TSTP Solution File: SET063+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:16:54 EDT 2022
% Result : Theorem 8.36s 2.58s
% Output : Proof 14.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET063+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 19:42:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.56/0.59 ____ _
% 0.56/0.59 ___ / __ \_____(_)___ ________ __________
% 0.56/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.56/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.56/0.59
% 0.56/0.59 A Theorem Prover for First-Order Logic
% 0.56/0.59 (ePrincess v.1.0)
% 0.56/0.59
% 0.56/0.59 (c) Philipp Rümmer, 2009-2015
% 0.56/0.59 (c) Peter Backeman, 2014-2015
% 0.56/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.59 Bug reports to peter@backeman.se
% 0.56/0.59
% 0.56/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.59
% 0.56/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.00 Prover 0: Preprocessing ...
% 2.95/1.37 Prover 0: Warning: ignoring some quantifiers
% 3.37/1.40 Prover 0: Constructing countermodel ...
% 6.16/2.07 Prover 0: gave up
% 6.16/2.07 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.53/2.11 Prover 1: Preprocessing ...
% 6.94/2.25 Prover 1: Warning: ignoring some quantifiers
% 6.94/2.26 Prover 1: Constructing countermodel ...
% 8.36/2.58 Prover 1: proved (510ms)
% 8.36/2.58
% 8.36/2.58 No countermodel exists, formula is valid
% 8.36/2.58 % SZS status Theorem for theBenchmark
% 8.36/2.58
% 8.36/2.58 Generating proof ... Warning: ignoring some quantifiers
% 13.92/3.89 found it (size 16)
% 13.92/3.89
% 13.92/3.89 % SZS output start Proof for theBenchmark
% 13.92/3.89 Assumed formulas after preprocessing and simplification:
% 13.92/3.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v2 = null_class) & function(v3) = 0 & inductive(v4) = 0 & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & subclass(v2, null_class) = 0 & subclass(successor_relation, v0) = 0 & subclass(element_relation, v0) = 0 & member(v4, universal_class) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (flip(v8) = v11) | ~ (ordered_pair(v9, v7) = v10) | ~ (ordered_pair(v5, v6) = v9) | ~ (member(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v7) = v15 & ordered_pair(v6, v5) = v14 & member(v15, v8) = v16 & member(v10, v1) = v13 & ( ~ (v16 = 0) | ~ (v13 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (rotate(v5) = v11) | ~ (ordered_pair(v9, v8) = v10) | ~ (ordered_pair(v6, v7) = v9) | ~ (member(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v14, v6) = v15 & ordered_pair(v7, v8) = v14 & member(v15, v5) = v16 & member(v10, v1) = v13 & ( ~ (v16 = 0) | ~ (v13 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image(v6, v10) = v11) | ~ (image(v5, v9) = v10) | ~ (singleton(v7) = v9) | ~ (member(v8, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (compose(v6, v5) = v14 & ordered_pair(v7, v8) = v13 & member(v13, v14) = v15 & member(v7, universal_class) = v16 & ( ~ (v15 = 0) | (v16 = 0 & v12 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (cross_product(v7, v8) = v10) | ~ (ordered_pair(v5, v6) = v9) | ~ (member(v9, v10) = v11) | ? [v12] : ? [v13] : (member(v6, v8) = v13 & member(v5, v7) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image(v6, v10) = v11) | ~ (image(v5, v9) = v10) | ~ (singleton(v7) = v9) | ~ (member(v8, v11) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (compose(v6, v5) = v14 & ordered_pair(v7, v8) = v13 & member(v13, v14) = v15 & member(v7, universal_class) = v12 & ( ~ (v12 = 0) | v15 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (flip(v8) = v11) | ~ (ordered_pair(v9, v7) = v10) | ~ (ordered_pair(v5, v6) = v9) | ~ (member(v10, v11) = 0) | ? [v12] : ? [v13] : (ordered_pair(v12, v7) = v13 & ordered_pair(v6, v5) = v12 & member(v13, v8) = 0 & member(v10, v1) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (rotate(v5) = v11) | ~ (ordered_pair(v9, v8) = v10) | ~ (ordered_pair(v6, v7) = v9) | ~ (member(v10, v11) = 0) | ? [v12] : ? [v13] : (ordered_pair(v12, v6) = v13 & ordered_pair(v7, v8) = v12 & member(v13, v5) = 0 & member(v10, v1) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cross_product(v7, v8) = v10) | ~ (ordered_pair(v5, v6) = v9) | ~ (member(v9, v10) = 0) | (member(v6, v8) = 0 & member(v5, v7) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v6) = v8) | ~ (singleton(v5) = v7) | ~ (unordered_pair(v7, v9) = v10) | ~ (unordered_pair(v5, v8) = v9) | ordered_pair(v5, v6) = v10) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (union(v5, v6) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v10 = 0) & member(v7, v6) = v11 & member(v7, v5) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection(v5, v6) = v8) | ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : (member(v7, v6) = v11 & member(v7, v5) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (sum_class(v6) = v7) | ~ (member(v5, v9) = 0) | ~ (member(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (restrict(v9, v8, v7) = v6) | ~ (restrict(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (intersection(v6, v8) = v9) | ~ (cross_product(v5, v7) = v8) | restrict(v6, v5, v7) = v9) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = null_class | ~ (restrict(v5, v7, universal_class) = v8) | ~ (singleton(v6) = v7) | ? [v9] : ? [v10] : ? [v11] : (domain_of(v5) = v10 & member(v6, v10) = v11 & member(v6, universal_class) = v9 & ( ~ (v9 = 0) | v11 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (power_class(v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ? [v10] : (subclass(v5, v6) = v10 & member(v5, universal_class) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (complement(v5) = v7) | ~ (member(v6, v7) = v8) | ? [v9] : ? [v10] : (member(v6, v5) = v10 & member(v6, universal_class) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v6, v5) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v5, universal_class) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unordered_pair(v5, v6) = v7) | ~ (member(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & member(v5, universal_class) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v7 = v5 | v6 = v5 | ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apply(v8, v7) = v6) | ~ (apply(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (disjoint(v8, v7) = v6) | ~ (disjoint(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (compose(v8, v7) = v6) | ~ (compose(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (image(v8, v7) = v6) | ~ (image(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (union(v8, v7) = v6) | ~ (union(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection(v8, v7) = v6) | ~ (intersection(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cross_product(v8, v7) = v6) | ~ (cross_product(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (ordered_pair(v8, v7) = v6) | ~ (ordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unordered_pair(v8, v7) = v6) | ~ (unordered_pair(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (subclass(v8, v7) = v6) | ~ (subclass(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (member(v8, v7) = v6) | ~ (member(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (image(v5, v7) = v8) | ~ (singleton(v6) = v7) | ? [v9] : (apply(v5, v6) = v9 & sum_class(v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (union(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : ? [v10] : (member(v7, v6) = v10 & member(v7, v5) = v9 & (v10 = 0 | v9 = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (restrict(v5, v7, universal_class) = v8) | ~ (singleton(v6) = v7) | ? [v9] : ? [v10] : ? [v11] : (domain_of(v5) = v9 & member(v6, v9) = v10 & member(v6, universal_class) = v11 & ( ~ (v10 = 0) | (v11 = 0 & ~ (v8 = null_class))))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection(v5, v6) = v8) | ~ (member(v7, v8) = 0) | (member(v7, v6) = 0 & member(v7, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cross_product(v5, v6) = v8) | ~ (member(v7, v8) = 0) | ? [v9] : ? [v10] : (first(v7) = v9 & second(v7) = v10 & ordered_pair(v9, v10) = v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unordered_pair(v6, v7) = v8) | ~ (member(v5, v8) = 0) | member(v5, universal_class) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (member(v6, universal_class) = v8) | ~ (member(v5, universal_class) = v7) | ? [v9] : ? [v10] : ? [v11] : (successor(v5) = v11 & ordered_pair(v5, v6) = v9 & member(v9, successor_relation) = v10 & ( ~ (v10 = 0) | (v11 = v6 & v8 = 0 & v7 = 0)))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = null_class | ~ (apply(v3, v5) = v6) | ~ (member(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & member(v5, universal_class) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (disjoint(v5, v6) = v7) | ? [v8] : (member(v8, v6) = 0 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (subclass(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (function(v7) = v6) | ~ (function(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (power_class(v7) = v6) | ~ (power_class(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (sum_class(v7) = v6) | ~ (sum_class(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (inductive(v7) = v6) | ~ (inductive(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (range_of(v7) = v6) | ~ (range_of(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (inverse(v7) = v6) | ~ (inverse(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (successor(v7) = v6) | ~ (successor(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (flip(v7) = v6) | ~ (flip(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (rotate(v7) = v6) | ~ (rotate(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (domain_of(v7) = v6) | ~ (domain_of(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (complement(v7) = v6) | ~ (complement(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (first(v7) = v6) | ~ (first(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (second(v7) = v6) | ~ (second(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (singleton(v7) = v6) | ~ (singleton(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = 0 | ~ (member(v7, universal_class) = 0) | ~ (member(v5, identity_relation) = v6) | ? [v8] : ( ~ (v8 = v5) & ordered_pair(v7, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (disjoint(v5, v6) = 0) | ~ (member(v7, v5) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (compose(v6, v5) = v7) | subclass(v7, v0) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (power_class(v6) = v7) | ~ (member(v5, v7) = 0) | (subclass(v5, v6) = 0 & member(v5, universal_class) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (sum_class(v6) = v7) | ~ (member(v5, v7) = 0) | ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (image(successor_relation, v5) = v6) | ~ (subclass(v6, v5) = v7) | ? [v8] : ? [v9] : (inductive(v5) = v8 & member(null_class, v5) = v9 & ( ~ (v8 = 0) | (v9 = 0 & v7 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (union(v5, v6) = v7) | ~ (singleton(v5) = v6) | successor(v5) = v7) & ! [v5] : ! [v6] : ! [v7] : ( ~ (restrict(v6, v5, universal_class) = v7) | ? [v8] : (image(v6, v5) = v8 & range_of(v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (complement(v5) = v7) | ~ (member(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & member(v6, v5) = v8 & member(v6, universal_class) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (member(v7, element_relation) = v10 & member(v6, universal_class) = v8 & member(v5, v6) = v9 & ( ~ (v9 = 0) | ~ (v8 = 0) | v10 = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (member(v7, element_relation) = v8 & member(v6, universal_class) = v9 & member(v5, v6) = v10 & ( ~ (v8 = 0) | (v10 = 0 & v9 = 0)))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (unordered_pair(v5, v6) = v7) | member(v7, universal_class) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (subclass(v5, v6) = 0) | ~ (member(v7, v5) = 0) | member(v7, v6) = 0) & ! [v5] : ! [v6] : (v6 = v5 | ~ (subclass(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & subclass(v6, v5) = v7)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subclass(v5, v5) = v6)) & ! [v5] : ! [v6] : (v6 = 0 | ~ (subclass(v5, universal_class) = v6)) & ! [v5] : ! [v6] : ( ~ (function(v6) = 0) | ~ (member(v5, universal_class) = 0) | ? [v7] : (image(v6, v5) = v7 & member(v7, universal_class) = 0)) & ! [v5] : ! [v6] : ( ~ (image(successor_relation, v5) = v6) | ~ (subclass(v6, v5) = 0) | ? [v7] : ? [v8] : (inductive(v5) = v8 & member(null_class, v5) = v7 & ( ~ (v7 = 0) | v8 = 0))) & ! [v5] : ! [v6] : ( ~ (range_of(v5) = v6) | ? [v7] : (inverse(v5) = v7 & domain_of(v7) = v6)) & ! [v5] : ! [v6] : ( ~ (flip(v5) = v6) | subclass(v6, v1) = 0) & ! [v5] : ! [v6] : ( ~ (rotate(v5) = v6) | subclass(v6, v1) = 0) & ! [v5] : ! [v6] : ( ~ (cross_product(v5, universal_class) = v6) | ? [v7] : ? [v8] : (inverse(v5) = v7 & flip(v6) = v8 & domain_of(v8) = v7)) & ! [v5] : ! [v6] : ( ~ (unordered_pair(v5, v5) = v6) | singleton(v5) = v6) & ! [v5] : ! [v6] : ( ~ (subclass(v5, v0) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (function(v5) = v7 & compose(v5, v8) = v9 & inverse(v5) = v8 & subclass(v9, identity_relation) = v10 & ( ~ (v7 = 0) | (v10 = 0 & v6 = 0)))) & ! [v5] : ! [v6] : ( ~ (member(v6, universal_class) = 0) | ~ (member(v5, universal_class) = 0) | ? [v7] : ? [v8] : ? [v9] : (successor(v5) = v7 & ordered_pair(v5, v6) = v8 & member(v8, successor_relation) = v9 & ( ~ (v7 = v6) | v9 = 0))) & ! [v5] : ! [v6] : ( ~ (member(v6, universal_class) = 0) | ~ (member(v5, universal_class) = 0) | ? [v7] : (first(v7) = v5 & second(v7) = v6 & ordered_pair(v5, v6) = v7)) & ! [v5] : ( ~ (inductive(v5) = 0) | subclass(v4, v5) = 0) & ! [v5] : ( ~ (subclass(v5, v0) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (function(v5) = v9 & compose(v5, v6) = v7 & inverse(v5) = v6 & subclass(v7, identity_relation) = v8 & ( ~ (v8 = 0) | v9 = 0))) & ! [v5] : ( ~ (member(v5, identity_relation) = 0) | ? [v6] : (ordered_pair(v6, v6) = v5 & member(v6, universal_class) = 0)) & ! [v5] : ~ (member(v5, null_class) = 0) & ! [v5] : ( ~ (member(v5, universal_class) = 0) | ? [v6] : (power_class(v5) = v6 & member(v6, universal_class) = 0)) & ! [v5] : ( ~ (member(v5, universal_class) = 0) | ? [v6] : (sum_class(v5) = v6 & member(v6, universal_class) = 0)) & ? [v5] : (v5 = null_class | ? [v6] : (disjoint(v6, v5) = 0 & member(v6, v5) = 0 & member(v6, universal_class) = 0)))
