields:
% 56.84/18.57 | (323) ~ (all_111_0_65 = 0)
% 56.84/18.57 | (324) in(all_111_1_66, all_0_7_7) = all_111_0_65
% 56.84/18.57 | (325) in(all_111_1_66, all_0_8_8) = 0
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (116) with all_0_9_9, all_71_0_44, all_86_0_55 and discharging atoms relation_rng(all_0_9_9) = all_86_0_55, relation_rng(all_0_9_9) = all_71_0_44, yields:
% 56.84/18.57 | (326) all_86_0_55 = all_71_0_44
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (116) with all_0_9_9, all_65_0_38, all_71_0_44 and discharging atoms relation_rng(all_0_9_9) = all_71_0_44, relation_rng(all_0_9_9) = all_65_0_38, yields:
% 56.84/18.57 | (327) all_71_0_44 = all_65_0_38
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (116) with all_0_9_9, all_63_0_36, all_86_0_55 and discharging atoms relation_rng(all_0_9_9) = all_86_0_55, relation_rng(all_0_9_9) = all_63_0_36, yields:
% 56.84/18.57 | (328) all_86_0_55 = all_63_0_36
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (202) with all_0_9_9, all_94_1_61, 0 and discharging atoms relation(all_0_9_9) = all_94_1_61, relation(all_0_9_9) = 0, yields:
% 56.84/18.57 | (329) all_94_1_61 = 0
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (202) with all_0_9_9, all_86_1_56, all_94_1_61 and discharging atoms relation(all_0_9_9) = all_94_1_61, relation(all_0_9_9) = all_86_1_56, yields:
% 56.84/18.57 | (330) all_94_1_61 = all_86_1_56
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (202) with all_0_9_9, all_71_1_45, all_94_1_61 and discharging atoms relation(all_0_9_9) = all_94_1_61, relation(all_0_9_9) = all_71_1_45, yields:
% 56.84/18.57 | (331) all_94_1_61 = all_71_1_45
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (202) with all_0_9_9, all_65_1_39, all_86_1_56 and discharging atoms relation(all_0_9_9) = all_86_1_56, relation(all_0_9_9) = all_65_1_39, yields:
% 56.84/18.57 | (332) all_86_1_56 = all_65_1_39
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (202) with all_0_9_9, all_63_1_37, all_86_1_56 and discharging atoms relation(all_0_9_9) = all_86_1_56, relation(all_0_9_9) = all_63_1_37, yields:
% 56.84/18.57 | (333) all_86_1_56 = all_63_1_37
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (330,331) yields a new equation:
% 56.84/18.57 | (334) all_86_1_56 = all_71_1_45
% 56.84/18.57 |
% 56.84/18.57 | Simplifying 334 yields:
% 56.84/18.57 | (335) all_86_1_56 = all_71_1_45
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (329,331) yields a new equation:
% 56.84/18.57 | (336) all_71_1_45 = 0
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (326,328) yields a new equation:
% 56.84/18.57 | (337) all_71_0_44 = all_63_0_36
% 56.84/18.57 |
% 56.84/18.57 | Simplifying 337 yields:
% 56.84/18.57 | (338) all_71_0_44 = all_63_0_36
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (333,332) yields a new equation:
