%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU198+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n017.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 08:47:33 EDT 2022 % Result : Theorem 25.22s 6.89s % Output : Proof 41.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEU198+2 : TPTP v8.1.0. Released v3.3.0. % 0.11/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n017.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sun Jun 19 01:18:58 EDT 2022 % 0.11/0.33 % CPUTime : % 0.18/0.55 ____ _ % 0.18/0.55 ___ / __ \_____(_)___ ________ __________ % 0.18/0.55 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.55 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.55 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.55 % 0.18/0.55 A Theorem Prover for First-Order Logic % 0.18/0.55 (ePrincess v.1.0) % 0.18/0.55 % 0.18/0.55 (c) Philipp Rümmer, 2009-2015 % 0.18/0.55 (c) Peter Backeman, 2014-2015 % 0.18/0.55 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.55 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.55 Bug reports to peter@backeman.se % 0.18/0.55 % 0.18/0.55 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.55 % 0.18/0.55 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.60 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.21/1.11 Prover 0: Preprocessing ... % 5.74/1.82 Prover 0: Warning: ignoring some quantifiers % 5.74/1.86 Prover 0: Constructing countermodel ... % 21.33/5.89 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 21.72/6.05 Prover 1: Preprocessing ... % 23.41/6.44 Prover 1: Warning: ignoring some quantifiers % 23.41/6.46 Prover 1: Constructing countermodel ... % 25.22/6.88 Prover 1: proved (989ms) % 25.22/6.89 Prover 0: stopped % 25.22/6.89 % 25.22/6.89 No countermodel exists, formula is valid % 25.22/6.89 % SZS status Theorem for theBenchmark % 25.22/6.89 % 25.22/6.89 Generating proof ... Warning: ignoring some quantifiers % 40.16/10.43 found it (size 26) % 40.16/10.43 % 40.16/10.43 % SZS output start Proof for theBenchmark % 40.16/10.43 Assumed formulas after preprocessing and simplification: % 40.16/10.43 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v5 = 0) & relation_rng(v3) = v4 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_rng_restriction(v1, v2) = v3 & subset(v4, v1) = 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] : ( ~ (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_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(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] : ( ~ (singleton(v12) = v15) | ~ (unordered_pair(v14, v15) = v16) | ~ (unordered_pair(v12, v13) = v14) | ordered_pair(v12, v13) = v16) & ! [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_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_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(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] : ( ~ (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] : ( ~ (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 | ~ (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) | ? [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) | ~ (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(v13) = 0) | ~ (relation(v12) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : (subset(v12, v13) = v14 & ( ~ (v14 = 0) | ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ~ (in(v22, v12) = 0) | in(v22, v13) = 0)) & (v14 = 0 | (v18 = 0 & ~ (v19 = 0) & ordered_pair(v15, v16) = v17 & in(v17, v13) = v19 & in(v17, v12) = 0)))) & ! [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)) % 40.70/10.56 | 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: % 40.70/10.56 | (1) ~ (all_0_2_2 = 0) & ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & relation_rng(all_0_8_8) = all_0_7_7 & relation_rng(empty_set) = empty_set & relation_dom(empty_set) = empty_set & powerset(empty_set) = all_0_11_11 & singleton(empty_set) = all_0_11_11 & relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8 & subset(all_0_7_7, all_0_10_10) = 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] : ( ~ (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_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(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] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [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_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_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(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] : ( ~ (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] : ( ~ (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 | ~ (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) | ? [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) | ~ (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(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset(v0, v1) = v2 & ( ~ (v2 = 0) | ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ (in(v10, v0) = 0) | in(v10, v1) = 0)) & (v2 = 0 | (v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0)))) & ! [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) % 40.70/10.60 | % 40.70/10.60 | Applying alpha-rule on (1) yields: % 40.70/10.60 | (2) ! [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))))))) % 40.70/10.60 | (3) ! [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))))) % 40.70/10.60 | (4) ! [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))) % 40.70/10.60 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 40.70/10.60 | (6) ! [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))) % 40.70/10.60 | (7) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 40.70/10.60 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) % 40.70/10.60 | (9) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) % 40.70/10.60 | (10) empty(all_0_1_1) = 0 % 40.70/10.60 | (11) empty(empty_set) = 0 % 40.70/10.60 | (12) ! [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)))))) % 40.70/10.60 | (13) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 40.70/10.60 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 40.70/10.60 | (15) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 40.70/10.60 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & powerset(v0) = v2 & empty(v3) = v4)) % 40.70/10.60 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 40.70/10.60 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 40.70/10.60 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) % 40.70/10.60 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 40.70/10.60 | (21) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 40.70/10.60 | (22) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) % 40.70/10.60 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 40.70/10.60 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) % 40.70/10.60 | (25) ! [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))))) % 40.70/10.61 | (26) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) % 40.70/10.61 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) % 40.70/10.61 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 40.70/10.61 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 40.70/10.61 | (30) ? [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))))) % 41.13/10.61 | (31) ! [v0] : ! [v1] : ( ~ (relation(v1) = 0) | ~ (relation(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (subset(v0, v1) = v2 & ( ~ (v2 = 0) | ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ (in(v10, v0) = 0) | in(v10, v1) = 0)) & (v2 = 0 | (v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0)))) % 41.13/10.61 | (32) ! [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))) % 41.13/10.61 | (33) ! [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)) % 41.13/10.61 | (34) ! [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))))) % 41.13/10.61 | (35) relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8 % 41.13/10.61 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 41.13/10.61 | (37) ! [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)) % 41.13/10.61 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) % 41.13/10.61 | (39) ! [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)))) % 41.13/10.61 | (40) ? [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)))) % 41.13/10.61 | (41) ! [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)))) % 41.13/10.61 | (42) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 41.13/10.61 | (43) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 41.13/10.61 | (44) ! [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))) % 41.13/10.61 | (45) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 41.13/10.61 | (46) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 41.13/10.61 | (47) ! [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)))) % 41.13/10.61 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 41.13/10.61 | (49) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 41.13/10.61 | (50) ! [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))))) % 41.13/10.61 | (51) ! [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))))) % 41.13/10.61 | (52) ! [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)) % 41.13/10.61 | (53) ! [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)))))) % 41.13/10.61 | (54) ! [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))) % 41.13/10.61 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 41.13/10.61 | (56) ? [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)))) % 41.13/10.61 | (57) ! [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)))))) % 41.13/10.61 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) % 41.13/10.61 | (59) ! [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)) % 41.13/10.62 | (60) ! [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))) % 41.13/10.62 | (61) ! [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))) % 41.13/10.62 | (62) ! [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)) % 41.13/10.62 | (63) ! [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))) % 41.13/10.62 | (64) ! [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)) % 41.13/10.62 | (65) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 41.13/10.62 | (66) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 41.13/10.62 | (67) ! [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))))) % 41.13/10.62 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 41.13/10.62 | (69) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 41.13/10.62 | (70) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 41.13/10.62 | (71) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) % 41.13/10.62 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 41.13/10.62 | (73) ! [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)) % 41.13/10.62 | (74) ! [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))) % 41.13/10.62 | (75) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 41.13/10.62 | (76) ? [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))) % 41.13/10.62 | (77) subset(all_0_7_7, all_0_10_10) = all_0_6_6 % 41.13/10.62 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 41.13/10.62 | (79) powerset(empty_set) = all_0_11_11 % 41.13/10.62 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 41.13/10.62 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 41.13/10.62 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 41.13/10.62 | (83) ! [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))) % 41.13/10.62 | (84) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 41.13/10.62 | (85) ! [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)))) % 41.13/10.62 | (86) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) % 41.13/10.62 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 41.13/10.62 | (88) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 41.13/10.62 | (89) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 41.13/10.62 | (90) ! [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)))) % 41.13/10.62 | (91) ! [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)) % 41.13/10.62 | (92) ! [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))) % 41.13/10.62 | (93) ! [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)) % 41.13/10.62 | (94) ! [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)) % 41.13/10.62 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) % 41.13/10.62 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 41.13/10.62 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) % 41.13/10.62 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) % 41.13/10.62 | (99) ! [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)))) % 41.13/10.62 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) % 41.13/10.62 | (101) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) % 41.13/10.62 | (102) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 41.13/10.62 | (103) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 41.13/10.62 | (104) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 41.13/10.62 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 41.13/10.62 | (106) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 41.13/10.62 | (107) ! [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))) % 41.13/10.63 | (108) ? [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))))) % 41.13/10.63 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 41.13/10.63 | (110) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 41.13/10.63 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 41.13/10.63 | (112) singleton(empty_set) = all_0_11_11 % 41.13/10.63 | (113) empty(all_0_0_0) = 0 % 41.13/10.63 | (114) ! [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))) % 41.13/10.63 | (115) ! [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))))) % 41.13/10.63 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) % 41.13/10.63 | (117) ! [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))) % 41.13/10.63 | (118) ! [v0] : ! [v1] : ( ~ (relation_dom(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 41.13/10.63 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) % 41.13/10.63 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 41.13/10.63 | (121) ! [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)) % 41.13/10.63 | (122) ! [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)) % 41.13/10.63 | (123) ! [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))))) % 41.13/10.63 | (124) ! [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)))) % 41.13/10.63 | (125) ! [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)))) % 41.13/10.63 | (126) ~ (all_0_4_4 = 0) % 41.13/10.63 | (127) ! [v0] : ~ (singleton(v0) = empty_set) % 41.13/10.63 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4)) % 41.13/10.63 | (129) ! [v0] : ~ (in(v0, empty_set) = 0) % 41.13/10.63 | (130) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 41.13/10.63 | (131) ? [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)))) % 41.13/10.63 | (132) ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 41.13/10.63 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 41.13/10.63 | (134) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v2 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v2 = 0))) % 41.13/10.63 | (135) ~ (all_0_6_6 = 0) % 41.13/10.63 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 