TSTP Solution File: SET067+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET067+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.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 00:17:00 EDT 2022
% Result : Theorem 15.75s 4.24s
% Output : Proof 30.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET067+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.32 % Computer : n023.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Sun Jul 10 11:13:10 EDT 2022
% 0.12/0.33 % 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
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.87/0.95 Prover 0: Preprocessing ...
% 3.21/1.36 Prover 0: Warning: ignoring some quantifiers
% 3.50/1.39 Prover 0: Constructing countermodel ...
% 13.90/3.86 Prover 0: gave up
% 13.90/3.86 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 14.28/3.91 Prover 1: Preprocessing ...
% 14.66/4.05 Prover 1: Warning: ignoring some quantifiers
% 14.66/4.06 Prover 1: Constructing countermodel ...
% 15.75/4.24 Prover 1: proved (379ms)
% 15.75/4.24
% 15.75/4.24 No countermodel exists, formula is valid
% 15.75/4.24 % SZS status Theorem for theBenchmark
% 15.75/4.24
% 15.75/4.24 Generating proof ... Warning: ignoring some quantifiers
% 29.92/7.69 found it (size 33)
% 29.92/7.69
% 29.92/7.69 % SZS output start Proof for theBenchmark
% 29.92/7.69 Assumed formulas after preprocessing and simplification:
% 29.92/7.69 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v6 = 0) & function(v7) = 0 & inductive(v8) = 0 & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & unordered_pair(v2, v3) = v5 & unordered_pair(v2, v2) = v4 & subclass(v4, v5) = v6 & subclass(successor_relation, v0) = 0 & subclass(element_relation, v0) = 0 & member(v8, universal_class) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (flip(v12) = v15) | ~ (ordered_pair(v13, v11) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ (member(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v11) = v19 & ordered_pair(v10, v9) = v18 & member(v19, v12) = v20 & member(v14, v1) = v17 & ( ~ (v20 = 0) | ~ (v17 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (rotate(v9) = v15) | ~ (ordered_pair(v13, v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ (member(v14, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (ordered_pair(v18, v10) = v19 & ordered_pair(v11, v12) = v18 & member(v19, v9) = v20 & member(v14, v1) = v17 & ( ~ (v20 = 0) | ~ (v17 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (image(v10, v14) = v15) | ~ (image(v9, v13) = v14) | ~ (singleton(v11) = v13) | ~ (member(v12, v15) = v16) | ? [v17] : ? [v18] : ? [v19] : ? [v20] : (compose(v10, v9) = v18 & ordered_pair(v11, v12) = v17 & member(v17, v18) = v19 & member(v11, universal_class) = v20 & ( ~ (v19 = 0) | (v20 = 0 & v16 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (cross_product(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ (member(v13, v14) = v15) | ? [v16] : ? [v17] : (member(v10, v12) = v17 & member(v9, v11) = v16 & ( ~ (v17 = 0) | ~ (v16 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image(v10, v14) = v15) | ~ (image(v9, v13) = v14) | ~ (singleton(v11) = v13) | ~ (member(v12, v15) = 0) | ? [v16] : ? [v17] : ? [v18] : ? [v19] : (compose(v10, v9) = v18 & ordered_pair(v11, v12) = v17 & member(v17, v18) = v19 & member(v11, universal_class) = v16 & ( ~ (v16 = 0) | v19 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (flip(v12) = v15) | ~ (ordered_pair(v13, v11) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ (member(v14, v15) = 0) | ? [v16] : ? [v17] : (ordered_pair(v16, v11) = v17 & ordered_pair(v10, v9) = v16 & member(v17, v12) = 0 & member(v14, v1) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (rotate(v9) = v15) | ~ (ordered_pair(v13, v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ (member(v14, v15) = 0) | ? [v16] : ? [v17] : (ordered_pair(v16, v10) = v17 & ordered_pair(v11, v12) = v16 & member(v17, v9) = 0 & member(v14, v1) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cross_product(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ (member(v13, v14) = 0) | (member(v10, v12) = 0 & member(v9, v11) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v12) | ~ (singleton(v9) = v11) | ~ (unordered_pair(v11, v13) = v14) | ~ (unordered_pair(v9, v12) = v13) | ordered_pair(v9, v10) = v14) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (union(v9, v10) = v12) | ~ (member(v11, v12) = v13) | ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v14 = 0) & member(v11, v10) = v15 & member(v11, v9) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (intersection(v9, v10) = v12) | ~ (member(v11, v12) = v13) | ? [v14] : ? [v15] : (member(v11, v10) = v15 & member(v11, v9) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (sum_class(v10) = v11) | ~ (member(v9, v13) = 0) | ~ (member(v9, v11) = v12) | ? [v14] : ( ~ (v14 = 0) & member(v13, v10) = v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (restrict(v13, v12, v11) = v10) | ~ (restrict(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v10, v12) = v13) | ~ (cross_product(v9, v11) = v12) | restrict(v10, v9, v11) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = null_class | ~ (restrict(v9, v11, universal_class) = v12) | ~ (singleton(v10) = v11) | ? [v13] : ? [v14] : ? [v15] : (domain_of(v9) = v14 & member(v10, v14) = v15 & member(v10, universal_class) = v13 & ( ~ (v13 = 0) | v15 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (power_class(v10) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ? [v14] : (subclass(v9, v10) = v14 & member(v9, universal_class) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (complement(v9) = v11) | ~ (member(v10, v11) = v12) | ? [v13] : ? [v14] : (member(v10, v9) = v14 & member(v10, universal_class) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v10, v9) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & member(v9, universal_class) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v9, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & member(v9, universal_class) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | v10 = v9 | ~ (unordered_pair(v10, v11) = v12) | ~ (member(v9, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (apply(v12, v11) = v10) | ~ (apply(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (disjoint(v12, v11) = v10) | ~ (disjoint(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (compose(v12, v11) = v10) | ~ (compose(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (image(v12, v11) = v10) | ~ (image(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (union(v12, v11) = v10) | ~ (union(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (intersection(v12, v11) = v10) | ~ (intersection(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cross_product(v12, v11) = v10) | ~ (cross_product(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (subclass(v12, v11) = v10) | ~ (subclass(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (member(v12, v11) = v10) | ~ (member(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image(v9, v11) = v12) | ~ (singleton(v10) = v11) | ? [v13] : (apply(v9, v10) = v13 & sum_class(v12) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : ? [v14] : (member(v11, v10) = v14 & member(v11, v9) = v13 & (v14 = 0 | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (restrict(v9, v11, universal_class) = v12) | ~ (singleton(v10) = v11) | ? [v13] : ? [v14] : ? [v15] : (domain_of(v9) = v13 & member(v10, v13) = v14 & member(v10, universal_class) = v15 & ( ~ (v14 = 0) | (v15 = 0 & ~ (v12 = null_class))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v9, v10) = v12) | ~ (member(v11, v12) = 0) | (member(v11, v10) = 0 & member(v11, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cross_product(v9, v10) = v12) | ~ (member(v11, v12) = 0) | ? [v13] : ? [v14] : (first(v11) = v13 & second(v11) = v14 & ordered_pair(v13, v14) = v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ~ (member(v9, v12) = 0) | member(v9, universal_class) = 0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (member(v10, universal_class) = v12) | ~ (member(v9, universal_class) = v11) | ? [v13] : ? [v14] : ? [v15] : (successor(v9) = v15 & ordered_pair(v9, v10) = v13 & member(v13, successor_relation) = v14 & ( ~ (v14 = 0) | (v15 = v10 & v12 = 0 & v11 = 0)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = null_class | ~ (apply(v7, v9) = v10) | ~ (member(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v9, universal_class) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (disjoint(v9, v10) = v11) | ? [v12] : (member(v12, v10) = 0 & member(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subclass(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & member(v12, v10) = v13 & member(v12, v9) = 0)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (function(v11) = v10) | ~ (function(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (power_class(v11) = v10) | ~ (power_class(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (sum_class(v11) = v10) | ~ (sum_class(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (inductive(v11) = v10) | ~ (inductive(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (range_of(v11) = v10) | ~ (range_of(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (inverse(v11) = v10) | ~ (inverse(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (successor(v11) = v10) | ~ (successor(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (flip(v11) = v10) | ~ (flip(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (rotate(v11) = v10) | ~ (rotate(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (domain_of(v11) = v10) | ~ (domain_of(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (complement(v11) = v10) | ~ (complement(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (first(v11) = v10) | ~ (first(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (second(v11) = v10) | ~ (second(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (member(v11, universal_class) = 0) | ~ (member(v9, identity_relation) = v10) | ? [v12] : ( ~ (v12 = v9) & ordered_pair(v11, v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (disjoint(v9, v10) = 0) | ~ (member(v11, v9) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v11, v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (compose(v10, v9) = v11) | subclass(v11, v0) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (power_class(v10) = v11) | ~ (member(v9, v11) = 0) | (subclass(v9, v10) = 0 & member(v9, universal_class) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sum_class(v10) = v11) | ~ (member(v9, v11) = 0) | ? [v12] : (member(v12, v10) = 0 & member(v9, v12) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (image(successor_relation, v9) = v10) | ~ (subclass(v10, v9) = v11) | ? [v12] : ? [v13] : (inductive(v9) = v12 & member(null_class, v9) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (singleton(v9) = v10) | successor(v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (restrict(v10, v9, universal_class) = v11) | ? [v12] : (image(v10, v9) = v12 & range_of(v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (complement(v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & member(v10, v9) = v12 & member(v10, universal_class) = 0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (member(v11, element_relation) = v14 & member(v10, universal_class) = v12 & member(v9, v10) = v13 & ( ~ (v13 = 0) | ~ (v12 = 0) | v14 = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (member(v11, element_relation) = v12 & member(v10, universal_class) = v13 & member(v9, v10) = v14 & ( ~ (v12 = 0) | (v14 = 0 & v13 = 0)))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | member(v11, universal_class) = 0) & ! [v9] : ! [v10] : ! [v11] : ( ~ (subclass(v9, v10) = 0) | ~ (member(v11, v9) = 0) | member(v11, v10) = 0) & ! [v9] : ! [v10] : (v10 = v9 | ~ (subclass(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & subclass(v10, v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subclass(v9, v9) = v10)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (subclass(v9, universal_class) = v10)) & ! [v9] : ! [v10] : ( ~ (function(v10) = 0) | ~ (member(v9, universal_class) = 0) | ? [v11] : (image(v10, v9) = v11 & member(v11, universal_class) = 0)) & ! [v9] : ! [v10] : ( ~ (image(successor_relation, v9) = v10) | ~ (subclass(v10, v9) = 0) | ? [v11] : ? [v12] : (inductive(v9) = v12 & member(null_class, v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (range_of(v9) = v10) | ? [v11] : (inverse(v9) = v11 & domain_of(v11) = v10)) & ! [v9] : ! [v10] : ( ~ (flip(v9) = v10) | subclass(v10, v1) = 0) & ! [v9] : ! [v10] : ( ~ (rotate(v9) = v10) | subclass(v10, v1) = 0) & ! [v9] : ! [v10] : ( ~ (cross_product(v9, universal_class) = v10) | ? [v11] : ? [v12] : (inverse(v9) = v11 & flip(v10) = v12 & domain_of(v12) = v11)) & ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v9) = v10) | singleton(v9) = v10) & ! [v9] : ! [v10] : ( ~ (subclass(v9, v0) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (function(v9) = v11 & compose(v9, v12) = v13 & inverse(v9) = v12 & subclass(v13, identity_relation) = v14 & ( ~ (v11 = 0) | (v14 = 0 & v10 = 0)))) & ! [v9] : ! [v10] : ( ~ (member(v10, universal_class) = 0) | ~ (member(v9, universal_class) = 0) | ? [v11] : ? [v12] : ? [v13] : (successor(v9) = v11 & ordered_pair(v9, v10) = v12 & member(v12, successor_relation) = v13 & ( ~ (v11 = v10) | v13 = 0))) & ! [v9] : ! [v10] : ( ~ (member(v10, universal_class) = 0) | ~ (member(v9, universal_class) = 0) | ? [v11] : (first(v11) = v9 & second(v11) = v10 & ordered_pair(v9, v10) = v11)) & ! [v9] : ( ~ (inductive(v9) = 0) | subclass(v8, v9) = 0) & ! [v9] : ( ~ (subclass(v9, v0) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : (function(v9) = v13 & compose(v9, v10) = v11 & inverse(v9) = v10 & subclass(v11, identity_relation) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v9] : ( ~ (member(v9, identity_relation) = 0) | ? [v10] : (ordered_pair(v10, v10) = v9 & member(v10, universal_class) = 0)) & ! [v9] : ~ (member(v9, null_class) = 0) & ! [v9] : ( ~ (member(v9, universal_class) = 0) | ? [v10] : (power_class(v9) = v10 & member(v10, universal_class) = 0)) & ! [v9] : ( ~ (member(v9, universal_class) = 0) | ? [v10] : (sum_class(v9) = v10 & member(v10, universal_class) = 0)) & ? [v9] : (v9 = null_class | ? [v10] : (disjoint(v10, v9) = 0 & member(v10, v9) = 0 & member(v10, universal_class) = 0)))
% 30.35/7.75 | 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 yields:
% 30.35/7.75 | (1) ~ (all_0_2_2 = 0) & function(all_0_1_1) = 0 & inductive(all_0_0_0) = 0 & cross_product(all_0_8_8, universal_class) = all_0_7_7 & cross_product(universal_class, universal_class) = all_0_8_8 & unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3 & unordered_pair(all_0_6_6, all_0_6_6) = all_0_4_4 & subclass(all_0_4_4, all_0_3_3) = all_0_2_2 & subclass(successor_relation, all_0_8_8) = 0 & subclass(element_relation, all_0_8_8) = 0 & member(all_0_0_0, universal_class) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v9, v2) = v10 & ordered_pair(v1, v0) = v9 & member(v10, v3) = v11 & member(v5, all_0_7_7) = v8 & ( ~ (v11 = 0) | ~ (v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (member(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v9, v1) = v10 & ordered_pair(v2, v3) = v9 & member(v10, v0) = v11 & member(v5, all_0_7_7) = v8 & ( ~ (v11 = 0) | ~ (v8 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (singleton(v2) = v4) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10 & member(v2, universal_class) = v11 & ( ~ (v10 = 0) | (v11 = 0 & v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v4, v5) = v6) | ? [v7] : ? [v8] : (member(v1, v3) = v8 & member(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (singleton(v2) = v4) | ~ (member(v3, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10 & member(v2, universal_class) = v7 & ( ~ (v7 = 0) | v10 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v5, v6) = 0) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3) = 0 & member(v5, all_0_7_7) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (member(v5, v6) = 0) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0) = 0 & member(v5, all_0_7_7) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v4, v5) = 0) | (member(v1, v3) = 0 & member(v0, v2) = 0)) & ! [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] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum_class(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, 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) | ? [v4] : ? [v5] : ? [v6] : (domain_of(v0) = v5 & member(v1, v5) = v6 & member(v1, universal_class) = v4 & ( ~ (v4 = 0) | v6 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_class(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : (subclass(v0, v1) = v5 & member(v0, universal_class) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ? [v5] : (member(v1, v0) = v5 & member(v1, universal_class) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(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] : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [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) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (domain_of(v0) = v4 & member(v1, v4) = v5 & member(v1, universal_class) = v6 & ( ~ (v5 = 0) | (v6 = 0 & ~ (v3 = null_class))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (first(v2) = v4 & second(v2) = v5 & ordered_pair(v4, v5) = v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v1, universal_class) = v3) | ~ (member(v0, universal_class) = v2) | ? [v4] : ? [v5] : ? [v6] : (successor(v0) = v6 & ordered_pair(v0, v1) = v4 & member(v4, successor_relation) = v5 & ( ~ (v5 = 0) | (v6 = v1 & v3 = 0 & v2 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ (member(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v0, universal_class) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [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 | ~ (inductive(v2) = v1) | ~ (inductive(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] : (v1 = 0 | ~ (member(v2, universal_class) = 0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_8_8) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (image(successor_relation, v0) = v1) | ~ (subclass(v1, v0) = v2) | ? [v3] : ? [v4] : (inductive(v0) = v3 & member(null_class, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [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] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (member(v2, element_relation) = v5 & member(v1, universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (member(v2, element_relation) = v3 & member(v1, universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = 0 & v4 = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, universal_class) = v1)) & ! [v0] : ! [v1] : ( ~ (function(v1) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : (image(v1, v0) = v2 & member(v2, universal_class) = 0)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ (subclass(v1, v0) = 0) | ? [v2] : ? [v3] : (inductive(v0) = v3 & member(null_class, v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1)) & ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_7_7) = 0) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_7_7) = 0) & ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (subclass(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (function(v0) = v2 & compose(v0, v3) = v4 & inverse(v0) = v3 & subclass(v4, identity_relation) = v5 & ( ~ (v2 = 0) | (v5 = 0 & v1 = 0)))) & ! [v0] : ! [v1] : ( ~ (member(v1, universal_class) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : ? [v3] : ? [v4] : (successor(v0) = v2 & ordered_pair(v0, v1) = v3 & member(v3, successor_relation) = v4 & ( ~ (v2 = v1) | v4 = 0))) & ! [v0] : ! [v1] : ( ~ (member(v1, universal_class) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : (first(v2) = v0 & second(v2) = v1 & ordered_pair(v0, v1) = v2)) & ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0) & ! [v0] : ( ~ (subclass(v0, all_0_8_8) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (function(v0) = v4 & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ( ~ (member(v0, identity_relation) = 0) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0)) & ! [v0] : ~ (member(v0, null_class) = 0) & ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0)) & ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0)) & ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 30.35/7.77 |
% 30.35/7.77 | Applying alpha-rule on (1) yields:
% 30.35/7.77 | (2) ! [v0] : ! [v1] : ( ~ (member(v1, universal_class) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : (first(v2) = v0 & second(v2) = v1 & ordered_pair(v0, v1) = v2))
% 30.35/7.77 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0))
% 30.35/7.78 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 30.35/7.78 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 30.35/7.78 | (6) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ (member(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & member(v0, universal_class) = v3))
