%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SEU224+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 08:47:51 EDT 2022 % Result : Theorem 101.05s 57.87s % Output : Proof 114.08s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU224+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n026.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jun 19 12:40:55 EDT 2022 % 0.12/0.33 % CPUTime : % 0.52/0.59 ____ _ % 0.52/0.59 ___ / __ \_____(_)___ ________ __________ % 0.52/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.59 % 0.52/0.59 A Theorem Prover for First-Order Logic % 0.52/0.59 (ePrincess v.1.0) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2015 % 0.52/0.60 (c) Peter Backeman, 2014-2015 % 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.60 Bug reports to peter@backeman.se % 0.52/0.60 % 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.77/1.20 Prover 0: Preprocessing ... % 7.09/2.12 Prover 0: Warning: ignoring some quantifiers % 7.27/2.17 Prover 0: Constructing countermodel ... % 22.29/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 22.59/6.05 Prover 1: Preprocessing ... % 24.41/6.47 Prover 1: Warning: ignoring some quantifiers % 24.41/6.49 Prover 1: Constructing countermodel ... % 32.93/8.53 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 33.60/8.71 Prover 2: Preprocessing ... % 36.74/9.50 Prover 2: Warning: ignoring some quantifiers % 37.07/9.54 Prover 2: Constructing countermodel ... % 41.71/11.56 Prover 0: stopped % 41.94/11.76 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 42.17/11.89 Prover 3: Preprocessing ... % 42.88/12.05 Prover 3: Warning: ignoring some quantifiers % 42.88/12.06 Prover 3: Constructing countermodel ... % 90.38/53.15 Prover 3: stopped % 90.62/53.35 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete % 91.10/53.50 Prover 4: Preprocessing ... % 93.22/54.13 Prover 4: Warning: ignoring some quantifiers % 93.22/54.15 Prover 4: Constructing countermodel ... % 101.05/57.87 Prover 1: proved (4383ms) % 101.05/57.87 Prover 2: stopped % 101.05/57.87 Prover 4: stopped % 101.05/57.87 % 101.05/57.87 No countermodel exists, formula is valid % 101.05/57.87 % SZS status Theorem for theBenchmark % 101.05/57.87 % 101.05/57.87 Generating proof ... Warning: ignoring some quantifiers % 112.77/61.55 found it (size 99) % 112.77/61.55 % 112.77/61.55 % SZS output start Proof for theBenchmark % 112.77/61.55 Assumed formulas after preprocessing and simplification: % 112.77/61.55 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ( ~ (v15 = 0) & ~ (v13 = 0) & relation_empty_yielding(v10) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(empty_set) = empty_set & relation_dom(v4) = v5 & relation_dom(v3) = v7 & relation_dom(empty_set) = empty_set & powerset(empty_set) = v0 & singleton(empty_set) = v0 & relation_dom_restriction(v3, v1) = v4 & one_to_one(v11) = 0 & relation(v19) = 0 & relation(v18) = 0 & relation(v16) = 0 & relation(v14) = 0 & relation(v11) = 0 & relation(v10) = 0 & relation(v3) = 0 & relation(empty_set) = 0 & function(v19) = 0 & function(v16) = 0 & function(v11) = 0 & function(v3) = 0 & empty(v18) = 0 & empty(v17) = 0 & empty(v16) = 0 & empty(v14) = v15 & empty(v12) = v13 & empty(empty_set) = 0 & in(v2, v7) = v8 & in(v2, v5) = v6 & in(v2, v1) = v9 & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ! [v28] : (v26 = 0 | ~ (relation_composition(v20, v21) = v22) | ~ (ordered_pair(v23, v27) = v28) | ~ (ordered_pair(v23, v24) = v25) | ~ (relation(v22) = 0) | ~ (relation(v20) = 0) | ~ (in(v28, v20) = 0) | ~ (in(v25, v22) = v26) | ? [v29] : ? [v30] : (( ~ (v30 = 0) & ordered_pair(v27, v24) = v29 & in(v29, v21) = v30) | ( ~ (v29 = 0) & relation(v21) = v29))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_composition(v25, v23) = v26) | ~ (identity_relation(v22) = v25) | ~ (ordered_pair(v20, v21) = v24) | ~ (in(v24, v26) = v27) | ? [v28] : ? [v29] : ? [v30] : (relation(v23) = v28 & in(v24, v23) = v30 & in(v20, v22) = v29 & ( ~ (v28 = 0) | (( ~ (v30 = 0) | ~ (v29 = 0) | v27 = 0) & ( ~ (v27 = 0) | (v30 = 0 & v29 = 0)))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (relation_rng(v22) = v25) | ~ (relation_dom(v22) = v23) | ~ (in(v21, v25) = v26) | ~ (in(v20, v23) = v24) | ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v20, v21) = v28 & relation(v22) = v27 & in(v28, v22) = v29 & ( ~ (v29 = 0) | ~ (v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (cartesian_product2(v22, v23) = v25) | ~ (ordered_pair(v20, v21) = v24) | ~ (in(v24, v25) = v26) | ? [v27] : ? [v28] : (in(v21, v23) = v28 & in(v20, v22) = v27 & ( ~ (v28 = 0) | ~ (v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v26 = 0 | ~ (cartesian_product2(v21, v23) = v25) | ~ (cartesian_product2(v20, v22) = v24) | ~ (subset(v24, v25) = v26) | ? [v27] : ? [v28] : (subset(v22, v23) = v28 & subset(v20, v21) = v27 & ( ~ (v28 = 0) | ~ (v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v24 = 0 | ~ (relation_rng(v22) = v25) | ~ (relation_dom(v22) = v23) | ~ (in(v21, v25) = v26) | ~ (in(v20, v23) = v24) | ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v20, v21) = v28 & relation(v22) = v27 & in(v28, v22) = v29 & ( ~ (v29 = 0) | ~ (v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v24 = 0 | ~ (cartesian_product2(v20, v21) = v22) | ~ (ordered_pair(v25, v26) = v23) | ~ (in(v23, v22) = v24) | ? [v27] : ? [v28] : (in(v26, v21) = v28 & in(v25, v20) = v27 & ( ~ (v28 = 0) | ~ (v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v24 = 0 | ~ (relation_inverse_image(v20, v21) = v22) | ~ (ordered_pair(v23, v25) = v26) | ~ (relation(v20) = 0) | ~ (in(v26, v20) = 0) | ~ (in(v23, v22) = v24) | ? [v27] : ( ~ (v27 = 0) & in(v25, v21) = v27)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : (v24 = 0 | ~ (relation_image(v20, v21) = v22) | ~ (ordered_pair(v25, v23) = v26) | ~ (relation(v20) = 0) | ~ (in(v26, v20) = 0) | ~ (in(v23, v22) = v24) | ? [v27] : ( ~ (v27 = 0) & in(v25, v21) = v27)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_rng_restriction(v20, v21) = v22) | ~ (ordered_pair(v23, v24) = v25) | ~ (relation(v22) = 0) | ~ (in(v25, v21) = v26) | ? [v27] : ? [v28] : (( ~ (v27 = 0) & relation(v21) = v27) | (in(v25, v22) = v27 & in(v24, v20) = v28 & ( ~ (v27 = 0) | (v28 = 0 & v26 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_dom_restriction(v20, v21) = v22) | ~ (ordered_pair(v23, v24) = v25) | ~ (relation(v22) = 0) | ~ (relation(v20) = 0) | ~ (in(v25, v20) = v26) | ? [v27] : ? [v28] : (in(v25, v22) = v27 & in(v23, v21) = v28 & ( ~ (v27 = 0) | (v28 = 0 & v26 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (subset_difference(v20, v21, v22) = v24) | ~ (element(v24, v23) = v25) | ~ (powerset(v20) = v23) | ? [v26] : ? [v27] : (element(v22, v23) = v27 & element(v21, v23) = v26 & ( ~ (v27 = 0) | ~ (v26 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (complements_of_subsets(v20, v21) = v24) | ~ (element(v24, v23) = v25) | ~ (powerset(v22) = v23) | ~ (powerset(v20) = v22) | ? [v26] : ( ~ (v26 = 0) & element(v21, v23) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_composition(v20, v22) = v23) | ~ (relation_dom(v23) = v24) | ~ (relation_dom(v20) = v21) | ~ (subset(v24, v21) = v25) | ? [v26] : (( ~ (v26 = 0) & relation(v22) = v26) | ( ~ (v26 = 0) & relation(v20) = v26))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_composition(v20, v21) = v22) | ~ (relation_rng(v22) = v23) | ~ (relation_rng(v21) = v24) | ~ (subset(v23, v24) = v25) | ~ (relation(v20) = 0) | ? [v26] : ( ~ (v26 = 0) & relation(v21) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_inverse(v20) = v21) | ~ (ordered_pair(v22, v23) = v24) | ~ (relation(v21) = 0) | ~ (in(v24, v21) = v25) | ? [v26] : ? [v27] : (( ~ (v27 = 0) & ordered_pair(v23, v22) = v26 & in(v26, v20) = v27) | ( ~ (v26 = 0) & relation(v20) = v26))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_field(v22) = v23) | ~ (in(v21, v23) = v25) | ~ (in(v20, v23) = v24) | ? [v26] : ? [v27] : ? [v28] : (ordered_pair(v20, v21) = v27 & relation(v22) = v26 & in(v27, v22) = v28 & ( ~ (v28 = 0) | ~ (v26 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_rng(v22) = v23) | ~ (relation_rng(v21) = v24) | ~ (relation_rng_restriction(v20, v21) = v22) | ~ (subset(v23, v24) = v25) | ? [v26] : ( ~ (v26 = 0) & relation(v21) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_rng(v22) = v23) | ~ (relation_rng(v21) = v24) | ~ (relation_dom_restriction(v21, v20) = v22) | ~ (subset(v23, v24) = v25) | ? [v26] : ( ~ (v26 = 0) & relation(v21) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (set_difference(v21, v23) = v24) | ~ (singleton(v22) = v23) | ~ (subset(v20, v24) = v25) | ? [v26] : ? [v27] : (subset(v20, v21) = v26 & in(v22, v20) = v27 & ( ~ (v26 = 0) | v27 = 0))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (set_difference(v21, v22) = v24) | ~ (set_difference(v20, v22) = v23) | ~ (subset(v23, v24) = v25) | ? [v26] : ( ~ (v26 = 0) & subset(v20, v21) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (relation_inverse_image(v22, v21) = v24) | ~ (relation_inverse_image(v22, v20) = v23) | ~ (subset(v23, v24) = v25) | ? [v26] : ? [v27] : (subset(v20, v21) = v27 & relation(v22) = v26 & ( ~ (v27 = 0) | ~ (v26 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (subset(v23, v24) = v25) | ~ (set_intersection2(v21, v22) = v24) | ~ (set_intersection2(v20, v22) = v23) | ? [v26] : ( ~ (v26 = 0) & subset(v20, v21) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v24 = 0 | ~ (relation_field(v22) = v23) | ~ (in(v21, v23) = v25) | ~ (in(v20, v23) = v24) | ? [v26] : ? [v27] : ? [v28] : (ordered_pair(v20, v21) = v27 & relation(v22) = v26 & in(v27, v22) = v28 & ( ~ (v28 = 0) | ~ (v26 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = 0 | ~ (relation_rng(v20) = v21) | ~ (ordered_pair(v24, v22) = v25) | ~ (in(v25, v20) = 0) | ~ (in(v22, v21) = v23) | ? [v26] : ( ~ (v26 = 0) & relation(v20) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : (v23 = 0 | ~ (relation_dom(v20) = v21) | ~ (ordered_pair(v22, v24) = v25) | ~ (in(v25, v20) = 0) | ~ (in(v22, v21) = v23) | ? [v26] : ( ~ (v26 = 0) & relation(v20) = v26)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_composition(v20, v21) = v22) | ~ (ordered_pair(v23, v24) = v25) | ~ (relation(v22) = 0) | ~ (relation(v20) = 0) | ~ (in(v25, v22) = 0) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ((v30 = 0 & v28 = 0 & ordered_pair(v26, v24) = v29 & ordered_pair(v23, v26) = v27 & in(v29, v21) = 0 & in(v27, v20) = 0) | ( ~ (v26 = 0) & relation(v21) = v26))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (subset_complement(v20, v23) = v24) | ~ (element(v21, v22) = 0) | ~ (powerset(v20) = v22) | ~ (subset(v21, v24) = v25) | ? [v26] : ? [v27] : (disjoint(v21, v23) = v27 & element(v23, v22) = v26 & ( ~ (v26 = 0) | (( ~ (v27 = 0) | v25 = 0) & ( ~ (v25 = 0) | v27 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_rng(v23) = v24) | ~ (relation_rng_restriction(v21, v22) = v23) | ~ (in(v20, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : (relation_rng(v22) = v28 & relation(v22) = v26 & in(v20, v28) = v29 & in(v20, v21) = v27 & ( ~ (v26 = 0) | (( ~ (v29 = 0) | ~ (v27 = 0) | v25 = 0) & ( ~ (v25 = 0) | (v29 = 0 & v27 = 0)))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_dom(v23) = v24) | ~ (relation_dom_restriction(v22, v21) = v23) | ~ (in(v20, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : (relation_dom(v22) = v28 & relation(v22) = v26 & in(v20, v28) = v29 & in(v20, v21) = v27 & ( ~ (v26 = 0) | (( ~ (v29 = 0) | ~ (v27 = 0) | v25 = 0) & ( ~ (v25 = 0) | (v29 = 0 & v27 = 0)))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (cartesian_product2(v22, v23) = v25) | ~ (ordered_pair(v20, v21) = v24) | ~ (in(v24, v25) = 0) | (in(v21, v23) = 0 & in(v20, v22) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (cartesian_product2(v21, v22) = v24) | ~ (cartesian_product2(v20, v22) = v23) | ~ (subset(v23, v24) = v25) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : (cartesian_product2(v22, v21) = v28 & cartesian_product2(v22, v20) = v27 & subset(v27, v28) = v29 & subset(v20, v21) = v26 & ( ~ (v26 = 0) | (v29 = 0 & v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_rng_restriction(v20, v21) = v22) | ~ (ordered_pair(v23, v24) = v25) | ~ (relation(v22) = 0) | ~ (in(v25, v21) = 0) | ? [v26] : ? [v27] : (( ~ (v26 = 0) & relation(v21) = v26) | (in(v25, v22) = v27 & in(v24, v20) = v26 & ( ~ (v26 = 0) | v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ! [v25] : ( ~ (relation_dom_restriction(v20, v21) = v22) | ~ (ordered_pair(v23, v24) = v25) | ~ (relation(v22) = 0) | ~ (relation(v20) = 0) | ~ (in(v25, v20) = 0) | ? [v26] : ? [v27] : (in(v25, v22) = v27 & in(v23, v21) = v26 & ( ~ (v26 = 0) | v27 = 0))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | v20 = empty_set | ~ (set_meet(v20) = v21) | ~ (in(v22, v23) = v24) | ~ (in(v22, v21) = 0) | ? [v25] : ( ~ (v25 = 0) & in(v23, v20) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (meet_of_subsets(v20, v21) = v23) | ~ (element(v23, v22) = v24) | ~ (powerset(v20) = v22) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & element(v21, v25) = v26 & powerset(v22) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (union_of_subsets(v20, v21) = v23) | ~ (element(v23, v22) = v24) | ~ (powerset(v20) = v22) | ? [v25] : ? [v26] : ( ~ (v26 = 0) & element(v21, v25) = v26 & powerset(v22) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset_complement(v20, v21) = v23) | ~ (element(v23, v22) = v24) | ~ (powerset(v20) = v22) | ? [v25] : ( ~ (v25 = 0) & element(v21, v22) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (relation_rng(v22) = v23) | ~ (relation_rng_restriction(v20, v21) = v22) | ~ (subset(v23, v20) = v24) | ? [v25] : ( ~ (v25 = 0) & relation(v21) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (relation_rng(v21) = v23) | ~ (relation_image(v21, v20) = v22) | ~ (subset(v22, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & relation(v21) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (relation_rng(v20) = v22) | ~ (relation_dom(v20) = v21) | ~ (cartesian_product2(v21, v22) = v23) | ~ (subset(v20, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & relation(v20) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (relation_dom(v21) = v23) | ~ (relation_inverse_image(v21, v20) = v22) | ~ (subset(v22, v23) = v24) | ? [v25] : ( ~ (v25 = 0) & relation(v21) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (element(v21, v23) = 0) | ~ (element(v20, v22) = v24) | ~ (powerset(v22) = v23) | ? [v25] : ( ~ (v25 = 0) & in(v20, v21) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (element(v21, v22) = 0) | ~ (powerset(v20) = v22) | ~ (in(v23, v20) = v24) | ? [v25] : ( ~ (v25 = 0) & in(v23, v21) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v23, v22) = v24) | ~ (unordered_pair(v20, v21) = v23) | ? [v25] : ? [v26] : (in(v21, v22) = v26 & in(v20, v22) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v23, v21) = v24) | ~ (set_union2(v20, v22) = v23) | ? [v25] : ? [v26] : (subset(v22, v21) = v26 & subset(v20, v21) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (subset(v20, v23) = v24) | ~ (set_intersection2(v21, v22) = v23) | ? [v25] : ? [v26] : (subset(v20, v22) = v26 & subset(v20, v21) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (identity_relation(v20) = v21) | ~ (ordered_pair(v22, v22) = v23) | ~ (relation(v21) = 0) | ~ (in(v23, v21) = v24) | ? [v25] : ( ~ (v25 = 0) & in(v22, v20) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (set_union2(v20, v21) = v22) | ~ (in(v23, v20) = v24) | ? [v25] : ? [v26] : (in(v23, v22) = v25 & in(v23, v21) = v26 & ( ~ (v25 = 0) | v26 = 0))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v23 = v22 | ~ (identity_relation(v20) = v21) | ~ (ordered_pair(v22, v23) = v24) | ~ (relation(v21) = 0) | ~ (in(v24, v21) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v23 = v21 | ~ (ordered_pair(v22, v23) = v24) | ~ (ordered_pair(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v23 = v20 | v22 = v20 | ~ (unordered_pair(v22, v23) = v24) | ~ (unordered_pair(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v23 = 0 | ~ (union(v20) = v21) | ~ (in(v22, v24) = 0) | ~ (in(v22, v21) = v23) | ? [v25] : ( ~ (v25 = 0) & in(v24, v20) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v22 = v20 | ~ (ordered_pair(v22, v23) = v24) | ~ (ordered_pair(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v21 = v20 | ~ (subset_difference(v24, v23, v22) = v21) | ~ (subset_difference(v24, v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v21 = empty_set | ~ (subset_difference(v20, v22, v23) = v24) | ~ (meet_of_subsets(v20, v21) = v23) | ~ (cast_to_subset(v20) = v22) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (union_of_subsets(v20, v28) = v29 & complements_of_subsets(v20, v21) = v28 & element(v21, v26) = v27 & powerset(v25) = v26 & powerset(v20) = v25 & ( ~ (v27 = 0) | v29 = v24))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : (v21 = empty_set | ~ (subset_difference(v20, v22, v23) = v24) | ~ (union_of_subsets(v20, v21) = v23) | ~ (cast_to_subset(v20) = v22) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (meet_of_subsets(v20, v28) = v29 & complements_of_subsets(v20, v21) = v28 & element(v21, v26) = v27 & powerset(v25) = v26 & powerset(v20) = v25 & ( ~ (v27 = 0) | v29 = v24))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (function_inverse(v21) = v22) | ~ (relation_composition(v22, v21) = v23) | ~ (apply(v23, v20) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (relation_rng(v21) = v28 & apply(v22, v20) = v30 & apply(v21, v30) = v31 & one_to_one(v21) = v27 & relation(v21) = v25 & function(v21) = v26 & in(v20, v28) = v29 & ( ~ (v29 = 0) | ~ (v27 = 0) | ~ (v26 = 0) | ~ (v25 = 0) | (v31 = v20 & v24 = v20)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_composition(v22, v21) = v23) | ~ (relation_dom(v23) = v24) | ~ (function(v21) = 0) | ~ (in(v20, v24) = 0) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (( ~ (v25 = 0) & relation(v21) = v25) | (apply(v23, v20) = v27 & apply(v22, v20) = v28 & apply(v21, v28) = v29 & relation(v22) = v25 & function(v22) = v26 & ( ~ (v26 = 0) | ~ (v25 = 0) | v29 = v27)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_inverse(v20) = v21) | ~ (ordered_pair(v22, v23) = v24) | ~ (relation(v21) = 0) | ~ (in(v24, v21) = 0) | ? [v25] : ? [v26] : ((v26 = 0 & ordered_pair(v23, v22) = v25 & in(v25, v20) = 0) | ( ~ (v25 = 0) & relation(v20) = v25))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (set_difference(v20, v21) = v22) | ~ (in(v23, v20) = v24) | ? [v25] : ? [v26] : (in(v23, v22) = v25 & in(v23, v21) = v26 & ( ~ (v25 = 0) | (v24 = 0 & ~ (v26 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v23) = v24) | ~ (relation_dom_restriction(v22, v20) = v23) | ~ (in(v21, v24) = 0) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : (apply(v23, v21) = v27 & apply(v22, v21) = v28 & relation(v22) = v25 & function(v22) = v26 & ( ~ (v26 = 0) | ~ (v25 = 0) | v28 = v27))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_dom(v21) = v22) | ~ (relation_image(v21, v23) = v24) | ~ (set_intersection2(v22, v20) = v23) | ? [v25] : ? [v26] : (relation_image(v21, v20) = v26 & relation(v21) = v25 & ( ~ (v25 = 0) | v26 = v24))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (singleton(v20) = v23) | ~ (unordered_pair(v22, v23) = v24) | ~ (unordered_pair(v20, v21) = v22) | ordered_pair(v20, v21) = v24) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_inverse_image(v22, v21) = v23) | ~ (in(v20, v23) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (relation_rng(v22) = v26 & relation(v22) = v25 & ( ~ (v25 = 0) | (( ~ (v24 = 0) | (v31 = 0 & v30 = 0 & v28 = 0 & ordered_pair(v20, v27) = v29 & in(v29, v22) = 0 & in(v27, v26) = 0 & in(v27, v21) = 0)) & (v24 = 0 | ! [v32] : ( ~ (in(v32, v26) = 0) | ? [v33] : ? [v34] : ? [v35] : (ordered_pair(v20, v32) = v33 & in(v33, v22) = v34 & in(v32, v21) = v35 & ( ~ (v35 = 0) | ~ (v34 = 0))))))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_image(v22, v21) = v23) | ~ (in(v20, v23) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : (relation_dom(v22) = v26 & relation(v22) = v25 & ( ~ (v25 = 0) | (( ~ (v24 = 0) | (v31 = 0 & v30 = 0 & v28 = 0 & ordered_pair(v27, v20) = v29 & in(v29, v22) = 0 & in(v27, v26) = 0 & in(v27, v21) = 0)) & (v24 = 0 | ! [v32] : ( ~ (in(v32, v26) = 0) | ? [v33] : ? [v34] : ? [v35] : (ordered_pair(v32, v20) = v33 & in(v33, v22) = v34 & in(v32, v21) = v35 & ( ~ (v35 = 0) | ~ (v34 = 0))))))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (relation_rng_restriction(v20, v23) = v24) | ~ (relation_dom_restriction(v22, v21) = v23) | ? [v25] : ? [v26] : ? [v27] : (relation_rng_restriction(v20, v22) = v26 & relation_dom_restriction(v26, v21) = v27 & relation(v22) = v25 & ( ~ (v25 = 0) | v27 = v24))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (subset(v20, v21) = 0) | ~ (ordered_pair(v22, v23) = v24) | ~ (relation(v20) = 0) | ~ (in(v24, v20) = 0) | ? [v25] : ((v25 = 0 & in(v24, v21) = 0) | ( ~ (v25 = 0) & relation(v21) = v25))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (identity_relation(v20) = v21) | ~ (ordered_pair(v22, v23) = v24) | ~ (relation(v21) = 0) | ~ (in(v24, v21) = 0) | in(v22, v20) = 0) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (ordered_pair(v20, v21) = v23) | ~ (in(v23, v22) = v24) | ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (relation_dom(v22) = v27 & apply(v22, v20) = v29 & relation(v22) = v25 & function(v22) = v26 & in(v20, v27) = v28 & ( ~ (v26 = 0) | ~ (v25 = 0) | (( ~ (v29 = v21) | ~ (v28 = 0) | v24 = 0) & ( ~ (v24 = 0) | (v29 = v21 & v28 = 0)))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (set_intersection2(v20, v21) = v22) | ~ (in(v23, v20) = v24) | ? [v25] : ? [v26] : (in(v23, v22) = v25 & in(v23, v21) = v26 & ( ~ (v25 = 0) | (v26 = 0 & v24 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ! [v24] : ( ~ (set_union2(v20, v21) = v22) | ~ (in(v23, v20) = v24) | ? [v25] : ? [v26] : (in(v23, v22) = v26 & in(v23, v21) = v25 & (v26 = 0 | ( ~ (v25 = 0) & ~ (v24 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (relation_composition(v20, v21) = v22) | ~ (relation(v23) = 0) | ~ (relation(v20) = 0) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : (( ~ (v24 = 0) & relation(v21) = v24) | (ordered_pair(v24, v25) = v26 & in(v26, v23) = v27 & ( ~ (v27 = 0) | ! [v33] : ! [v34] : ( ~ (ordered_pair(v24, v33) = v34) | ~ (in(v34, v20) = 0) | ? [v35] : ? [v36] : ( ~ (v36 = 0) & ordered_pair(v33, v25) = v35 & in(v35, v21) = v36))) & (v27 = 0 | (v32 = 0 & v30 = 0 & ordered_pair(v28, v25) = v31 & ordered_pair(v24, v28) = v29 & in(v31, v21) = 0 & in(v29, v20) = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (relation_rng_restriction(v20, v21) = v22) | ~ (relation(v23) = 0) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (( ~ (v24 = 0) & relation(v21) = v24) | (ordered_pair(v24, v25) = v26 & in(v26, v23) = v27 & in(v26, v21) = v29 & in(v25, v20) = v28 & ( ~ (v29 = 0) | ~ (v28 = 0) | ~ (v27 = 0)) & (v27 = 0 | (v29 = 0 & v28 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v22 | ~ (relation_dom_restriction(v20, v21) = v23) | ~ (relation(v22) = 0) | ~ (relation(v20) = 0) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (ordered_pair(v24, v25) = v26 & in(v26, v22) = v27 & in(v26, v20) = v29 & in(v24, v21) = v28 & ( ~ (v29 = 0) | ~ (v28 = 0) | ~ (v27 = 0)) & (v27 = 0 | (v29 = 0 & v28 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | v23 = v20 | ~ (unordered_pair(v20, v21) = v22) | ~ (in(v23, v22) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (subset_complement(v20, v22) = v23) | ~ (subset_complement(v20, v21) = v22) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & element(v21, v24) = v25 & powerset(v20) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (set_difference(v21, v20) = v22) | ~ (set_union2(v20, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & subset(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (apply(v22, v21) = v23) | ~ (identity_relation(v20) = v22) | ? [v24] : ( ~ (v24 = 0) & in(v21, v20) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v21 | ~ (singleton(v20) = v22) | ~ (set_union2(v22, v21) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (set_difference(v20, v22) = v23) | ~ (singleton(v21) = v22) | in(v21, v20) = 0) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | v20 = empty_set | ~ (set_meet(v20) = v21) | ~ (in(v22, v21) = v23) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & in(v24, v20) = 0 & in(v22, v24) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (disjoint(v22, v21) = v23) | ~ (singleton(v20) = v22) | in(v20, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (disjoint(v21, v22) = 0) | ~ (disjoint(v20, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & subset(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (set_difference(v20, v21) = v22) | ~ (subset(v22, v20) = v23)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (union(v21) = v22) | ~ (subset(v20, v22) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (cast_to_subset(v20) = v21) | ~ (element(v21, v22) = v23) | ~ (powerset(v20) = v22)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v20, v22) = v23) | ~ (powerset(v21) = v22) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & in(v24, v21) = v25 & in(v24, v20) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (element(v20, v22) = v23) | ~ (powerset(v21) = v22) | ? [v24] : ( ~ (v24 = 0) & subset(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (powerset(v20) = v21) | ~ (subset(v22, v20) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v22, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (singleton(v20) = v22) | ~ (subset(v22, v21) = v23) | ? [v24] : ( ~ (v24 = 0) & in(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (relation_rng_restriction(v20, v21) = v22) | ~ (subset(v22, v21) = v23) | ? [v24] : ( ~ (v24 = 0) & relation(v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (relation_dom_restriction(v21, v20) = v22) | ~ (subset(v22, v21) = v23) | ? [v24] : ( ~ (v24 = 0) & relation(v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v22, v20) = v23) | ~ (set_intersection2(v20, v21) = v22)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v20, v22) = v23) | ~ (subset(v20, v21) = 0) | ? [v24] : ( ~ (v24 = 0) & subset(v21, v22) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (subset(v20, v22) = v23) | ~ (set_union2(v20, v21) = v22)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (unordered_pair(v20, v21) = v22) | ~ (in(v21, v22) = v23)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = 0 | ~ (unordered_pair(v20, v21) = v22) | ~ (in(v20, v22) = v23)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v22 = v21 | ~ (singleton(v20) = v23) | ~ (unordered_pair(v21, v22) = v23)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (are_equipotent(v23, v22) = v21) | ~ (are_equipotent(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (meet_of_subsets(v23, v22) = v21) | ~ (meet_of_subsets(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (union_of_subsets(v23, v22) = v21) | ~ (union_of_subsets(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (complements_of_subsets(v23, v22) = v21) | ~ (complements_of_subsets(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (relation_composition(v23, v22) = v21) | ~ (relation_composition(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (disjoint(v23, v22) = v21) | ~ (disjoint(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (subset_complement(v23, v22) = v21) | ~ (subset_complement(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (set_difference(v23, v22) = v21) | ~ (set_difference(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (apply(v23, v22) = v21) | ~ (apply(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (cartesian_product2(v23, v22) = v21) | ~ (cartesian_product2(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (element(v23, v22) = v21) | ~ (element(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (singleton(v21) = v23) | ~ (singleton(v20) = v22) | ~ (subset(v22, v23) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (singleton(v20) = v23) | ~ (unordered_pair(v21, v22) = v23)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (relation_inverse_image(v23, v22) = v21) | ~ (relation_inverse_image(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (relation_image(v23, v22) = v21) | ~ (relation_image(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (relation_rng_restriction(v23, v22) = v21) | ~ (relation_rng_restriction(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (relation_dom_restriction(v23, v22) = v21) | ~ (relation_dom_restriction(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (subset(v23, v22) = v21) | ~ (subset(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (ordered_pair(v23, v22) = v21) | ~ (ordered_pair(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (set_intersection2(v23, v22) = v21) | ~ (set_intersection2(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (set_union2(v23, v22) = v21) | ~ (set_union2(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (unordered_pair(v23, v22) = v21) | ~ (unordered_pair(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (proper_subset(v23, v22) = v21) | ~ (proper_subset(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = v20 | ~ (in(v23, v22) = v21) | ~ (in(v23, v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : (v21 = empty_set | ~ (element(v21, v23) = 0) | ~ (powerset(v22) = v23) | ~ (powerset(v20) = v22) | ? [v24] : ( ~ (v24 = empty_set) & complements_of_subsets(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_composition(v22, v21) = v23) | ~ (identity_relation(v20) = v22) | ? [v24] : ? [v25] : (relation_dom_restriction(v21, v20) = v25 & relation(v21) = v24 & ( ~ (v24 = 0) | v25 = v23))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_rng(v21) = v22) | ~ (set_intersection2(v22, v20) = v23) | ? [v24] : ? [v25] : ? [v26] : (relation_rng(v25) = v26 & relation_rng_restriction(v20, v21) = v25 & relation(v21) = v24 & ( ~ (v24 = 0) | v26 = v23))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_rng(v20) = v22) | ~ (relation_dom(v20) = v21) | ~ (set_union2(v21, v22) = v23) | ? [v24] : ? [v25] : (relation_field(v20) = v25 & relation(v20) = v24 & ( ~ (v24 = 0) | v25 = v23))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_rng(v20) = v21) | ~ (relation_image(v22, v21) = v23) | ? [v24] : ? [v25] : ? [v26] : (( ~ (v24 = 0) & relation(v20) = v24) | (relation_composition(v20, v22) = v25 & relation_rng(v25) = v26 & relation(v22) = v24 & ( ~ (v24 = 0) | v26 = v23)))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (set_difference(v22, v21) = v23) | ~ (set_union2(v20, v21) = v22) | set_difference(v20, v21) = v23) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (set_difference(v21, v20) = v22) | ~ (set_union2(v20, v22) = v23) | set_union2(v20, v21) = v23) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (set_difference(v20, v22) = v23) | ~ (set_difference(v20, v21) = v22) | set_intersection2(v20, v21) = v23) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (set_difference(v20, v21) = v22) | ~ (in(v23, v20) = 0) | ? [v24] : ? [v25] : (in(v23, v22) = v25 & in(v23, v21) = v24 & (v25 = 0 | v24 = 0))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v21) = v22) | ~ (set_intersection2(v22, v20) = v23) | ? [v24] : ? [v25] : ? [v26] : (relation_dom(v25) = v26 & relation_dom_restriction(v21, v20) = v25 & relation(v21) = v24 & ( ~ (v24 = 0) | v26 = v23))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_dom(v21) = v22) | ~ (in(v20, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : (apply(v21, v20) = v26 & relation(v21) = v24 & function(v21) = v25 & ( ~ (v25 = 0) | ~ (v24 = 0) | ! [v27] : ! [v28] : ! [v29] : ( ~ (v23 = 0) | ~ (relation_composition(v21, v27) = v28) | ~ (apply(v28, v20) = v29) | ? [v30] : ? [v31] : ? [v32] : (apply(v27, v26) = v32 & relation(v27) = v30 & function(v27) = v31 & ( ~ (v31 = 0) | ~ (v30 = 0) | v32 = v29)))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (cartesian_product2(v20, v21) = v22) | ~ (in(v23, v22) = 0) | ? [v24] : ? [v25] : (ordered_pair(v24, v25) = v23 & in(v25, v21) = 0 & in(v24, v20) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v22, v23) = 0) | ~ (element(v21, v23) = 0) | ~ (powerset(v20) = v23) | ? [v24] : (subset_difference(v20, v21, v22) = v24 & set_difference(v21, v22) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v22, v23) = 0) | ~ (powerset(v20) = v23) | ~ (in(v21, v22) = 0) | ? [v24] : ? [v25] : ( ~ (v25 = 0) & subset_complement(v20, v22) = v24 & in(v21, v24) = v25)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v21, v23) = 0) | ~ (powerset(v22) = v23) | ~ (powerset(v20) = v22) | ? [v24] : (meet_of_subsets(v20, v21) = v24 & set_meet(v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v21, v23) = 0) | ~ (powerset(v22) = v23) | ~ (powerset(v20) = v22) | ? [v24] : (union_of_subsets(v20, v21) = v24 & union(v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v21, v23) = 0) | ~ (powerset(v22) = v23) | ~ (powerset(v20) = v22) | ? [v24] : (complements_of_subsets(v20, v24) = v21 & complements_of_subsets(v20, v21) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v21, v23) = 0) | ~ (powerset(v22) = v23) | ~ (powerset(v20) = v22) | ? [v24] : (complements_of_subsets(v20, v21) = v24 & ! [v25] : (v25 = v24 | ~ (element(v25, v23) = 0) | ? [v26] : ? [v27] : ? [v28] : ? [v29] : (subset_complement(v20, v26) = v28 & element(v26, v22) = 0 & in(v28, v21) = v29 & in(v26, v25) = v27 & ( ~ (v29 = 0) | ~ (v27 = 0)) & (v29 = 0 | v27 = 0))) & ! [v25] : ( ~ (element(v25, v22) = 0) | ~ (element(v24, v23) = 0) | ? [v26] : ? [v27] : ? [v28] : (subset_complement(v20, v25) = v27 & in(v27, v21) = v28 & in(v25, v24) = v26 & ( ~ (v28 = 0) | v26 = 0) & ( ~ (v26 = 0) | v28 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (element(v21, v23) = 0) | ~ (powerset(v22) = v23) | ~ (in(v20, v21) = 0) | ? [v24] : ( ~ (v24 = 0) & empty(v22) = v24)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_inverse_image(v20, v21) = v22) | ~ (relation(v20) = 0) | ~ (in(v23, v22) = 0) | ? [v24] : ? [v25] : (ordered_pair(v23, v24) = v25 & in(v25, v20) = 0 & in(v24, v21) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (relation_image(v20, v21) = v22) | ~ (relation(v20) = 0) | ~ (in(v23, v22) = 0) | ? [v24] : ? [v25] : (ordered_pair(v24, v23) = v25 & in(v25, v20) = 0 & in(v24, v21) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (subset(v23, v22) = 0) | ~ (unordered_pair(v20, v21) = v23) | (in(v21, v22) = 0 & in(v20, v22) = 0)) & ! [v20] : ! [v21] : ! [v22] : ! [v23] : ( ~ (set_intersection2(v20, v21) = v22) | ~ (in(v23, v20) = 0) | ? [v24] : ? [v25] : (in(v23, v22) = v25 & in(v23, v21) = v24 & ( ~ (v24 = 0) | v25 = 0))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (set_difference(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v24, v22) = v27 & in(v24, v21) = v26 & in(v24, v20) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0) | v27 = 0) & (v25 = 0 | (v26 = 0 & ~ (v27 = 0))))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (cartesian_product2(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (in(v24, v20) = v25 & ( ~ (v25 = 0) | ! [v31] : ! [v32] : ( ~ (ordered_pair(v31, v32) = v24) | ? [v33] : ? [v34] : (in(v32, v22) = v34 & in(v31, v21) = v33 & ( ~ (v34 = 0) | ~ (v33 = 0))))) & (v25 = 0 | (v30 = v24 & v29 = 0 & v28 = 0 & ordered_pair(v26, v27) = v24 & in(v27, v22) = 0 & in(v26, v21) = 0)))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (relation_inverse_image(v21, v22) = v23) | ~ (relation(v21) = 0) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (in(v24, v20) = v25 & ( ~ (v25 = 0) | ! [v30] : ! [v31] : ( ~ (ordered_pair(v24, v30) = v31) | ~ (in(v31, v21) = 0) | ? [v32] : ( ~ (v32 = 0) & in(v30, v22) = v32))) & (v25 = 0 | (v29 = 0 & v28 = 0 & ordered_pair(v24, v26) = v27 & in(v27, v21) = 0 & in(v26, v22) = 0)))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (relation_image(v21, v22) = v23) | ~ (relation(v21) = 0) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : (in(v24, v20) = v25 & ( ~ (v25 = 0) | ! [v30] : ! [v31] : ( ~ (ordered_pair(v30, v24) = v31) | ~ (in(v31, v21) = 0) | ? [v32] : ( ~ (v32 = 0) & in(v30, v22) = v32))) & (v25 = 0 | (v29 = 0 & v28 = 0 & ordered_pair(v26, v24) = v27 & in(v27, v21) = 0 & in(v26, v22) = 0)))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (set_intersection2(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v24, v22) = v27 & in(v24, v21) = v26 & in(v24, v20) = v25 & ( ~ (v27 = 0) | ~ (v26 = 0) | ~ (v25 = 0)) & (v25 = 0 | (v27 = 0 & v26 = 0)))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (set_union2(v21, v22) = v23) | ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v24, v22) = v27 & in(v24, v21) = v26 & in(v24, v20) = v25 & ( ~ (v25 = 0) | ( ~ (v27 = 0) & ~ (v26 = 0))) & (v27 = 0 | v26 = 0 | v25 = 0))) & ? [v20] : ! [v21] : ! [v22] : ! [v23] : (v23 = v20 | ~ (unordered_pair(v21, v22) = v23) | ? [v24] : ? [v25] : (in(v24, v20) = v25 & ( ~ (v25 = 0) | ( ~ (v24 = v22) & ~ (v24 = v21))) & (v25 = 0 | v24 = v22 | v24 = v21))) & ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (relation_inverse(v20) = v21) | ~ (relation(v22) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (( ~ (v23 = 0) & relation(v20) = v23) | (ordered_pair(v24, v23) = v27 & ordered_pair(v23, v24) = v25 & in(v27, v20) = v28 & in(v25, v22) = v26 & ( ~ (v28 = 0) | ~ (v26 = 0)) & (v28 = 0 | v26 = 0)))) & ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (identity_relation(v20) = v22) | ~ (relation(v21) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (ordered_pair(v23, v24) = v25 & in(v25, v21) = v26 & in(v23, v20) = v27 & ( ~ (v27 = 0) | ~ (v26 = 0) | ~ (v24 = v23)) & (v26 = 0 | (v27 = 0 & v24 = v23)))) & ! [v20] : ! [v21] : ! [v22] : (v22 = v21 | ~ (set_union2(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | v20 = empty_set | ~ (singleton(v21) = v22) | ~ (subset(v20, v22) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (singleton(v20) = v21) | ~ (in(v22, v21) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (set_intersection2(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = empty_set | ~ (set_difference(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | v21 = v20 | ~ (proper_subset(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & subset(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (disjoint(v20, v21) = v22) | ? [v23] : ? [v24] : (set_intersection2(v20, v21) = v23 & in(v24, v23) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (disjoint(v20, v21) = v22) | ? [v23] : ( ~ (v23 = v20) & set_difference(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (disjoint(v20, v21) = v22) | ? [v23] : ( ~ (v23 = empty_set) & set_intersection2(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (disjoint(v20, v21) = v22) | ? [v23] : (in(v23, v21) = 0 & in(v23, v20) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (element(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & in(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (singleton(v21) = v20) | ~ (subset(v20, v20) = v22)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (singleton(v20) = v21) | ~ (subset(empty_set, v21) = v22)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (singleton(v20) = v21) | ~ (in(v20, v21) = v22)) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v20, v21) = v22) | ~ (relation(v20) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v26 = 0 & ~ (v27 = 0) & ordered_pair(v23, v24) = v25 & in(v25, v21) = v27 & in(v25, v20) = 0) | ( ~ (v23 = 0) & relation(v21) = v23))) & ! [v20] : ! [v21] : ! [v22] : (v22 = 0 | ~ (subset(v20, v21) = v22) | ? [v23] : ? [v24] : ( ~ (v24 = 0) & in(v23, v21) = v24 & in(v23, v20) = 0)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation_empty_yielding(v22) = v21) | ~ (relation_empty_yielding(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (function_inverse(v22) = v21) | ~ (function_inverse(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation_inverse(v22) = v21) | ~ (relation_inverse(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation_field(v22) = v21) | ~ (relation_field(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation_rng(v22) = v21) | ~ (relation_rng(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (union(v22) = v21) | ~ (union(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (cast_to_subset(v22) = v21) | ~ (cast_to_subset(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation_dom(v22) = v21) | ~ (relation_dom(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (powerset(v22) = v21) | ~ (powerset(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (singleton(v22) = v21) | ~ (singleton(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (set_meet(v22) = v21) | ~ (set_meet(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (identity_relation(v22) = v21) | ~ (identity_relation(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (one_to_one(v22) = v21) | ~ (one_to_one(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (relation(v22) = v21) | ~ (relation(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (function(v22) = v21) | ~ (function(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v21 = v20 | ~ (empty(v22) = v21) | ~ (empty(v22) = v20)) & ! [v20] : ! [v21] : ! [v22] : (v20 = empty_set | ~ (relation_rng(v21) = v22) | ~ (subset(v20, v22) = 0) | ? [v23] : ? [v24] : (relation_inverse_image(v21, v20) = v24 & relation(v21) = v23 & ( ~ (v24 = empty_set) | ~ (v23 = 0)))) & ! [v20] : ! [v21] : ! [v22] : (v20 = empty_set | ~ (element(v22, v21) = 0) | ~ (powerset(v20) = v21) | ? [v23] : (subset_complement(v20, v22) = v23 & ! [v24] : ! [v25] : (v25 = 0 | ~ (in(v24, v23) = v25) | ? [v26] : ? [v27] : (element(v24, v20) = v26 & in(v24, v22) = v27 & ( ~ (v26 = 0) | v27 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v21, v20) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation(v22) = v26 & relation(v21) = v24 & empty(v22) = v25 & empty(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v26 = 0 & v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (relation(v22) = v27 & relation(v21) = v25 & relation(v20) = v23 & function(v22) = v28 & function(v21) = v26 & function(v20) = v24 & ( ~ (v26 = 0) | ~ (v25 = 0) | ~ (v24 = 0) | ~ (v23 = 0) | (v28 = 0 & v27 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation(v22) = v26 & relation(v21) = v24 & empty(v22) = v25 & empty(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v26 = 0 & v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_composition(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (relation(v22) = v25 & relation(v21) = v24 & relation(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (disjoint(v22, v21) = 0) | ~ (singleton(v20) = v22) | ? [v23] : ( ~ (v23 = 0) & in(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (disjoint(v20, v21) = 0) | ~ (in(v22, v20) = 0) | ? [v23] : ( ~ (v23 = 0) & in(v22, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng(v20) = v21) | ~ (in(v22, v21) = 0) | ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & ordered_pair(v23, v22) = v24 & in(v24, v20) = 0) | ( ~ (v23 = 0) & relation(v20) = v23))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_difference(v20, v22) = v20) | ~ (singleton(v21) = v22) | ? [v23] : ( ~ (v23 = 0) & in(v21, v20) = v23)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (union(v20) = v21) | ~ (in(v22, v21) = 0) | ? [v23] : (in(v23, v20) = 0 & in(v22, v23) = 0)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v20) = v21) | ~ (relation_image(v20, v21) = v22) | ? [v23] : ? [v24] : (relation_rng(v20) = v24 & relation(v20) = v23 & ( ~ (v23 = 0) | v24 = v22))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom(v20) = v21) | ~ (in(v22, v21) = 0) | ? [v23] : ? [v24] : ? [v25] : ((v25 = 0 & ordered_pair(v22, v23) = v24 & in(v24, v20) = 0) | ( ~ (v23 = 0) & relation(v20) = v23))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (cartesian_product2(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (empty(v22) = v25 & empty(v21) = v24 & empty(v20) = v23 & ( ~ (v25 = 0) | v24 = 0 | v23 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (element(v21, v22) = 0) | ~ (powerset(v20) = v22) | ? [v23] : (subset_complement(v20, v21) = v23 & set_difference(v20, v21) = v23)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (element(v21, v20) = v22) | ? [v23] : ? [v24] : (empty(v21) = v24 & empty(v20) = v23 & ( ~ (v23 = 0) | (( ~ (v24 = 0) | v22 = 0) & ( ~ (v22 = 0) | v24 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (element(v21, v20) = v22) | ? [v23] : ? [v24] : (empty(v20) = v23 & in(v21, v20) = v24 & (v23 = 0 | (( ~ (v24 = 0) | v22 = 0) & ( ~ (v22 = 0) | v24 = 0))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (element(v20, v22) = 0) | ~ (powerset(v21) = v22) | subset(v20, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ( ~ (powerset(v20) = v21) | ~ (subset(v22, v20) = 0) | in(v22, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ( ~ (singleton(v20) = v22) | ~ (subset(v22, v21) = 0) | in(v20, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_rng_restriction(v20, v21) = v22) | ? [v23] : ? [v24] : (relation(v22) = v24 & relation(v21) = v23 & ( ~ (v23 = 0) | v24 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_empty_yielding(v22) = v26 & relation_empty_yielding(v20) = v24 & relation(v22) = v25 & relation(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v26 = 0 & v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation(v22) = v25 & relation(v20) = v23 & function(v22) = v26 & function(v20) = v24 & ( ~ (v24 = 0) | ~ (v23 = 0) | (v26 = 0 & v25 = 0)))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (relation_dom_restriction(v20, v21) = v22) | ? [v23] : ? [v24] : (relation(v22) = v24 & relation(v20) = v23 & ( ~ (v23 = 0) | v24 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (subset(v20, v21) = 0) | ~ (in(v22, v20) = 0) | in(v22, v21) = 0) & ! [v20] : ! [v21] : ! [v22] : ( ~ (identity_relation(v20) = v22) | ~ (function(v21) = 0) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (relation_dom(v21) = v24 & relation(v21) = v23 & ( ~ (v23 = 0) | (( ~ (v24 = v20) | v22 = v21 | (v26 = 0 & ~ (v27 = v25) & apply(v21, v25) = v27 & in(v25, v20) = 0)) & ( ~ (v22 = v21) | (v24 = v20 & ! [v28] : ! [v29] : (v29 = v28 | ~ (apply(v21, v28) = v29) | ? [v30] : ( ~ (v30 = 0) & in(v28, v20) = v30)))))))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (ordered_pair(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_intersection2(v20, v21) = v22) | set_intersection2(v21, v20) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_intersection2(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (relation(v22) = v25 & relation(v21) = v24 & relation(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v21, v20) = v22) | ? [v23] : ? [v24] : (empty(v22) = v24 & empty(v20) = v23 & ( ~ (v24 = 0) | v23 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v20, v21) = v22) | set_union2(v21, v20) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v20, v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (relation(v22) = v25 & relation(v21) = v24 & relation(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (set_union2(v20, v21) = v22) | ? [v23] : ? [v24] : (empty(v22) = v24 & empty(v20) = v23 & ( ~ (v24 = 0) | v23 = 0))) & ! [v20] : ! [v21] : ! [v22] : ( ~ (unordered_pair(v20, v21) = v22) | unordered_pair(v21, v20) = v22) & ! [v20] : ! [v21] : ! [v22] : ( ~ (unordered_pair(v20, v21) = v22) | ? [v23] : ( ~ (v23 = 0) & empty(v22) = v23)) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | v21 = empty_set | ~ (set_meet(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v23, v20) = v24 & ( ~ (v24 = 0) | (v26 = 0 & ~ (v27 = 0) & in(v25, v21) = 0 & in(v23, v25) = v27)) & (v24 = 0 | ! [v28] : ! [v29] : (v29 = 0 | ~ (in(v23, v28) = v29) | ? [v30] : ( ~ (v30 = 0) & in(v28, v21) = v30))))) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_rng(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (( ~ (v23 = 0) & relation(v21) = v23) | (in(v23, v20) = v24 & ( ~ (v24 = 0) | ! [v28] : ! [v29] : ( ~ (ordered_pair(v28, v23) = v29) | ~ (in(v29, v21) = 0))) & (v24 = 0 | (v27 = 0 & ordered_pair(v25, v23) = v26 & in(v26, v21) = 0))))) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (union(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (in(v23, v20) = v24 & ( ~ (v24 = 0) | ! [v28] : ( ~ (in(v23, v28) = 0) | ? [v29] : ( ~ (v29 = 0) & in(v28, v21) = v29))) & (v24 = 0 | (v27 = 0 & v26 = 0 & in(v25, v21) = 0 & in(v23, v25) = 0)))) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (relation_dom(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : (( ~ (v23 = 0) & relation(v21) = v23) | (in(v23, v20) = v24 & ( ~ (v24 = 0) | ! [v28] : ! [v29] : ( ~ (ordered_pair(v23, v28) = v29) | ~ (in(v29, v21) = 0))) & (v24 = 0 | (v27 = 0 & ordered_pair(v23, v25) = v26 & in(v26, v21) = 0))))) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (powerset(v21) = v22) | ? [v23] : ? [v24] : ? [v25] : (subset(v23, v21) = v25 & in(v23, v20) = v24 & ( ~ (v25 = 0) | ~ (v24 = 0)) & (v25 = 0 | v24 = 0))) & ? [v20] : ! [v21] : ! [v22] : (v22 = v20 | ~ (singleton(v21) = v22) | ? [v23] : ? [v24] : (in(v23, v20) = v24 & ( ~ (v24 = 0) | ~ (v23 = v21)) & (v24 = 0 | v23 = v21))) & ! [v20] : ! [v21] : (v21 = v20 | ~ (set_difference(v20, empty_set) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (cast_to_subset(v20) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (subset(v20, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & subset(v21, v20) = v22)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (set_intersection2(v20, v20) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (set_union2(v20, v20) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (set_union2(v20, empty_set) = v21)) & ! [v20] : ! [v21] : (v21 = v20 | ~ (relation(v21) = 0) | ~ (relation(v20) = 0) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (ordered_pair(v22, v23) = v24 & in(v24, v21) = v26 & in(v24, v20) = v25 & ( ~ (v26 = 0) | ~ (v25 = 0)) & (v26 = 0 | v25 = 0))) & ! [v20] : ! [v21] : (v21 = v20 | ~ (empty(v21) = 0) | ~ (empty(v20) = 0)) & ! [v20] : ! [v21] : (v21 = empty_set | ~ (set_difference(empty_set, v20) = v21)) & ! [v20] : ! [v21] : (v21 = empty_set | ~ (set_intersection2(v20, empty_set) = v21)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(v20, v20) = v21)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (subset(empty_set, v20) = v21)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (relation(v20) = v21) | ? [v22] : (in(v22, v20) = 0 & ! [v23] : ! [v24] : ~ (ordered_pair(v23, v24) = v22))) & ! [v20] : ! [v21] : (v21 = 0 | ~ (function(v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v20) = v22)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (empty(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ( ~ (v24 = 0) & element(v23, v22) = 0 & powerset(v20) = v22 & empty(v23) = v24)) & ! [v20] : ! [v21] : (v21 = 0 | ~ (empty(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation_rng(v20) = v23 & relation(v20) = v22 & empty(v23) = v24 & ( ~ (v24 = 0) | ~ (v22 = 0)))) & ! [v20] : ! [v21] : (v21 = 0 | ~ (empty(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation_dom(v20) = v23 & relation(v20) = v22 & empty(v23) = v24 & ( ~ (v24 = 0) | ~ (v22 = 0)))) & ! [v20] : ! [v21] : (v20 = empty_set | ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | ( ~ (v23 = empty_set) & ~ (v21 = empty_set))))) & ! [v20] : ! [v21] : ( ~ (function_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : (relation_rng(v21) = v28 & relation_rng(v20) = v25 & relation_dom(v21) = v26 & relation_dom(v20) = v27 & one_to_one(v20) = v24 & relation(v20) = v22 & function(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | (v28 = v27 & v26 = v25)))) & ! [v20] : ! [v21] : ( ~ (function_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v20) = v25 & relation_dom(v20) = v26 & one_to_one(v20) = v24 & relation(v20) = v22 & function(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | ! [v27] : ( ~ (function(v27) = 0) | ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : ? [v34] : ? [v35] : (relation_dom(v27) = v29 & relation(v27) = v28 & ( ~ (v28 = 0) | (( ~ (v29 = v25) | v27 = v21 | (apply(v27, v30) = v33 & apply(v20, v31) = v35 & in(v31, v26) = v34 & in(v30, v25) = v32 & ((v35 = v30 & v34 = 0 & ( ~ (v33 = v31) | ~ (v32 = 0))) | (v33 = v31 & v32 = 0 & ( ~ (v35 = v30) | ~ (v34 = 0)))))) & ( ~ (v27 = v21) | (v29 = v25 & ! [v36] : ! [v37] : ! [v38] : ( ~ (in(v37, v26) = v38) | ~ (in(v36, v25) = 0) | ? [v39] : ? [v40] : (apply(v21, v36) = v39 & apply(v20, v37) = v40 & ( ~ (v39 = v37) | (v40 = v36 & v38 = 0)))) & ! [v36] : ! [v37] : ! [v38] : ( ~ (in(v37, v26) = 0) | ~ (in(v36, v25) = v38) | ? [v39] : ? [v40] : (apply(v21, v36) = v40 & apply(v20, v37) = v39 & ( ~ (v39 = v36) | (v40 = v37 & v38 = 0))))))))))))) & ! [v20] : ! [v21] : ( ~ (function_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_inverse(v20) = v25 & one_to_one(v20) = v24 & relation(v20) = v22 & function(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v25 = v21))) & ! [v20] : ! [v21] : ( ~ (function_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (one_to_one(v21) = v25 & one_to_one(v20) = v24 & relation(v20) = v22 & function(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v25 = 0))) & ! [v20] : ! [v21] : ( ~ (function_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation(v21) = v24 & relation(v20) = v22 & function(v21) = v25 & function(v20) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0) | (v25 = 0 & v24 = 0)))) & ! [v20] : ! [v21] : ( ~ (disjoint(v20, v21) = 0) | disjoint(v21, v20) = 0) & ! [v20] : ! [v21] : ( ~ (disjoint(v20, v21) = 0) | set_difference(v20, v21) = v20) & ! [v20] : ! [v21] : ( ~ (disjoint(v20, v21) = 0) | set_intersection2(v20, v21) = empty_set) & ! [v20] : ! [v21] : ( ~ (disjoint(v20, v21) = 0) | ? [v22] : (set_intersection2(v20, v21) = v22 & ! [v23] : ~ (in(v23, v22) = 0))) & ! [v20] : ! [v21] : ( ~ (relation_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : (relation_rng(v21) = v26 & relation_rng(v20) = v23 & relation_dom(v21) = v24 & relation_dom(v20) = v25 & relation(v20) = v22 & ( ~ (v22 = 0) | (v26 = v25 & v24 = v23)))) & ! [v20] : ! [v21] : ( ~ (relation_inverse(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation(v21) = v24 & empty(v21) = v23 & empty(v20) = v22 & ( ~ (v22 = 0) | (v24 = 0 & v23 = 0)))) & ! [v20] : ! [v21] : ( ~ (relation_inverse(v20) = v21) | ? [v22] : ? [v23] : (relation_inverse(v21) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | v23 = v20))) & ! [v20] : ! [v21] : ( ~ (relation_inverse(v20) = v21) | ? [v22] : ? [v23] : (relation(v21) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | v23 = 0))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_rng(v24) = v25) | ~ (subset(v21, v25) = v26) | ? [v27] : ? [v28] : ? [v29] : ? [v30] : (relation_dom(v24) = v29 & subset(v23, v29) = v30 & subset(v20, v24) = v28 & relation(v24) = v27 & ( ~ (v28 = 0) | ~ (v27 = 0) | (v30 = 0 & v26 = 0))))))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | ! [v24] : ! [v25] : ( ~ (relation_rng(v24) = v25) | ~ (subset(v23, v25) = 0) | ? [v26] : ? [v27] : ? [v28] : (relation_composition(v24, v20) = v27 & relation_rng(v27) = v28 & relation(v24) = v26 & ( ~ (v26 = 0) | v28 = v21)))))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | ! [v24] : ! [v25] : ( ~ (relation_dom(v24) = v25) | ~ (subset(v21, v25) = 0) | ? [v26] : ? [v27] : ? [v28] : (relation_composition(v20, v24) = v27 & relation_dom(v27) = v28 & relation(v24) = v26 & ( ~ (v26 = 0) | v28 = v23)))))) & ! [v20] : ! [v21] : ( ~ (relation_rng(v20) = v21) | ? [v22] : ? [v23] : (relation_dom(v20) = v23 & relation(v20) = v22 & ( ~ (v22 = 0) | (( ~ (v23 = empty_set) | v21 = empty_set) & ( ~ (v21 = empty_set) | v23 = empty_set))))) & ! [v20] : ! [v21] : ( ~ (set_difference(v20, v21) = empty_set) | subset(v20, v21) = 0) & ! [v20] : ! [v21] : ( ~ (element(v20, v21) = 0) | ? [v22] : ? [v23] : (empty(v21) = v22 & in(v20, v21) = v23 & (v23 = 0 | v22 = 0))) & ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | union(v21) = v20) & ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) & ! [v20] : ! [v21] : ( ~ (powerset(v20) = v21) | ? [v22] : (element(v22, v21) = 0 & empty(v22) = 0)) & ! [v20] : ! [v21] : ( ~ (singleton(v20) = v21) | ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) & ! [v20] : ! [v21] : ( ~ (identity_relation(v20) = v21) | relation_rng(v21) = v20) & ! [v20] : ! [v21] : ( ~ (identity_relation(v20) = v21) | relation_dom(v21) = v20) & ! [v20] : ! [v21] : ( ~ (identity_relation(v20) = v21) | relation(v21) = 0) & ! [v20] : ! [v21] : ( ~ (identity_relation(v20) = v21) | function(v21) = 0) & ! [v20] : ! [v21] : ( ~ (unordered_pair(v20, v20) = v21) | singleton(v20) = v21) & ! [v20] : ! [v21] : ( ~ (one_to_one(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ? [v29] : ? [v30] : (relation_dom(v20) = v24 & relation(v20) = v22 & function(v20) = v23 & ( ~ (v23 = 0) | ~ (v22 = 0) | (( ~ (v21 = 0) | ! [v31] : ! [v32] : (v32 = v31 | ~ (in(v32, v24) = 0) | ~ (in(v31, v24) = 0) | ? [v33] : ? [v34] : ( ~ (v34 = v33) & apply(v20, v32) = v34 & apply(v20, v31) = v33))) & (v21 = 0 | (v30 = v29 & v28 = 0 & v27 = 0 & ~ (v26 = v25) & apply(v20, v26) = v29 & apply(v20, v25) = v29 & in(v26, v24) = 0 & in(v25, v24) = 0)))))) & ! [v20] : ! [v21] : ( ~ (one_to_one(v20) = v21) | ? [v22] : ? [v23] : ? [v24] : (relation(v20) = v22 & function(v20) = v24 & empty(v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0) | ~ (v22 = 0) | v21 = 0))) & ! [v20] : ! [v21] : ( ~ (relation(v20) = 0) | ~ (in(v21, v20) = 0) | ? [v22] : ? [v23] : ordered_pair(v22, v23) = v21) & ! [v20] : ! [v21] : ( ~ (proper_subset(v21, v20) = 0) | ? [v22] : ( ~ (v22 = 0) & subset(v20, v21) = v22)) & ! [v20] : ! [v21] : ( ~ (proper_subset(v20, v21) = 0) | subset(v20, v21) = 0) & ! [v20] : ! [v21] : ( ~ (proper_subset(v20, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & proper_subset(v21, v20) = v22)) & ! [v20] : ! [v21] : ( ~ (in(v20, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & empty(v21) = v22)) & ! [v20] : ! [v21] : ( ~ (in(v20, v21) = 0) | ? [v22] : ( ~ (v22 = 0) & in(v21, v20) = v22)) & ? [v20] : ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : (relation_dom(v21) = v23 & relation(v21) = v22 & ( ~ (v22 = 0) | ! [v24] : ! [v25] : ! [v26] : ! [v27] : ( ~ (relation_composition(v24, v21) = v25) | ~ (relation_dom(v25) = v26) | ~ (in(v20, v26) = v27) | ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : (relation_dom(v24) = v30 & apply(v24, v20) = v32 & relation(v24) = v28 & function(v24) = v29 & in(v32, v23) = v33 & in(v20, v30) = v31 & ( ~ (v29 = 0) | ~ (v28 = 0) | (( ~ (v33 = 0) | ~ (v31 = 0) | v27 = 0) & ( ~ (v27 = 0) | (v33 = 0 & v31 = 0))))))))) & ? [v20] : ! [v21] : ( ~ (function(v21) = 0) | ? [v22] : ? [v23] : (relation_dom(v21) = v23 & relation(v21) = v22 & ( ~ (v22 = 0) | ! [v24] : ! [v25] : ! [v26] : ( ~ (relation_dom(v24) = v25) | ~ (set_intersection2(v25, v20) = v26) | ? [v27] : ? [v28] : ? [v29] : ? [v30] : ? [v31] : ? [v32] : ? [v33] : (relation_dom_restriction(v24, v20) = v29 & relation(v24) = v27 & function(v24) = v28 & ( ~ (v28 = 0) | ~ (v27 = 0) | (( ~ (v29 = v21) | (v26 = v23 & ! [v34] : ( ~ (in(v34, v23) = 0) | ? [v35] : (apply(v24, v34) = v35 & apply(v21, v34) = v35)))) & ( ~ (v26 = v23) | v29 = v21 | (v31 = 0 & ~ (v33 = v32) & apply(v24, v30) = v33 & apply(v21, v30) = v32 & in(v30, v23) = 0))))))))) & ! [v20] : (v20 = empty_set | ~ (set_meet(empty_set) = v20)) & ! [v20] : (v20 = empty_set | ~ (subset(v20, empty_set) = 0)) & ! [v20] : (v20 = empty_set | ~ (relation(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : (ordered_pair(v21, v22) = v23 & in(v23, v20) = 0)) & ! [v20] : (v20 = empty_set | ~ (empty(v20) = 0)) & ! [v20] : ~ (singleton(v20) = empty_set) & ! [v20] : ( ~ (one_to_one(v20) = 0) | ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : (relation_inverse(v20) = v23 & relation(v23) = v24 & relation(v20) = v21 & function(v23) = v25 & function(v20) = v22 & ( ~ (v22 = 0) | ~ (v21 = 0) | (v25 = 0 & v24 = 0)))) & ! [v20] : ( ~ (function(v20) = 0) | ? [v21] : ? [v22] : (relation_dom(v20) = v22 & relation(v20) = v21 & ( ~ (v21 = 0) | ( ! [v23] : ! [v24] : ! [v25] : ! [v26] : ( ~ (ordered_pair(v23, v24) = v25) | ~ (in(v25, v20) = v26) | ? [v27] : ? [v28] : (apply(v20, v23) = v28 & in(v23, v22) = v27 & ( ~ (v27 = 0) | (( ~ (v28 = v24) | v26 = 0) & ( ~ (v26 = 0) | v28 = v24))))) & ? [v23] : ! [v24] : ! [v25] : (v25 = 0 | ~ (in(v24, v22) = v25) | ? [v26] : (apply(v20, v24) = v26 & ( ~ (v26 = v23) | v23 = empty_set) & ( ~ (v23 = empty_set) | v26 = empty_set))))))) & ! [v20] : ( ~ (empty(v20) = 0) | relation(v20) = 0) & ! [v20] : ( ~ (empty(v20) = 0) | ? [v21] : (relation_rng(v20) = v21 & relation(v21) = 0 & empty(v21) = 0)) & ! [v20] : ( ~ (empty(v20) = 0) | ? [v21] : (relation_dom(v20) = v21 & relation(v21) = 0 & empty(v21) = 0)) & ! [v20] : ~ (proper_subset(v20, v20) = 0) & ! [v20] : ~ (in(v20, empty_set) = 0) & ? [v20] : ? [v21] : (v21 = v20 | ? [v22] : ? [v23] : ? [v24] : (in(v22, v21) = v24 & in(v22, v20) = v23 & ( ~ (v24 = 0) | ~ (v23 = 0)) & (v24 = 0 | v23 = 0))) & ? [v20] : ? [v21] : element(v21, v20) = 0 & ? [v20] : ? [v21] : (in(v20, v21) = 0 & ! [v22] : ! [v23] : ! [v24] : (v24 = 0 | ~ (powerset(v22) = v23) | ~ (in(v23, v21) = v24) | ? [v25] : ( ~ (v25 = 0) & in(v22, v21) = v25)) & ! [v22] : ! [v23] : (v23 = 0 | ~ (are_equipotent(v22, v21) = v23) | ? [v24] : ? [v25] : (subset(v22, v21) = v24 & in(v22, v21) = v25 & ( ~ (v24 = 0) | v25 = 0))) & ! [v22] : ! [v23] : ( ~ (subset(v23, v22) = 0) | ? [v24] : ? [v25] : (in(v23, v21) = v25 & in(v22, v21) = v24 & ( ~ (v24 = 0) | v25 = 0)))) & ? [v20] : ? [v21] : (in(v20, v21) = 0 & ! [v22] : ! [v23] : (v23 = 0 | ~ (are_equipotent(v22, v21) = v23) | ? [v24] : ? [v25] : (subset(v22, v21) = v24 & in(v22, v21) = v25 & ( ~ (v24 = 0) | v25 = 0))) & ! [v22] : ! [v23] : ( ~ (subset(v23, v22) = 0) | ? [v24] : ? [v25] : (in(v23, v21) = v25 & in(v22, v21) = v24 & ( ~ (v24 = 0) | v25 = 0))) & ! [v22] : ( ~ (in(v22, v21) = 0) | ? [v23] : (in(v23, v21) = 0 & ! [v24] : ( ~ (subset(v24, v22) = 0) | in(v24, v23) = 0)))) & ? [v20] : (v20 = empty_set | ? [v21] : in(v21, v20) = 0) & ((v9 = 0 & v8 = 0 & ~ (v6 = 0)) | (v6 = 0 & ( ~ (v9 = 0) | ~ (v8 = 0))))) % 113.45/61.70 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10, all_0_11_11, all_0_12_12, all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_17_17, all_0_18_18, all_0_19_19 yields: % 113.45/61.70 | (1) ~ (all_0_4_4 = 0) & ~ (all_0_6_6 = 0) & relation_empty_yielding(all_0_9_9) = 0 & relation_empty_yielding(empty_set) = 0 & relation_rng(empty_set) = empty_set & relation_dom(all_0_15_15) = all_0_14_14 & relation_dom(all_0_16_16) = all_0_12_12 & relation_dom(empty_set) = empty_set & powerset(empty_set) = all_0_19_19 & singleton(empty_set) = all_0_19_19 & relation_dom_restriction(all_0_16_16, all_0_18_18) = all_0_15_15 & one_to_one(all_0_8_8) = 0 & relation(all_0_0_0) = 0 & relation(all_0_1_1) = 0 & relation(all_0_3_3) = 0 & relation(all_0_5_5) = 0 & relation(all_0_8_8) = 0 & relation(all_0_9_9) = 0 & relation(all_0_16_16) = 0 & relation(empty_set) = 0 & function(all_0_0_0) = 0 & function(all_0_3_3) = 0 & function(all_0_8_8) = 0 & function(all_0_16_16) = 0 & empty(all_0_1_1) = 0 & empty(all_0_2_2) = 0 & empty(all_0_3_3) = 0 & empty(all_0_5_5) = all_0_4_4 & empty(all_0_7_7) = all_0_6_6 & empty(empty_set) = 0 & in(all_0_17_17, all_0_12_12) = all_0_11_11 & in(all_0_17_17, all_0_14_14) = all_0_13_13 & in(all_0_17_17, all_0_18_18) = all_0_10_10 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v7) = v8) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v8, v0) = 0) | ~ (in(v5, v2) = v6) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v7, v4) = v9 & in(v9, v1) = v10) | ( ~ (v9 = 0) & relation(v1) = v9))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v5, v3) = v6) | ~ (identity_relation(v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (relation(v3) = v8 & in(v4, v3) = v10 & in(v0, v2) = v9 & ( ~ (v8 = 0) | (( ~ (v10 = 0) | ~ (v9 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v10 = 0 & v9 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v0, v1) = v8 & relation(v2) = v7 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = v6) | ? [v7] : ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ (cartesian_product2(v0, v2) = v4) | ~ (subset(v4, v5) = v6) | ? [v7] : ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_rng(v2) = v5) | ~ (relation_dom(v2) = v3) | ~ (in(v1, v5) = v6) | ~ (in(v0, v3) = v4) | ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v0, v1) = v8 & relation(v2) = v7 & in(v8, v2) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ? [v7] : ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (in(v5, v1) = v6) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & relation(v1) = v7) | (in(v5, v2) = v7 & in(v4, v0) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = v6) | ? [v7] : ? [v8] : (in(v5, v2) = v7 & in(v3, v1) = v8 & ( ~ (v7 = 0) | (v8 = 0 & v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset_difference(v0, v1, v2) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v0) = v3) | ? [v6] : ? [v7] : (element(v2, v3) = v7 & element(v1, v3) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (complements_of_subsets(v0, v1) = v4) | ~ (element(v4, v3) = v5) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_composition(v0, v2) = v3) | ~ (relation_dom(v3) = v4) | ~ (relation_dom(v0) = v1) | ~ (subset(v4, v1) = v5) | ? [v6] : (( ~ (v6 = 0) & relation(v2) = v6) | ( ~ (v6 = 0) & relation(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_composition(v0, v1) = v2) | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (subset(v3, v4) = v5) | ~ (relation(v0) = 0) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = v5) | ? [v6] : ? [v7] : (( ~ (v7 = 0) & ordered_pair(v3, v2) = v6 & in(v6, v0) = v7) | ( ~ (v6 = 0) & relation(v0) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v0, v1) = v7 & relation(v2) = v6 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v3) = v4) | ~ (singleton(v2) = v3) | ~ (subset(v0, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (set_difference(v1, v2) = v4) | ~ (set_difference(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v7 & relation(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (subset(v3, v4) = v5) | ~ (set_intersection2(v1, v2) = v4) | ~ (set_intersection2(v0, v2) = v3) | ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v4 = 0 | ~ (relation_field(v2) = v3) | ~ (in(v1, v3) = v5) | ~ (in(v0, v3) = v4) | ? [v6] : ? [v7] : ? [v8] : (ordered_pair(v0, v1) = v7 & relation(v2) = v6 & in(v7, v2) = v8 & ( ~ (v8 = 0) | ~ (v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_rng(v0) = v1) | ~ (ordered_pair(v4, v2) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v3 = 0 | ~ (relation_dom(v0) = v1) | ~ (ordered_pair(v2, v4) = v5) | ~ (in(v5, v0) = 0) | ~ (in(v2, v1) = v3) | ? [v6] : ( ~ (v6 = 0) & relation(v0) = v6)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v2) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & ordered_pair(v6, v4) = v9 & ordered_pair(v3, v6) = v7 & in(v9, v1) = 0 & in(v7, v0) = 0) | ( ~ (v6 = 0) & relation(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (subset_complement(v0, v3) = v4) | ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ~ (subset(v1, v4) = v5) | ? [v6] : ? [v7] : (disjoint(v1, v3) = v7 & element(v3, v2) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | v7 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng(v3) = v4) | ~ (relation_rng_restriction(v1, v2) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_rng(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ~ (in(v0, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v8 & relation(v2) = v6 & in(v0, v8) = v9 & in(v0, v1) = v7 & ( ~ (v6 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v9 = 0 & v7 = 0)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) | ~ (cartesian_product2(v0, v2) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (in(v5, v1) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & relation(v1) = v6) | (in(v5, v2) = v7 & in(v4, v0) = v6 & ( ~ (v6 = 0) | v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ~ (ordered_pair(v3, v4) = v5) | ~ (relation(v2) = 0) | ~ (relation(v0) = 0) | ~ (in(v5, v0) = 0) | ? [v6] : ? [v7] : (in(v5, v2) = v7 & in(v3, v1) = v6 & ( ~ (v6 = 0) | v7 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v3) = v4) | ~ (in(v2, v1) = 0) | ? [v5] : ( ~ (v5 = 0) & in(v3, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (meet_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union_of_subsets(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & element(v1, v5) = v6 & powerset(v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (subset_complement(v0, v1) = v3) | ~ (element(v3, v2) = v4) | ~ (powerset(v0) = v2) | ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v1) = v3) | ~ (relation_image(v1, v0) = v2) | ~ (subset(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (cartesian_product2(v1, v2) = v3) | ~ (subset(v0, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_dom(v1) = v3) | ~ (relation_inverse_image(v1, v0) = v2) | ~ (subset(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = 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] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v1) = v8 & apply(v2, v0) = v10 & apply(v1, v10) = v11 & one_to_one(v1) = v7 & relation(v1) = v5 & function(v1) = v6 & in(v0, v8) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v11 = v0 & v4 = v0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (relation_dom(v3) = v4) | ~ (function(v1) = 0) | ~ (in(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v5 = 0) & relation(v1) = v5) | (apply(v3, v0) = v7 & apply(v2, v0) = v8 & apply(v1, v8) = v9 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = v7)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0) | ? [v5] : ? [v6] : ((v6 = 0 & ordered_pair(v3, v2) = v5 & in(v5, v0) = 0) | ( ~ (v5 = 0) & relation(v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ? [v5] : ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ (in(v1, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v3, v1) = v7 & apply(v2, v1) = v8 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ? [v5] : ? [v6] : (relation_image(v1, v0) = v6 & relation(v1) = v5 & ( ~ (v5 = 0) | v6 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v0, v7) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0))))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v7, v0) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0))))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v0, v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ~ (in(v4, v0) = 0) | ? [v5] : ((v5 = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & relation(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0) | in(v2, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v7 & apply(v2, v0) = v9 & relation(v2) = v5 & function(v2) = v6 & in(v0, v7) = v8 & ( ~ (v6 = 0) | ~ (v5 = 0) | (( ~ (v9 = v1) | ~ (v8 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 = v1 & v8 = 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 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ( ~ (v4 = 0) & in(v1, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | v0 = empty_set | ~ (set_meet(v0) = v1) | ~ (in(v2, v1) = v3) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = 0 & in(v2, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = empty_set | ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : ( ~ (v4 = empty_set) & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ? [v5] : (relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v5) = v6 & relation_rng_restriction(v0, v1) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v2) | ~ (relation_dom(v0) = v1) | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : (relation_field(v0) = v5 & relation(v0) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_dom(v5) = v6 & relation_dom_restriction(v1, v0) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v0) = v6 & relation(v1) = v4 & function(v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ! [v7] : ! [v8] : ! [v9] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v7) = v8) | ~ (apply(v8, v0) = v9) | ? [v10] : ? [v11] : ? [v12] : (apply(v7, v6) = v12 & relation(v7) = v10 & function(v7) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9)))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (element(v1, v3) = 0) | ~ (powerset(v0) = v3) | ? [v4] : (subset_difference(v0, v1, v2) = v4 & set_difference(v1, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v2, v3) = 0) | ~ (powerset(v0) = v3) | ~ (in(v1, v2) = 0) | ? [v4] : ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (meet_of_subsets(v0, v1) = v4 & set_meet(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (complements_of_subsets(v0, v1) = v4 & ! [v5] : (v5 = v4 | ~ (element(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) | ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) & ! [v5] : ( ~ (element(v5, v2) = 0) | ~ (element(v4, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ? [v4] : ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = 0))))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (cartesian_product2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) | ? [v13] : ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) & ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ? [v4] : ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (relation_inverse(v0) = v1) | ~ (relation(v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (( ~ (v3 = 0) & relation(v0) = v3) | (ordered_pair(v4, v3) = v7 & ordered_pair(v3, v4) = v5 & in(v7, v0) = v8 & in(v5, v2) = v6 & ( ~ (v8 = 0) | ~ (v6 = 0)) & (v8 = 0 | v6 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (identity_relation(v0) = v2) | ~ (relation(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (ordered_pair(v3, v4) = v5 & in(v5, v1) = v6 & in(v3, v0) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v4 = v3)) & (v6 = 0 | (v7 = 0 & v4 = v3)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0) | ( ~ (v3 = 0) & relation(v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (relation_rng(v1) = v2) | ~ (subset(v0, v2) = 0) | ? [v3] : ? [v4] : (relation_inverse_image(v1, v0) = v4 & relation(v1) = v3 & ( ~ (v4 = empty_set) | ~ (v3 = 0)))) & ! [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] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v7 & relation(v1) = v5 & relation(v0) = v3 & function(v2) = v8 & function(v1) = v6 & function(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v8 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (relation(v2) = v5 & relation(v1) = v4 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v3, v2) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ? [v3] : ? [v4] : (relation_rng(v0) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = v2))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & ordered_pair(v2, v3) = v4 & in(v4, v0) = 0) | ( ~ (v3 = 0) & relation(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cartesian_product2(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (empty(v2) = v5 & empty(v1) = v4 & empty(v0) = v3 & ( ~ (v5 = 0) | v4 = 0 | v3 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [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] : ? [v5] : ? [v6] : (relation_empty_yielding(v2) = v6 & relation_empty_yielding(v0) = v4 & relation(v2) = v5 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v5 & relation(v0) = v3 & function(v2) = v6 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 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] : ( ~ (identity_relation(v0) = v2) | ~ (function(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v0) | v2 = v1 | (v6 = 0 & ~ (v7 = v5) & apply(v1, v5) = v7 & in(v5, v0) = 0)) & ( ~ (v2 = v1) | (v4 = v0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (apply(v1, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v0) = v10)))))))) & ! [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] : (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 | ~ (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 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 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 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) & ! [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 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set))))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v1) = v8 & relation_rng(v0) = v5 & relation_dom(v1) = v6 & relation_dom(v0) = v7 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | (v8 = v7 & v6 = v5)))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & relation_dom(v0) = v6 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ! [v7] : ( ~ (function(v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_dom(v7) = v9 & relation(v7) = v8 & ( ~ (v8 = 0) | (( ~ (v9 = v5) | v7 = v1 | (apply(v7, v10) = v13 & apply(v0, v11) = v15 & in(v11, v6) = v14 & in(v10, v5) = v12 & ((v15 = v10 & v14 = 0 & ( ~ (v13 = v11) | ~ (v12 = 0))) | (v13 = v11 & v12 = 0 & ( ~ (v15 = v10) | ~ (v14 = 0)))))) & ( ~ (v7 = v1) | (v9 = v5 & ! [v16] : ! [v17] : ! [v18] : ( ~ (in(v17, v6) = v18) | ~ (in(v16, v5) = 0) | ? [v19] : ? [v20] : (apply(v1, v16) = v19 & apply(v0, v17) = v20 & ( ~ (v19 = v17) | (v20 = v16 & v18 = 0)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (in(v17, v6) = 0) | ~ (in(v16, v5) = v18) | ? [v19] : ? [v20] : (apply(v1, v16) = v20 & apply(v0, v17) = v19 & ( ~ (v19 = v16) | (v20 = v17 & v18 = 0))))))))))))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_inverse(v0) = v5 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (one_to_one(v1) = v5 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation(v1) = v4 & relation(v0) = v2 & function(v1) = v5 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) & ! [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] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) & ! [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] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & relation(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = 0))))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v1)))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ~ (subset(v1, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v3)))))) & ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set))))) & ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) & ! [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] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v11] : ! [v12] : (v12 = v11 | ~ (in(v12, v4) = 0) | ~ (in(v11, v4) = 0) | ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v0, v12) = v14 & apply(v0, v11) = v13))) & (v1 = 0 | (v10 = v9 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v6) = v9 & apply(v0, v5) = v9 & in(v6, v4) = 0 & in(v5, v4) = 0)))))) & ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 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] : ! [v1] : ( ~ (function(v1) = 0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation(v1) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v4, v1) = v5) | ~ (relation_dom(v5) = v6) | ~ (in(v0, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (relation_dom(v4) = v10 & apply(v4, v0) = v12 & relation(v4) = v8 & function(v4) = v9 & in(v12, v3) = v13 & in(v0, v10) = v11 & ( ~ (v9 = 0) | ~ (v8 = 0) | (( ~ (v13 = 0) | ~ (v11 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v13 = 0 & v11 = 0))))))))) & ? [v0] : ! [v1] : ( ~ (function(v1) = 0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation(v1) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom(v4) = v5) | ~ (set_intersection2(v5, v0) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (relation_dom_restriction(v4, v0) = v9 & relation(v4) = v7 & function(v4) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = v1) | (v6 = v3 & ! [v14] : ( ~ (in(v14, v3) = 0) | ? [v15] : (apply(v4, v14) = v15 & apply(v1, v14) = v15)))) & ( ~ (v6 = v3) | v9 = v1 | (v11 = 0 & ~ (v13 = v12) & apply(v4, v10) = v13 & apply(v1, v10) = v12 & in(v10, v3) = 0))))))))) & ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) & ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) & ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0)) & ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) & ! [v0] : ~ (singleton(v0) = empty_set) & ! [v0] : ( ~ (one_to_one(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_inverse(v0) = v3 & relation(v3) = v4 & relation(v0) = v1 & function(v3) = v5 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ? [v7] : ? [v8] : (apply(v0, v3) = v8 & in(v3, v2) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4))))) & ? [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : (apply(v0, v4) = v6 & ( ~ (v6 = v3) | v3 = empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) & ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) & ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 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) & ((all_0_10_10 = 0 & all_0_11_11 = 0 & ~ (all_0_13_13 = 0)) | (all_0_13_13 = 0 & ( ~ (all_0_10_10 = 0) | ~ (all_0_11_11 = 0)))) % 113.45/61.76 | % 113.45/61.76 | Applying alpha-rule on (1) yields: % 113.45/61.76 | (2) ! [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)) % 113.45/61.76 | (3) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 113.45/61.76 | (4) ! [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))) % 113.45/61.76 | (5) relation(all_0_5_5) = 0 % 113.45/61.76 | (6) ! [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))))) % 113.45/61.76 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v0 | v2 = v0 | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v4)) % 113.45/61.76 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) % 113.45/61.76 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_dom(v1) = v3) | ~ (relation_inverse_image(v1, v0) = v2) | ~ (subset(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) % 113.45/61.76 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 113.45/61.76 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) % 113.45/61.76 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v2, v1) = v3) | ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) % 113.45/61.76 | (13) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) % 113.45/61.76 | (14) ! [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))))) % 113.45/61.76 | (15) ! [v0] : ~ (singleton(v0) = empty_set) % 113.45/61.76 | (16) function(all_0_3_3) = 0 % 113.45/61.76 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation(v2) = v7 & relation(v1) = v5 & relation(v0) = v3 & function(v2) = v8 & function(v1) = v6 & function(v0) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0) | (v8 = 0 & v7 = 0)))) % 113.45/61.76 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_rng_restriction(v3, v2) = v1) | ~ (relation_rng_restriction(v3, v2) = v0)) % 113.45/61.76 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation(v2) = v1) | ~ (relation(v2) = v0)) % 113.45/61.76 | (20) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(empty_set, v0) = v1)) % 113.45/61.76 | (21) relation(all_0_16_16) = 0 % 113.45/61.76 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & powerset(v0) = v2 & empty(v3) = v4)) % 113.45/61.76 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (complements_of_subsets(v3, v2) = v1) | ~ (complements_of_subsets(v3, v2) = v0)) % 113.45/61.76 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v0) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) % 113.45/61.76 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (subset(empty_set, v1) = v2)) % 113.45/61.76 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, empty_set) = v1)) % 113.45/61.76 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) % 113.45/61.76 | (28) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_rng(v0) = v5 & relation_dom(v0) = v6 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | ! [v7] : ( ~ (function(v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (relation_dom(v7) = v9 & relation(v7) = v8 & ( ~ (v8 = 0) | (( ~ (v9 = v5) | v7 = v1 | (apply(v7, v10) = v13 & apply(v0, v11) = v15 & in(v11, v6) = v14 & in(v10, v5) = v12 & ((v15 = v10 & v14 = 0 & ( ~ (v13 = v11) | ~ (v12 = 0))) | (v13 = v11 & v12 = 0 & ( ~ (v15 = v10) | ~ (v14 = 0)))))) & ( ~ (v7 = v1) | (v9 = v5 & ! [v16] : ! [v17] : ! [v18] : ( ~ (in(v17, v6) = v18) | ~ (in(v16, v5) = 0) | ? [v19] : ? [v20] : (apply(v1, v16) = v19 & apply(v0, v17) = v20 & ( ~ (v19 = v17) | (v20 = v16 & v18 = 0)))) & ! [v16] : ! [v17] : ! [v18] : ( ~ (in(v17, v6) = 0) | ~ (in(v16, v5) = v18) | ? [v19] : ? [v20] : (apply(v1, v16) = v20 & apply(v0, v17) = v19 & ( ~ (v19 = v16) | (v20 = v17 & v18 = 0))))))))))))) % 113.45/61.76 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_rng_restriction(v0, v3) = v4) | ~ (relation_dom_restriction(v2, v1) = v3) | ? [v5] : ? [v6] : ? [v7] : (relation_rng_restriction(v0, v2) = v6 & relation_dom_restriction(v6, v1) = v7 & relation(v2) = v5 & ( ~ (v5 = 0) | v7 = v4))) % 113.45/61.76 | (30) ? [v0] : ! [v1] : ( ~ (function(v1) = 0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation(v1) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (relation_composition(v4, v1) = v5) | ~ (relation_dom(v5) = v6) | ~ (in(v0, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (relation_dom(v4) = v10 & apply(v4, v0) = v12 & relation(v4) = v8 & function(v4) = v9 & in(v12, v3) = v13 & in(v0, v10) = v11 & ( ~ (v9 = 0) | ~ (v8 = 0) | (( ~ (v13 = 0) | ~ (v11 = 0) | v7 = 0) & ( ~ (v7 = 0) | (v13 = 0 & v11 = 0))))))))) % 113.45/61.76 | (31) ! [v0] : ( ~ (empty(v0) = 0) | relation(v0) = 0) % 113.45/61.76 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_dom(v2) = v1) | ~ (relation_dom(v2) = v0)) % 113.45/61.76 | (33) ? [v0] : ? [v1] : (v1 = v0 | ? [v2] : ? [v3] : ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) % 113.45/61.76 | (34) powerset(empty_set) = all_0_19_19 % 113.45/61.76 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (set_difference(v0, v2) = v3) | ~ (singleton(v1) = v2) | in(v1, v0) = 0) % 113.45/61.76 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_difference(v0, v2) = v0) | ~ (singleton(v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) % 113.45/61.76 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v2 = v0 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 113.45/61.76 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ordered_pair(v0, v1) = v3) | ~ (in(v3, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v2) = v7 & apply(v2, v0) = v9 & relation(v2) = v5 & function(v2) = v6 & in(v0, v7) = v8 & ( ~ (v6 = 0) | ~ (v5 = 0) | (( ~ (v9 = v1) | ~ (v8 = 0) | v4 = 0) & ( ~ (v4 = 0) | (v9 = v1 & v8 = 0)))))) % 113.87/61.77 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v2 | ~ (identity_relation(v0) = v1) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v1) = 0) | ~ (in(v4, v1) = 0)) % 113.87/61.77 | (40) ! [v0] : ( ~ (one_to_one(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_inverse(v0) = v3 & relation(v3) = v4 & relation(v0) = v1 & function(v3) = v5 & function(v0) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | (v5 = 0 & v4 = 0)))) % 113.87/61.77 | (41) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_dom(v1) = v0) % 113.87/61.77 | (42) ! [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)) % 113.87/61.77 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v1, v2) = 0) | ~ (disjoint(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 113.87/61.77 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v7, v0) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v12, v0) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0))))))))) % 113.87/61.77 | (45) ! [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))))) % 113.87/61.77 | (46) ! [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)))) % 113.87/61.77 | (47) (all_0_10_10 = 0 & all_0_11_11 = 0 & ~ (all_0_13_13 = 0)) | (all_0_13_13 = 0 & ( ~ (all_0_10_10 = 0) | ~ (all_0_11_11 = 0))) % 113.87/61.77 | (48) ! [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)) % 113.87/61.77 | (49) function(all_0_16_16) = 0 % 113.87/61.77 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (element(v0, v2) = v3) | ~ (powerset(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 113.87/61.77 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v0, v2) = v3) | ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) % 113.87/61.77 | (52) ! [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)) % 113.87/61.77 | (53) ! [v0] : (v0 = empty_set | ~ (empty(v0) = 0)) % 113.87/61.77 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v0) = v1) | ~ (relation_image(v2, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & relation(v0) = v4) | (relation_composition(v0, v2) = v5 & relation_rng(v5) = v6 & relation(v2) = v4 & ( ~ (v4 = 0) | v6 = v3)))) % 113.87/61.77 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (subset(v3, v2) = 0) | ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) % 113.87/61.77 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (are_equipotent(v3, v2) = v1) | ~ (are_equipotent(v3, v2) = v0)) % 113.87/61.77 | (57) ! [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)))))) % 113.87/61.77 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 113.87/61.77 | (59) ! [v0] : ! [v1] : ! [v2] : (v0 = empty_set | ~ (relation_rng(v1) = v2) | ~ (subset(v0, v2) = 0) | ? [v3] : ? [v4] : (relation_inverse_image(v1, v0) = v4 & relation(v1) = v3 & ( ~ (v4 = empty_set) | ~ (v3 = 0)))) % 113.87/61.77 | (60) ! [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)))) % 113.87/61.77 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (powerset(v0) = v2) | ? [v4] : (union_of_subsets(v0, v1) = v4 & union(v1) = v4)) % 113.87/61.77 | (62) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_difference(empty_set, v0) = v1)) % 113.87/61.77 | (63) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_dom(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 113.87/61.77 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 113.87/61.77 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) % 113.87/61.77 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (relation_image(v0, v1) = v2) | ? [v3] : ? [v4] : (relation_rng(v0) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = v2))) % 113.87/61.77 | (67) ! [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))))) % 113.87/61.77 | (68) relation_empty_yielding(empty_set) = 0 % 113.87/61.77 | (69) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) % 113.87/61.77 | (70) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_dom(v4) = v5) | ~ (subset(v1, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v0, v4) = v7 & relation_dom(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v3)))))) % 113.87/61.77 | (71) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_rng(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) % 113.87/61.77 | (72) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) % 113.87/61.77 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v2, v0) = v3) | ~ (set_intersection2(v0, v1) = v2)) % 113.87/61.77 | (74) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (one_to_one(v1) = v5 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v5 = 0))) % 113.87/61.77 | (75) ! [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)) % 113.87/61.77 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v0) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 113.87/61.77 | (77) empty(all_0_5_5) = all_0_4_4 % 113.87/61.77 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) % 113.87/61.77 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (set_meet(v2) = v1) | ~ (set_meet(v2) = v0)) % 113.87/61.77 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v0) = v1) | ~ (in(v2, v1) = 0)) % 113.87/61.77 | (81) ! [v0] : ! [v1] : (v1 = 0 | ~ (empty(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation_rng(v0) = v3 & relation(v0) = v2 & empty(v3) = v4 & ( ~ (v4 = 0) | ~ (v2 = 0)))) % 113.87/61.77 | (82) relation_empty_yielding(all_0_9_9) = 0 % 113.87/61.77 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_inverse_image(v2, v1) = v4) | ~ (relation_inverse_image(v2, v0) = v3) | ~ (subset(v3, v4) = v5) | ? [v6] : ? [v7] : (subset(v0, v1) = v7 & relation(v2) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 113.87/61.77 | (84) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) % 113.87/61.77 | (85) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_inverse(v2) = v1) | ~ (relation_inverse(v2) = v0)) % 113.87/61.77 | (86) ! [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)))) % 113.87/61.77 | (87) empty(all_0_3_3) = 0 % 113.87/61.77 | (88) ? [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (singleton(v1) = v2) | ? [v3] : ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) % 113.87/61.77 | (89) ! [v0] : ! [v1] : (v1 = v0 | ~ (cast_to_subset(v0) = v1)) % 113.87/61.77 | (90) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (( ~ (v1 = 0) | ! [v11] : ! [v12] : (v12 = v11 | ~ (in(v12, v4) = 0) | ~ (in(v11, v4) = 0) | ? [v13] : ? [v14] : ( ~ (v14 = v13) & apply(v0, v12) = v14 & apply(v0, v11) = v13))) & (v1 = 0 | (v10 = v9 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v6) = v9 & apply(v0, v5) = v9 & in(v6, v4) = 0 & in(v5, v4) = 0)))))) % 113.87/61.77 | (91) ! [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)) % 113.87/61.77 | (92) relation_rng(empty_set) = empty_set % 113.87/61.77 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v4, v3) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) % 113.87/61.77 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (union(v1) = v2) | ~ (subset(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 113.87/61.77 | (95) relation_dom(all_0_15_15) = all_0_14_14 % 113.87/61.77 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) % 113.87/61.77 | (97) relation(all_0_0_0) = 0 % 113.87/61.77 | (98) ! [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))) % 113.87/61.77 | (99) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_intersection2(v0, v0) = v1)) % 113.87/61.77 | (100) ? [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))))) % 113.87/61.78 | (101) in(all_0_17_17, all_0_12_12) = all_0_11_11 % 113.87/61.78 | (102) ~ (all_0_6_6 = 0) % 113.87/61.78 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 113.87/61.78 | (104) ! [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)))) % 113.87/61.78 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (subset(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) % 113.87/61.78 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (relation_dom_restriction(v1, v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & relation(v1) = v4)) % 113.87/61.78 | (107) ! [v0] : ! [v1] : (v1 = empty_set | ~ (set_intersection2(v0, empty_set) = v1)) % 113.87/61.78 | (108) ! [v0] : ! [v1] : ( ~ (element(v0, v1) = 0) | ? [v2] : ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) % 113.87/61.78 | (109) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) % 113.87/61.78 | (110) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_union2(v0, v0) = v1)) % 113.87/61.78 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) % 113.87/61.78 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_field(v2) = v1) | ~ (relation_field(v2) = v0)) % 113.87/61.78 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) % 113.87/61.78 | (114) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation_rng(v1) = v0) % 113.87/61.78 | (115) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation(v1) = v4 & relation(v0) = v2 & function(v1) = v5 & function(v0) = v3 & ( ~ (v3 = 0) | ~ (v2 = 0) | (v5 = 0 & v4 = 0)))) % 113.87/61.78 | (116) function(all_0_0_0) = 0 % 113.87/61.78 | (117) ! [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))) % 113.87/61.78 | (118) ! [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)) % 113.87/61.78 | (119) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) % 113.87/61.78 | (120) relation(all_0_9_9) = 0 % 113.87/61.78 | (121) empty(empty_set) = 0 % 113.87/61.78 | (122) singleton(empty_set) = all_0_19_19 % 113.87/61.78 | (123) ! [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))) % 113.87/61.78 | (124) ! [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))) % 113.87/61.78 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (cast_to_subset(v0) = v1) | ~ (element(v1, v2) = v3) | ~ (powerset(v0) = v2)) % 113.87/61.78 | (126) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 113.87/61.78 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_dom(v1) = v2) | ~ (in(v0, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (apply(v1, v0) = v6 & relation(v1) = v4 & function(v1) = v5 & ( ~ (v5 = 0) | ~ (v4 = 0) | ! [v7] : ! [v8] : ! [v9] : ( ~ (v3 = 0) | ~ (relation_composition(v1, v7) = v8) | ~ (apply(v8, v0) = v9) | ? [v10] : ? [v11] : ? [v12] : (apply(v7, v6) = v12 & relation(v7) = v10 & function(v7) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0) | v12 = v9)))))) % 113.87/61.78 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union_of_subsets(v3, v2) = v1) | ~ (union_of_subsets(v3, v2) = v0)) % 113.87/61.78 | (129) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v3, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (relation_composition(v4, v0) = v7 & relation_rng(v7) = v8 & relation(v4) = v6 & ( ~ (v6 = 0) | v8 = v1)))))) % 113.87/61.78 | (130) ! [v0] : ! [v1] : ! [v2] : (v2 = empty_set | ~ (set_difference(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 113.87/61.78 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = v1 | ~ (ordered_pair(v2, v3) = v4) | ~ (ordered_pair(v0, v1) = v4)) % 113.87/61.78 | (132) ! [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)))) % 113.87/61.78 | (133) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (relation_rng(v1) = v8 & relation_rng(v0) = v5 & relation_dom(v1) = v6 & relation_dom(v0) = v7 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | (v8 = v7 & v6 = v5)))) % 113.87/61.78 | (134) ! [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)))))) % 113.87/61.78 | (135) ! [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))))) % 113.87/61.78 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function_inverse(v2) = v1) | ~ (function_inverse(v2) = v0)) % 113.87/61.78 | (137) ! [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)))) % 113.87/61.78 | (138) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) % 113.87/61.78 | (139) ! [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))) % 113.87/61.78 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (apply(v2, v1) = v3) | ~ (identity_relation(v0) = v2) | ? [v4] : ( ~ (v4 = 0) & in(v1, v0) = v4)) % 113.87/61.78 | (141) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v1) = v0) | ~ (subset(v0, v0) = v2)) % 113.87/61.78 | (142) relation(all_0_8_8) = 0 % 113.87/61.78 | (143) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | ? [v2] : (set_intersection2(v0, v1) = v2 & ! [v3] : ~ (in(v3, v2) = 0))) % 113.87/61.78 | (144) ! [v0] : ! [v1] : (v1 = 0 | ~ (subset(v0, v0) = v1)) % 113.87/61.78 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v0, v2) = v3)) % 113.87/61.78 | (146) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_empty_yielding(v2) = v1) | ~ (relation_empty_yielding(v2) = v0)) % 113.87/61.78 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (element(v3, v2) = v1) | ~ (element(v3, v2) = v0)) % 113.87/61.78 | (148) relation_dom_restriction(all_0_16_16, all_0_18_18) = all_0_15_15 % 113.87/61.78 | (149) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_rng(v4) = v5) | ~ (subset(v1, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (relation_dom(v4) = v9 & subset(v3, v9) = v10 & subset(v0, v4) = v8 & relation(v4) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0) | (v10 = 0 & v6 = 0))))))) % 113.87/61.78 | (150) ! [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)))) % 113.94/61.78 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_dom_restriction(v3, v2) = v1) | ~ (relation_dom_restriction(v3, v2) = v0)) % 113.94/61.78 | (152) ! [v0] : ! [v1] : ! [v2] : (v2 = v1 | ~ (set_union2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 113.94/61.78 | (153) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 113.94/61.78 | (154) ! [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))))) % 113.94/61.78 | (155) ! [v0] : (v0 = empty_set | ~ (set_meet(empty_set) = v0)) % 113.94/61.78 | (156) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (identity_relation(v2) = v1) | ~ (identity_relation(v2) = v0)) % 113.94/61.78 | (157) ? [v0] : ? [v1] : element(v1, v0) = 0 % 113.94/61.78 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 113.94/61.78 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation_empty_yielding(v2) = v6 & relation_empty_yielding(v0) = v4 & relation(v2) = v5 & relation(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 113.94/61.78 | (160) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (one_to_one(v2) = v1) | ~ (one_to_one(v2) = v0)) % 113.94/61.78 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = v3)) % 113.94/61.78 | (162) ? [v0] : (v0 = empty_set | ? [v1] : in(v1, v0) = 0) % 113.94/61.78 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (function_inverse(v1) = v2) | ~ (relation_composition(v2, v1) = v3) | ~ (apply(v3, v0) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v1) = v8 & apply(v2, v0) = v10 & apply(v1, v10) = v11 & one_to_one(v1) = v7 & relation(v1) = v5 & function(v1) = v6 & in(v0, v8) = v9 & ( ~ (v9 = 0) | ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0) | (v11 = v0 & v4 = v0)))) % 113.94/61.78 | (164) ! [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)))) % 113.94/61.79 | (165) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (singleton(v0) = v3) | ~ (unordered_pair(v2, v3) = v4) | ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) % 113.94/61.79 | (166) ! [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))))) % 113.94/61.79 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subset(v0, v2) = v3) | ~ (set_union2(v0, v1) = v2)) % 113.94/61.79 | (168) ! [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))) % 113.94/61.79 | (169) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) % 113.94/61.79 | (170) ! [v0] : ! [v1] : (v1 = v0 | ~ (empty(v1) = 0) | ~ (empty(v0) = 0)) % 113.94/61.79 | (171) relation(all_0_1_1) = 0 % 113.94/61.79 | (172) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) % 113.94/61.79 | (173) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v2, v1) = 0) | ~ (singleton(v0) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 113.94/61.79 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (element(v1, v3) = 0) | ~ (powerset(v2) = v3) | ~ (in(v0, v1) = 0) | ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) % 113.94/61.79 | (175) ! [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))) % 113.94/61.79 | (176) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_image(v0, v1) = v2) | ~ (ordered_pair(v5, v3) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) % 113.94/61.79 | (177) ! [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)) % 113.94/61.79 | (178) ! [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))) % 113.94/61.79 | (179) ! [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)))) % 113.94/61.79 | (180) relation(all_0_3_3) = 0 % 113.94/61.79 | (181) ! [v0] : ! [v1] : ( ~ (in(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 113.94/61.79 | (182) ! [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))) % 113.94/61.79 | (183) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 113.94/61.79 | (184) ! [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)))) % 113.94/61.79 | (185) ? [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))))) % 113.94/61.79 | (186) ! [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))) % 113.94/61.79 | (187) ! [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)) % 113.94/61.79 | (188) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (relation_rng(v2) = v3) | ~ (relation_rng(v1) = v4) | ~ (relation_rng_restriction(v0, v1) = v2) | ~ (subset(v3, v4) = v5) | ? [v6] : ( ~ (v6 = 0) & relation(v1) = v6)) % 113.94/61.79 | (189) ! [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)) % 113.94/61.79 | (190) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) % 113.94/61.79 | (191) ? [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))))) % 113.94/61.79 | (192) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) % 113.94/61.79 | (193) ! [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)) % 113.94/61.79 | (194) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_rng_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : (relation(v2) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 113.94/61.79 | (195) ! [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))) % 113.94/61.79 | (196) ! [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)))))) % 113.94/61.79 | (197) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (subset_difference(v4, v3, v2) = v1) | ~ (subset_difference(v4, v3, v2) = v0)) % 113.94/61.79 | (198) ! [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)) % 113.94/61.79 | (199) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_rng(v1) = v2) | ~ (set_intersection2(v2, v0) = v3) | ? [v4] : ? [v5] : ? [v6] : (relation_rng(v5) = v6 & relation_rng_restriction(v0, v1) = v5 & relation(v1) = v4 & ( ~ (v4 = 0) | v6 = v3))) % 113.94/61.79 | (200) ? [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)))) % 113.94/61.79 | (201) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (relation_rng(v2) = v1) | ~ (relation_rng(v2) = v0)) % 113.94/61.79 | (202) ! [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)))) % 113.94/61.79 | (203) ! [v0] : ! [v1] : (v1 = v0 | ~ (set_difference(v0, empty_set) = v1)) % 113.94/61.79 | (204) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation_inverse(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = v0))) % 113.94/61.79 | (205) ! [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))) % 113.94/61.79 | (206) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (disjoint(v2, v1) = v3) | ~ (singleton(v0) = v2) | in(v0, v1) = 0) % 113.94/61.79 | (207) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_composition(v2, v1) = v3) | ~ (relation_dom(v3) = v4) | ~ (function(v1) = 0) | ~ (in(v0, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (( ~ (v5 = 0) & relation(v1) = v5) | (apply(v3, v0) = v7 & apply(v2, v0) = v8 & apply(v1, v8) = v9 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v9 = v7)))) % 113.94/61.79 | (208) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | function(v1) = 0) % 113.94/61.79 | (209) in(all_0_17_17, all_0_18_18) = all_0_10_10 % 113.94/61.79 | (210) ! [v0] : ! [v1] : ! [v2] : ( ~ (identity_relation(v0) = v2) | ~ (function(v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (relation_dom(v1) = v4 & relation(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = v0) | v2 = v1 | (v6 = 0 & ~ (v7 = v5) & apply(v1, v5) = v7 & in(v5, v0) = 0)) & ( ~ (v2 = v1) | (v4 = v0 & ! [v8] : ! [v9] : (v9 = v8 | ~ (apply(v1, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & in(v8, v0) = v10)))))))) % 113.94/61.79 | (211) ! [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)) % 113.94/61.79 | (212) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 113.94/61.79 | (213) ! [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)))) % 113.94/61.79 | (214) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3)) % 113.94/61.79 | (215) ! [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))) % 113.94/61.79 | (216) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (meet_of_subsets(v3, v2) = v1) | ~ (meet_of_subsets(v3, v2) = v0)) % 113.94/61.79 | (217) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_inverse_image(v0, v1) = v2) | ~ (relation(v0) = 0) | ~ (in(v3, v2) = 0) | ? [v4] : ? [v5] : (ordered_pair(v3, v4) = v5 & in(v5, v0) = 0 & in(v4, v1) = 0)) % 113.94/61.79 | (218) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) % 113.94/61.79 | (219) ! [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))) % 113.94/61.79 | (220) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | ~ (set_intersection2(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 113.94/61.79 | (221) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (subset(v0, v1) = 0) | ~ (ordered_pair(v2, v3) = v4) | ~ (relation(v0) = 0) | ~ (in(v4, v0) = 0) | ? [v5] : ((v5 = 0 & in(v4, v1) = 0) | ( ~ (v5 = 0) & relation(v1) = v5))) % 113.94/61.80 | (222) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v1) = v4 & empty(v1) = v3 & empty(v0) = v2 & ( ~ (v2 = 0) | (v4 = 0 & v3 = 0)))) % 113.94/61.80 | (223) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 113.94/61.80 | (224) ! [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))) % 113.94/61.80 | (225) ! [v0] : ! [v1] : (v0 = empty_set | ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | ( ~ (v3 = empty_set) & ~ (v1 = empty_set))))) % 113.94/61.80 | (226) ! [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)) % 113.94/61.80 | (227) ! [v0] : ! [v1] : ( ~ (function_inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (relation_inverse(v0) = v5 & one_to_one(v0) = v4 & relation(v0) = v2 & function(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v5 = v1))) % 113.94/61.80 | (228) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (element(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) % 113.94/61.80 | (229) ! [v0] : ! [v1] : ( ~ (relation_rng(v0) = v1) | ? [v2] : ? [v3] : (relation_dom(v0) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = empty_set) | v1 = empty_set) & ( ~ (v1 = empty_set) | v3 = empty_set))))) % 113.94/61.80 | (230) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_inverse_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v4, v10) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v4, v6) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) % 113.94/61.80 | (231) ? [v0] : ! [v1] : ( ~ (function(v1) = 0) | ? [v2] : ? [v3] : (relation_dom(v1) = v3 & relation(v1) = v2 & ( ~ (v2 = 0) | ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_dom(v4) = v5) | ~ (set_intersection2(v5, v0) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (relation_dom_restriction(v4, v0) = v9 & relation(v4) = v7 & function(v4) = v8 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v9 = v1) | (v6 = v3 & ! [v14] : ( ~ (in(v14, v3) = 0) | ? [v15] : (apply(v4, v14) = v15 & apply(v1, v14) = v15)))) & ( ~ (v6 = v3) | v9 = v1 | (v11 = 0 & ~ (v13 = v12) & apply(v4, v10) = v13 & apply(v1, v10) = v12 & in(v10, v3) = 0))))))))) % 113.94/61.80 | (232) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) % 113.94/61.80 | (233) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 113.94/61.80 | (234) ! [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)) % 113.94/61.80 | (235) ! [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))) % 113.94/61.80 | (236) ! [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)) % 113.94/61.80 | (237) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v1) = v2) | ~ (relation_image(v1, v3) = v4) | ~ (set_intersection2(v2, v0) = v3) | ? [v5] : ? [v6] : (relation_image(v1, v0) = v6 & relation(v1) = v5 & ( ~ (v5 = 0) | v6 = v4))) % 113.94/61.80 | (238) ? [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))))) % 113.94/61.80 | (239) ! [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)))) % 113.94/61.80 | (240) ! [v0] : ! [v1] : ! [v2] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0)) % 113.94/61.80 | (241) ! [v0] : ! [v1] : ! [v2] : ( ~ (set_union2(v0, v1) = v2) | ? [v3] : ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) % 113.94/61.80 | (242) empty(all_0_1_1) = 0 % 113.94/61.80 | (243) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set) % 113.94/61.80 | (244) ! [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))) % 113.94/61.80 | (245) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) % 113.94/61.80 | (246) ! [v0] : (v0 = empty_set | ~ (relation(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : (ordered_pair(v1, v2) = v3 & in(v3, v0) = 0)) % 113.94/61.80 | (247) function(all_0_8_8) = 0 % 113.94/61.80 | (248) ! [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)) % 113.94/61.80 | (249) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_composition(v3, v2) = v1) | ~ (relation_composition(v3, v2) = v0)) % 113.94/61.80 | (250) ! [v0] : ! [v1] : ! [v2] : ( ~ (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | in(v2, v1) = 0) % 113.94/61.80 | (251) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) % 113.94/61.80 | (252) ! [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))) % 113.94/61.80 | (253) ! [v0] : (v0 = empty_set | ~ (subset(v0, empty_set) = 0)) % 113.94/61.80 | (254) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) % 113.94/61.80 | (255) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ( ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v3, v4) = v5) | ~ (in(v5, v0) = v6) | ? [v7] : ? [v8] : (apply(v0, v3) = v8 & in(v3, v2) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = v4) | v6 = 0) & ( ~ (v6 = 0) | v8 = v4))))) & ? [v3] : ! [v4] : ! [v5] : (v5 = 0 | ~ (in(v4, v2) = v5) | ? [v6] : (apply(v0, v4) = v6 & ( ~ (v6 = v3) | v3 = empty_set) & ( ~ (v3 = empty_set) | v6 = empty_set))))))) % 113.94/61.80 | (256) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_image(v3, v2) = v1) | ~ (relation_image(v3, v2) = v0)) % 113.94/61.80 | (257) ! [v0] : ! [v1] : (v1 = v0 | ~ (subset(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) % 113.94/61.80 | (258) ! [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)) % 113.94/61.80 | (259) ! [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)) % 113.94/61.80 | (260) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ (relation(v0) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v6 = 0 & ~ (v7 = 0) & ordered_pair(v3, v4) = v5 & in(v5, v1) = v7 & in(v5, v0) = 0) | ( ~ (v3 = 0) & relation(v1) = v3))) % 113.94/61.80 | (261) ! [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))) % 113.94/61.80 | (262) ! [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))))) % 113.94/61.80 | (263) ! [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)))) % 113.94/61.80 | (264) ! [v0] : ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) % 113.94/61.80 | (265) ! [v0] : ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) % 113.94/61.80 | (266) relation_dom(empty_set) = empty_set % 113.94/61.80 | (267) ? [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))) % 113.94/61.80 | (268) ! [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)))) % 113.94/61.80 | (269) ! [v0] : ! [v1] : ( ~ (relation_inverse(v0) = v1) | ? [v2] : ? [v3] : (relation(v1) = v3 & relation(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) % 113.94/61.80 | (270) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (relation_inverse_image(v3, v2) = v1) | ~ (relation_inverse_image(v3, v2) = v0)) % 113.94/61.80 | (271) one_to_one(all_0_8_8) = 0 % 113.94/61.80 | (272) relation(empty_set) = 0 % 113.94/61.80 | (273) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v0) = v2) | ? [v3] : ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) % 113.94/61.80 | (274) ! [v0] : ! [v1] : ( ~ (identity_relation(v0) = v1) | relation(v1) = 0) % 113.94/61.80 | (275) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_inverse_image(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_rng(v2) = v6 & relation(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | (v11 = 0 & v10 = 0 & v8 = 0 & ordered_pair(v0, v7) = v9 & in(v9, v2) = 0 & in(v7, v6) = 0 & in(v7, v1) = 0)) & (v4 = 0 | ! [v12] : ( ~ (in(v12, v6) = 0) | ? [v13] : ? [v14] : ? [v15] : (ordered_pair(v0, v12) = v13 & in(v13, v2) = v14 & in(v12, v1) = v15 & ( ~ (v15 = 0) | ~ (v14 = 0))))))))) % 113.94/61.80 | (276) relation_dom(all_0_16_16) = all_0_12_12 % 113.94/61.80 | (277) ! [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)))) % 113.94/61.80 | (278) ! [v0] : ! [v1] : ( ~ (relation(v0) = 0) | ~ (in(v1, v0) = 0) | ? [v2] : ? [v3] : ordered_pair(v2, v3) = v1) % 113.94/61.81 | (279) ~ (all_0_4_4 = 0) % 113.94/61.81 | (280) ! [v0] : ! [v1] : ( ~ (powerset(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 113.94/61.81 | (281) empty(all_0_7_7) = all_0_6_6 % 113.94/61.81 | (282) ? [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)))) % 113.94/61.81 | (283) ! [v0] : ! [v1] : (v1 = 0 | ~ (relation(v0) = v1) | ? [v2] : (in(v2, v0) = 0 & ! [v3] : ! [v4] : ~ (ordered_pair(v3, v4) = v2))) % 113.94/61.81 | (284) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v4 = 0 | ~ (relation_inverse_image(v0, v1) = v2) | ~ (ordered_pair(v3, v5) = v6) | ~ (relation(v0) = 0) | ~ (in(v6, v0) = 0) | ~ (in(v3, v2) = v4) | ? [v7] : ( ~ (v7 = 0) & in(v5, v1) = v7)) % 113.94/61.81 | (285) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cast_to_subset(v2) = v1) | ~ (cast_to_subset(v2) = v0)) % 113.94/61.81 | (286) ! [v0] : ~ (in(v0, empty_set) = 0) % 113.94/61.81 | (287) ! [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)) % 113.94/61.81 | (288) ! [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)) % 113.94/61.81 | (289) ! [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)) % 113.94/61.81 | (290) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (subset(v2, v3) = 0)) % 113.94/61.81 | (291) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom_restriction(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v5 & relation(v0) = v3 & function(v2) = v6 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 113.94/61.81 | (292) ! [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)))) % 113.94/61.81 | (293) ! [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)) % 113.94/61.81 | (294) ! [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)) % 113.94/61.81 | (295) ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_composition(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (relation(v2) = v6 & relation(v1) = v4 & empty(v2) = v5 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | (v6 = 0 & v5 = 0)))) % 113.94/61.81 | (296) ? [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (relation_image(v1, v2) = v3) | ~ (relation(v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ! [v10] : ! [v11] : ( ~ (ordered_pair(v10, v4) = v11) | ~ (in(v11, v1) = 0) | ? [v12] : ( ~ (v12 = 0) & in(v10, v2) = v12))) & (v5 = 0 | (v9 = 0 & v8 = 0 & ordered_pair(v6, v4) = v7 & in(v7, v1) = 0 & in(v6, v2) = 0)))) % 113.94/61.81 | (297) in(all_0_17_17, all_0_14_14) = all_0_13_13 % 113.94/61.81 | (298) ? [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)))) % 113.94/61.81 | (299) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v1 | ~ (singleton(v0) = v3) | ~ (unordered_pair(v1, v2) = v3)) % 113.94/61.81 | (300) ! [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)) % 113.94/61.81 | (301) ! [v0] : ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) % 113.94/61.81 | (302) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) % 113.94/61.81 | (303) ! [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) % 113.94/61.81 | (304) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v1, v2) = 0) | ~ (powerset(v0) = v2) | ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) % 113.94/61.81 | (305) ! [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))) % 113.94/61.81 | (306) ! [v0] : ! [v1] : ! [v2] : ( ~ (element(v0, v2) = 0) | ~ (powerset(v1) = v2) | subset(v0, v1) = 0) % 113.94/61.81 | (307) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) % 113.94/61.81 | (308) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (set_difference(v1, v0) = v2) | ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) % 113.94/61.81 | (309) ! [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))))) % 113.94/61.81 | (310) ? [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))) % 113.94/61.81 | (311) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 113.94/61.81 | (312) ? [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)))) % 113.94/61.81 | (313) ! [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)))) % 113.94/61.81 | (314) empty(all_0_2_2) = 0 % 113.94/61.81 | (315) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 113.94/61.81 | (316) ! [v0] : ~ (proper_subset(v0, v0) = 0) % 113.94/61.81 | (317) ? [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)))) % 113.94/61.81 | (318) ! [v0] : ( ~ (empty(v0) = 0) | ? [v1] : (relation_dom(v0) = v1 & relation(v1) = 0 & empty(v1) = 0)) % 113.94/61.81 | (319) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v3) = v4) | ~ (relation_dom_restriction(v2, v0) = v3) | ~ (in(v1, v4) = 0) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : (apply(v3, v1) = v7 & apply(v2, v1) = v8 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | v8 = v7))) % 113.94/61.81 | (320) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 113.94/61.81 | (321) ! [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)))) % 113.94/61.81 | (322) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (relation_rng(v1) = v3) | ~ (relation_image(v1, v0) = v2) | ~ (subset(v2, v3) = v4) | ? [v5] : ( ~ (v5 = 0) & relation(v1) = v5)) % 113.94/61.81 | (323) ? [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))) % 113.94/61.81 | (324) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | v3 = v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0)) % 113.94/61.81 | (325) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 113.94/61.81 | (326) ! [v0] : ! [v1] : ( ~ (one_to_one(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (relation(v0) = v2 & function(v0) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0) | v1 = 0))) % 113.94/61.81 | (327) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subset_complement(v3, v2) = v1) | ~ (subset_complement(v3, v2) = v0)) % 113.94/61.81 | (328) ! [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))) % 113.94/61.81 | (329) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v0) = v2)) % 113.94/61.81 | (330) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (proper_subset(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) % 113.94/61.81 | (331) ! [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)) % 113.94/61.81 | (332) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = v2)) % 113.94/61.81 | (333) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) % 113.94/61.81 | (334) ! [v0] : ! [v1] : ( ~ (proper_subset(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) % 114.08/61.81 | (335) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v1 | ~ (singleton(v0) = v2) | ~ (set_union2(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) % 114.08/61.81 | (336) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (subset(v2, v0) = v3)) % 114.08/61.81 | % 114.08/61.82 | Instantiating (30) with all_4_0_22 yields: % 114.08/61.82 | (337) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (relation_composition(v3, v0) = v4) | ~ (relation_dom(v4) = v5) | ~ (in(all_4_0_22, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_dom(v3) = v9 & apply(v3, all_4_0_22) = v11 & relation(v3) = v7 & function(v3) = v8 & in(v11, v2) = v12 & in(all_4_0_22, v9) = v10 & ( ~ (v8 = 0) | ~ (v7 = 0) | (( ~ (v12 = 0) | ~ (v10 = 0) | v6 = 0) & ( ~ (v6 = 0) | (v12 = 0 & v10 = 0))))))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating (231) with all_12_0_27 yields: % 114.08/61.82 | (338) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (relation_dom(v0) = v2 & relation(v0) = v1 & ( ~ (v1 = 0) | ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_dom(v3) = v4) | ~ (set_intersection2(v4, all_12_0_27) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (relation_dom_restriction(v3, all_12_0_27) = v8 & relation(v3) = v6 & function(v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v8 = v0) | (v5 = v2 & ! [v13] : ( ~ (in(v13, v2) = 0) | ? [v14] : (apply(v3, v13) = v14 & apply(v0, v13) = v14)))) & ( ~ (v5 = v2) | v8 = v0 | (v10 = 0 & ~ (v12 = v11) & apply(v3, v9) = v12 & apply(v0, v9) = v11 & in(v9, v2) = 0))))))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (159) with all_0_15_15, all_0_18_18, all_0_16_16 and discharging atoms relation_dom_restriction(all_0_16_16, all_0_18_18) = all_0_15_15, yields: % 114.08/61.82 | (339) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_empty_yielding(all_0_15_15) = v3 & relation_empty_yielding(all_0_16_16) = v1 & relation(all_0_15_15) = v2 & relation(all_0_16_16) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (291) with all_0_15_15, all_0_18_18, all_0_16_16 and discharging atoms relation_dom_restriction(all_0_16_16, all_0_18_18) = all_0_15_15, yields: % 114.08/61.82 | (340) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation(all_0_15_15) = v2 & relation(all_0_16_16) = v0 & function(all_0_15_15) = v3 & function(all_0_16_16) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | (v3 = 0 & v2 = 0))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (76) with all_0_15_15, all_0_18_18, all_0_16_16 and discharging atoms relation_dom_restriction(all_0_16_16, all_0_18_18) = all_0_15_15, yields: % 114.08/61.82 | (341) ? [v0] : ? [v1] : (relation(all_0_15_15) = v1 & relation(all_0_16_16) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (337) with all_0_16_16 and discharging atoms function(all_0_16_16) = 0, yields: % 114.08/61.82 | (342) ? [v0] : ? [v1] : (relation_dom(all_0_16_16) = v1 & relation(all_0_16_16) = v0 & ( ~ (v0 = 0) | ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (relation_composition(v2, all_0_16_16) = v3) | ~ (relation_dom(v3) = v4) | ~ (in(all_4_0_22, v4) = v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom(v2) = v8 & apply(v2, all_4_0_22) = v10 & relation(v2) = v6 & function(v2) = v7 & in(v10, v1) = v11 & in(all_4_0_22, v8) = v9 & ( ~ (v7 = 0) | ~ (v6 = 0) | (( ~ (v11 = 0) | ~ (v9 = 0) | v5 = 0) & ( ~ (v5 = 0) | (v11 = 0 & v9 = 0)))))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (338) with all_0_16_16 and discharging atoms function(all_0_16_16) = 0, yields: % 114.08/61.82 | (343) ? [v0] : ? [v1] : (relation_dom(all_0_16_16) = v1 & relation(all_0_16_16) = v0 & ( ~ (v0 = 0) | ! [v2] : ! [v3] : ! [v4] : ( ~ (relation_dom(v2) = v3) | ~ (set_intersection2(v3, all_12_0_27) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (relation_dom_restriction(v2, all_12_0_27) = v7 & relation(v2) = v5 & function(v2) = v6 & ( ~ (v6 = 0) | ~ (v5 = 0) | (( ~ (v7 = all_0_16_16) | (v4 = v1 & ! [v12] : ( ~ (in(v12, v1) = 0) | ? [v13] : (apply(v2, v12) = v13 & apply(all_0_16_16, v12) = v13)))) & ( ~ (v4 = v1) | v7 = all_0_16_16 | (v9 = 0 & ~ (v11 = v10) & apply(v2, v8) = v11 & apply(all_0_16_16, v8) = v10 & in(v8, v1) = 0)))))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (255) with all_0_16_16 and discharging atoms function(all_0_16_16) = 0, yields: % 114.08/61.82 | (344) ? [v0] : ? [v1] : (relation_dom(all_0_16_16) = v1 & relation(all_0_16_16) = v0 & ( ~ (v0 = 0) | ( ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v2, v3) = v4) | ~ (in(v4, all_0_16_16) = v5) | ? [v6] : ? [v7] : (apply(all_0_16_16, v2) = v7 & in(v2, v1) = v6 & ( ~ (v6 = 0) | (( ~ (v7 = v3) | v5 = 0) & ( ~ (v5 = 0) | v7 = v3))))) & ? [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (in(v3, v1) = v4) | ? [v5] : (apply(all_0_16_16, v3) = v5 & ( ~ (v5 = v2) | v2 = empty_set) & ( ~ (v2 = empty_set) | v5 = empty_set)))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (127) with all_0_11_11, all_0_12_12, all_0_16_16, all_0_17_17 and discharging atoms relation_dom(all_0_16_16) = all_0_12_12, in(all_0_17_17, all_0_12_12) = all_0_11_11, yields: % 114.08/61.82 | (345) ? [v0] : ? [v1] : ? [v2] : (apply(all_0_16_16, all_0_17_17) = v2 & relation(all_0_16_16) = v0 & function(all_0_16_16) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | ! [v3] : ! [v4] : ! [v5] : ( ~ (all_0_11_11 = 0) | ~ (relation_composition(all_0_16_16, v3) = v4) | ~ (apply(v4, all_0_17_17) = v5) | ? [v6] : ? [v7] : ? [v8] : (apply(v3, v2) = v8 & relation(v3) = v6 & function(v3) = v7 & ( ~ (v7 = 0) | ~ (v6 = 0) | v8 = v5))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating formula (134) with all_0_13_13, all_0_14_14, all_0_15_15, all_0_16_16, all_0_18_18, all_0_17_17 and discharging atoms relation_dom(all_0_15_15) = all_0_14_14, relation_dom_restriction(all_0_16_16, all_0_18_18) = all_0_15_15, in(all_0_17_17, all_0_14_14) = all_0_13_13, yields: % 114.08/61.82 | (346) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (relation_dom(all_0_16_16) = v2 & relation(all_0_16_16) = v0 & in(all_0_17_17, v2) = v3 & in(all_0_17_17, all_0_18_18) = v1 & ( ~ (v0 = 0) | (( ~ (v3 = 0) | ~ (v1 = 0) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | (v3 = 0 & v1 = 0))))) % 114.08/61.82 | % 114.08/61.82 | Instantiating (346) with all_59_0_47, all_59_1_48, all_59_2_49, all_59_3_50 yields: % 114.08/61.82 | (347) relation_dom(all_0_16_16) = all_59_1_48 & relation(all_0_16_16) = all_59_3_50 & in(all_0_17_17, all_59_1_48) = all_59_0_47 & in(all_0_17_17, all_0_18_18) = all_59_2_49 & ( ~ (all_59_3_50 = 0) | (( ~ (all_59_0_47 = 0) | ~ (all_59_2_49 = 0) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | (all_59_0_47 = 0 & all_59_2_49 = 0)))) % 114.08/61.82 | % 114.08/61.82 | Applying alpha-rule on (347) yields: % 114.08/61.82 | (348) in(all_0_17_17, all_59_1_48) = all_59_0_47 % 114.08/61.82 | (349) relation_dom(all_0_16_16) = all_59_1_48 % 114.08/61.82 | (350) relation(all_0_16_16) = all_59_3_50 % 114.08/61.82 | (351) in(all_0_17_17, all_0_18_18) = all_59_2_49 % 114.08/61.82 | (352) ~ (all_59_3_50 = 0) | (( ~ (all_59_0_47 = 0) | ~ (all_59_2_49 = 0) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | (all_59_0_47 = 0 & all_59_2_49 = 0))) % 114.08/61.82 | % 114.08/61.82 | Instantiating (345) with all_61_0_51, all_61_1_52, all_61_2_53 yields: % 114.08/61.82 | (353) apply(all_0_16_16, all_0_17_17) = all_61_0_51 & relation(all_0_16_16) = all_61_2_53 & function(all_0_16_16) = all_61_1_52 & ( ~ (all_61_1_52 = 0) | ~ (all_61_2_53 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (all_0_11_11 = 0) | ~ (relation_composition(all_0_16_16, v0) = v1) | ~ (apply(v1, all_0_17_17) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(v0, all_61_0_51) = v5 & relation(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2)))) % 114.08/61.82 | % 114.08/61.82 | Applying alpha-rule on (353) yields: % 114.08/61.82 | (354) apply(all_0_16_16, all_0_17_17) = all_61_0_51 % 114.08/61.82 | (355) relation(all_0_16_16) = all_61_2_53 % 114.08/61.82 | (356) function(all_0_16_16) = all_61_1_52 % 114.08/61.82 | (357) ~ (all_61_1_52 = 0) | ~ (all_61_2_53 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (all_0_11_11 = 0) | ~ (relation_composition(all_0_16_16, v0) = v1) | ~ (apply(v1, all_0_17_17) = v2) | ? [v3] : ? [v4] : ? [v5] : (apply(v0, all_61_0_51) = v5 & relation(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = v2))) % 114.08/61.82 | % 114.08/61.82 | Instantiating (344) with all_84_0_68, all_84_1_69 yields: % 114.08/61.82 | (358) relation_dom(all_0_16_16) = all_84_0_68 & relation(all_0_16_16) = all_84_1_69 & ( ~ (all_84_1_69 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_0_16_16) = v3) | ? [v4] : ? [v5] : (apply(all_0_16_16, v0) = v5 & in(v0, all_84_0_68) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 = v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_84_0_68) = v2) | ? [v3] : (apply(all_0_16_16, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set))))) % 114.08/61.82 | % 114.08/61.82 | Applying alpha-rule on (358) yields: % 114.08/61.82 | (359) relation_dom(all_0_16_16) = all_84_0_68 % 114.08/61.82 | (360) relation(all_0_16_16) = all_84_1_69 % 114.08/61.82 | (361) ~ (all_84_1_69 = 0) | ( ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ordered_pair(v0, v1) = v2) | ~ (in(v2, all_0_16_16) = v3) | ? [v4] : ? [v5] : (apply(all_0_16_16, v0) = v5 & in(v0, all_84_0_68) = v4 & ( ~ (v4 = 0) | (( ~ (v5 = v1) | v3 = 0) & ( ~ (v3 = 0) | v5 = v1))))) & ? [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (in(v1, all_84_0_68) = v2) | ? [v3] : (apply(all_0_16_16, v1) = v3 & ( ~ (v3 = v0) | v0 = empty_set) & ( ~ (v0 = empty_set) | v3 = empty_set)))) % 114.08/61.82 | % 114.08/61.82 | Instantiating (340) with all_110_0_98, all_110_1_99, all_110_2_100, all_110_3_101 yields: % 114.08/61.82 | (362) relation(all_0_15_15) = all_110_1_99 & relation(all_0_16_16) = all_110_3_101 & function(all_0_15_15) = all_110_0_98 & function(all_0_16_16) = all_110_2_100 & ( ~ (all_110_2_100 = 0) | ~ (all_110_3_101 = 0) | (all_110_0_98 = 0 & all_110_1_99 = 0)) % 114.08/61.82 | % 114.08/61.82 | Applying alpha-rule on (362) yields: % 114.08/61.82 | (363) relation(all_0_15_15) = all_110_1_99 % 114.08/61.82 | (364) relation(all_0_16_16) = all_110_3_101 % 114.08/61.82 | (365) ~ (all_110_2_100 = 0) | ~ (all_110_3_101 = 0) | (all_110_0_98 = 0 & all_110_1_99 = 0) % 114.08/61.82 | (366) function(all_0_16_16) = all_110_2_100 % 114.08/61.82 | (367) function(all_0_15_15) = all_110_0_98 % 114.08/61.82 | % 114.08/61.82 | Instantiating (339) with all_112_0_102, all_112_1_103, all_112_2_104, all_112_3_105 yields: % 114.08/61.82 | (368) relation_empty_yielding(all_0_15_15) = all_112_0_102 & relation_empty_yielding(all_0_16_16) = all_112_2_104 & relation(all_0_15_15) = all_112_1_103 & relation(all_0_16_16) = all_112_3_105 & ( ~ (all_112_2_104 = 0) | ~ (all_112_3_105 = 0) | (all_112_0_102 = 0 & all_112_1_103 = 0)) % 114.08/61.82 | % 114.08/61.82 | Applying alpha-rule on (368) yields: % 114.08/61.82 | (369) relation(all_0_15_15) = all_112_1_103 % 114.08/61.82 | (370) relation(all_0_16_16) = all_112_3_105 % 114.08/61.82 | (371) ~ (all_112_2_104 = 0) | ~ (all_112_3_105 = 0) | (all_112_0_102 = 0 & all_112_1_103 = 0) % 114.08/61.82 | (372) relation_empty_yielding(all_0_16_16) = all_112_2_104 % 114.08/61.82 | (373) relation_empty_yielding(all_0_15_15) = all_112_0_102 % 114.08/61.82 | % 114.08/61.82 | Instantiating (341) with all_114_0_106, all_114_1_107 yields: % 114.08/61.82 | (374) relation(all_0_15_15) = all_114_0_106 & relation(all_0_16_16) = all_114_1_107 & ( ~ (all_114_1_107 = 0) | all_114_0_106 = 0) % 114.08/61.82 | % 114.08/61.82 | Applying alpha-rule on (374) yields: % 114.08/61.82 | (375) relation(all_0_15_15) = all_114_0_106 % 114.08/61.82 | (376) relation(all_0_16_16) = all_114_1_107 % 114.08/61.82 | (377) ~ (all_114_1_107 = 0) | all_114_0_106 = 0 % 114.08/61.82 | % 114.08/61.82 | Instantiating (343) with all_116_0_108, all_116_1_109 yields: % 114.08/61.82 | (378) relation_dom(all_0_16_16) = all_116_0_108 & relation(all_0_16_16) = all_116_1_109 & ( ~ (all_116_1_109 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (set_intersection2(v1, all_12_0_27) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v0, all_12_0_27) = v5 & relation(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = all_0_16_16) | (v2 = all_116_0_108 & ! [v10] : ( ~ (in(v10, all_116_0_108) = 0) | ? [v11] : (apply(v0, v10) = v11 & apply(all_0_16_16, v10) = v11)))) & ( ~ (v2 = all_116_0_108) | v5 = all_0_16_16 | (v7 = 0 & ~ (v9 = v8) & apply(v0, v6) = v9 & apply(all_0_16_16, v6) = v8 & in(v6, all_116_0_108) = 0))))))) % 114.08/61.83 | % 114.08/61.83 | Applying alpha-rule on (378) yields: % 114.08/61.83 | (379) relation_dom(all_0_16_16) = all_116_0_108 % 114.08/61.83 | (380) relation(all_0_16_16) = all_116_1_109 % 114.08/61.83 | (381) ~ (all_116_1_109 = 0) | ! [v0] : ! [v1] : ! [v2] : ( ~ (relation_dom(v0) = v1) | ~ (set_intersection2(v1, all_12_0_27) = v2) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom_restriction(v0, all_12_0_27) = v5 & relation(v0) = v3 & function(v0) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | (( ~ (v5 = all_0_16_16) | (v2 = all_116_0_108 & ! [v10] : ( ~ (in(v10, all_116_0_108) = 0) | ? [v11] : (apply(v0, v10) = v11 & apply(all_0_16_16, v10) = v11)))) & ( ~ (v2 = all_116_0_108) | v5 = all_0_16_16 | (v7 = 0 & ~ (v9 = v8) & apply(v0, v6) = v9 & apply(all_0_16_16, v6) = v8 & in(v6, all_116_0_108) = 0)))))) % 114.08/61.83 | % 114.08/61.83 | Instantiating (342) with all_118_0_110, all_118_1_111 yields: % 114.08/61.83 | (382) relation_dom(all_0_16_16) = all_118_0_110 & relation(all_0_16_16) = all_118_1_111 & ( ~ (all_118_1_111 = 0) | ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, all_0_16_16) = v1) | ~ (relation_dom(v1) = v2) | ~ (in(all_4_0_22, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v0) = v6 & apply(v0, all_4_0_22) = v8 & relation(v0) = v4 & function(v0) = v5 & in(v8, all_118_0_110) = v9 & in(all_4_0_22, v6) = v7 & ( ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v3 = 0) & ( ~ (v3 = 0) | (v9 = 0 & v7 = 0))))))) % 114.08/61.83 | % 114.08/61.83 | Applying alpha-rule on (382) yields: % 114.08/61.83 | (383) relation_dom(all_0_16_16) = all_118_0_110 % 114.08/61.83 | (384) relation(all_0_16_16) = all_118_1_111 % 114.08/61.83 | (385) ~ (all_118_1_111 = 0) | ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (relation_composition(v0, all_0_16_16) = v1) | ~ (relation_dom(v1) = v2) | ~ (in(all_4_0_22, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : (relation_dom(v0) = v6 & apply(v0, all_4_0_22) = v8 & relation(v0) = v4 & function(v0) = v5 & in(v8, all_118_0_110) = v9 & in(all_4_0_22, v6) = v7 & ( ~ (v5 = 0) | ~ (v4 = 0) | (( ~ (v9 = 0) | ~ (v7 = 0) | v3 = 0) & ( ~ (v3 = 0) | (v9 = 0 & v7 = 0)))))) % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (32) with all_0_16_16, all_116_0_108, all_0_12_12 and discharging atoms relation_dom(all_0_16_16) = all_116_0_108, relation_dom(all_0_16_16) = all_0_12_12, yields: % 114.08/61.83 | (386) all_116_0_108 = all_0_12_12 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (32) with all_0_16_16, all_116_0_108, all_118_0_110 and discharging atoms relation_dom(all_0_16_16) = all_118_0_110, relation_dom(all_0_16_16) = all_116_0_108, yields: % 114.08/61.83 | (387) all_118_0_110 = all_116_0_108 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (32) with all_0_16_16, all_84_0_68, all_118_0_110 and discharging atoms relation_dom(all_0_16_16) = all_118_0_110, relation_dom(all_0_16_16) = all_84_0_68, yields: % 114.08/61.83 | (388) all_118_0_110 = all_84_0_68 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (32) with all_0_16_16, all_59_1_48, all_116_0_108 and discharging atoms relation_dom(all_0_16_16) = all_116_0_108, relation_dom(all_0_16_16) = all_59_1_48, yields: % 114.08/61.83 | (389) all_116_0_108 = all_59_1_48 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_116_1_109, all_118_1_111 and discharging atoms relation(all_0_16_16) = all_118_1_111, relation(all_0_16_16) = all_116_1_109, yields: % 114.08/61.83 | (390) all_118_1_111 = all_116_1_109 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_114_1_107, all_118_1_111 and discharging atoms relation(all_0_16_16) = all_118_1_111, relation(all_0_16_16) = all_114_1_107, yields: % 114.08/61.83 | (391) all_118_1_111 = all_114_1_107 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_112_3_105, 0 and discharging atoms relation(all_0_16_16) = all_112_3_105, relation(all_0_16_16) = 0, yields: % 114.08/61.83 | (392) all_112_3_105 = 0 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_110_3_101, all_114_1_107 and discharging atoms relation(all_0_16_16) = all_114_1_107, relation(all_0_16_16) = all_110_3_101, yields: % 114.08/61.83 | (393) all_114_1_107 = all_110_3_101 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_110_3_101, all_112_3_105 and discharging atoms relation(all_0_16_16) = all_112_3_105, relation(all_0_16_16) = all_110_3_101, yields: % 114.08/61.83 | (394) all_112_3_105 = all_110_3_101 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_84_1_69, all_112_3_105 and discharging atoms relation(all_0_16_16) = all_112_3_105, relation(all_0_16_16) = all_84_1_69, yields: % 114.08/61.83 | (395) all_112_3_105 = all_84_1_69 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_61_2_53, all_118_1_111 and discharging atoms relation(all_0_16_16) = all_118_1_111, relation(all_0_16_16) = all_61_2_53, yields: % 114.08/61.83 | (396) all_118_1_111 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (19) with all_0_16_16, all_59_3_50, all_112_3_105 and discharging atoms relation(all_0_16_16) = all_112_3_105, relation(all_0_16_16) = all_59_3_50, yields: % 114.08/61.83 | (397) all_112_3_105 = all_59_3_50 % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (153) with all_0_17_17, all_0_12_12, all_59_0_47, all_0_11_11 and discharging atoms in(all_0_17_17, all_0_12_12) = all_0_11_11, yields: % 114.08/61.83 | (398) all_59_0_47 = all_0_11_11 | ~ (in(all_0_17_17, all_0_12_12) = all_59_0_47) % 114.08/61.83 | % 114.08/61.83 | Instantiating formula (153) with all_0_17_17, all_0_18_18, all_59_2_49, all_0_10_10 and discharging atoms in(all_0_17_17, all_0_18_18) = all_59_2_49, in(all_0_17_17, all_0_18_18) = all_0_10_10, yields: % 114.08/61.83 | (399) all_59_2_49 = all_0_10_10 % 114.08/61.83 | % 114.08/61.83 | Combining equations (387,388) yields a new equation: % 114.08/61.83 | (400) all_116_0_108 = all_84_0_68 % 114.08/61.83 | % 114.08/61.83 | Simplifying 400 yields: % 114.08/61.83 | (401) all_116_0_108 = all_84_0_68 % 114.08/61.83 | % 114.08/61.83 | Combining equations (391,390) yields a new equation: % 114.08/61.83 | (402) all_116_1_109 = all_114_1_107 % 114.08/61.83 | % 114.08/61.83 | Combining equations (396,390) yields a new equation: % 114.08/61.83 | (403) all_116_1_109 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Combining equations (386,401) yields a new equation: % 114.08/61.83 | (404) all_84_0_68 = all_0_12_12 % 114.08/61.83 | % 114.08/61.83 | Combining equations (389,401) yields a new equation: % 114.08/61.83 | (405) all_84_0_68 = all_59_1_48 % 114.08/61.83 | % 114.08/61.83 | Combining equations (402,403) yields a new equation: % 114.08/61.83 | (406) all_114_1_107 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Simplifying 406 yields: % 114.08/61.83 | (407) all_114_1_107 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Combining equations (393,407) yields a new equation: % 114.08/61.83 | (408) all_110_3_101 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Simplifying 408 yields: % 114.08/61.83 | (409) all_110_3_101 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Combining equations (394,395) yields a new equation: % 114.08/61.83 | (410) all_110_3_101 = all_84_1_69 % 114.08/61.83 | % 114.08/61.83 | Simplifying 410 yields: % 114.08/61.83 | (411) all_110_3_101 = all_84_1_69 % 114.08/61.83 | % 114.08/61.83 | Combining equations (392,395) yields a new equation: % 114.08/61.83 | (412) all_84_1_69 = 0 % 114.08/61.83 | % 114.08/61.83 | Combining equations (397,395) yields a new equation: % 114.08/61.83 | (413) all_84_1_69 = all_59_3_50 % 114.08/61.83 | % 114.08/61.83 | Combining equations (411,409) yields a new equation: % 114.08/61.83 | (414) all_84_1_69 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Simplifying 414 yields: % 114.08/61.83 | (415) all_84_1_69 = all_61_2_53 % 114.08/61.83 | % 114.08/61.83 | Combining equations (405,404) yields a new equation: % 114.08/61.83 | (416) all_59_1_48 = all_0_12_12 % 114.08/61.83 | % 114.08/61.83 | Simplifying 416 yields: % 114.08/61.83 | (417) all_59_1_48 = all_0_12_12 % 114.08/61.83 | % 114.08/61.83 | Combining equations (412,415) yields a new equation: % 114.08/61.83 | (418) all_61_2_53 = 0 % 114.08/61.83 | % 114.08/61.83 | Combining equations (413,415) yields a new equation: % 114.08/61.83 | (419) all_61_2_53 = all_59_3_50 % 114.08/61.83 | % 114.08/61.83 | Combining equations (418,419) yields a new equation: % 114.08/61.83 | (420) all_59_3_50 = 0 % 114.08/61.83 | % 114.08/61.83 | From (417) and (348) follows: % 114.08/61.83 | (421) in(all_0_17_17, all_0_12_12) = all_59_0_47 % 114.08/61.83 | % 114.08/61.83 +-Applying beta-rule and splitting (398), into two cases. % 114.08/61.83 |-Branch one: % 114.08/61.83 | (422) ~ (in(all_0_17_17, all_0_12_12) = all_59_0_47) % 114.08/61.83 | % 114.08/61.83 | Using (421) and (422) yields: % 114.08/61.83 | (423) $false % 114.08/61.83 | % 114.08/61.83 |-The branch is then unsatisfiable % 114.08/61.83 |-Branch two: % 114.08/61.83 | (421) in(all_0_17_17, all_0_12_12) = all_59_0_47 % 114.08/61.83 | (425) all_59_0_47 = all_0_11_11 % 114.08/61.83 | % 114.08/61.83 +-Applying beta-rule and splitting (47), into two cases. % 114.08/61.83 |-Branch one: % 114.08/61.83 | (426) all_0_10_10 = 0 & all_0_11_11 = 0 & ~ (all_0_13_13 = 0) % 114.08/61.83 | % 114.08/61.83 | Applying alpha-rule on (426) yields: % 114.08/61.83 | (427) all_0_10_10 = 0 % 114.08/61.83 | (428) all_0_11_11 = 0 % 114.08/61.83 | (429) ~ (all_0_13_13 = 0) % 114.08/61.83 | % 114.08/61.83 | Combining equations (427,399) yields a new equation: % 114.08/61.83 | (430) all_59_2_49 = 0 % 114.08/61.83 | % 114.08/61.83 | Combining equations (428,425) yields a new equation: % 114.08/61.83 | (431) all_59_0_47 = 0 % 114.08/61.83 | % 114.08/61.83 +-Applying beta-rule and splitting (352), into two cases. % 114.08/61.83 |-Branch one: % 114.08/61.83 | (432) ~ (all_59_3_50 = 0) % 114.08/61.83 | % 114.08/61.84 | Equations (420) can reduce 432 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (420) all_59_3_50 = 0 % 114.08/61.84 | (435) ( ~ (all_59_0_47 = 0) | ~ (all_59_2_49 = 0) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | (all_59_0_47 = 0 & all_59_2_49 = 0)) % 114.08/61.84 | % 114.08/61.84 | Applying alpha-rule on (435) yields: % 114.08/61.84 | (436) ~ (all_59_0_47 = 0) | ~ (all_59_2_49 = 0) | all_0_13_13 = 0 % 114.08/61.84 | (437) ~ (all_0_13_13 = 0) | (all_59_0_47 = 0 & all_59_2_49 = 0) % 114.08/61.84 | % 114.08/61.84 +-Applying beta-rule and splitting (436), into two cases. % 114.08/61.84 |-Branch one: % 114.08/61.84 | (438) ~ (all_59_0_47 = 0) % 114.08/61.84 | % 114.08/61.84 | Equations (431) can reduce 438 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (431) all_59_0_47 = 0 % 114.08/61.84 | (441) ~ (all_59_2_49 = 0) | all_0_13_13 = 0 % 114.08/61.84 | % 114.08/61.84 +-Applying beta-rule and splitting (441), into two cases. % 114.08/61.84 |-Branch one: % 114.08/61.84 | (442) ~ (all_59_2_49 = 0) % 114.08/61.84 | % 114.08/61.84 | Equations (430) can reduce 442 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (430) all_59_2_49 = 0 % 114.08/61.84 | (445) all_0_13_13 = 0 % 114.08/61.84 | % 114.08/61.84 | Equations (445) can reduce 429 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (447) all_0_13_13 = 0 & ( ~ (all_0_10_10 = 0) | ~ (all_0_11_11 = 0)) % 114.08/61.84 | % 114.08/61.84 | Applying alpha-rule on (447) yields: % 114.08/61.84 | (445) all_0_13_13 = 0 % 114.08/61.84 | (449) ~ (all_0_10_10 = 0) | ~ (all_0_11_11 = 0) % 114.08/61.84 | % 114.08/61.84 +-Applying beta-rule and splitting (352), into two cases. % 114.08/61.84 |-Branch one: % 114.08/61.84 | (432) ~ (all_59_3_50 = 0) % 114.08/61.84 | % 114.08/61.84 | Equations (420) can reduce 432 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (420) all_59_3_50 = 0 % 114.08/61.84 | (435) ( ~ (all_59_0_47 = 0) | ~ (all_59_2_49 = 0) | all_0_13_13 = 0) & ( ~ (all_0_13_13 = 0) | (all_59_0_47 = 0 & all_59_2_49 = 0)) % 114.08/61.84 | % 114.08/61.84 | Applying alpha-rule on (435) yields: % 114.08/61.84 | (436) ~ (all_59_0_47 = 0) | ~ (all_59_2_49 = 0) | all_0_13_13 = 0 % 114.08/61.84 | (437) ~ (all_0_13_13 = 0) | (all_59_0_47 = 0 & all_59_2_49 = 0) % 114.08/61.84 | % 114.08/61.84 +-Applying beta-rule and splitting (437), into two cases. % 114.08/61.84 |-Branch one: % 114.08/61.84 | (429) ~ (all_0_13_13 = 0) % 114.08/61.84 | % 114.08/61.84 | Equations (445) can reduce 429 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (445) all_0_13_13 = 0 % 114.08/61.84 | (459) all_59_0_47 = 0 & all_59_2_49 = 0 % 114.08/61.84 | % 114.08/61.84 | Applying alpha-rule on (459) yields: % 114.08/61.84 | (431) all_59_0_47 = 0 % 114.08/61.84 | (430) all_59_2_49 = 0 % 114.08/61.84 | % 114.08/61.84 | Combining equations (431,425) yields a new equation: % 114.08/61.84 | (428) all_0_11_11 = 0 % 114.08/61.84 | % 114.08/61.84 | Combining equations (430,399) yields a new equation: % 114.08/61.84 | (427) all_0_10_10 = 0 % 114.08/61.84 | % 114.08/61.84 +-Applying beta-rule and splitting (449), into two cases. % 114.08/61.84 |-Branch one: % 114.08/61.84 | (464) ~ (all_0_10_10 = 0) % 114.08/61.84 | % 114.08/61.84 | Equations (427) can reduce 464 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 |-Branch two: % 114.08/61.84 | (427) all_0_10_10 = 0 % 114.08/61.84 | (467) ~ (all_0_11_11 = 0) % 114.08/61.84 | % 114.08/61.84 | Equations (428) can reduce 467 to: % 114.08/61.84 | (433) $false % 114.08/61.84 | % 114.08/61.84 |-The branch is then unsatisfiable % 114.08/61.84 % SZS output end Proof for theBenchmark % 114.08/61.84 % 114.08/61.84 61234ms %------------------------------------------------------------------------------