% 56.84/18.57 | (339) all_65_1_39 = all_63_1_37
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (335,332) yields a new equation:
% 56.84/18.57 | (340) all_71_1_45 = all_65_1_39
% 56.84/18.57 |
% 56.84/18.57 | Simplifying 340 yields:
% 56.84/18.57 | (341) all_71_1_45 = all_65_1_39
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (327,338) yields a new equation:
% 56.84/18.57 | (342) all_65_0_38 = all_63_0_36
% 56.84/18.57 |
% 56.84/18.57 | Simplifying 342 yields:
% 56.84/18.57 | (343) all_65_0_38 = all_63_0_36
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (341,336) yields a new equation:
% 56.84/18.57 | (344) all_65_1_39 = 0
% 56.84/18.57 |
% 56.84/18.57 | Simplifying 344 yields:
% 56.84/18.57 | (345) all_65_1_39 = 0
% 56.84/18.57 |
% 56.84/18.57 | Combining equations (339,345) yields a new equation:
% 56.84/18.57 | (346) all_63_1_37 = 0
% 56.84/18.57 |
% 56.84/18.57 | Simplifying 346 yields:
% 56.84/18.57 | (347) all_63_1_37 = 0
% 56.84/18.57 |
% 56.84/18.57 | From (343) and (302) follows:
% 56.84/18.57 | (298) relation_rng(all_0_9_9) = all_63_0_36
% 56.84/18.57 |
% 56.84/18.57 | From (347) and (299) follows:
% 56.84/18.57 | (154) relation(all_0_9_9) = 0
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (18) with all_63_0_36, all_0_9_9 and discharging atoms relation_rng(all_0_9_9) = all_63_0_36, yields:
% 56.84/18.57 | (350) ? [v0] : ? [v1] : ? [v2] : (empty(all_63_0_36) = v2 & empty(all_0_9_9) = v0 & relation(all_0_9_9) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | v0 = 0))
% 56.84/18.57 |
% 56.84/18.57 | Instantiating formula (151) with 0, all_0_8_8, all_0_9_9, all_0_10_10, all_111_1_66 and discharging atoms relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8, in(all_111_1_66, all_0_8_8) = 0, yields:
% 57.19/18.57 | (351) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | (v6 = 0 & v5 = 0 & v3 = 0 & ordered_pair(all_111_1_66, v2) = v4 & in(v4, all_0_9_9) = 0 & in(v2, v1) = 0 & in(v2, all_0_10_10) = 0)))
% 57.19/18.57 |
% 57.19/18.57 | Instantiating formula (188) with all_111_1_66, all_0_8_8, all_0_10_10, all_0_9_9 and discharging atoms relation_inverse_image(all_0_9_9, all_0_10_10) = all_0_8_8, relation(all_0_9_9) = 0, in(all_111_1_66, all_0_8_8) = 0, yields:
% 57.19/18.57 | (352) ? [v0] : ? [v1] : (ordered_pair(all_111_1_66, v0) = v1 & in(v1, all_0_9_9) = 0 & in(v0, all_0_10_10) = 0)
% 57.19/18.57 |
% 57.19/18.57 | Instantiating (352) with all_174_0_80, all_174_1_81 yields:
% 57.19/18.57 | (353) ordered_pair(all_111_1_66, all_174_1_81) = all_174_0_80 & in(all_174_0_80, all_0_9_9) = 0 & in(all_174_1_81, all_0_10_10) = 0
% 57.19/18.57 |
% 57.19/18.57 | Applying alpha-rule on (353) yields:
% 57.19/18.57 | (354) ordered_pair(all_111_1_66, all_174_1_81) = all_174_0_80
% 57.19/18.57 | (355) in(all_174_0_80, all_0_9_9) = 0