% 30.35/7.78 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = null_class | ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (domain_of(v0) = v5 & member(v1, v5) = v6 & member(v1, universal_class) = v4 & ( ~ (v4 = 0) | v6 = 0)))
% 30.35/7.78 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (member(v2, element_relation) = v5 & member(v1, universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~ (v3 = 0) | v5 = 0)))
% 30.35/7.78 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0)
% 30.35/7.78 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0))
% 30.35/7.78 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0))
% 30.35/7.78 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (member(v2, universal_class) = 0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3))
% 30.35/7.78 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 30.35/7.78 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 30.35/7.78 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0))
% 30.35/7.78 | (16) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0))
% 30.35/7.78 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 30.35/7.78 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 30.35/7.78 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 30.35/7.78 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v4, v5) = v6) | ? [v7] : ? [v8] : (member(v1, v3) = v8 & member(v0, v2) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0))))
% 30.35/7.78 | (21) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 30.35/7.78 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, universal_class) = v1))
% 30.35/7.78 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (member(v5, v6) = 0) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0) = 0 & member(v5, all_0_7_7) = 0))
% 30.35/7.78 | (24) cross_product(all_0_8_8, universal_class) = all_0_7_7
% 30.35/7.78 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ (member(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v9, v1) = v10 & ordered_pair(v2, v3) = v9 & member(v10, v0) = v11 & member(v5, all_0_7_7) = v8 & ( ~ (v11 = 0) | ~ (v8 = 0))))
% 30.35/7.78 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 30.35/7.78 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 30.35/7.78 | (28) cross_product(universal_class, universal_class) = all_0_8_8
% 30.35/7.78 | (29) inductive(all_0_0_0) = 0
% 30.35/7.78 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum_class(v1) = v2) | ~ (member(v0, v4) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 30.35/7.78 | (31) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 30.35/7.78 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0))
% 30.35/7.78 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2)
% 30.35/7.78 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 30.35/7.79 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (singleton(v2) = v4) | ~ (member(v3, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10 & member(v2, universal_class) = v7 & ( ~ (v7 = 0) | v10 = 0)))
% 30.35/7.79 | (36) member(all_0_0_0, universal_class) = 0
% 30.35/7.79 | (37) unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3
% 30.35/7.79 | (38) function(all_0_1_1) = 0
% 30.35/7.79 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (member(v2, element_relation) = v3 & member(v1, universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = 0 & v4 = 0))))
% 30.35/7.79 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v4, v5) = 0) | (member(v1, v3) = 0 & member(v0, v2) = 0))
% 30.35/7.79 | (41) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0))
% 30.35/7.79 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 30.35/7.79 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 30.35/7.79 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ? [v5] : (member(v1, v0) = v5 & member(v1, universal_class) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 30.35/7.79 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0))
% 30.35/7.79 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 30.35/7.79 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cross_product(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (first(v2) = v4 & second(v2) = v5 & ordered_pair(v4, v5) = v2))
% 30.35/7.79 | (48) ~ (all_0_2_2 = 0)
% 30.35/7.79 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(successor_relation, v0) = v1) | ~ (subclass(v1, v0) = v2) | ? [v3] : ? [v4] : (inductive(v0) = v3 & member(null_class, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0))))
% 30.35/7.79 | (50) ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2))
% 30.35/7.79 | (51) ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0)
% 30.35/7.79 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0))
% 30.35/7.79 | (53) ! [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)
% 30.35/7.79 | (54) ! [v0] : ( ~ (subclass(v0, all_0_8_8) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (function(v0) = v4 & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 30.35/7.79 | (55) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 30.71/7.79 | (56) subclass(successor_relation, all_0_8_8) = 0
