TSTP Solution File: SET082+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n021.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 00:17:13 EDT 2022
% Result : Theorem 21.90s 5.91s
% Output : Proof 36.97s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET082+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.03/0.14 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jul 9 22:09:37 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.46/0.61 ____ _
% 0.46/0.61 ___ / __ \_____(_)___ ________ __________
% 0.46/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.61
% 0.46/0.61 A Theorem Prover for First-Order Logic
% 0.46/0.61 (ePrincess v.1.0)
% 0.46/0.61
% 0.46/0.61 (c) Philipp Rümmer, 2009-2015
% 0.46/0.61 (c) Peter Backeman, 2014-2015
% 0.46/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.61 Bug reports to peter@backeman.se
% 0.46/0.61
% 0.46/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.61
% 0.46/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.86/1.02 Prover 0: Preprocessing ...
% 3.22/1.42 Prover 0: Warning: ignoring some quantifiers
% 3.50/1.46 Prover 0: Constructing countermodel ...
% 7.04/2.25 Prover 0: gave up
% 7.04/2.25 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 7.26/2.30 Prover 1: Preprocessing ...
% 7.76/2.45 Prover 1: Warning: ignoring some quantifiers
% 7.98/2.45 Prover 1: Constructing countermodel ...
% 19.86/5.41 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.98/5.44 Prover 2: Preprocessing ...
% 20.65/5.58 Prover 2: Warning: ignoring some quantifiers
% 20.65/5.59 Prover 2: Constructing countermodel ...
% 21.90/5.91 Prover 2: proved (497ms)
% 21.90/5.91 Prover 1: stopped
% 21.90/5.91
% 21.90/5.91 No countermodel exists, formula is valid
% 21.90/5.91 % SZS status Theorem for theBenchmark
% 21.90/5.91
% 21.90/5.91 Generating proof ... Warning: ignoring some quantifiers
% 36.06/10.44 found it (size 121)
% 36.06/10.44
% 36.06/10.44 % SZS output start Proof for theBenchmark
% 36.06/10.44 Assumed formulas after preprocessing and simplification:
% 36.06/10.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v4 = null_class) & ~ (v3 = 0) & function(v5) = 0 & inductive(v6) = 0 & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & singleton(v2) = v4 & subclass(successor_relation, v0) = 0 & subclass(element_relation, v0) = 0 & member(v6, universal_class) = 0 & member(v2, universal_class) = v3 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (flip(v10) = v13) | ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ (member(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v17 = 0) & ordered_pair(v15, v9) = v16 & ordered_pair(v8, v7) = v15 & member(v16, v10) = v17) | ( ~ (v15 = 0) & member(v12, v1) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (rotate(v7) = v13) | ~ (ordered_pair(v11, v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ (member(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v17 = 0) & ordered_pair(v15, v8) = v16 & ordered_pair(v9, v10) = v15 & member(v16, v7) = v17) | ( ~ (v15 = 0) & member(v12, v1) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image(v8, v12) = v13) | ~ (image(v7, v11) = v12) | ~ (singleton(v9) = v11) | ~ (member(v10, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ((v15 = 0 & v14 = 0 & member(v9, universal_class) = 0) | ( ~ (v17 = 0) & compose(v8, v7) = v16 & ordered_pair(v9, v10) = v15 & member(v15, v16) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (compose(v8, v7) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ (member(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (( ~ (v17 = 0) & image(v8, v15) = v16 & image(v7, v14) = v15 & singleton(v9) = v14 & member(v10, v16) = v17) | ( ~ (v14 = 0) & member(v9, universal_class) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (cross_product(v9, v10) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ (member(v11, v12) = v13) | ? [v14] : (( ~ (v14 = 0) & member(v8, v10) = v14) | ( ~ (v14 = 0) & member(v7, v9) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (image(v8, v12) = v13) | ~ (image(v7, v11) = v12) | ~ (singleton(v9) = v11) | ~ (member(v10, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : ((v16 = 0 & compose(v8, v7) = v15 & ordered_pair(v9, v10) = v14 & member(v14, v15) = 0) | ( ~ (v14 = 0) & member(v9, universal_class) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (flip(v10) = v13) | ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ (member(v12, v13) = 0) | ? [v14] : ? [v15] : (ordered_pair(v14, v9) = v15 & ordered_pair(v8, v7) = v14 & member(v15, v10) = 0 & member(v12, v1) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (rotate(v7) = v13) | ~ (ordered_pair(v11, v10) = v12) | ~ (ordered_pair(v8, v9) = v11) | ~ (member(v12, v13) = 0) | ? [v14] : ? [v15] : (ordered_pair(v14, v8) = v15 & ordered_pair(v9, v10) = v14 & member(v15, v7) = 0 & member(v12, v1) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v8, v7) = v11) | ~ (member(v12, v10) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v14, v9) = v15 & ordered_pair(v7, v8) = v14 & ((v16 = 0 & v13 = 0 & member(v15, v1) = 0) | ( ~ (v17 = 0) & flip(v10) = v16 & member(v15, v16) = v17)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v11, v8) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ (member(v12, v7) = v13) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v14, v10) = v15 & ordered_pair(v8, v9) = v14 & ((v16 = 0 & v13 = 0 & member(v15, v1) = 0) | ( ~ (v17 = 0) & rotate(v7) = v16 & member(v15, v16) = v17)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (compose(v8, v7) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ (member(v11, v12) = 0) | ? [v13] : ? [v14] : ? [v15] : (image(v8, v14) = v15 & image(v7, v13) = v14 & singleton(v9) = v13 & member(v10, v15) = 0 & member(v9, universal_class) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cross_product(v9, v10) = v12) | ~ (ordered_pair(v7, v8) = v11) | ~ (member(v11, v12) = 0) | (member(v8, v10) = 0 & member(v7, v9) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v9) = v12) | ~ (ordered_pair(v8, v7) = v11) | ~ (member(v12, v10) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v13, v9) = v14 & ordered_pair(v7, v8) = v13 & ((v16 = 0 & flip(v10) = v15 & member(v14, v15) = 0) | ( ~ (v15 = 0) & member(v14, v1) = v15)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ordered_pair(v11, v8) = v12) | ~ (ordered_pair(v9, v10) = v11) | ~ (member(v12, v7) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (ordered_pair(v13, v10) = v14 & ordered_pair(v8, v9) = v13 & ((v16 = 0 & rotate(v7) = v15 & member(v14, v15) = 0) | ( ~ (v15 = 0) & member(v14, v1) = v15)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (union(v7, v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : ? [v13] : ( ~ (v13 = 0) & ~ (v12 = 0) & member(v9, v8) = v13 & member(v9, v7) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (intersection(v7, v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & member(v9, v8) = v12) | ( ~ (v12 = 0) & member(v9, v7) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum_class(v8) = v9) | ~ (member(v11, v8) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (sum_class(v8) = v9) | ~ (member(v7, v11) = 0) | ~ (member(v7, v9) = v10) | ? [v12] : ( ~ (v12 = 0) & member(v11, v8) = v12)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (restrict(v11, v10, v9) = v8) | ~ (restrict(v11, v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v10) = v11) | ~ (cross_product(v7, v9) = v10) | restrict(v8, v7, v9) = v11) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = null_class | ~ (restrict(v7, v9, universal_class) = v10) | ~ (singleton(v8) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & domain_of(v7) = v11 & member(v8, v11) = 0) | ( ~ (v11 = 0) & member(v8, universal_class) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (power_class(v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & subclass(v7, v8) = v11) | ( ~ (v11 = 0) & member(v7, universal_class) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (domain_of(v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = null_class & restrict(v7, v11, universal_class) = null_class & singleton(v8) = v11) | ( ~ (v11 = 0) & member(v8, universal_class) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (complement(v7) = v9) | ~ (member(v8, v9) = v10) | ? [v11] : ((v11 = 0 & member(v8, v7) = 0) | ( ~ (v11 = 0) & member(v8, universal_class) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v8, v7) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v7, universal_class) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unordered_pair(v7, v8) = v9) | ~ (member(v7, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v7, universal_class) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subclass(v7, v8) = 0) | ~ (member(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & member(v9, v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = v7 | v8 = v7 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (apply(v10, v9) = v8) | ~ (apply(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (disjoint(v10, v9) = v8) | ~ (disjoint(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (compose(v10, v9) = v8) | ~ (compose(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (image(v10, v9) = v8) | ~ (image(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (union(v10, v9) = v8) | ~ (union(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (intersection(v10, v9) = v8) | ~ (intersection(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (cross_product(v10, v9) = v8) | ~ (cross_product(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (ordered_pair(v10, v9) = v8) | ~ (ordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (unordered_pair(v10, v9) = v8) | ~ (unordered_pair(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (subclass(v10, v9) = v8) | ~ (subclass(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (member(v10, v9) = v8) | ~ (member(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (image(v7, v9) = v10) | ~ (singleton(v8) = v9) | ? [v11] : (apply(v7, v8) = v11 & sum_class(v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : ((v11 = 0 & member(v9, v8) = 0) | (v11 = 0 & member(v9, v7) = 0))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v8, v7, v9) = v10) | ? [v11] : (intersection(v8, v11) = v10 & cross_product(v7, v9) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v7, v9, universal_class) = v10) | ~ (singleton(v8) = v9) | ? [v11] : ? [v12] : ((v11 = 0 & ~ (v10 = null_class) & member(v8, universal_class) = 0) | ( ~ (v12 = 0) & domain_of(v7) = v11 & member(v8, v11) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection(v7, v8) = v10) | ~ (member(v9, v10) = 0) | (member(v9, v8) = 0 & member(v9, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cross_product(v7, v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : ? [v12] : (first(v9) = v11 & second(v9) = v12 & ordered_pair(v11, v12) = v9)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (singleton(v8) = v9) | ~ (unordered_pair(v7, v9) = v10) | ? [v11] : ? [v12] : (ordered_pair(v7, v8) = v11 & singleton(v7) = v12 & unordered_pair(v12, v10) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | ~ (member(v7, v10) = 0) | member(v7, universal_class) = 0) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (disjoint(v7, v8) = v9) | ? [v10] : (member(v10, v8) = 0 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (subclass(v7, v8) = v9) | ? [v10] : ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11 & member(v10, v7) = 0)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (member(v8, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & complement(v7) = v10 & member(v8, v10) = 0) | ( ~ (v10 = 0) & member(v8, universal_class) = v10))) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (function(v9) = v8) | ~ (function(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (power_class(v9) = v8) | ~ (power_class(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (sum_class(v9) = v8) | ~ (sum_class(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (inductive(v9) = v8) | ~ (inductive(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (range_of(v9) = v8) | ~ (range_of(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (inverse(v9) = v8) | ~ (inverse(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (successor(v9) = v8) | ~ (successor(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (flip(v9) = v8) | ~ (flip(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (rotate(v9) = v8) | ~ (rotate(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (domain_of(v9) = v8) | ~ (domain_of(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (complement(v9) = v8) | ~ (complement(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (first(v9) = v8) | ~ (first(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (second(v9) = v8) | ~ (second(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singleton(v9) = v8) | ~ (singleton(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (ordered_pair(v9, v9) = v7) | ~ (member(v7, identity_relation) = v8) | ? [v10] : ( ~ (v10 = 0) & member(v9, universal_class) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (member(v9, universal_class) = 0) | ~ (member(v7, identity_relation) = v8) | ? [v10] : ( ~ (v10 = v7) & ordered_pair(v9, v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (apply(v7, v8) = v9) | ? [v10] : ? [v11] : (sum_class(v11) = v9 & image(v7, v10) = v11 & singleton(v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v7, v8) = 0) | ~ (member(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v7) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (disjoint(v7, v8) = 0) | ~ (member(v9, v7) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v9, v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (compose(v8, v7) = v9) | subclass(v9, v0) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (power_class(v8) = v9) | ~ (member(v7, v9) = 0) | (subclass(v7, v8) = 0 & member(v7, universal_class) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (sum_class(v8) = v9) | ~ (member(v7, v9) = 0) | ? [v10] : (member(v10, v8) = 0 & member(v7, v10) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (image(v8, v7) = v9) | ? [v10] : (range_of(v10) = v9 & restrict(v8, v7, universal_class) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (image(v8, v7) = v9) | ? [v10] : ((v10 = 0 & member(v9, universal_class) = 0) | ( ~ (v10 = 0) & function(v8) = v10) | ( ~ (v10 = 0) & member(v7, universal_class) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (domain_of(v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : ? [v11] : ( ~ (v11 = null_class) & restrict(v7, v10, universal_class) = v11 & singleton(v8) = v10 & member(v8, universal_class) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (restrict(v8, v7, universal_class) = v9) | ? [v10] : (image(v8, v7) = v10 & range_of(v9) = v10)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (complement(v7) = v9) | ~ (member(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & member(v8, v7) = v10 & member(v8, universal_class) = 0)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (singleton(v8) = v11 & singleton(v7) = v10 & unordered_pair(v10, v12) = v9 & unordered_pair(v7, v11) = v12)) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & v10 = 0 & successor(v7) = v8 & member(v8, universal_class) = 0 & member(v7, universal_class) = 0) | ( ~ (v10 = 0) & member(v9, successor_relation) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = v8 & v10 = v7 & first(v9) = v7 & second(v9) = v8) | ( ~ (v10 = 0) & member(v8, universal_class) = v10) | ( ~ (v10 = 0) & member(v7, universal_class) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & member(v8, universal_class) = 0 & member(v7, v8) = 0) | ( ~ (v10 = 0) & member(v9, element_relation) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ((v10 = 0 & member(v9, successor_relation) = 0) | ( ~ (v10 = v8) & successor(v7) = v10) | ( ~ (v10 = 0) & member(v8, universal_class) = v10) | ( ~ (v10 = 0) & member(v7, universal_class) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ordered_pair(v7, v8) = v9) | ? [v10] : ((v10 = 0 & member(v9, element_relation) = 0) | ( ~ (v10 = 0) & member(v8, universal_class) = v10) | ( ~ (v10 = 0) & member(v7, v8) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | member(v9, universal_class) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subclass(v7, v8) = v9) | ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & member(v7, universal_class) = 0) | ( ~ (v11 = 0) & power_class(v8) = v10 & member(v7, v10) = v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (subclass(v7, v8) = 0) | ~ (member(v9, v7) = 0) | member(v9, v8) = 0) & ! [v7] : ! [v8] : ! [v9] : ( ~ (member(v8, v7) = v9) | ? [v10] : ? [v11] : ((v10 = 0 & ~ (v9 = 0) & member(v8, universal_class) = 0) | ( ~ (v11 = 0) & complement(v7) = v10 & member(v8, v10) = v11))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (member(v7, v8) = v9) | ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & member(v8, universal_class) = 0) | ( ~ (v11 = 0) & ordered_pair(v7, v8) = v10 & member(v10, element_relation) = v11))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subclass(v8, v7) = 0) | ? [v9] : ( ~ (v9 = 0) & subclass(v7, v8) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (subclass(v7, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & subclass(v8, v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (function(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (( ~ (v11 = 0) & compose(v7, v9) = v10 & inverse(v7) = v9 & subclass(v10, identity_relation) = v11) | ( ~ (v9 = 0) & subclass(v7, v0) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (inductive(v7) = v8) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & image(successor_relation, v7) = v9 & subclass(v9, v7) = v10) | ( ~ (v9 = 0) & member(null_class, v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subclass(v7, v7) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subclass(v7, universal_class) = v8)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (subclass(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & inductive(v7) = v9)) & ! [v7] : ! [v8] : (v7 = null_class | ~ (apply(v5, v7) = v8) | ? [v9] : ((v9 = 0 & member(v8, v7) = 0) | ( ~ (v9 = 0) & member(v7, universal_class) = v9))) & ! [v7] : ! [v8] : ( ~ (power_class(v7) = v8) | ? [v9] : ((v9 = 0 & member(v8, universal_class) = 0) | ( ~ (v9 = 0) & member(v7, universal_class) = v9))) & ! [v7] : ! [v8] : ( ~ (sum_class(v7) = v8) | ? [v9] : ((v9 = 0 & member(v8, universal_class) = 0) | ( ~ (v9 = 0) & member(v7, universal_class) = v9))) & ! [v7] : ! [v8] : ( ~ (image(successor_relation, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & subclass(v8, v7) = 0 & member(null_class, v7) = 0) | ( ~ (v9 = 0) & inductive(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (image(successor_relation, v7) = v8) | ? [v9] : ((v9 = 0 & inductive(v7) = 0) | ( ~ (v9 = 0) & subclass(v8, v7) = v9) | ( ~ (v9 = 0) & member(null_class, v7) = v9))) & ! [v7] : ! [v8] : ( ~ (range_of(v7) = v8) | ? [v9] : (inverse(v7) = v9 & domain_of(v9) = v8)) & ! [v7] : ! [v8] : ( ~ (inverse(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & compose(v7, v8) = v10 & subclass(v10, identity_relation) = 0 & subclass(v7, v0) = 0) | ( ~ (v9 = 0) & function(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (inverse(v7) = v8) | ? [v9] : ? [v10] : (flip(v9) = v10 & domain_of(v10) = v8 & cross_product(v7, universal_class) = v9)) & ! [v7] : ! [v8] : ( ~ (inverse(v7) = v8) | ? [v9] : ? [v10] : ((v9 = 0 & function(v7) = 0) | ( ~ (v10 = 0) & compose(v7, v8) = v9 & subclass(v9, identity_relation) = v10) | ( ~ (v9 = 0) & subclass(v7, v0) = v9))) & ! [v7] : ! [v8] : ( ~ (inverse(v7) = v8) | ? [v9] : (range_of(v7) = v9 & domain_of(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (successor(v7) = v8) | ? [v9] : (union(v7, v9) = v8 & singleton(v7) = v9)) & ! [v7] : ! [v8] : ( ~ (flip(v7) = v8) | subclass(v8, v1) = 0) & ! [v7] : ! [v8] : ( ~ (rotate(v7) = v8) | subclass(v8, v1) = 0) & ! [v7] : ! [v8] : ( ~ (cross_product(v7, universal_class) = v8) | ? [v9] : ? [v10] : (inverse(v7) = v9 & flip(v8) = v10 & domain_of(v10) = v9)) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) & ! [v7] : ! [v8] : ( ~ (singleton(v7) = v8) | ? [v9] : (successor(v7) = v9 & union(v7, v8) = v9)) & ! [v7] : ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) & ! [v7] : ! [v8] : ( ~ (subclass(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & power_class(v8) = v9 & member(v7, v9) = 0) | ( ~ (v9 = 0) & member(v7, universal_class) = v9))) & ! [v7] : ! [v8] : ( ~ (subclass(v7, v0) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v8 = 0 & compose(v7, v9) = v10 & inverse(v7) = v9 & subclass(v10, identity_relation) = 0) | ( ~ (v9 = 0) & function(v7) = v9))) & ! [v7] : ! [v8] : ( ~ (member(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & ordered_pair(v7, v8) = v9 & member(v9, element_relation) = 0) | ( ~ (v9 = 0) & member(v8, universal_class) = v9))) & ! [v7] : ! [v8] : ( ~ (member(null_class, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & image(successor_relation, v7) = v9 & subclass(v9, v7) = 0) | ( ~ (v9 = 0) & inductive(v7) = v9))) & ! [v7] : (v7 = null_class | ~ (member(v7, universal_class) = 0) | ? [v8] : (apply(v5, v7) = v8 & member(v8, v7) = 0)) & ! [v7] : ( ~ (function(v7) = 0) | ? [v8] : ? [v9] : (compose(v7, v8) = v9 & inverse(v7) = v8 & subclass(v9, identity_relation) = 0 & subclass(v7, v0) = 0)) & ! [v7] : ( ~ (inductive(v7) = 0) | subclass(v6, v7) = 0) & ! [v7] : ( ~ (inductive(v7) = 0) | ? [v8] : (image(successor_relation, v7) = v8 & subclass(v8, v7) = 0 & member(null_class, v7) = 0)) & ! [v7] : ( ~ (subclass(v7, v0) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v8 = 0 & function(v7) = 0) | ( ~ (v10 = 0) & compose(v7, v8) = v9 & inverse(v7) = v8 & subclass(v9, identity_relation) = v10))) & ! [v7] : ( ~ (member(v7, identity_relation) = 0) | ? [v8] : (ordered_pair(v8, v8) = v7 & member(v8, universal_class) = 0)) & ! [v7] : ~ (member(v7, null_class) = 0) & ! [v7] : ( ~ (member(v7, universal_class) = 0) | ? [v8] : (power_class(v7) = v8 & member(v8, universal_class) = 0)) & ! [v7] : ( ~ (member(v7, universal_class) = 0) | ? [v8] : (sum_class(v7) = v8 & member(v8, universal_class) = 0)) & ! [v7] : ( ~ (member(null_class, v7) = 0) | ? [v8] : ? [v9] : ((v8 = 0 & inductive(v7) = 0) | ( ~ (v9 = 0) & image(successor_relation, v7) = v8 & subclass(v8, v7) = v9))) & ? [v7] : ? [v8] : ? [v9] : ? [v10] : restrict(v9, v8, v7) = v10 & ? [v7] : ? [v8] : ? [v9] : apply(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : disjoint(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : compose(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : image(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : union(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : intersection(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : cross_product(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : ordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : unordered_pair(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : subclass(v8, v7) = v9 & ? [v7] : ? [v8] : ? [v9] : member(v8, v7) = v9 & ? [v7] : ? [v8] : function(v7) = v8 & ? [v7] : ? [v8] : power_class(v7) = v8 & ? [v7] : ? [v8] : sum_class(v7) = v8 & ? [v7] : ? [v8] : inductive(v7) = v8 & ? [v7] : ? [v8] : range_of(v7) = v8 & ? [v7] : ? [v8] : inverse(v7) = v8 & ? [v7] : ? [v8] : successor(v7) = v8 & ? [v7] : ? [v8] : flip(v7) = v8 & ? [v7] : ? [v8] : rotate(v7) = v8 & ? [v7] : ? [v8] : domain_of(v7) = v8 & ? [v7] : ? [v8] : complement(v7) = v8 & ? [v7] : ? [v8] : first(v7) = v8 & ? [v7] : ? [v8] : second(v7) = v8 & ? [v7] : ? [v8] : singleton(v7) = v8 & ? [v7] : (v7 = null_class | ? [v8] : (disjoint(v8, v7) = 0 & member(v8, v7) = 0 & member(v8, universal_class) = 0)))
% 36.55/10.54 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 36.55/10.54 | (1) ~ (all_0_2_2 = null_class) & ~ (all_0_3_3 = 0) & function(all_0_1_1) = 0 & inductive(all_0_0_0) = 0 & cross_product(all_0_6_6, universal_class) = all_0_5_5 & cross_product(universal_class, universal_class) = all_0_6_6 & singleton(all_0_4_4) = all_0_2_2 & subclass(successor_relation, all_0_6_6) = 0 & subclass(element_relation, all_0_6_6) = 0 & member(all_0_0_0, universal_class) = 0 & member(all_0_4_4, universal_class) = all_0_3_3 & ! [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] : (( ~ (v10 = 0) & ordered_pair(v8, v2) = v9 & ordered_pair(v1, v0) = v8 & member(v9, v3) = v10) | ( ~ (v8 = 0) & member(v5, all_0_5_5) = v8))) & ! [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] : (( ~ (v10 = 0) & ordered_pair(v8, v1) = v9 & ordered_pair(v2, v3) = v8 & member(v9, v0) = v10) | ( ~ (v8 = 0) & member(v5, all_0_5_5) = v8))) & ! [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] : ((v8 = 0 & v7 = 0 & member(v2, universal_class) = 0) | ( ~ (v10 = 0) & compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ~ (v10 = 0) & image(v1, v8) = v9 & image(v0, v7) = v8 & singleton(v2) = v7 & member(v3, v9) = v10) | ( ~ (v7 = 0) & member(v2, universal_class) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v1, v3) = v7) | ( ~ (v7 = 0) & member(v0, v2) = v7))) & ! [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] : ((v9 = 0 & compose(v1, v0) = v8 & ordered_pair(v2, v3) = v7 & member(v7, v8) = 0) | ( ~ (v7 = 0) & member(v2, universal_class) = v7))) & ! [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_5_5) = 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_5_5) = 0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ (member(v5, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_5_5) = 0) | ( ~ (v10 = 0) & flip(v3) = v9 & member(v8, v9) = v10)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v5, v0) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_5_5) = 0) | ( ~ (v10 = 0) & rotate(v0) = v9 & member(v8, v9) = v10)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8) = 0 & member(v2, universal_class) = 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] : ( ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ (member(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v6, v2) = v7 & ordered_pair(v0, v1) = v6 & ((v9 = 0 & flip(v3) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_5_5) = v8)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v5, v0) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v6, v3) = v7 & ordered_pair(v1, v2) = v6 & ((v9 = 0 & rotate(v0) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_5_5) = v8)))) & ! [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] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum_class(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) & ! [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] : ((v5 = 0 & domain_of(v0) = v4 & member(v1, v4) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_class(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & subclass(v0, v1) = v4) | ( ~ (v4 = 0) & member(v0, universal_class) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (domain_of(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = null_class & restrict(v0, v4, universal_class) = null_class & singleton(v1) = v4) | ( ~ (v4 = 0) & member(v1, universal_class) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ((v4 = 0 & member(v1, v0) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4))) & ! [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] : (v3 = 0 | ~ (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = 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] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ? [v4] : ? [v5] : ((v4 = 0 & ~ (v3 = null_class) & member(v1, universal_class) = 0) | ( ~ (v5 = 0) & domain_of(v0) = v4 & member(v1, v4) = v5))) & ! [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] : ( ~ (singleton(v1) = v2) | ~ (unordered_pair(v0, v2) = v3) | ? [v4] : ? [v5] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & unordered_pair(v5, v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0) & ! [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] : (v2 = 0 | ~ (member(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & complement(v0) = v3 & member(v1, v3) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3))) & ! [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 | ~ (ordered_pair(v2, v2) = v0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = 0) & member(v2, universal_class) = v3)) & ! [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] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = 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_6_6) = 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(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : ((v3 = 0 & member(v2, universal_class) = 0) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (domain_of(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = null_class) & restrict(v0, v3, universal_class) = v4 & singleton(v1) = v3 & member(v1, universal_class) = 0)) & ! [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] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v1 & v4 = 0 & v3 = 0 & successor(v0) = v1 & member(v1, universal_class) = 0 & member(v0, universal_class) = 0) | ( ~ (v3 = 0) & member(v2, successor_relation) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = v1 & v3 = v0 & first(v2) = v0 & second(v2) = v1) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & member(v1, universal_class) = 0 & member(v0, v1) = 0) | ( ~ (v3 = 0) & member(v2, element_relation) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ((v3 = 0 & member(v2, successor_relation) = 0) | ( ~ (v3 = v1) & successor(v0) = v3) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ((v3 = 0 & member(v2, element_relation) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & member(v0, universal_class) = 0) | ( ~ (v4 = 0) & power_class(v1) = v3 & member(v0, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v1, v0) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & ~ (v2 = 0) & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & complement(v0) = v3 & member(v1, v3) = v4))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v0, v1) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = v4) | ( ~ (v2 = 0) & subclass(v0, all_0_6_6) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (inductive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & image(successor_relation, v0) = v2 & subclass(v2, v0) = v3) | ( ~ (v2 = 0) & member(null_class, v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, v0) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, universal_class) = v1)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(all_0_0_0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & inductive(v0) = v2)) & ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, v0) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) & ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) & ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & subclass(v1, v0) = 0 & member(null_class, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ? [v2] : ((v2 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & subclass(v1, v0) = v2) | ( ~ (v2 = 0) & member(null_class, v0) = v2))) & ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1)) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & compose(v0, v1) = v3 & subclass(v3, identity_relation) = 0 & subclass(v0, all_0_6_6) = 0) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2)) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : ((v2 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & subclass(v2, identity_relation) = v3) | ( ~ (v2 = 0) & subclass(v0, all_0_6_6) = v2))) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_5_5) = 0) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_5_5) = 0) & ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (successor(v0) = v2 & union(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ! [v1] : ( ~ (subclass(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & power_class(v1) = v2 & member(v0, v2) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) & ! [v0] : ! [v1] : ( ~ (subclass(v0, all_0_6_6) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v1 = 0 & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = 0) | ( ~ (v2 = 0) & function(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (member(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & ordered_pair(v0, v1) = v2 & member(v2, element_relation) = 0) | ( ~ (v2 = 0) & member(v1, universal_class) = v2))) & ! [v0] : ! [v1] : ( ~ (member(null_class, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v1 = 0 & image(successor_relation, v0) = v2 & subclass(v2, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2))) & ! [v0] : (v0 = null_class | ~ (member(v0, universal_class) = 0) | ? [v1] : (apply(all_0_1_1, v0) = v1 & member(v1, v0) = 0)) & ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = 0 & subclass(v0, all_0_6_6) = 0)) & ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0) & ! [v0] : ( ~ (inductive(v0) = 0) | ? [v1] : (image(successor_relation, v0) = v1 & subclass(v1, v0) = 0 & member(null_class, v0) = 0)) & ! [v0] : ( ~ (subclass(v0, all_0_6_6) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v1 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3))) & ! [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] : ( ~ (member(null_class, v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & image(successor_relation, v0) = v1 & subclass(v1, v0) = v2))) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : restrict(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : compose(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : image(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : cross_product(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : subclass(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2 & ? [v0] : ? [v1] : function(v0) = v1 & ? [v0] : ? [v1] : power_class(v0) = v1 & ? [v0] : ? [v1] : sum_class(v0) = v1 & ? [v0] : ? [v1] : inductive(v0) = v1 & ? [v0] : ? [v1] : range_of(v0) = v1 & ? [v0] : ? [v1] : inverse(v0) = v1 & ? [v0] : ? [v1] : successor(v0) = v1 & ? [v0] : ? [v1] : flip(v0) = v1 & ? [v0] : ? [v1] : rotate(v0) = v1 & ? [v0] : ? [v1] : domain_of(v0) = v1 & ? [v0] : ? [v1] : complement(v0) = v1 & ? [v0] : ? [v1] : first(v0) = v1 & ? [v0] : ? [v1] : second(v0) = v1 & ? [v0] : ? [v1] : singleton(v0) = v1 & ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 36.55/10.57 |
% 36.55/10.57 | Applying alpha-rule on (1) yields:
% 36.55/10.57 | (2) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 36.55/10.57 | (3) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 36.55/10.57 | (4) ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0)
% 36.55/10.57 | (5) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & compose(v0, v1) = v3 & subclass(v3, identity_relation) = 0 & subclass(v0, all_0_6_6) = 0) | ( ~ (v2 = 0) & function(v0) = v2)))
% 36.55/10.57 | (6) ! [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] : (( ~ (v10 = 0) & ordered_pair(v8, v2) = v9 & ordered_pair(v1, v0) = v8 & member(v9, v3) = v10) | ( ~ (v8 = 0) & member(v5, all_0_5_5) = v8)))
% 36.55/10.57 | (7) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_5_5) = 0)
% 36.55/10.57 | (8) cross_product(all_0_6_6, universal_class) = all_0_5_5
% 36.55/10.57 | (9) ! [v0] : ( ~ (member(null_class, v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & image(successor_relation, v0) = v1 & subclass(v1, v0) = v2)))
% 36.55/10.57 | (10) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 36.55/10.57 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 36.55/10.57 | (12) cross_product(universal_class, universal_class) = all_0_6_6
% 36.55/10.57 | (13) ! [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))
% 36.55/10.57 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (member(v2, universal_class) = 0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3))
% 36.55/10.57 | (15) ? [v0] : ? [v1] : successor(v0) = v1
% 36.55/10.57 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (domain_of(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ? [v4] : ( ~ (v4 = null_class) & restrict(v0, v3, universal_class) = v4 & singleton(v1) = v3 & member(v1, universal_class) = 0))
% 36.55/10.57 | (17) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0))
% 36.55/10.57 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2))
% 36.55/10.57 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v3 = 0 | ~ (sum_class(v1) = v2) | ~ (member(v4, v1) = 0) | ~ (member(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 36.55/10.58 | (20) ? [v0] : ? [v1] : second(v0) = v1
% 36.55/10.58 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0))
% 36.55/10.58 | (22) ! [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))
% 36.55/10.58 | (23) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 36.55/10.58 | (24) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = v1 & v3 = v0 & first(v2) = v0 & second(v2) = v1) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3)))
% 36.55/10.58 | (25) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 36.55/10.58 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0))
% 36.55/10.58 | (27) ~ (all_0_2_2 = null_class)
% 36.55/10.58 | (28) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(all_0_0_0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & inductive(v0) = v2))
% 36.55/10.58 | (29) ? [v0] : ? [v1] : inductive(v0) = v1
% 36.55/10.58 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0))
% 36.55/10.58 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v5, v0) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v6, v3) = v7 & ordered_pair(v1, v2) = v6 & ((v9 = 0 & rotate(v0) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_5_5) = v8))))
% 36.55/10.58 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3))
% 36.55/10.58 | (33) ? [v0] : ? [v1] : ? [v2] : compose(v1, v0) = v2
% 36.55/10.58 | (34) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 36.55/10.58 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0)
% 36.55/10.58 | (36) member(all_0_0_0, universal_class) = 0
% 36.55/10.58 | (37) ! [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] : ((v9 = 0 & compose(v1, v0) = v8 & ordered_pair(v2, v3) = v7 & member(v7, v8) = 0) | ( ~ (v7 = 0) & member(v2, universal_class) = v7)))
% 36.55/10.58 | (38) ? [v0] : ? [v1] : function(v0) = v1
% 36.55/10.58 | (39) ~ (all_0_3_3 = 0)
% 36.55/10.58 | (40) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0))
% 36.55/10.58 | (41) ? [v0] : ? [v1] : sum_class(v0) = v1
% 36.55/10.58 | (42) ! [v0] : ( ~ (member(v0, identity_relation) = 0) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0))
% 36.55/10.58 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = v1 & v4 = 0 & v3 = 0 & successor(v0) = v1 & member(v1, universal_class) = 0 & member(v0, universal_class) = 0) | ( ~ (v3 = 0) & member(v2, successor_relation) = v3)))
% 36.55/10.58 | (44) ! [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] : (( ~ (v10 = 0) & ordered_pair(v8, v1) = v9 & ordered_pair(v2, v3) = v8 & member(v9, v0) = v10) | ( ~ (v8 = 0) & member(v5, all_0_5_5) = v8)))
% 36.55/10.58 | (45) ? [v0] : ? [v1] : flip(v0) = v1
% 36.55/10.58 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, universal_class) = v1))
% 36.55/10.58 | (47) ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2
% 36.55/10.58 | (48) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0))
% 36.55/10.58 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (singleton(v1) = v2) | ~ (unordered_pair(v0, v2) = v3) | ? [v4] : ? [v5] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & unordered_pair(v5, v3) = v4))
% 36.55/10.58 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 36.55/10.58 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & member(v1, v3) = v7) | ( ~ (v7 = 0) & member(v0, v2) = v7)))
% 36.55/10.58 | (52) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ? [v2] : ((v2 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & subclass(v1, v0) = v2) | ( ~ (v2 = 0) & member(null_class, v0) = v2)))
% 36.55/10.58 | (53) ! [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] : ((v8 = 0 & v7 = 0 & member(v2, universal_class) = 0) | ( ~ (v10 = 0) & compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10)))
% 36.55/10.58 | (54) ! [v0] : ! [v1] : ( ~ (subclass(v0, all_0_6_6) = v1) | ? [v2] : ? [v3] : ? [v4] : ((v4 = 0 & v1 = 0 & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = 0) | ( ~ (v2 = 0) & function(v0) = v2)))
% 36.55/10.59 | (55) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 36.55/10.59 | (56) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0))
% 36.55/10.59 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ((v3 = 0 & member(v2, element_relation) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, v1) = v3)))
% 36.55/10.59 | (58) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (member(v1, v0) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & complement(v0) = v3 & member(v1, v3) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3)))
% 36.55/10.59 | (59) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, v0) = v1))
% 36.55/10.59 | (60) ! [v0] : ! [v1] : ( ~ (subclass(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & power_class(v1) = v2 & member(v0, v2) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 36.55/10.59 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_6_6) = 0)
% 36.55/10.59 | (62) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 36.55/10.59 | (63) ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v0, v1) = v2))
% 36.55/10.59 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3))
% 36.55/10.59 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0))
% 36.55/10.59 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0))
% 36.55/10.59 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 36.55/10.59 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (function(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = v4) | ( ~ (v2 = 0) & subclass(v0, all_0_6_6) = v2)))
% 36.55/10.59 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & member(v0, universal_class) = 0) | ( ~ (v4 = 0) & power_class(v1) = v3 & member(v0, v3) = v4)))
% 36.55/10.59 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ? [v4] : ? [v5] : ((v4 = 0 & ~ (v3 = null_class) & member(v1, universal_class) = 0) | ( ~ (v5 = 0) & domain_of(v0) = v4 & member(v1, v4) = v5)))
% 36.55/10.59 | (71) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 36.55/10.59 | (72) ! [v0] : ~ (member(v0, null_class) = 0)
% 36.55/10.59 | (73) ? [v0] : ? [v1] : ? [v2] : ? [v3] : restrict(v2, v1, v0) = v3
% 36.55/10.59 | (74) member(all_0_4_4, universal_class) = all_0_3_3
% 36.55/10.59 | (75) ! [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_5_5) = 0))
% 36.55/10.59 | (76) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_5_5) = 0)
% 36.55/10.59 | (77) ? [v0] : ? [v1] : ? [v2] : image(v1, v0) = v2
% 36.55/10.59 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 36.55/10.59 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 36.55/10.59 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 36.55/10.59 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v1, v0) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & ~ (v2 = 0) & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & complement(v0) = v3 & member(v1, v3) = v4)))
% 36.55/10.59 | (82) ? [v0] : ? [v1] : power_class(v0) = v1