41.13/10.63 | (137) ? [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))) % 41.13/10.63 | (138) ! [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)))) % 41.13/10.63 | (139) ! [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))))) % 41.13/10.63 | (140) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 41.13/10.63 | (141) ! [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)))) % 41.13/10.63 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) % 41.13/10.63 | (143) ~ (all_0_2_2 = 0) % 41.13/10.63 | (144) ! [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)) % 41.13/10.63 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 41.13/10.63 | (146) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 41.13/10.63 | (147) ! [v0] : ~ (proper_subset(v0, v0) = 0) % 41.13/10.63 | (148) ! [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)) % 41.13/10.63 | (149) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 41.13/10.63 | (150) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 41.13/10.63 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 41.13/10.63 | (152) ! [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))) % 41.13/10.63 | (153) ! [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)) % 41.13/10.63 | (154) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) % 41.13/10.64 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 41.13/10.64 | (156) ! [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)))) % 41.13/10.64 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 41.13/10.64 | (158) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 41.13/10.64 | (159) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 41.13/10.64 | (160) relation(all_0_3_3) = 0 % 41.13/10.64 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 41.13/10.64 | (162) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 41.13/10.64 | (163) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) % 41.13/10.64 | (164) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) % 41.13/10.64 | (165) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 41.13/10.64 | (166) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 41.13/10.64 | (167) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 41.13/10.64 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 41.13/10.64 | (169) ! [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))))) % 41.13/10.64 | (170) ! [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)) % 41.13/10.64 | (171) ! [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))) % 41.13/10.64 | (172) ! [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)))))) % 41.13/10.64 | (173) ! [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) % 41.13/10.64 | (174) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 41.13/10.64 | (175) relation_rng(empty_set) = empty_set % 41.13/10.64 | (176) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 41.13/10.64 | (177) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) % 41.13/10.64 | (178) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0))) % 41.13/10.64 | (179) ? [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)))) % 41.13/10.64 | (180) ! [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)))) % 41.13/10.64 | (181) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 41.13/10.64 | (182) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 41.13/10.64 | (183) ! [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))) % 41.13/10.64 | (184) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 41.13/10.64 | (185) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) % 41.13/10.64 | (186) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 41.13/10.64 | (187) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 41.13/10.64 | (188) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) % 41.13/10.64 | (189) relation_dom(empty_set) = empty_set % 41.13/10.64 | (190) ! [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)))))) % 41.13/10.64 | (191) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 41.13/10.64 | (192) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) % 41.13/10.64 | (193) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 41.13/10.64 | (194) ! [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)))) % 41.13/10.64 | (195) ! [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))) % 41.13/10.64 | (196) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 41.13/10.64 | (197) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 41.13/10.64 | (198) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 41.13/10.64 | (199) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 41.13/10.64 | (200) ! [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)) % 41.13/10.64 | (201) ? [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))))) % 41.13/10.65 | (202) relation(all_0_9_9) = 0 % 41.13/10.65 | (203) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 41.13/10.65 | (204) ! [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)))) % 41.13/10.65 | (205) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) % 41.13/10.65 | (206) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 41.13/10.65 | (207) ! [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)) % 41.13/10.65 | (208) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 41.13/10.65 | (209) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) % 41.13/10.65 | (210) ! [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)))) % 41.13/10.65 | (211) ! [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)) % 41.13/10.65 | (212) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) % 41.13/10.65 | (213) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2)) % 41.13/10.65 | (214) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 41.13/10.65 | (215) ! [v0] : ! [v1] : ! [v2] : ( ~ (empty(v1) = v2) | ~ (empty(v0) = 0) | ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) % 41.13/10.65 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 41.13/10.65 | (217) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0) % 41.13/10.65 | (218) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 41.13/10.65 | (219) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 41.13/10.65 | (220) ! [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))) % 41.13/10.65 | (221) ? [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))) % 41.13/10.65 | (222) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) % 41.13/10.65 | (223) ! [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)) % 41.13/10.65 | (224) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0)) % 41.13/10.65 | (225) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 41.13/10.65 | (226) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) % 41.13/10.65 | (227) ! [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)))) % 41.13/10.65 | (228) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 41.13/10.65 | (229) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) % 41.13/10.65 | (230) ! [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))) % 41.13/10.65 | (231) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 41.13/10.65 | (232) ! [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)) % 41.13/10.65 | (233) ! [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)) % 41.13/10.65 | (234) ! [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))) % 41.13/10.65 | (235) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 41.13/10.65 | (236) relation(empty_set) = 0 % 41.13/10.65 | (237) empty(all_0_5_5) = all_0_4_4 % 41.13/10.65 | (238) ! [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)))) % 41.13/10.65 | (239) ! [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))) % 41.13/10.65 | (240) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 41.13/10.65 | (241) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 41.13/10.65 | (242) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 41.13/10.65 | (243) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) % 41.13/10.65 | (244) ! [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)))) % 41.13/10.65 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 41.13/10.65 | (246) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (empty(v1) = v3 & empty(v0) = v2 & relation(v1) = v4 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 41.13/10.65 | (247) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 41.13/10.65 | (248) ! [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)) % 41.13/10.65 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 41.13/10.65 | (250) ! [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)))) % 41.13/10.66 | (251) ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0)) % 41.13/10.66 | (252) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 41.13/10.66 | (253) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 41.13/10.66 | (254) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 41.13/10.66 | (255) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 41.13/10.66 | (256) relation(all_0_0_0) = 0 % 41.13/10.66 | (257) ! [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)) % 41.13/10.66 | (258) ? [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)))) % 41.13/10.66 | (259) ? [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))))) % 41.13/10.66 | (260) ! [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)))) % 41.13/10.66 | (261) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 41.13/10.66 | (262) ! [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)) % 41.13/10.66 | (263) relation_rng(all_0_8_8) = all_0_7_7 % 41.13/10.66 | (264) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) % 41.13/10.66 | (265) ? [v0] : ? [v1] : element(v1, v0) = 0 % 41.13/10.66 | (266) ! [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)))) % 41.13/10.66 | (267) empty(all_0_3_3) = all_0_2_2 % 41.13/10.66 | (268) ! [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))))) % 41.13/10.66 | (269) ! [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)) % 41.13/10.66 | % 41.13/10.66 | Instantiating formula (96) with all_0_8_8, all_0_9_9, all_0_10_10 and discharging atoms relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8, yields: % 41.13/10.66 | (270) ? [v0] : ? [v1] : (relation(all_0_8_8) = v1 & relation(all_0_9_9) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 41.13/10.66 | % 41.13/10.66 | Instantiating formula (176) with all_0_6_6, all_0_10_10, all_0_7_7 and discharging atoms subset(all_0_7_7, all_0_10_10) = all_0_6_6, yields: % 41.13/10.66 | (271) all_0_6_6 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = 0 & in(v0, all_0_10_10) = v1) % 41.13/10.66 | % 41.13/10.66 | Instantiating (270) with all_93_0_78, all_93_1_79 yields: % 41.13/10.66 | (272) relation(all_0_8_8) = all_93_0_78 & relation(all_0_9_9) = all_93_1_79 & ( ~ (all_93_1_79 = 0) | all_93_0_78 = 0) % 41.13/10.66 | % 41.13/10.66 | Applying alpha-rule on (272) yields: % 41.13/10.66 | (273) relation(all_0_8_8) = all_93_0_78 % 41.13/10.66 | (274) relation(all_0_9_9) = all_93_1_79 % 41.13/10.66 | (275) ~ (all_93_1_79 = 0) | all_93_0_78 = 0 % 41.13/10.66 | % 41.13/10.66 +-Applying beta-rule and splitting (271), into two cases. % 41.13/10.66 |-Branch one: % 41.13/10.66 | (276) all_0_6_6 = 0 % 41.13/10.66 | % 41.13/10.66 | Equations (276) can reduce 135 to: % 41.13/10.66 | (277) $false % 41.13/10.66 | % 41.13/10.66 |-The branch is then unsatisfiable % 41.13/10.66 |-Branch two: % 41.13/10.66 | (135) ~ (all_0_6_6 = 0) % 41.13/10.66 | (279) ? [v0] : ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_7_7) = 0 & in(v0, all_0_10_10) = v1) % 41.13/10.66 | % 41.13/10.66 | Instantiating (279) with all_141_0_117, all_141_1_118 yields: % 41.13/10.66 | (280) ~ (all_141_0_117 = 0) & in(all_141_1_118, all_0_7_7) = 0 & in(all_141_1_118, all_0_10_10) = all_141_0_117 % 41.13/10.66 | % 41.13/10.66 | Applying alpha-rule on (280) yields: % 41.13/10.66 | (281) ~ (all_141_0_117 = 0) % 41.13/10.66 | (282) in(all_141_1_118, all_0_7_7) = 0 % 41.13/10.66 | (283) in(all_141_1_118, all_0_10_10) = all_141_0_117 % 41.13/10.66 | % 41.13/10.66 | Instantiating formula (231) with all_0_9_9, all_93_1_79, 0 and discharging atoms relation(all_0_9_9) = all_93_1_79, relation(all_0_9_9) = 0, yields: % 41.13/10.66 | (284) all_93_1_79 = 0 % 41.13/10.66 | % 41.13/10.66 | From (284) and (274) follows: % 41.13/10.66 | (202) relation(all_0_9_9) = 0 % 41.13/10.66 | % 41.13/10.66 | Instantiating formula (12) with 0, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_141_1_118 and discharging atoms relation_rng(all_0_8_8) = all_0_7_7, relation_rng_restriction(all_0_10_10, all_0_9_9) = all_0_8_8, in(all_141_1_118, all_0_7_7) = 0, yields: % 41.13/10.66 | (286) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_rng(all_0_9_9) = v2 & relation(all_0_9_9) = v0 & in(all_141_1_118, v2) = v3 & in(all_141_1_118, all_0_10_10) = v1 & ( ~ (v0 = 0) | (v3 = 0 & v1 = 0))) % 41.13/10.66 | % 41.13/10.66 | Instantiating (286) with all_289_0_166, all_289_1_167, all_289_2_168, all_289_3_169 yields: % 41.13/10.66 | (287) relation_rng(all_0_9_9) = all_289_1_167 & relation(all_0_9_9) = all_289_3_169 & in(all_141_1_118, all_289_1_167) = all_289_0_166 & in(all_141_1_118, all_0_10_10) = all_289_2_168 & ( ~ (all_289_3_169 = 0) | (all_289_0_166 = 0 & all_289_2_168 = 0)) % 41.13/10.66 | % 41.13/10.66 | Applying alpha-rule on (287) yields: % 41.13/10.66 | (288) ~ (all_289_3_169 = 0) | (all_289_0_166 = 0 & all_289_2_168 = 0) % 41.13/10.66 | (289) relation(all_0_9_9) = all_289_3_169 % 41.13/10.66 | (290) in(all_141_1_118, all_289_1_167) = all_289_0_166 % 41.13/10.66 | (291) relation_rng(all_0_9_9) = all_289_1_167 % 41.13/10.66 | (292) in(all_141_1_118, all_0_10_10) = all_289_2_168 % 41.13/10.66 | % 41.13/10.67 | Instantiating formula (231) with all_0_9_9, all_289_3_169, 0 and discharging atoms relation(all_0_9_9) = all_289_3_169, relation(all_0_9_9) = 0, yields: % 41.13/10.67 | (293) all_289_3_169 = 0 % 41.13/10.67 | % 41.13/10.67 | Instantiating formula (28) with all_141_1_118, all_0_10_10, all_289_2_168, all_141_0_117 and discharging atoms in(all_141_1_118, all_0_10_10) = all_289_2_168, in(all_141_1_118, all_0_10_10) = all_141_0_117, yields: % 41.13/10.67 | (294) all_289_2_168 = all_141_0_117 % 41.13/10.67 | % 41.13/10.67 +-Applying beta-rule and splitting (288), into two cases. % 41.13/10.67 |-Branch one: % 41.13/10.67 | (295) ~ (all_289_3_169 = 0) % 41.13/10.67 | % 41.13/10.67 | Equations (293) can reduce 295 to: % 41.13/10.67 | (277) $false % 41.13/10.67 | % 41.13/10.67 |-The branch is then unsatisfiable % 41.13/10.67 |-Branch two: % 41.13/10.67 | (293) all_289_3_169 = 0 % 41.13/10.67 | (298) all_289_0_166 = 0 & all_289_2_168 = 0 % 41.13/10.67 | % 41.13/10.67 | Applying alpha-rule on (298) yields: % 41.13/10.67 | (299) all_289_0_166 = 0 % 41.13/10.67 | (300) all_289_2_168 = 0 % 41.13/10.67 | % 41.13/10.67 | Combining equations (294,300) yields a new equation: % 41.13/10.67 | (301) all_141_0_117 = 0 % 41.13/10.67 | % 41.13/10.67 | Simplifying 301 yields: % 41.13/10.67 | (302) all_141_0_117 = 0 % 41.13/10.67 | % 41.13/10.67 | Equations (302) can reduce 281 to: % 41.13/10.67 | (277) $false % 41.13/10.67 | % 41.13/10.67 |-The branch is then unsatisfiable % 41.13/10.67 % SZS output end Proof for theBenchmark % 41.13/10.67 % 41.13/10.67 10104ms %------------------------------------------------------------------------------