% 30.71/7.79 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ? [v5] : (member(v2, v1) = v5 & member(v2, v0) = v4 & (v5 = 0 | v4 = 0)))
% 30.71/7.79 | (58) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 30.71/7.79 | (59) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 30.71/7.79 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (ordered_pair(v9, v2) = v10 & ordered_pair(v1, v0) = v9 & member(v10, v3) = v11 & member(v5, all_0_7_7) = v8 & ( ~ (v11 = 0) | ~ (v8 = 0))))
% 30.71/7.79 | (61) ! [v0] : ! [v1] : ( ~ (member(v1, universal_class) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : ? [v3] : ? [v4] : (successor(v0) = v2 & ordered_pair(v0, v1) = v3 & member(v3, successor_relation) = v4 & ( ~ (v2 = v1) | v4 = 0)))
% 30.71/7.79 | (62) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_7_7) = 0)
% 30.71/7.79 | (63) subclass(all_0_4_4, all_0_3_3) = all_0_2_2
% 30.71/7.79 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 30.71/7.79 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 30.71/7.80 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 30.71/7.80 | (67) subclass(element_relation, all_0_8_8) = 0
% 30.71/7.80 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 30.71/7.80 | (69) ! [v0] : ! [v1] : ( ~ (function(v1) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : (image(v1, v0) = v2 & member(v2, universal_class) = 0))
% 30.71/7.80 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0))
% 30.71/7.80 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0)
% 30.71/7.80 | (72) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0))
% 30.71/7.80 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0))
% 30.71/7.80 | (74) ! [v0] : ( ~ (member(v0, identity_relation) = 0) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0))
% 30.71/7.80 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 30.71/7.80 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_8_8) = 0)
% 30.71/7.80 | (77) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 30.71/7.80 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v5, v6) = 0) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3) = 0 & member(v5, all_0_7_7) = 0))
% 30.71/7.80 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (singleton(v2) = v4) | ~ (member(v3, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ? [v11] : (compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10 & member(v2, universal_class) = v11 & ( ~ (v10 = 0) | (v11 = 0 & v7 = 0))))
% 30.71/7.80 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 30.71/7.80 | (81) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0))
% 30.71/7.80 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : ( ~ (v6 = 0) & ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5))
% 30.71/7.80 | (83) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ (subclass(v1, v0) = 0) | ? [v2] : ? [v3] : (inductive(v0) = v3 & member(null_class, v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.71/7.80 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ? [v4] : ? [v5] : ? [v6] : (domain_of(v0) = v4 & member(v1, v4) = v5 & member(v1, universal_class) = v6 & ( ~ (v5 = 0) | (v6 = 0 & ~ (v3 = null_class)))))
% 30.71/7.80 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 30.71/7.80 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 30.71/7.80 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (member(v1, universal_class) = v3) | ~ (member(v0, universal_class) = v2) | ? [v4] : ? [v5] : ? [v6] : (successor(v0) = v6 & ordered_pair(v0, v1) = v4 & member(v4, successor_relation) = v5 & ( ~ (v5 = 0) | (v6 = v1 & v3 = 0 & v2 = 0))))
% 30.71/7.80 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0))
% 30.71/7.80 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0))
% 30.71/7.80 | (90) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_7_7) = 0)
% 30.71/7.80 | (91) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0))
% 30.71/7.80 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_class(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ? [v5] : (subclass(v0, v1) = v5 & member(v0, universal_class) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 30.71/7.80 | (93) ! [v0] : ! [v1] : ( ~ (subclass(v0, all_0_8_8) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : (function(v0) = v2 & compose(v0, v3) = v4 & inverse(v0) = v3 & subclass(v4, identity_relation) = v5 & ( ~ (v2 = 0) | (v5 = 0 & v1 = 0))))
% 30.71/7.81 | (94) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, v0) = v1))
% 30.71/7.81 | (95) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0))
% 30.71/7.81 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : ? [v6] : (member(v2, v1) = v6 & member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))
% 30.71/7.81 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 30.71/7.81 | (98) unordered_pair(all_0_6_6, all_0_6_6) = all_0_4_4
% 30.71/7.81 | (99) ! [v0] : ~ (member(v0, null_class) = 0)
% 30.71/7.81 | (100) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (77) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms subclass(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 30.71/7.81 | (101) all_0_2_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0)
% 30.71/7.81 |
% 30.71/7.81 +-Applying beta-rule and splitting (101), into two cases.