% 36.55/10.59 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (member(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4)))
% 36.55/10.59 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 36.55/10.59 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) = v5))
% 36.55/10.59 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v5, v0) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_5_5) = 0) | ( ~ (v10 = 0) & rotate(v0) = v9 & member(v8, v9) = v10))))
% 36.55/10.60 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5)))
% 36.55/10.60 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (power_class(v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : (( ~ (v4 = 0) & subclass(v0, v1) = v4) | ( ~ (v4 = 0) & member(v0, universal_class) = v4)))
% 36.55/10.60 | (89) ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 36.55/10.60 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0))
% 36.55/10.60 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (( ~ (v10 = 0) & image(v1, v8) = v9 & image(v0, v7) = v8 & singleton(v2) = v7 & member(v3, v9) = v10) | ( ~ (v7 = 0) & member(v2, universal_class) = v7)))
% 36.55/10.60 | (92) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 36.55/10.60 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 36.55/10.60 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : ((v3 = 0 & member(v2, universal_class) = 0) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3)))
% 36.55/10.60 | (95) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = 0 & subclass(v1, v0) = 0 & member(null_class, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2)))
% 36.55/10.60 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0)))
% 36.55/10.60 | (97) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 36.55/10.60 | (98) ? [v0] : ? [v1] : rotate(v0) = v1
% 36.55/10.60 | (99) ! [v0] : (v0 = null_class | ~ (member(v0, universal_class) = 0) | ? [v1] : (apply(all_0_1_1, v0) = v1 & member(v1, v0) = 0))
% 36.55/10.60 | (100) ? [v0] : ? [v1] : inverse(v0) = v1
% 36.55/10.60 | (101) ? [v0] : ? [v1] : singleton(v0) = v1
% 36.55/10.60 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0))
% 36.55/10.60 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 36.55/10.60 | (104) ? [v0] : ? [v1] : domain_of(v0) = v1
% 36.55/10.60 | (105) ? [v0] : ? [v1] : range_of(v0) = v1
% 36.55/10.60 | (106) ! [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))
% 36.55/10.60 | (107) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 36.55/10.60 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 36.55/10.60 | (109) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 36.55/10.60 | (110) subclass(successor_relation, all_0_6_6) = 0
% 36.55/10.60 | (111) ! [v0] : ( ~ (inductive(v0) = 0) | ? [v1] : (image(successor_relation, v0) = v1 & subclass(v1, v0) = 0 & member(null_class, v0) = 0))
% 36.55/10.60 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 36.55/10.60 | (113) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 36.55/10.60 | (114) ? [v0] : ? [v1] : ? [v2] : subclass(v1, v0) = v2
% 36.55/10.60 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0))
% 36.55/10.60 | (116) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2))
% 36.55/10.60 | (117) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0))
% 36.55/10.60 | (118) ? [v0] : ? [v1] : first(v0) = v1
% 36.55/10.60 | (119) function(all_0_1_1) = 0
% 36.55/10.60 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (domain_of(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = null_class & restrict(v0, v4, universal_class) = null_class & singleton(v1) = v4) | ( ~ (v4 = 0) & member(v1, universal_class) = v4)))
% 36.55/10.60 | (121) ! [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))
% 36.55/10.60 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = null_class | ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ? [v4] : ? [v5] : ((v5 = 0 & domain_of(v0) = v4 & member(v1, v4) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4)))
% 36.55/10.61 | (123) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0))
% 36.55/10.61 | (124) ! [v0] : ! [v1] : (v1 = 0 | ~ (inductive(v0) = v1) | ? [v2] : ? [v3] : (( ~ (v3 = 0) & image(successor_relation, v0) = v2 & subclass(v2, v0) = v3) | ( ~ (v2 = 0) & member(null_class, v0) = v2)))
% 36.55/10.61 | (125) inductive(all_0_0_0) = 0
% 36.55/10.61 | (126) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : ((v2 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & subclass(v2, identity_relation) = v3) | ( ~ (v2 = 0) & subclass(v0, all_0_6_6) = v2)))
% 36.55/10.61 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ((v3 = 0 & member(v2, successor_relation) = 0) | ( ~ (v3 = v1) & successor(v0) = v3) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3)))
% 36.55/10.61 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0))
% 36.55/10.61 | (129) ? [v0] : ? [v1] : complement(v0) = v1
% 36.55/10.61 | (130) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = 0 & subclass(v0, all_0_6_6) = 0))
% 36.55/10.61 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 36.55/10.61 | (132) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (successor(v0) = v2 & union(v0, v1) = v2))
% 36.55/10.61 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0))
% 36.55/10.61 | (134) ! [v0] : ( ~ (subclass(v0, all_0_6_6) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v1 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3)))
% 36.55/10.61 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ (member(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8) = 0 & member(v2, universal_class) = 0))
% 36.55/10.61 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 36.55/10.61 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 36.55/10.61 | (138) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3))
% 36.55/10.61 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 36.55/10.61 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ (member(v5, v3) = v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_5_5) = 0) | ( ~ (v10 = 0) & flip(v3) = v9 & member(v8, v9) = v10))))
% 36.55/10.61 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 36.55/10.61 | (142) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (ordered_pair(v2, v2) = v0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = 0) & member(v2, universal_class) = v3))
% 36.55/10.61 | (143) subclass(element_relation, all_0_6_6) = 0
% 36.55/10.61 | (144) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 36.55/10.61 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 36.55/10.61 | (146) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0))
% 36.55/10.61 | (147) ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 36.55/10.61 | (148) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2))
% 36.55/10.61 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ (member(v5, v3) = 0) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : (ordered_pair(v6, v2) = v7 & ordered_pair(v0, v1) = v6 & ((v9 = 0 & flip(v3) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_5_5) = v8))))
% 36.55/10.61 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ? [v4] : ((v4 = 0 & member(v1, v0) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4)))
% 36.55/10.61 | (151) ! [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_5_5) = 0))
% 36.55/10.62 | (152) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 36.55/10.62 | (153) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & member(v1, universal_class) = 0 & member(v0, v1) = 0) | ( ~ (v3 = 0) & member(v2, element_relation) = v3)))
% 36.55/10.62 | (154) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0)
% 36.55/10.62 | (155) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 36.55/10.62 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4))
% 36.55/10.62 | (157) ! [v0] : ! [v1] : ( ~ (member(null_class, v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v1 = 0 & image(successor_relation, v0) = v2 & subclass(v2, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2)))
% 36.55/10.62 | (158) ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2))
% 36.55/10.62 | (159) ? [v0] : ? [v1] : ? [v2] : cross_product(v1, v0) = v2
% 36.55/10.62 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 36.55/10.62 | (161) ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, v0) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 36.55/10.62 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 36.55/10.62 | (163) ! [v0] : ! [v1] : ( ~ (member(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & ordered_pair(v0, v1) = v2 & member(v2, element_relation) = 0) | ( ~ (v2 = 0) & member(v1, universal_class) = v2)))
% 36.55/10.62 | (164) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 36.55/10.62 | (165) singleton(all_0_4_4) = all_0_2_2
% 36.55/10.62 |
% 36.55/10.62 | Instantiating formula (3) with all_0_2_2, all_0_4_4 and discharging atoms singleton(all_0_4_4) = all_0_2_2, yields:
% 36.55/10.62 | (166) unordered_pair(all_0_4_4, all_0_4_4) = all_0_2_2
% 36.55/10.62 |
% 36.55/10.62 | Instantiating formula (81) with 0, all_0_0_0, universal_class and discharging atoms member(all_0_0_0, universal_class) = 0, yields:
% 36.55/10.62 | (167) ? [v0] : ? [v1] : ( ~ (v1 = 0) & complement(universal_class) = v0 & member(all_0_0_0, v0) = v1)
% 36.55/10.62 |
% 36.55/10.62 | Instantiating formula (58) with all_0_3_3, all_0_4_4, universal_class and discharging atoms member(all_0_4_4, universal_class) = all_0_3_3, yields:
% 36.55/10.62 | (168) all_0_3_3 = 0 | ? [v0] : ? [v1] : ((v1 = 0 & complement(universal_class) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.55/10.62 |
% 36.55/10.62 | Instantiating formula (81) with all_0_3_3, all_0_4_4, universal_class and discharging atoms member(all_0_4_4, universal_class) = all_0_3_3, yields:
% 36.55/10.62 | (169) ? [v0] : ? [v1] : ((v0 = 0 & ~ (all_0_3_3 = 0) & member(all_0_4_4, universal_class) = 0) | ( ~ (v1 = 0) & complement(universal_class) = v0 & member(all_0_4_4, v0) = v1))
% 36.55/10.62 |
% 36.55/10.62 | Instantiating (167) with all_75_0_98, all_75_1_99 yields:
% 36.55/10.62 | (170) ~ (all_75_0_98 = 0) & complement(universal_class) = all_75_1_99 & member(all_0_0_0, all_75_1_99) = all_75_0_98
% 36.97/10.62 |
% 36.97/10.62 | Applying alpha-rule on (170) yields:
% 36.97/10.62 | (171) ~ (all_75_0_98 = 0)
% 36.97/10.62 | (172) complement(universal_class) = all_75_1_99
% 36.97/10.62 | (173) member(all_0_0_0, all_75_1_99) = all_75_0_98
% 36.97/10.62 |
% 36.97/10.62 | Instantiating (169) with all_85_0_104, all_85_1_105 yields:
% 36.97/10.62 | (174) (all_85_1_105 = 0 & ~ (all_0_3_3 = 0) & member(all_0_4_4, universal_class) = 0) | ( ~ (all_85_0_104 = 0) & complement(universal_class) = all_85_1_105 & member(all_0_4_4, all_85_1_105) = all_85_0_104)
% 36.97/10.62 |
% 36.97/10.62 +-Applying beta-rule and splitting (174), into two cases.