% 57.19/18.58 | (356) in(all_174_1_81, all_0_10_10) = 0
% 57.19/18.58 |
% 57.19/18.58 | Instantiating (351) with all_178_0_83, all_178_1_84, all_178_2_85, all_178_3_86, all_178_4_87, all_178_5_88, all_178_6_89 yields:
% 57.19/18.58 | (357) relation_rng(all_0_9_9) = all_178_5_88 & relation(all_0_9_9) = all_178_6_89 & ( ~ (all_178_6_89 = 0) | (all_178_0_83 = 0 & all_178_1_84 = 0 & all_178_3_86 = 0 & ordered_pair(all_111_1_66, all_178_4_87) = all_178_2_85 & in(all_178_2_85, all_0_9_9) = 0 & in(all_178_4_87, all_178_5_88) = 0 & in(all_178_4_87, all_0_10_10) = 0))
% 57.19/18.58 |
% 57.19/18.58 | Applying alpha-rule on (357) yields:
% 57.19/18.58 | (358) relation_rng(all_0_9_9) = all_178_5_88
% 57.19/18.58 | (359) relation(all_0_9_9) = all_178_6_89
% 57.19/18.58 | (360) ~ (all_178_6_89 = 0) | (all_178_0_83 = 0 & all_178_1_84 = 0 & all_178_3_86 = 0 & ordered_pair(all_111_1_66, all_178_4_87) = all_178_2_85 & in(all_178_2_85, all_0_9_9) = 0 & in(all_178_4_87, all_178_5_88) = 0 & in(all_178_4_87, all_0_10_10) = 0)
% 57.19/18.58 |
% 57.19/18.58 | Instantiating (350) with all_208_0_108, all_208_1_109, all_208_2_110 yields:
% 57.19/18.58 | (361) empty(all_63_0_36) = all_208_0_108 & empty(all_0_9_9) = all_208_2_110 & relation(all_0_9_9) = all_208_1_109 & ( ~ (all_208_0_108 = 0) | ~ (all_208_1_109 = 0) | all_208_2_110 = 0)
% 57.19/18.58 |
% 57.19/18.58 | Applying alpha-rule on (361) yields:
% 57.19/18.58 | (362) empty(all_63_0_36) = all_208_0_108
% 57.19/18.58 | (363) empty(all_0_9_9) = all_208_2_110
% 57.19/18.58 | (364) relation(all_0_9_9) = all_208_1_109
% 57.19/18.58 | (365) ~ (all_208_0_108 = 0) | ~ (all_208_1_109 = 0) | all_208_2_110 = 0
% 57.19/18.58 |
% 57.19/18.58 | Instantiating formula (202) with all_0_9_9, all_208_1_109, 0 and discharging atoms relation(all_0_9_9) = all_208_1_109, relation(all_0_9_9) = 0, yields:
% 57.19/18.58 | (366) all_208_1_109 = 0
% 57.19/18.58 |
% 57.19/18.58 | Instantiating formula (202) with all_0_9_9, all_178_6_89, all_208_1_109 and discharging atoms relation(all_0_9_9) = all_208_1_109, relation(all_0_9_9) = all_178_6_89, yields:
% 57.19/18.58 | (367) all_208_1_109 = all_178_6_89
% 57.19/18.58 |
% 57.19/18.58 | Instantiating formula (59) with all_174_0_80 yields:
% 57.19/18.58 | (368) ~ (in(all_174_0_80, empty_set) = 0)
% 57.19/18.58 |
% 57.19/18.58 | Combining equations (367,366) yields a new equation:
% 57.19/18.58 | (369) all_178_6_89 = 0
% 57.19/18.58 |
% 57.19/18.58 | Simplifying 369 yields:
% 57.19/18.58 | (370) all_178_6_89 = 0
% 57.19/18.58 |
% 57.19/18.58 | From (370) and (359) follows:
% 57.19/18.58 | (154) relation(all_0_9_9) = 0
% 57.19/18.58 |
% 57.19/18.58 | Using (355) and (368) yields:
% 57.19/18.58 | (372) ~ (all_0_9_9 = empty_set)
% 57.19/18.58 |
% 57.19/18.58 +-Applying beta-rule and splitting (290), into two cases.