% 30.71/7.81 |-Branch one:
% 30.71/7.81 | (102) all_0_2_2 = 0
% 30.71/7.81 |
% 30.71/7.81 | Equations (102) can reduce 48 to:
% 30.71/7.81 | (103) $false
% 30.71/7.81 |
% 30.71/7.81 |-The branch is then unsatisfiable
% 30.71/7.81 |-Branch two:
% 30.71/7.81 | (48) ~ (all_0_2_2 = 0)
% 30.71/7.81 | (105) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0)
% 30.71/7.81 |
% 30.71/7.81 | Instantiating (105) with all_54_0_40, all_54_1_41 yields:
% 30.71/7.81 | (106) ~ (all_54_0_40 = 0) & member(all_54_1_41, all_0_3_3) = all_54_0_40 & member(all_54_1_41, all_0_4_4) = 0
% 30.71/7.81 |
% 30.71/7.81 | Applying alpha-rule on (106) yields:
% 30.71/7.81 | (107) ~ (all_54_0_40 = 0)
% 30.71/7.81 | (108) member(all_54_1_41, all_0_3_3) = all_54_0_40
% 30.71/7.81 | (109) member(all_54_1_41, all_0_4_4) = 0
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (68) with all_0_4_4, all_0_6_6, all_0_6_6, all_54_1_41 and discharging atoms unordered_pair(all_0_6_6, all_0_6_6) = all_0_4_4, member(all_54_1_41, all_0_4_4) = 0, yields:
% 30.71/7.81 | (110) all_54_1_41 = all_0_6_6
% 30.71/7.81 |
% 30.71/7.81 | From (110) and (108) follows:
% 30.71/7.81 | (111) member(all_0_6_6, all_0_3_3) = all_54_0_40
% 30.71/7.81 |
% 30.71/7.81 | From (110) and (109) follows:
% 30.71/7.81 | (112) member(all_0_6_6, all_0_4_4) = 0
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (46) with all_54_0_40, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_5_5) = all_0_3_3, member(all_0_6_6, all_0_3_3) = all_54_0_40, yields:
% 30.71/7.81 | (113) all_54_0_40 = 0 | ? [v0] : ( ~ (v0 = 0) & member(all_0_6_6, universal_class) = v0)
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (9) with all_0_4_4, all_0_6_6, all_0_6_6, all_0_6_6 and discharging atoms unordered_pair(all_0_6_6, all_0_6_6) = all_0_4_4, member(all_0_6_6, all_0_4_4) = 0, yields:
% 30.71/7.81 | (114) member(all_0_6_6, universal_class) = 0
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (69) with all_0_1_1, all_0_6_6 and discharging atoms function(all_0_1_1) = 0, yields:
% 30.71/7.81 | (115) ~ (member(all_0_6_6, universal_class) = 0) | ? [v0] : (image(all_0_1_1, all_0_6_6) = v0 & member(v0, universal_class) = 0)
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (91) with all_0_6_6 yields:
% 30.71/7.81 | (116) ~ (member(all_0_6_6, universal_class) = 0) | ? [v0] : (power_class(all_0_6_6) = v0 & member(v0, universal_class) = 0)
% 30.71/7.81 |
% 30.71/7.81 | Instantiating formula (81) with all_0_6_6 yields:
% 30.71/7.81 | (117) ~ (member(all_0_6_6, universal_class) = 0) | ? [v0] : (sum_class(all_0_6_6) = v0 & member(v0, universal_class) = 0)
% 30.71/7.81 |
% 30.71/7.81 +-Applying beta-rule and splitting (113), into two cases.