% 36.97/10.62 |-Branch one:
% 36.97/10.62 | (175) all_85_1_105 = 0 & ~ (all_0_3_3 = 0) & member(all_0_4_4, universal_class) = 0
% 36.97/10.62 |
% 36.97/10.62 | Applying alpha-rule on (175) yields:
% 36.97/10.62 | (176) all_85_1_105 = 0
% 36.97/10.62 | (39) ~ (all_0_3_3 = 0)
% 36.97/10.62 | (178) member(all_0_4_4, universal_class) = 0
% 36.97/10.62 |
% 36.97/10.62 +-Applying beta-rule and splitting (168), into two cases.
% 36.97/10.62 |-Branch one:
% 36.97/10.62 | (179) all_0_3_3 = 0
% 36.97/10.62 |
% 36.97/10.62 | Equations (179) can reduce 39 to:
% 36.97/10.62 | (180) $false
% 36.97/10.62 |
% 36.97/10.63 |-The branch is then unsatisfiable
% 36.97/10.63 |-Branch two:
% 36.97/10.63 | (39) ~ (all_0_3_3 = 0)
% 36.97/10.63 | (182) ? [v0] : ? [v1] : ((v1 = 0 & complement(universal_class) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (136) with all_0_4_4, universal_class, 0, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_0_3_3, member(all_0_4_4, universal_class) = 0, yields:
% 36.97/10.63 | (179) all_0_3_3 = 0
% 36.97/10.63 |
% 36.97/10.63 | Equations (179) can reduce 39 to:
% 36.97/10.63 | (180) $false
% 36.97/10.63 |
% 36.97/10.63 |-The branch is then unsatisfiable
% 36.97/10.63 |-Branch two:
% 36.97/10.63 | (185) ~ (all_85_0_104 = 0) & complement(universal_class) = all_85_1_105 & member(all_0_4_4, all_85_1_105) = all_85_0_104
% 36.97/10.63 |
% 36.97/10.63 | Applying alpha-rule on (185) yields:
% 36.97/10.63 | (186) ~ (all_85_0_104 = 0)
% 36.97/10.63 | (187) complement(universal_class) = all_85_1_105
% 36.97/10.63 | (188) member(all_0_4_4, all_85_1_105) = all_85_0_104
% 36.97/10.63 |
% 36.97/10.63 +-Applying beta-rule and splitting (168), into two cases.
% 36.97/10.63 |-Branch one:
% 36.97/10.63 | (179) all_0_3_3 = 0
% 36.97/10.63 |
% 36.97/10.63 | Equations (179) can reduce 39 to:
% 36.97/10.63 | (180) $false
% 36.97/10.63 |
% 36.97/10.63 |-The branch is then unsatisfiable
% 36.97/10.63 |-Branch two:
% 36.97/10.63 | (39) ~ (all_0_3_3 = 0)
% 36.97/10.63 | (182) ? [v0] : ? [v1] : ((v1 = 0 & complement(universal_class) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.97/10.63 |
% 36.97/10.63 | Instantiating (182) with all_101_0_115, all_101_1_116 yields:
% 36.97/10.63 | (193) (all_101_0_115 = 0 & complement(universal_class) = all_101_1_116 & member(all_0_4_4, all_101_1_116) = 0) | ( ~ (all_101_1_116 = 0) & member(all_0_4_4, universal_class) = all_101_1_116)
% 36.97/10.63 |
% 36.97/10.63 +-Applying beta-rule and splitting (193), into two cases.
% 36.97/10.63 |-Branch one:
% 36.97/10.63 | (194) all_101_0_115 = 0 & complement(universal_class) = all_101_1_116 & member(all_0_4_4, all_101_1_116) = 0
% 36.97/10.63 |
% 36.97/10.63 | Applying alpha-rule on (194) yields:
% 36.97/10.63 | (195) all_101_0_115 = 0
% 36.97/10.63 | (196) complement(universal_class) = all_101_1_116
% 36.97/10.63 | (197) member(all_0_4_4, all_101_1_116) = 0
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (62) with universal_class, all_85_1_105, all_101_1_116 and discharging atoms complement(universal_class) = all_101_1_116, complement(universal_class) = all_85_1_105, yields:
% 36.97/10.63 | (198) all_101_1_116 = all_85_1_105
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (62) with universal_class, all_75_1_99, all_101_1_116 and discharging atoms complement(universal_class) = all_101_1_116, complement(universal_class) = all_75_1_99, yields:
% 36.97/10.63 | (199) all_101_1_116 = all_75_1_99
% 36.97/10.63 |
% 36.97/10.63 | Combining equations (199,198) yields a new equation:
% 36.97/10.63 | (200) all_85_1_105 = all_75_1_99
% 36.97/10.63 |
% 36.97/10.63 | Combining equations (200,198) yields a new equation:
% 36.97/10.63 | (199) all_101_1_116 = all_75_1_99
% 36.97/10.63 |
% 36.97/10.63 | From (199) and (197) follows:
% 36.97/10.63 | (202) member(all_0_4_4, all_75_1_99) = 0
% 36.97/10.63 |
% 36.97/10.63 | From (200) and (188) follows:
% 36.97/10.63 | (203) member(all_0_4_4, all_75_1_99) = all_85_0_104
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (136) with all_0_4_4, all_75_1_99, 0, all_85_0_104 and discharging atoms member(all_0_4_4, all_75_1_99) = all_85_0_104, member(all_0_4_4, all_75_1_99) = 0, yields:
% 36.97/10.63 | (204) all_85_0_104 = 0
% 36.97/10.63 |
% 36.97/10.63 | Equations (204) can reduce 186 to:
% 36.97/10.63 | (180) $false
% 36.97/10.63 |
% 36.97/10.63 |-The branch is then unsatisfiable
% 36.97/10.63 |-Branch two:
% 36.97/10.63 | (206) ~ (all_101_1_116 = 0) & member(all_0_4_4, universal_class) = all_101_1_116
% 36.97/10.63 |
% 36.97/10.63 | Applying alpha-rule on (206) yields:
% 36.97/10.63 | (207) ~ (all_101_1_116 = 0)
% 36.97/10.63 | (208) member(all_0_4_4, universal_class) = all_101_1_116
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (62) with universal_class, all_75_1_99, all_85_1_105 and discharging atoms complement(universal_class) = all_85_1_105, complement(universal_class) = all_75_1_99, yields:
% 36.97/10.63 | (200) all_85_1_105 = all_75_1_99
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (136) with all_0_4_4, universal_class, all_101_1_116, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_101_1_116, member(all_0_4_4, universal_class) = all_0_3_3, yields:
% 36.97/10.63 | (210) all_101_1_116 = all_0_3_3
% 36.97/10.63 |
% 36.97/10.63 | Equations (210) can reduce 207 to:
% 36.97/10.63 | (39) ~ (all_0_3_3 = 0)
% 36.97/10.63 |
% 36.97/10.63 | From (200) and (188) follows:
% 36.97/10.63 | (203) member(all_0_4_4, all_75_1_99) = all_85_0_104
% 36.97/10.63 |
% 36.97/10.63 | From (210) and (208) follows:
% 36.97/10.63 | (74) member(all_0_4_4, universal_class) = all_0_3_3
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (154) with all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unordered_pair(all_0_4_4, all_0_4_4) = all_0_2_2, yields:
% 36.97/10.63 | (214) member(all_0_2_2, universal_class) = 0
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (58) with all_75_0_98, all_0_0_0, all_75_1_99 and discharging atoms member(all_0_0_0, all_75_1_99) = all_75_0_98, yields:
% 36.97/10.63 | (215) all_75_0_98 = 0 | ? [v0] : ? [v1] : ((v1 = 0 & complement(all_75_1_99) = v0 & member(all_0_0_0, v0) = 0) | ( ~ (v0 = 0) & member(all_0_0_0, universal_class) = v0))
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (58) with all_85_0_104, all_0_4_4, all_75_1_99 and discharging atoms member(all_0_4_4, all_75_1_99) = all_85_0_104, yields:
% 36.97/10.63 | (216) all_85_0_104 = 0 | ? [v0] : ? [v1] : ((v1 = 0 & complement(all_75_1_99) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.97/10.63 |
% 36.97/10.63 | Instantiating formula (81) with all_85_0_104, all_0_4_4, all_75_1_99 and discharging atoms member(all_0_4_4, all_75_1_99) = all_85_0_104, yields:
% 36.97/10.63 | (217) ? [v0] : ? [v1] : ((v0 = 0 & ~ (all_85_0_104 = 0) & member(all_0_4_4, universal_class) = 0) | ( ~ (v1 = 0) & complement(all_75_1_99) = v0 & member(all_0_4_4, v0) = v1))
% 36.97/10.63 |
% 36.97/10.63 | Instantiating (217) with all_134_0_140, all_134_1_141 yields:
% 36.97/10.63 | (218) (all_134_1_141 = 0 & ~ (all_85_0_104 = 0) & member(all_0_4_4, universal_class) = 0) | ( ~ (all_134_0_140 = 0) & complement(all_75_1_99) = all_134_1_141 & member(all_0_4_4, all_134_1_141) = all_134_0_140)
% 36.97/10.63 |
% 36.97/10.63 +-Applying beta-rule and splitting (218), into two cases.
