%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SET025+1 : TPTP v8.1.0. Bugfixed v5.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n024.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 00:16:18 EDT 2022 % Result : Theorem 3.96s 1.49s % Output : Proof 6.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : SET025+1 : TPTP v8.1.0. Bugfixed v5.4.0. % 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.33 % Computer : n024.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Mon Jul 11 09:22:43 EDT 2022 % 0.11/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.57 (ePrincess v.1.0) % 0.18/0.57 % 0.18/0.57 (c) Philipp Rümmer, 2009-2015 % 0.18/0.57 (c) Peter Backeman, 2014-2015 % 0.18/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.57 Bug reports to peter@backeman.se % 0.18/0.57 % 0.18/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.57 % 0.18/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.65/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.65/0.90 Prover 0: Preprocessing ... % 2.94/1.28 Prover 0: Warning: ignoring some quantifiers % 2.94/1.31 Prover 0: Constructing countermodel ... % 3.96/1.49 Prover 0: proved (870ms) % 3.96/1.49 % 3.96/1.49 No countermodel exists, formula is valid % 3.96/1.49 % SZS status Theorem for theBenchmark % 3.96/1.49 % 3.96/1.49 Generating proof ... Warning: ignoring some quantifiers % 5.64/1.86 found it (size 7) % 5.64/1.86 % 5.64/1.86 % SZS output start Proof for theBenchmark % 5.64/1.86 Assumed formulas after preprocessing and simplification: % 5.64/1.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : (cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & ordered_pair(v2, v3) = v4 & function(v5) & inductive(v6) & member(v6, universal_class) & subclass(successor_relation, v0) & subclass(element_relation, v0) & ~ member(v4, universal_class) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image(v8, v13) = v14) | ~ (image(v7, v12) = v13) | ~ (ordered_pair(v9, v10) = v11) | ~ (singleton(v9) = v12) | member(v10, v14) | ? [v15] : (compose(v8, v7) = v15 & ~ member(v11, v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image(v8, v13) = v14) | ~ (image(v7, v12) = v13) | ~ (ordered_pair(v9, v10) = v11) | ~ (singleton(v9) = v12) | member(v9, universal_class) | ? [v15] : (compose(v8, v7) = v15 & ~ member(v11, v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image(v8, v12) = v13) | ~ (image(v7, v11) = v12) | ~ (ordered_pair(v9, v10) = v14) | ~ (singleton(v9) = v11) | ~ member(v10, v13) | ~ member(v9, universal_class) | ? [v15] : (compose(v8, v7) = v15 & member(v14, v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v9 | ~ (first(v9) = v11) | ~ (second(v9) = v12) | ~ (cross_product(v7, v8) = v10) | ~ (ordered_pair(v11, v12) = v13) | ~ member(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (flip(v10) = v13) | ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v8, v7) = v11) | ~ member(v12, v10) | ? [v14] : ? [v15] : (ordered_pair(v14, v9) = v15 & ordered_pair(v7, v8) = v14 & ( ~ member(v15, v1) | member(v15, v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (flip(v10) = v13) | ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ member(v12, v13) | member(v12, v1)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (flip(v10) = v13) | ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ member(v12, v13) | ? [v14] : ? [v15] : (ordered_pair(v14, v9) = v15 & ordered_pair(v8, v7) = v14 & member(v15, v10))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (flip(v10) = v13) | ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ member(v12, v1) | member(v12, v13) | ? [v14] : ? [v15] : (ordered_pair(v14, v9) = v15 & ordered_pair(v8, v7) = v14 & ~ member(v15, v10))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (flip(v10) = v11) | ~ (ordered_pair(v12, v9) = v13) | ~ (ordered_pair(v8, v7) = v12) | ? [v14] : ? [v15] : (ordered_pair(v14, v9) = v15 & ordered_pair(v7, v8) = v14 & ( ~ member(v15, v11) | (member(v15, v1) & member(v13, v10))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (rotate(v7) = v13) | ~ (ordered_pair(v11, v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ member(v12, v13) | member(v12, v1)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (rotate(v7) = v13) | ~ (ordered_pair(v11, v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ member(v12, v13) | ? [v14] : ? [v15] : (ordered_pair(v14, v8) = v15 & ordered_pair(v9, v10) = v14 & member(v15, v7))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (rotate(v7) = v13) | ~ (ordered_pair(v11, v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ member(v12, v1) | member(v12, v13) | ? [v14] : ? [v15] : (ordered_pair(v14, v8) = v15 & ordered_pair(v9, v10) = v14 & ~ member(v15, v7))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (rotate(v7) = v13) | ~ (ordered_pair(v11, v8) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ member(v12, v7) | ? [v14] : ? [v15] : (ordered_pair(v14, v10) = v15 & ordered_pair(v8, v9) = v14 & ( ~ member(v15, v1) | member(v15, v13)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (rotate(v7) = v11) | ~ (ordered_pair(v12, v8) = v13) | ~ (ordered_pair(v9, v10) = v12) | ? [v14] : ? [v15] : (ordered_pair(v14, v10) = v15 & ordered_pair(v8, v9) = v14 & ( ~ member(v15, v11) | (member(v15, v1) & member(v13, v7))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose(v8, v7) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, v12) | member(v9, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose(v8, v7) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, v12) | ? [v13] : ? [v14] : ? [v15] : (image(v8, v14) = v15 & image(v7, v13) = v14 & singleton(v9) = v13 & member(v10, v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose(v8, v7) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ member(v9, universal_class) | member(v11, v12) | ? [v13] : ? [v14] : ? [v15] : (image(v8, v14) = v15 & image(v7, v13) = v14 & singleton(v9) = v13 & ~ member(v10, v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cross_product(v9, v10) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ member(v11, v12) | member(v8, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cross_product(v9, v10) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ member(v11, v12) | member(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cross_product(v9, v10) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ member(v8, v10) | ~ member(v7, v9) | member(v11, v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (singleton(v8) = v10) | ~ (singleton(v7) = v9) | ~ (unordered_pair(v9, v11) = v12) | ~ (unordered_pair(v7, v10) = v11) | ordered_pair(v7, v8) = v12) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (restrict(v11, v10, v9) = v8) | ~ (restrict(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v10) = v11) | ~ (cross_product(v7, v9) = v10) | restrict(v8, v7, v9) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = null_class | ~ (restrict(v7, v9, universal_class) = v10) | ~ (singleton(v8) = v9) | ~ member(v8, universal_class) | ? [v11] : (domain_of(v7) = v11 & member(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ member(v7, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (apply(v10, v9) = v8) | ~ (apply(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (compose(v10, v9) = v8) | ~ (compose(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (image(v10, v9) = v8) | ~ (image(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (cross_product(v10, v9) = v8) | ~ (cross_product(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (sum_class(v8) = v9) | ~ member(v10, v8) | ~ member(v7, v10) | member(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image(v7, v9) = v10) | ~ (singleton(v8) = v9) | ? [v11] : (apply(v7, v8) = v11 & sum_class(v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v7, v8) = v10) | ~ member(v9, v10) | member(v9, v8) | member(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v7, v8) = v10) | ~ member(v9, v8) | member(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v7, v8) = v10) | ~ member(v9, v7) | member(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v8, v7, v9) = v10) | ? [v11] : (intersection(v8, v11) = v10 & cross_product(v7, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v7, v9, universal_class) = v10) | ~ (singleton(v8) = v9) | member(v8, universal_class) | ? [v11] : (domain_of(v7) = v11 & ~ member(v8, v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v7, v8) = v10) | ~ member(v9, v10) | member(v9, v8)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v7, v8) = v10) | ~ member(v9, v10) | member(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v7, v8) = v10) | ~ member(v9, v8) | ~ member(v9, v7) | member(v9, v10)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | ~ member(v7, v10) | member(v7, universal_class)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_class(v9) = v8) | ~ (power_class(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum_class(v9) = v8) | ~ (sum_class(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (range_of(v9) = v8) | ~ (range_of(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (inverse(v9) = v8) | ~ (inverse(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (successor(v9) = v8) | ~ (successor(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (flip(v9) = v8) | ~ (flip(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (rotate(v9) = v8) | ~ (rotate(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (domain_of(v9) = v8) | ~ (domain_of(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (complement(v9) = v8) | ~ (complement(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (first(v9) = v8) | ~ (first(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (second(v9) = v8) | ~ (second(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (apply(v7, v8) = v9) | ? [v10] : ? [v11] : (sum_class(v11) = v9 & image(v7, v10) = v11 & singleton(v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (compose(v8, v7) = v9) | subclass(v9, v0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (compose(v7, v8) = v9) | ~ (inverse(v7) = v8) | ~ function(v7) | subclass(v9, identity_relation)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (compose(v7, v8) = v9) | ~ (inverse(v7) = v8) | ~ function(v7) | subclass(v7, v0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (compose(v7, v8) = v9) | ~ (inverse(v7) = v8) | ~ subclass(v9, identity_relation) | ~ subclass(v7, v0) | function(v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_class(v8) = v9) | ~ member(v7, v9) | member(v7, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_class(v8) = v9) | ~ member(v7, v9) | subclass(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_class(v8) = v9) | ~ member(v7, universal_class) | ~ subclass(v7, v8) | member(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum_class(v8) = v9) | ~ member(v7, v9) | ? [v10] : (member(v10, v8) & member(v7, v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (image(v8, v7) = v9) | ~ function(v8) | ~ member(v7, universal_class) | member(v9, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (image(v8, v7) = v9) | ? [v10] : (range_of(v10) = v9 & restrict(v8, v7, universal_class) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (union(v7, v8) = v9) | ~ (singleton(v7) = v8) | successor(v7) = v9) & ! [v7] : ! [v8] : ! [v9] : ( ~ (restrict(v8, v7, universal_class) = v9) | ? [v10] : (image(v8, v7) = v10 & range_of(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (restrict(v7, v9, universal_class) = null_class) | ~ (singleton(v8) = v9) | ? [v10] : (domain_of(v7) = v10 & ~ member(v8, v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (complement(v7) = v9) | ~ member(v8, v9) | ~ member(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (complement(v7) = v9) | ~ member(v8, v9) | member(v8, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (complement(v7) = v9) | ~ member(v8, universal_class) | member(v8, v9) | member(v8, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v9, successor_relation) | successor(v7) = v8) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v9, successor_relation) | member(v8, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v9, successor_relation) | member(v7, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v9, element_relation) | member(v8, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v9, element_relation) | member(v7, v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v8, universal_class) | ~ member(v7, v8) | member(v9, element_relation)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v8, universal_class) | ~ member(v7, universal_class) | member(v9, successor_relation) | ? [v10] : ( ~ (v10 = v8) & successor(v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ~ member(v8, universal_class) | ~ member(v7, universal_class) | (first(v9) = v7 & second(v9) = v8)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (singleton(v8) = v11 & singleton(v7) = v10 & unordered_pair(v10, v12) = v9 & unordered_pair(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | ~ member(v7, universal_class) | member(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | ~ member(v7, universal_class) | member(v7, v9)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | member(v9, universal_class)) & ! [v7] : ! [v8] : ! [v9] : ( ~ disjoint(v7, v8) | ~ member(v9, v8) | ~ member(v9, v7)) & ! [v7] : ! [v8] : ! [v9] : ( ~ member(v9, v7) | ~ subclass(v7, v8) | member(v9, v8)) & ! [v7] : ! [v8] : (v8 = v7 | ~ subclass(v8, v7) | ~ subclass(v7, v8)) & ! [v7] : ! [v8] : (v7 = null_class | ~ (apply(v5, v7) = v8) | ~ member(v7, universal_class) | member(v8, v7)) & ! [v7] : ! [v8] : ( ~ (power_class(v7) = v8) | ~ member(v7, universal_class) | member(v8, universal_class)) & ! [v7] : ! [v8] : ( ~ (sum_class(v7) = v8) | ~ member(v7, universal_class) | member(v8, universal_class)) & ! [v7] : ! [v8] : ( ~ (image(successor_relation, v7) = v8) | ~ inductive(v7) | member(null_class, v7)) & ! [v7] : ! [v8] : ( ~ (image(successor_relation, v7) = v8) | ~ inductive(v7) | subclass(v8, v7)) & ! [v7] : ! [v8] : ( ~ (image(successor_relation, v7) = v8) | ~ member(null_class, v7) | ~ subclass(v8, v7) | inductive(v7)) & ! [v7] : ! [v8] : ( ~ (range_of(v7) = v8) | ? [v9] : (inverse(v7) = v9 & domain_of(v9) = v8)) & ! [v7] : ! [v8] : ( ~ (inverse(v7) = v8) | ? [v9] : ? [v10] : (flip(v9) = v10 & domain_of(v10) = v8 & cross_product(v7, universal_class) = v9)) & ! [v7] : ! [v8] : ( ~ (inverse(v7) = v8) | ? [v9] : (range_of(v7) = v9 & domain_of(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (successor(v7) = v8) | ? [v9] : (union(v7, v9) = v8 & singleton(v7) = v9)) & ! [v7] : ! [v8] : ( ~ (flip(v7) = v8) | subclass(v8, v1)) & ! [v7] : ! [v8] : ( ~ (rotate(v7) = v8) | subclass(v8, v1)) & ! [v7] : ! [v8] : ( ~ (cross_product(v7, universal_class) = v8) | ? [v9] : ? [v10] : (inverse(v7) = v9 & flip(v8) = v10 & domain_of(v10) = v9)) & ! [v7] : ! [v8] : ( ~ (ordered_pair(v8, v8) = v7) | ~ member(v8, universal_class) | member(v7, identity_relation)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ! [v7] : ( ~ inductive(v7) | subclass(v6, v7)) & ! [v7] : ( ~ member(v7, identity_relation) | ? [v8] : (ordered_pair(v8, v8) = v7 & member(v8, universal_class))) & ! [v7] : ~ member(v7, null_class) & ? [v7] : ? [v8] : (disjoint(v7, v8) | ? [v9] : (member(v9, v8) & member(v9, v7))) & ? [v7] : ? [v8] : (subclass(v7, v8) | ? [v9] : (member(v9, v7) & ~ member(v9, v8))) & ? [v7] : (v7 = null_class | ? [v8] : (disjoint(v8, v7) & member(v8, v7) & member(v8, universal_class))) & ? [v7] : subclass(v7, v7) & ? [v7] : subclass(v7, universal_class)) % 5.99/1.94 | 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 yields: % 5.99/1.94 | (1) cross_product(all_0_6_6, universal_class) = all_0_5_5 & cross_product(universal_class, universal_class) = all_0_6_6 & ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & function(all_0_1_1) & inductive(all_0_0_0) & member(all_0_0_0, universal_class) & subclass(successor_relation, all_0_6_6) & subclass(element_relation, all_0_6_6) & ~ member(all_0_2_2, universal_class) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v3, v7) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (ordered_pair(v2, v3) = v7) | ~ (singleton(v2) = v4) | ~ member(v3, v6) | ~ member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & member(v7, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (first(v2) = v4) | ~ (second(v2) = v5) | ~ (cross_product(v0, v1) = v3) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ member(v5, v3) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, all_0_5_5) | member(v8, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | member(v5, all_0_5_5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, all_0_5_5) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & ~ member(v8, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v4) | ~ (ordered_pair(v5, v2) = v6) | ~ (ordered_pair(v1, v0) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_5_5) & member(v6, v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | member(v5, all_0_5_5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, all_0_5_5) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & ~ member(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v5, v0) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, all_0_5_5) | member(v8, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v4) | ~ (ordered_pair(v5, v1) = v6) | ~ (ordered_pair(v2, v3) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_5_5) & member(v6, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | member(v2, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v2, universal_class) | member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & ~ member(v3, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v1, v3) | ~ member(v0, v2) | member(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (unordered_pair(v2, v4) = v5) | ~ (unordered_pair(v0, v3) = v4) | ordered_pair(v0, v1) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = null_class | ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ~ member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & member(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(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 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum_class(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & ~ member(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_6_6)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v2, identity_relation)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v0, all_0_6_6)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ subclass(v2, identity_relation) | ~ subclass(v0, all_0_6_6) | function(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | member(v0, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | subclass(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, universal_class) | ~ subclass(v0, v1) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ~ function(v1) | ~ member(v0, universal_class) | member(v2, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v0, v2, universal_class) = null_class) | ~ (singleton(v1) = v2) | ? [v3] : (domain_of(v0) = v3 & ~ member(v1, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | ~ member(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | member(v1, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, universal_class) | member(v1, v2) | member(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | successor(v0) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v1, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v0, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v1, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, v1) | member(v2, element_relation)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | member(v2, successor_relation) | ? [v3] : ( ~ (v3 = v1) & successor(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | (first(v2) = v0 & second(v2) = v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ member(v2, v1) | ~ member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subclass(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subclass(v1, v0) | ~ subclass(v0, v1)) & ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ member(v0, universal_class) | member(v1, v0)) & ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class)) & ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | member(null_class, v0)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | subclass(v1, v0)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ member(null_class, v0) | ~ subclass(v1, v0) | inductive(v0)) & ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1)) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2)) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_5_5)) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_5_5)) & ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (ordered_pair(v1, v1) = v0) | ~ member(v1, universal_class) | member(v0, identity_relation)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ( ~ inductive(v0) | subclass(all_0_0_0, v0)) & ! [v0] : ( ~ member(v0, identity_relation) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class))) & ! [v0] : ~ member(v0, null_class) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) & ? [v0] : ? [v1] : (subclass(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) & member(v1, v0) & member(v1, universal_class))) & ? [v0] : subclass(v0, v0) & ? [v0] : subclass(v0, universal_class) % 5.99/1.97 | % 5.99/1.97 | Applying alpha-rule on (1) yields: % 5.99/1.97 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum_class(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) % 5.99/1.97 | (3) ? [v0] : subclass(v0, v0) % 5.99/1.97 | (4) cross_product(all_0_6_6, universal_class) = all_0_5_5 % 5.99/1.97 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | member(v5, all_0_5_5)) % 5.99/1.97 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) % 5.99/1.97 | (7) function(all_0_1_1) % 5.99/1.97 | (8) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) % 5.99/1.97 | (9) inductive(all_0_0_0) % 5.99/1.97 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v1, v3)) % 5.99/1.97 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3)) % 5.99/1.97 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) % 5.99/1.97 | (13) ! [v0] : ! [v1] : ( ~ (ordered_pair(v1, v1) = v0) | ~ member(v1, universal_class) | member(v0, identity_relation)) % 5.99/1.97 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) % 5.99/1.97 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | successor(v0) = v1) % 5.99/1.97 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0)) % 5.99/1.97 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | subclass(v0, v1)) % 5.99/1.97 | (18) ? [v0] : subclass(v0, universal_class) % 5.99/1.97 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) % 5.99/1.97 | (20) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0)) % 5.99/1.97 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | member(v1, universal_class)) % 5.99/1.97 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ member(v2, v1) | ~ member(v2, v0)) % 5.99/1.97 | (23) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | subclass(v1, v0)) % 5.99/1.97 | (24) ? [v0] : ? [v1] : (subclass(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) % 5.99/1.97 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8))) % 5.99/1.97 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v4) | ~ (ordered_pair(v5, v1) = v6) | ~ (ordered_pair(v2, v3) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_5_5) & member(v6, v0))))) % 5.99/1.97 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v0, v2)) % 5.99/1.97 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) % 5.99/1.97 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0)) % 5.99/1.97 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v0, universal_class)) % 5.99/1.97 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) % 5.99/1.97 | (32) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) % 5.99/1.97 | (33) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) % 5.99/1.97 | (34) ! [v0] : ~ member(v0, null_class) % 5.99/1.97 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4)) % 5.99/1.97 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ member(v5, v3) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, all_0_5_5) | member(v8, v6)))) % 5.99/1.97 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, universal_class) | ~ subclass(v0, v1) | member(v0, v2)) % 5.99/1.97 | (38) ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class)) % 5.99/1.97 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | (first(v2) = v0 & second(v2) = v1)) % 5.99/1.97 | (40) subclass(successor_relation, all_0_6_6) % 5.99/1.97 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2) % 5.99/1.97 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) % 5.99/1.97 | (43) member(all_0_0_0, universal_class) % 5.99/1.97 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & ~ member(v1, v4))) % 5.99/1.97 | (45) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) & member(v1, v0) & member(v1, universal_class))) % 5.99/1.97 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0))) % 5.99/1.97 | (47) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) % 5.99/1.97 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (first(v2) = v4) | ~ (second(v2) = v5) | ~ (cross_product(v0, v1) = v3) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v2, v3)) % 5.99/1.97 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) = v5)) % 5.99/1.97 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | ~ member(v0, universal_class) | member(v0, v2)) % 5.99/1.97 | (51) cross_product(universal_class, universal_class) = all_0_6_6 % 5.99/1.98 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, all_0_5_5) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & ~ member(v8, v3))) % 5.99/1.98 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3)) % 5.99/1.98 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, v1) | member(v2, element_relation)) % 5.99/1.98 | (55) ! [v0] : ( ~ member(v0, identity_relation) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class))) % 5.99/1.98 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8))) % 5.99/1.98 | (57) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2)) % 5.99/1.98 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, all_0_5_5) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & ~ member(v8, v0))) % 5.99/1.98 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) % 5.99/1.98 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) % 6.23/1.98 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v0, all_0_6_6)) % 6.23/1.98 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) % 6.23/1.98 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | member(v2, successor_relation) | ? [v3] : ( ~ (v3 = v1) & successor(v0) = v3)) % 6.23/1.98 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 6.23/1.98 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0)) % 6.23/1.98 | (66) ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2)) % 6.23/1.98 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ member(v0, universal_class) | member(v0, v2)) % 6.23/1.98 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4) % 6.23/1.98 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | member(v0, universal_class)) % 6.23/1.98 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ~ function(v1) | ~ member(v0, universal_class) | member(v2, universal_class)) % 6.23/1.98 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3)) % 6.23/1.98 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) % 6.23/1.98 | (73) ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 % 6.23/1.98 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) % 6.23/1.98 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_6_6)) % 6.23/1.98 | (76) ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class)) % 6.23/1.98 | (77) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2)) % 6.23/1.98 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v1, universal_class)) % 6.23/1.98 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) % 6.23/1.98 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4)) % 6.23/1.98 | (81) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2)) % 6.23/1.98 | (82) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_5_5)) % 6.23/1.98 | (83) ~ member(all_0_2_2, universal_class) % 6.23/1.98 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v2, universal_class) | member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & ~ member(v3, v8))) % 6.23/1.98 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (ordered_pair(v2, v3) = v7) | ~ (singleton(v2) = v4) | ~ member(v3, v6) | ~ member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & member(v7, v8))) % 6.23/1.98 | (86) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) % 6.23/1.98 | (87) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | member(null_class, v0)) % 6.23/1.98 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 6.23/1.98 