% 30.71/7.81 |-Branch one:
% 30.71/7.81 | (118) all_54_0_40 = 0
% 30.71/7.81 |
% 30.71/7.81 | Equations (118) can reduce 107 to:
% 30.71/7.81 | (103) $false
% 30.71/7.81 |
% 30.71/7.81 |-The branch is then unsatisfiable
% 30.71/7.81 |-Branch two:
% 30.71/7.81 | (107) ~ (all_54_0_40 = 0)
% 30.71/7.81 | (121) ? [v0] : ( ~ (v0 = 0) & member(all_0_6_6, universal_class) = v0)
% 30.71/7.81 |
% 30.71/7.81 | Instantiating (121) with all_338_0_308 yields:
% 30.71/7.81 | (122) ~ (all_338_0_308 = 0) & member(all_0_6_6, universal_class) = all_338_0_308
% 30.71/7.81 |
% 30.71/7.81 | Applying alpha-rule on (122) yields:
% 30.71/7.81 | (123) ~ (all_338_0_308 = 0)
% 30.71/7.81 | (124) member(all_0_6_6, universal_class) = all_338_0_308
% 30.71/7.81 |
% 30.71/7.81 +-Applying beta-rule and splitting (117), into two cases.
% 30.71/7.81 |-Branch one:
% 30.71/7.81 | (125) ~ (member(all_0_6_6, universal_class) = 0)
% 30.71/7.82 |
% 30.71/7.82 | Using (114) and (125) yields:
% 30.71/7.82 | (126) $false
% 30.71/7.82 |
% 30.71/7.82 |-The branch is then unsatisfiable
% 30.71/7.82 |-Branch two:
% 30.71/7.82 | (114) member(all_0_6_6, universal_class) = 0
% 30.71/7.82 | (128) ? [v0] : (sum_class(all_0_6_6) = v0 & member(v0, universal_class) = 0)
% 30.71/7.82 |
% 30.71/7.82 +-Applying beta-rule and splitting (115), into two cases.
% 30.71/7.82 |-Branch one:
% 30.71/7.82 | (125) ~ (member(all_0_6_6, universal_class) = 0)
% 30.71/7.82 |
% 30.71/7.82 | Using (114) and (125) yields:
% 30.71/7.82 | (126) $false
% 30.71/7.82 |
% 30.71/7.82 |-The branch is then unsatisfiable
% 30.71/7.82 |-Branch two:
% 30.71/7.82 | (114) member(all_0_6_6, universal_class) = 0
% 30.71/7.82 | (132) ? [v0] : (image(all_0_1_1, all_0_6_6) = v0 & member(v0, universal_class) = 0)
% 30.71/7.82 |
% 30.71/7.82 +-Applying beta-rule and splitting (116), into two cases.
% 30.71/7.82 |-Branch one:
% 30.71/7.82 | (125) ~ (member(all_0_6_6, universal_class) = 0)
% 30.71/7.82 |
% 30.71/7.82 | Using (114) and (125) yields:
% 30.71/7.82 | (126) $false
% 30.71/7.82 |
% 30.71/7.82 |-The branch is then unsatisfiable
% 30.71/7.82 |-Branch two:
% 30.71/7.82 | (114) member(all_0_6_6, universal_class) = 0
% 30.71/7.82 | (136) ? [v0] : (power_class(all_0_6_6) = v0 & member(v0, universal_class) = 0)
% 30.71/7.82 |
% 30.71/7.82 | Instantiating formula (97) with all_0_6_6, universal_class, all_338_0_308, 0 and discharging atoms member(all_0_6_6, universal_class) = all_338_0_308, member(all_0_6_6, universal_class) = 0, yields:
% 30.71/7.82 | (137) all_338_0_308 = 0
% 30.71/7.82 |
% 30.71/7.82 | Equations (137) can reduce 123 to:
% 30.71/7.82 | (103) $false
% 30.71/7.82 |
% 30.71/7.82 |-The branch is then unsatisfiable
% 30.71/7.82 % SZS output end Proof for theBenchmark
% 30.71/7.82
% 30.71/7.82 7232ms
%------------------------------------------------------------------------------