% 36.97/10.63 |-Branch one:
% 36.97/10.63 | (219) all_134_1_141 = 0 & ~ (all_85_0_104 = 0) & member(all_0_4_4, universal_class) = 0
% 36.97/10.63 |
% 36.97/10.63 | Applying alpha-rule on (219) yields:
% 36.97/10.63 | (220) all_134_1_141 = 0
% 36.97/10.63 | (186) ~ (all_85_0_104 = 0)
% 36.97/10.63 | (178) member(all_0_4_4, universal_class) = 0
% 36.97/10.63 |
% 36.97/10.64 | Instantiating formula (136) with all_0_4_4, universal_class, 0, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_0_3_3, member(all_0_4_4, universal_class) = 0, yields:
% 36.97/10.64 | (179) all_0_3_3 = 0
% 36.97/10.64 |
% 36.97/10.64 | Equations (179) can reduce 39 to:
% 36.97/10.64 | (180) $false
% 36.97/10.64 |
% 36.97/10.64 |-The branch is then unsatisfiable
% 36.97/10.64 |-Branch two:
% 36.97/10.64 | (225) ~ (all_134_0_140 = 0) & complement(all_75_1_99) = all_134_1_141 & member(all_0_4_4, all_134_1_141) = all_134_0_140
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (225) yields:
% 36.97/10.64 | (226) ~ (all_134_0_140 = 0)
% 36.97/10.64 | (227) complement(all_75_1_99) = all_134_1_141
% 36.97/10.64 | (228) member(all_0_4_4, all_134_1_141) = all_134_0_140
% 36.97/10.64 |
% 36.97/10.64 +-Applying beta-rule and splitting (215), into two cases.
% 36.97/10.64 |-Branch one:
% 36.97/10.64 | (229) all_75_0_98 = 0
% 36.97/10.64 |
% 36.97/10.64 | Equations (229) can reduce 171 to:
% 36.97/10.64 | (180) $false
% 36.97/10.64 |
% 36.97/10.64 |-The branch is then unsatisfiable
% 36.97/10.64 |-Branch two:
% 36.97/10.64 | (171) ~ (all_75_0_98 = 0)
% 36.97/10.64 | (232) ? [v0] : ? [v1] : ((v1 = 0 & complement(all_75_1_99) = v0 & member(all_0_0_0, v0) = 0) | ( ~ (v0 = 0) & member(all_0_0_0, universal_class) = v0))
% 36.97/10.64 |
% 36.97/10.64 | Instantiating (232) with all_186_0_200, all_186_1_201 yields:
% 36.97/10.64 | (233) (all_186_0_200 = 0 & complement(all_75_1_99) = all_186_1_201 & member(all_0_0_0, all_186_1_201) = 0) | ( ~ (all_186_1_201 = 0) & member(all_0_0_0, universal_class) = all_186_1_201)
% 36.97/10.64 |
% 36.97/10.64 +-Applying beta-rule and splitting (216), into two cases.
% 36.97/10.64 |-Branch one:
% 36.97/10.64 | (204) all_85_0_104 = 0
% 36.97/10.64 |
% 36.97/10.64 | Equations (204) can reduce 186 to:
% 36.97/10.64 | (180) $false
% 36.97/10.64 |
% 36.97/10.64 |-The branch is then unsatisfiable
% 36.97/10.64 |-Branch two:
% 36.97/10.64 | (186) ~ (all_85_0_104 = 0)
% 36.97/10.64 | (237) ? [v0] : ? [v1] : ((v1 = 0 & complement(all_75_1_99) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.97/10.64 |
% 36.97/10.64 | Instantiating (237) with all_190_0_202, all_190_1_203 yields:
% 36.97/10.64 | (238) (all_190_0_202 = 0 & complement(all_75_1_99) = all_190_1_203 & member(all_0_4_4, all_190_1_203) = 0) | ( ~ (all_190_1_203 = 0) & member(all_0_4_4, universal_class) = all_190_1_203)
% 36.97/10.64 |
% 36.97/10.64 +-Applying beta-rule and splitting (233), into two cases.
% 36.97/10.64 |-Branch one:
% 36.97/10.64 | (239) all_186_0_200 = 0 & complement(all_75_1_99) = all_186_1_201 & member(all_0_0_0, all_186_1_201) = 0
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (239) yields:
% 36.97/10.64 | (240) all_186_0_200 = 0
% 36.97/10.64 | (241) complement(all_75_1_99) = all_186_1_201
% 36.97/10.64 | (242) member(all_0_0_0, all_186_1_201) = 0
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (62) with all_75_1_99, all_134_1_141, all_186_1_201 and discharging atoms complement(all_75_1_99) = all_186_1_201, complement(all_75_1_99) = all_134_1_141, yields:
% 36.97/10.64 | (243) all_186_1_201 = all_134_1_141
% 36.97/10.64 |
% 36.97/10.64 | From (243) and (241) follows:
% 36.97/10.64 | (227) complement(all_75_1_99) = all_134_1_141
% 36.97/10.64 |
% 36.97/10.64 | From (243) and (242) follows:
% 36.97/10.64 | (245) member(all_0_0_0, all_134_1_141) = 0
% 36.97/10.64 |
% 36.97/10.64 +-Applying beta-rule and splitting (238), into two cases.
% 36.97/10.64 |-Branch one:
% 36.97/10.64 | (246) all_190_0_202 = 0 & complement(all_75_1_99) = all_190_1_203 & member(all_0_4_4, all_190_1_203) = 0
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (246) yields:
% 36.97/10.64 | (247) all_190_0_202 = 0
% 36.97/10.64 | (248) complement(all_75_1_99) = all_190_1_203
% 36.97/10.64 | (249) member(all_0_4_4, all_190_1_203) = 0
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (62) with all_75_1_99, all_190_1_203, all_134_1_141 and discharging atoms complement(all_75_1_99) = all_190_1_203, complement(all_75_1_99) = all_134_1_141, yields:
% 36.97/10.64 | (250) all_190_1_203 = all_134_1_141
% 36.97/10.64 |
% 36.97/10.64 | From (250) and (249) follows:
% 36.97/10.64 | (251) member(all_0_4_4, all_134_1_141) = 0
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (136) with all_0_4_4, all_134_1_141, 0, all_134_0_140 and discharging atoms member(all_0_4_4, all_134_1_141) = all_134_0_140, member(all_0_4_4, all_134_1_141) = 0, yields:
% 36.97/10.64 | (252) all_134_0_140 = 0
% 36.97/10.64 |
% 36.97/10.64 | Equations (252) can reduce 226 to:
% 36.97/10.64 | (180) $false
% 36.97/10.64 |
% 36.97/10.64 |-The branch is then unsatisfiable
% 36.97/10.64 |-Branch two:
% 36.97/10.64 | (254) ~ (all_190_1_203 = 0) & member(all_0_4_4, universal_class) = all_190_1_203
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (254) yields:
% 36.97/10.64 | (255) ~ (all_190_1_203 = 0)
% 36.97/10.64 | (256) member(all_0_4_4, universal_class) = all_190_1_203
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (136) with all_0_4_4, universal_class, all_190_1_203, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_190_1_203, member(all_0_4_4, universal_class) = all_0_3_3, yields:
% 36.97/10.64 | (257) all_190_1_203 = all_0_3_3
% 36.97/10.64 |
% 36.97/10.64 | Equations (257) can reduce 255 to:
% 36.97/10.64 | (39) ~ (all_0_3_3 = 0)
% 36.97/10.64 |
% 36.97/10.64 | From (257) and (256) follows:
% 36.97/10.64 | (74) member(all_0_4_4, universal_class) = all_0_3_3
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (81) with 0, all_0_0_0, all_134_1_141 and discharging atoms member(all_0_0_0, all_134_1_141) = 0, yields:
% 36.97/10.64 | (260) ? [v0] : ? [v1] : ( ~ (v1 = 0) & complement(all_134_1_141) = v0 & member(all_0_0_0, v0) = v1)
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (99) with all_0_2_2 and discharging atoms member(all_0_2_2, universal_class) = 0, yields:
% 36.97/10.64 | (261) all_0_2_2 = null_class | ? [v0] : (apply(all_0_1_1, all_0_2_2) = v0 & member(v0, all_0_2_2) = 0)
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (58) with all_134_0_140, all_0_4_4, all_134_1_141 and discharging atoms member(all_0_4_4, all_134_1_141) = all_134_0_140, yields:
% 36.97/10.64 | (262) all_134_0_140 = 0 | ? [v0] : ? [v1] : ((v1 = 0 & complement(all_134_1_141) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (81) with all_134_0_140, all_0_4_4, all_134_1_141 and discharging atoms member(all_0_4_4, all_134_1_141) = all_134_0_140, yields:
% 36.97/10.64 | (263) ? [v0] : ? [v1] : ((v0 = 0 & ~ (all_134_0_140 = 0) & member(all_0_4_4, universal_class) = 0) | ( ~ (v1 = 0) & complement(all_134_1_141) = v0 & member(all_0_4_4, v0) = v1))
% 36.97/10.64 |
% 36.97/10.64 | Instantiating (260) with all_266_0_230, all_266_1_231 yields:
% 36.97/10.64 | (264) ~ (all_266_0_230 = 0) & complement(all_134_1_141) = all_266_1_231 & member(all_0_0_0, all_266_1_231) = all_266_0_230
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (264) yields:
% 36.97/10.64 | (265) ~ (all_266_0_230 = 0)
% 36.97/10.64 | (266) complement(all_134_1_141) = all_266_1_231
% 36.97/10.64 | (267) member(all_0_0_0, all_266_1_231) = all_266_0_230
% 36.97/10.64 |
% 36.97/10.64 | Instantiating (263) with all_293_0_278, all_293_1_279 yields:
% 36.97/10.64 | (268) (all_293_1_279 = 0 & ~ (all_134_0_140 = 0) & member(all_0_4_4, universal_class) = 0) | ( ~ (all_293_0_278 = 0) & complement(all_134_1_141) = all_293_1_279 & member(all_0_4_4, all_293_1_279) = all_293_0_278)
% 36.97/10.64 |
% 36.97/10.64 +-Applying beta-rule and splitting (261), into two cases.