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0)) % 6.23/1.98 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v0, v2, universal_class) = null_class) | ~ (singleton(v1) = v2) | ? [v3] : (domain_of(v0) = v3 & ~ member(v1, v3))) % 6.23/1.98 | (91) ! [v0] : ! [v1] : (v1 = v0 | ~ subclass(v1, v0) | ~ subclass(v0, v1)) % 6.23/1.98 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) % 6.23/1.98 | (93) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v0, v1)) % 6.23/1.98 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0)) % 6.23/1.98 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, universal_class) | member(v1, v2) | member(v1, v0)) % 6.23/1.98 | (96) ! [v0] : ( ~ inductive(v0) | subclass(all_0_0_0, v0)) % 6.23/1.98 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) % 6.23/1.98 | (98) subclass(element_relation, all_0_6_6) % 6.23/1.98 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v4) | ~ (ordered_pair(v5, v2) = v6) | ~ (ordered_pair(v1, v0) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_5_5) & member(v6, v3))))) % 6.23/1.98 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | member(v5, all_0_5_5)) % 6.23/1.98 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | ~ member(v1, v0)) % 6.23/1.98 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v5, v0) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, all_0_5_5) | member(v8, v6)))) % 6.23/1.98 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | member(v2, universal_class)) % 6.23/1.98 | (104) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ member(null_class, v0) | ~ subclass(v1, v0) | inductive(v0)) % 6.23/1.98 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) % 6.23/1.98 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) % 6.23/1.98 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v3, v7) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8))) % 6.23/1.99 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3))) % 6.23/1.99 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = null_class | ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ~ member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & member(v1, v4))) % 6.23/1.99 | (110) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subclass(v0, v1) | member(v2, v1)) % 6.23/1.99 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ subclass(v2, identity_relation) | ~ subclass(v0, all_0_6_6) | function(v0)) % 6.23/1.99 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) % 6.23/1.99 | (113) ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ member(v0, universal_class) | member(v1, v0)) % 6.23/1.99 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v2, identity_relation)) % 6.23/1.99 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v1, universal_class)) % 6.23/1.99 | (116) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1)) % 6.23/1.99 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class)) % 6.23/1.99 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (unordered_pair(v2, v4) = v5) | ~ (unordered_pair(v0, v3) = v4) | ordered_pair(v0, v1) = v5) % 6.23/1.99 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) % 6.23/1.99 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v1, v3) | ~ member(v0, v2) | member(v4, v5)) % 6.23/1.99 | (121) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_5_5)) % 6.23/1.99 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3) | member(v0, universal_class)) % 6.23/1.99 | % 6.23/1.99 | Instantiating formula (49) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms ordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, yields: % 6.23/1.99 | (123) ? [v0] : ? [v1] : ? [v2] : (singleton(all_0_3_3) = v1 & singleton(all_0_4_4) = v0 & unordered_pair(v0, v2) = all_0_2_2 & unordered_pair(all_0_4_4, v1) = v2) % 6.23/1.99 | % 6.23/1.99 | Instantiating (123) with all_16_0_14, all_16_1_15, all_16_2_16 yields: % 6.23/1.99 | (124) singleton(all_0_3_3) = all_16_1_15 & singleton(all_0_4_4) = all_16_2_16 & unordered_pair(all_16_2_16, all_16_0_14) = all_0_2_2 & unordered_pair(all_0_4_4, all_16_1_15) = all_16_0_14 % 6.23/1.99 | % 6.23/1.99 | Applying alpha-rule on (124) yields: % 6.23/1.99 | (125) singleton(all_0_3_3) = all_16_1_15 % 6.23/1.99 | (126) singleton(all_0_4_4) = all_16_2_16 % 6.23/1.99 | (127) unordered_pair(all_16_2_16, all_16_0_14) = all_0_2_2 % 6.23/1.99 | (128) unordered_pair(all_0_4_4, all_16_1_15) = all_16_0_14 % 6.23/1.99 | % 6.23/1.99 | Instantiating formula (117) with all_0_2_2, all_16_0_14, all_16_2_16 and discharging atoms unordered_pair(all_16_2_16, all_16_0_14) = all_0_2_2, ~ member(all_0_2_2, universal_class), yields: % 6.23/1.99 | (129) $false % 6.23/1.99 | % 6.23/1.99 |-The branch is then unsatisfiable % 6.23/1.99 % SZS output end Proof for theBenchmark % 6.23/1.99 % 6.23/1.99 1411ms %------------------------------------------------------------------------------