% 57.19/18.58 |-Branch one:
% 57.19/18.58 | (373) all_0_9_9 = empty_set
% 57.19/18.58 |
% 57.19/18.58 | Equations (373) can reduce 372 to:
% 57.19/18.58 | (319) $false
% 57.19/18.58 |
% 57.19/18.58 |-The branch is then unsatisfiable
% 57.19/18.58 |-Branch two:
% 57.19/18.58 | (372) ~ (all_0_9_9 = empty_set)
% 57.19/18.58 | (376) ? [v0] : ? [v1] : (relation_rng(all_0_9_9) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | ( ~ (v1 = empty_set) & ~ (all_0_7_7 = empty_set))))
% 57.19/18.58 |
% 57.19/18.58 | Instantiating (376) with all_372_0_154, all_372_1_155 yields:
% 57.19/18.58 | (377) relation_rng(all_0_9_9) = all_372_0_154 & relation(all_0_9_9) = all_372_1_155 & ( ~ (all_372_1_155 = 0) | ( ~ (all_372_0_154 = empty_set) & ~ (all_0_7_7 = empty_set)))
% 57.19/18.58 |
% 57.19/18.58 | Applying alpha-rule on (377) yields:
% 57.19/18.58 | (378) relation_rng(all_0_9_9) = all_372_0_154
% 57.19/18.58 | (379) relation(all_0_9_9) = all_372_1_155
% 57.19/18.58 | (380) ~ (all_372_1_155 = 0) | ( ~ (all_372_0_154 = empty_set) & ~ (all_0_7_7 = empty_set))
% 57.19/18.58 |
% 57.19/18.58 | Instantiating formula (202) with all_0_9_9, all_372_1_155, 0 and discharging atoms relation(all_0_9_9) = all_372_1_155, relation(all_0_9_9) = 0, yields:
% 57.19/18.58 | (381) all_372_1_155 = 0
% 57.19/18.58 |
% 57.19/18.58 | From (381) and (379) follows:
% 57.19/18.58 | (154) relation(all_0_9_9) = 0
% 57.19/18.58 |
% 57.19/18.58 | Instantiating formula (146) with all_174_0_80, all_174_1_81, all_111_0_65, all_111_1_66, all_0_7_7, all_0_9_9 and discharging atoms relation_dom(all_0_9_9) = all_0_7_7, ordered_pair(all_111_1_66, all_174_1_81) = all_174_0_80, in(all_174_0_80, all_0_9_9) = 0, in(all_111_1_66, all_0_7_7) = all_111_0_65, yields:
% 57.19/18.58 | (383) all_111_0_65 = 0 | ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 57.19/18.58 |
% 57.19/18.58 +-Applying beta-rule and splitting (383), into two cases.
% 57.19/18.58 |-Branch one:
% 57.19/18.58 | (384) all_111_0_65 = 0
% 57.19/18.58 |
% 57.19/18.58 | Equations (384) can reduce 323 to:
% 57.19/18.58 | (319) $false
% 57.19/18.58 |
% 57.19/18.58 |-The branch is then unsatisfiable
% 57.19/18.58 |-Branch two:
% 57.19/18.58 | (323) ~ (all_111_0_65 = 0)
% 57.19/18.58 | (387) ? [v0] : ( ~ (v0 = 0) & relation(all_0_9_9) = v0)
% 57.19/18.58 |
% 57.19/18.58 | Instantiating (387) with all_1098_0_416 yields:
% 57.19/18.58 | (388) ~ (all_1098_0_416 = 0) & relation(all_0_9_9) = all_1098_0_416
% 57.19/18.58 |
% 57.19/18.58 | Applying alpha-rule on (388) yields:
% 57.19/18.58 | (389) ~ (all_1098_0_416 = 0)
% 57.19/18.58 | (390) relation(all_0_9_9) = all_1098_0_416
% 57.19/18.58 |
% 57.19/18.58 | Instantiating formula (202) with all_0_9_9, all_1098_0_416, 0 and discharging atoms relation(all_0_9_9) = all_1098_0_416, relation(all_0_9_9) = 0, yields:
% 57.19/18.58 | (391) all_1098_0_416 = 0
% 57.19/18.58 |
% 57.19/18.58 | Equations (391) can reduce 389 to:
% 57.19/18.58 | (319) $false
% 57.19/18.58 |
% 57.19/18.58 |-The branch is then unsatisfiable
% 57.19/18.58 % SZS output end Proof for theBenchmark
% 57.19/18.58
% 57.19/18.58 17977ms
%------------------------------------------------------------------------------