% 36.97/10.64 |-Branch one:
% 36.97/10.64 | (269) all_0_2_2 = null_class
% 36.97/10.64 |
% 36.97/10.64 | Equations (269) can reduce 27 to:
% 36.97/10.64 | (180) $false
% 36.97/10.64 |
% 36.97/10.64 |-The branch is then unsatisfiable
% 36.97/10.64 |-Branch two:
% 36.97/10.64 | (27) ~ (all_0_2_2 = null_class)
% 36.97/10.64 | (272) ? [v0] : (apply(all_0_1_1, all_0_2_2) = v0 & member(v0, all_0_2_2) = 0)
% 36.97/10.64 |
% 36.97/10.64 | Instantiating (272) with all_372_0_384 yields:
% 36.97/10.64 | (273) apply(all_0_1_1, all_0_2_2) = all_372_0_384 & member(all_372_0_384, all_0_2_2) = 0
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (273) yields:
% 36.97/10.64 | (274) apply(all_0_1_1, all_0_2_2) = all_372_0_384
% 36.97/10.64 | (275) member(all_372_0_384, all_0_2_2) = 0
% 36.97/10.64 |
% 36.97/10.64 +-Applying beta-rule and splitting (268), into two cases.
% 36.97/10.64 |-Branch one:
% 36.97/10.64 | (276) all_293_1_279 = 0 & ~ (all_134_0_140 = 0) & member(all_0_4_4, universal_class) = 0
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (276) yields:
% 36.97/10.64 | (277) all_293_1_279 = 0
% 36.97/10.64 | (226) ~ (all_134_0_140 = 0)
% 36.97/10.64 | (178) member(all_0_4_4, universal_class) = 0
% 36.97/10.64 |
% 36.97/10.64 | Instantiating formula (136) with all_0_4_4, universal_class, 0, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_0_3_3, member(all_0_4_4, universal_class) = 0, yields:
% 36.97/10.64 | (179) all_0_3_3 = 0
% 36.97/10.64 |
% 36.97/10.64 | Equations (179) can reduce 39 to:
% 36.97/10.64 | (180) $false
% 36.97/10.64 |
% 36.97/10.64 |-The branch is then unsatisfiable
% 36.97/10.64 |-Branch two:
% 36.97/10.64 | (282) ~ (all_293_0_278 = 0) & complement(all_134_1_141) = all_293_1_279 & member(all_0_4_4, all_293_1_279) = all_293_0_278
% 36.97/10.64 |
% 36.97/10.64 | Applying alpha-rule on (282) yields:
% 36.97/10.64 | (283) ~ (all_293_0_278 = 0)
% 36.97/10.64 | (284) complement(all_134_1_141) = all_293_1_279
% 36.97/10.64 | (285) member(all_0_4_4, all_293_1_279) = all_293_0_278
% 36.97/10.65 |
% 36.97/10.65 +-Applying beta-rule and splitting (262), into two cases.
% 36.97/10.65 |-Branch one:
% 36.97/10.65 | (252) all_134_0_140 = 0
% 36.97/10.65 |
% 36.97/10.65 | Equations (252) can reduce 226 to:
% 36.97/10.65 | (180) $false
% 36.97/10.65 |
% 36.97/10.65 |-The branch is then unsatisfiable
% 36.97/10.65 |-Branch two:
% 36.97/10.65 | (226) ~ (all_134_0_140 = 0)
% 36.97/10.65 | (289) ? [v0] : ? [v1] : ((v1 = 0 & complement(all_134_1_141) = v0 & member(all_0_4_4, v0) = 0) | ( ~ (v0 = 0) & member(all_0_4_4, universal_class) = v0))
% 36.97/10.65 |
% 36.97/10.65 | Instantiating (289) with all_446_0_400, all_446_1_401 yields:
% 36.97/10.65 | (290) (all_446_0_400 = 0 & complement(all_134_1_141) = all_446_1_401 & member(all_0_4_4, all_446_1_401) = 0) | ( ~ (all_446_1_401 = 0) & member(all_0_4_4, universal_class) = all_446_1_401)
% 36.97/10.65 |
% 36.97/10.65 +-Applying beta-rule and splitting (290), into two cases.
% 36.97/10.65 |-Branch one:
% 36.97/10.65 | (291) all_446_0_400 = 0 & complement(all_134_1_141) = all_446_1_401 & member(all_0_4_4, all_446_1_401) = 0
% 36.97/10.65 |
% 36.97/10.65 | Applying alpha-rule on (291) yields:
% 36.97/10.65 | (292) all_446_0_400 = 0
% 36.97/10.65 | (293) complement(all_134_1_141) = all_446_1_401
% 36.97/10.65 | (294) member(all_0_4_4, all_446_1_401) = 0
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (62) with all_134_1_141, all_293_1_279, all_446_1_401 and discharging atoms complement(all_134_1_141) = all_446_1_401, complement(all_134_1_141) = all_293_1_279, yields:
% 36.97/10.65 | (295) all_446_1_401 = all_293_1_279
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (62) with all_134_1_141, all_266_1_231, all_446_1_401 and discharging atoms complement(all_134_1_141) = all_446_1_401, complement(all_134_1_141) = all_266_1_231, yields:
% 36.97/10.65 | (296) all_446_1_401 = all_266_1_231
% 36.97/10.65 |
% 36.97/10.65 | Combining equations (296,295) yields a new equation:
% 36.97/10.65 | (297) all_293_1_279 = all_266_1_231
% 36.97/10.65 |
% 36.97/10.65 | Combining equations (297,295) yields a new equation:
% 36.97/10.65 | (296) all_446_1_401 = all_266_1_231
% 36.97/10.65 |
% 36.97/10.65 | From (296) and (294) follows:
% 36.97/10.65 | (299) member(all_0_4_4, all_266_1_231) = 0
% 36.97/10.65 |
% 36.97/10.65 | From (297) and (285) follows:
% 36.97/10.65 | (300) member(all_0_4_4, all_266_1_231) = all_293_0_278
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (136) with all_0_4_4, all_266_1_231, 0, all_293_0_278 and discharging atoms member(all_0_4_4, all_266_1_231) = all_293_0_278, member(all_0_4_4, all_266_1_231) = 0, yields:
% 36.97/10.65 | (301) all_293_0_278 = 0
% 36.97/10.65 |
% 36.97/10.65 | Equations (301) can reduce 283 to:
% 36.97/10.65 | (180) $false
% 36.97/10.65 |
% 36.97/10.65 |-The branch is then unsatisfiable
% 36.97/10.65 |-Branch two:
% 36.97/10.65 | (303) ~ (all_446_1_401 = 0) & member(all_0_4_4, universal_class) = all_446_1_401
% 36.97/10.65 |
% 36.97/10.65 | Applying alpha-rule on (303) yields:
% 36.97/10.65 | (304) ~ (all_446_1_401 = 0)
% 36.97/10.65 | (305) member(all_0_4_4, universal_class) = all_446_1_401
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (162) with all_0_2_2, all_0_4_4, all_0_4_4, all_372_0_384 and discharging atoms unordered_pair(all_0_4_4, all_0_4_4) = all_0_2_2, member(all_372_0_384, all_0_2_2) = 0, yields:
% 36.97/10.65 | (306) all_372_0_384 = all_0_4_4
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (136) with all_0_4_4, universal_class, all_446_1_401, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_446_1_401, member(all_0_4_4, universal_class) = all_0_3_3, yields:
% 36.97/10.65 | (307) all_446_1_401 = all_0_3_3
% 36.97/10.65 |
% 36.97/10.65 | Equations (307) can reduce 304 to:
% 36.97/10.65 | (39) ~ (all_0_3_3 = 0)
% 36.97/10.65 |
% 36.97/10.65 | From (306) and (275) follows:
% 36.97/10.65 | (309) member(all_0_4_4, all_0_2_2) = 0
% 36.97/10.65 |
% 36.97/10.65 | From (307) and (305) follows:
% 36.97/10.65 | (74) member(all_0_4_4, universal_class) = all_0_3_3
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (35) with all_0_2_2, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms unordered_pair(all_0_4_4, all_0_4_4) = all_0_2_2, member(all_0_4_4, all_0_2_2) = 0, yields:
% 36.97/10.65 | (178) member(all_0_4_4, universal_class) = 0
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (136) with all_0_4_4, universal_class, 0, all_0_3_3 and discharging atoms member(all_0_4_4, universal_class) = all_0_3_3, member(all_0_4_4, universal_class) = 0, yields:
% 36.97/10.65 | (179) all_0_3_3 = 0
% 36.97/10.65 |
% 36.97/10.65 | Equations (179) can reduce 39 to:
% 36.97/10.65 | (180) $false
% 36.97/10.65 |
% 36.97/10.65 |-The branch is then unsatisfiable
% 36.97/10.65 |-Branch two:
% 36.97/10.65 | (314) ~ (all_186_1_201 = 0) & member(all_0_0_0, universal_class) = all_186_1_201
% 36.97/10.65 |
% 36.97/10.65 | Applying alpha-rule on (314) yields:
% 36.97/10.65 | (315) ~ (all_186_1_201 = 0)
% 36.97/10.65 | (316) member(all_0_0_0, universal_class) = all_186_1_201
% 36.97/10.65 |
% 36.97/10.65 | Instantiating formula (136) with all_0_0_0, universal_class, all_186_1_201, 0 and discharging atoms member(all_0_0_0, universal_class) = all_186_1_201, member(all_0_0_0, universal_class) = 0, yields:
% 36.97/10.65 | (317) all_186_1_201 = 0
% 36.97/10.65 |
% 36.97/10.65 | Equations (317) can reduce 315 to:
% 36.97/10.65 | (180) $false
% 36.97/10.65 |
% 36.97/10.65 |-The branch is then unsatisfiable
% 36.97/10.65 % SZS output end Proof for theBenchmark
% 36.97/10.65
% 36.97/10.65 10026ms
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