% 14.27/3.96 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 14.27/3.96 | (1) ~ (all_0_2_2 = null_class) & function(all_0_1_1) = 0 & inductive(all_0_0_0) = 0 & cross_product(all_0_4_4, universal_class) = all_0_3_3 & cross_product(universal_class, universal_class) = all_0_4_4 & subclass(all_0_2_2, null_class) = 0 & subclass(successor_relation, all_0_4_4) = 0 & subclass(element_relation, all_0_4_4) = 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_3_3) = 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_3_3) = 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_3_3) = 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_3_3) = 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_4_4) = 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_3_3) = 0) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_3_3) = 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_4_4) = 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_4_4) = 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))
% 14.69/3.98 |
% 14.69/3.98 | Applying alpha-rule on (1) yields:
% 14.69/3.98 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0))
% 14.69/3.98 | (3) ! [v0] : ! [v1] : ( ~ (subclass(v0, all_0_4_4) = 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))))
% 14.69/3.98 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0))
% 14.69/3.98 | (5) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_3_3) = 0)
% 14.69/3.98 | (6) subclass(all_0_2_2, null_class) = 0
% 14.69/3.98 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 14.69/3.98 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 14.69/3.98 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0))
% 14.69/3.98 | (10) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 14.69/3.98 | (11) ! [v0] : ! [v1] : ( ~ (function(v1) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : (image(v1, v0) = v2 & member(v2, universal_class) = 0))
% 14.69/3.98 | (12) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0))
% 14.69/3.98 | (13) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 14.69/3.98 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0))
% 14.69/3.98 | (15) ! [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_3_3) = v8 & ( ~ (v11 = 0) | ~ (v8 = 0))))
% 14.69/3.99 | (16) inductive(all_0_0_0) = 0
% 14.69/3.99 | (17) ! [v0] : ~ (member(v0, null_class) = 0)
% 14.69/3.99 | (18) ! [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))
% 14.69/3.99 | (19) ! [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)))
% 14.69/3.99 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0)
% 14.69/3.99 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0))
% 14.69/3.99 | (22) ! [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)))
% 14.69/3.99 | (23) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0))
% 14.69/3.99 | (24) ! [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))))
% 14.69/3.99 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 14.69/3.99 | (26) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 14.69/3.99 | (27) ! [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)))
% 14.69/3.99 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2)
% 14.69/3.99 | (29) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0))
% 14.69/3.99 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0))
% 14.69/3.99 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_4_4) = 0)
% 14.69/3.99 | (32) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 14.69/3.99 | (33) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 14.69/3.99 | (34) subclass(successor_relation, all_0_4_4) = 0
% 14.69/3.99 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 14.69/3.99 | (36) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_3_3) = 0)
% 14.69/3.99 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 14.69/3.99 | (38) cross_product(universal_class, universal_class) = all_0_4_4
% 14.69/3.99 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 14.69/3.99 | (40) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 14.69/3.99 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0))
% 14.69/3.99 | (42) ! [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))
% 14.69/3.99 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 14.69/3.99 | (44) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 14.69/3.99 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0))
% 14.69/3.99 | (46) ! [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))))
% 14.69/4.00 | (47) member(all_0_0_0, universal_class) = 0
% 14.69/4.00 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (member(v2, universal_class) = 0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3))
% 14.69/4.00 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 14.69/4.00 | (50) ! [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))))
% 14.69/4.00 | (51) ! [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))
% 14.69/4.00 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 14.69/4.00 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 14.69/4.00 | (54) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 14.69/4.00 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 14.69/4.00 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 14.69/4.00 | (57) ! [v0] : ! [v1] : ( ~ (member(v1, universal_class) = 0) | ~ (member(v0, universal_class) = 0) | ? [v2] : (first(v2) = v0 & second(v2) = v1 & ordered_pair(v0, v1) = v2))
% 14.69/4.00 | (58) ! [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)))
% 14.69/4.00 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 14.69/4.00 | (60) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, universal_class) = v1))
% 14.69/4.00 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0))
% 14.69/4.00 | (62) subclass(element_relation, all_0_4_4) = 0
% 14.69/4.00 | (63) ! [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)))
% 14.69/4.00 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 14.69/4.00 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0))
% 14.69/4.00 | (66) ! [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_3_3) = v8 & ( ~ (v11 = 0) | ~ (v8 = 0))))
% 14.69/4.00 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 14.69/4.00 | (68) ! [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))))
% 14.69/4.00 | (69) ! [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))
% 14.69/4.00 | (70) ! [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)))
% 14.69/4.00 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2))
% 14.69/4.00 | (72) cross_product(all_0_4_4, universal_class) = all_0_3_3
% 14.69/4.00 | (73) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0))
% 14.69/4.00 | (74) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, v0) = v1))
% 14.69/4.00 | (75) function(all_0_1_1) = 0
% 14.69/4.00 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 14.69/4.00 | (77) ! [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)))
% 14.69/4.01 | (78) ! [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_3_3) = 0))
% 14.69/4.01 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 14.69/4.01 | (80) ! [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))))
% 14.69/4.01 | (81) ! [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_3_3) = 0))
% 14.69/4.01 | (82) ~ (all_0_2_2 = null_class)
% 14.69/4.01 | (83) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0))
% 14.69/4.01 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 14.69/4.01 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 14.69/4.01 | (86) ! [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))))
% 14.69/4.01 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0))
% 14.69/4.01 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0)
% 14.69/4.01 | (89) ! [v0] : ( ~ (subclass(v0, all_0_4_4) = 0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : (function(v0) = v4 & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 14.69/4.01 | (90) ! [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))))
% 14.69/4.01 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0))
% 14.69/4.01 | (92) ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0)
% 14.69/4.01 | (93) ! [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)))))
% 14.69/4.01 | (94) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 14.69/4.01 | (95) ! [v0] : ( ~ (member(v0, identity_relation) = 0) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0))
% 14.69/4.01 | (96) ! [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)
% 14.69/4.01 | (97) ! [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))
% 14.69/4.01 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 14.69/4.01 |
% 14.69/4.01 | Instantiating formula (71) with null_class, all_0_2_2 and discharging atoms subclass(all_0_2_2, null_class) = 0, yields:
% 14.69/4.01 | (99) all_0_2_2 = null_class | ? [v0] : ( ~ (v0 = 0) & subclass(null_class, all_0_2_2) = v0)
% 14.69/4.01 |
% 14.69/4.01 +-Applying beta-rule and splitting (99), into two cases.
% 14.69/4.01 |-Branch one:
% 14.69/4.01 | (100) all_0_2_2 = null_class
% 14.69/4.01 |
% 14.69/4.01 | Equations (100) can reduce 82 to:
% 14.69/4.01 | (101) $false
% 14.69/4.01 |
% 14.69/4.01 |-The branch is then unsatisfiable
% 14.69/4.01 |-Branch two:
% 14.69/4.01 | (82) ~ (all_0_2_2 = null_class)
% 14.69/4.02 | (103) ? [v0] : ( ~ (v0 = 0) & subclass(null_class, all_0_2_2) = v0)
% 14.69/4.02 |
% 14.69/4.02 | Instantiating (103) with all_46_0_36 yields:
% 14.69/4.02 | (104) ~ (all_46_0_36 = 0) & subclass(null_class, all_0_2_2) = all_46_0_36
% 14.69/4.02 |
% 14.69/4.02 | Applying alpha-rule on (104) yields:
% 14.69/4.02 | (105) ~ (all_46_0_36 = 0)
% 14.69/4.02 | (106) subclass(null_class, all_0_2_2) = all_46_0_36
% 14.69/4.02 |
% 14.69/4.02 | Instantiating formula (33) with all_46_0_36, all_0_2_2, null_class and discharging atoms subclass(null_class, all_0_2_2) = all_46_0_36, yields:
% 14.69/4.02 | (107) all_46_0_36 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, null_class) = 0)
% 14.69/4.02 |
% 14.69/4.02 +-Applying beta-rule and splitting (107), into two cases.
% 14.69/4.02 |-Branch one:
% 14.69/4.02 | (108) all_46_0_36 = 0
% 14.69/4.02 |
% 14.69/4.02 | Equations (108) can reduce 105 to:
% 14.69/4.02 | (101) $false
% 14.69/4.02 |
% 14.69/4.02 |-The branch is then unsatisfiable
% 14.69/4.02 |-Branch two:
% 14.69/4.02 | (105) ~ (all_46_0_36 = 0)
% 14.69/4.02 | (111) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_2_2) = v1 & member(v0, null_class) = 0)
% 14.69/4.02 |
% 14.69/4.02 | Instantiating (111) with all_198_0_157, all_198_1_158 yields:
% 14.69/4.02 | (112) ~ (all_198_0_157 = 0) & member(all_198_1_158, all_0_2_2) = all_198_0_157 & member(all_198_1_158, null_class) = 0
% 14.69/4.02 |
% 14.69/4.02 | Applying alpha-rule on (112) yields:
% 14.69/4.02 | (113) ~ (all_198_0_157 = 0)
% 14.69/4.02 | (114) member(all_198_1_158, all_0_2_2) = all_198_0_157
% 14.69/4.02 | (115) member(all_198_1_158, null_class) = 0
% 14.69/4.02 |
% 14.69/4.02 | Instantiating formula (17) with all_198_1_158 and discharging atoms member(all_198_1_158, null_class) = 0, yields:
% 14.69/4.02 | (116) $false
% 14.69/4.02 |
% 14.69/4.02 |-The branch is then unsatisfiable
% 14.69/4.02 % SZS output end Proof for theBenchmark
% 14.69/4.02
% 14.69/4.02 3415ms
%------------------------------------------------------------------------------