TSTP Solution File: SET095+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET095+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n022.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 00:17:24 EDT 2022
% Result : Theorem 23.14s 6.09s
% Output : Proof 25.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET095+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n022.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 10 13:18:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.20/0.58 ____ _
% 0.20/0.58 ___ / __ \_____(_)___ ________ __________
% 0.20/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.20/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.20/0.58
% 0.20/0.58 A Theorem Prover for First-Order Logic
% 0.20/0.58 (ePrincess v.1.0)
% 0.20/0.58
% 0.20/0.58 (c) Philipp Rümmer, 2009-2015
% 0.20/0.58 (c) Peter Backeman, 2014-2015
% 0.20/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.58 Bug reports to peter@backeman.se
% 0.20/0.59
% 0.20/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59
% 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.78/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/0.95 Prover 0: Preprocessing ...
% 3.25/1.34 Prover 0: Warning: ignoring some quantifiers
% 3.25/1.37 Prover 0: Constructing countermodel ...
% 9.11/2.68 Prover 0: gave up
% 9.11/2.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 9.32/2.73 Prover 1: Preprocessing ...
% 9.78/2.86 Prover 1: Warning: ignoring some quantifiers
% 9.78/2.87 Prover 1: Constructing countermodel ...
% 21.44/5.74 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 21.87/5.81 Prover 2: Preprocessing ...
% 22.70/6.01 Prover 2: Warning: ignoring some quantifiers
% 22.70/6.01 Prover 2: Constructing countermodel ...
% 23.14/6.09 Prover 2: proved (341ms)
% 23.14/6.09 Prover 1: stopped
% 23.14/6.09
% 23.14/6.09 No countermodel exists, formula is valid
% 23.14/6.09 % SZS status Theorem for theBenchmark
% 23.14/6.09
% 23.14/6.09 Generating proof ... Warning: ignoring some quantifiers
% 24.21/6.35 found it (size 14)
% 24.21/6.35
% 24.21/6.35 % SZS output start Proof for theBenchmark
% 24.21/6.35 Assumed formulas after preprocessing and simplification:
% 24.21/6.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v5 = 0) & function(v6) = 0 & inductive(v7) = 0 & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & singleton(v2) = v4 & subclass(v4, v3) = v5 & subclass(successor_relation, v0) = 0 & subclass(element_relation, v0) = 0 & member(v7, universal_class) = 0 & member(v2, v3) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (flip(v11) = v14) | ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (member(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (( ~ (v18 = 0) & ordered_pair(v16, v10) = v17 & ordered_pair(v9, v8) = v16 & member(v17, v11) = v18) | ( ~ (v16 = 0) & member(v13, v1) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (rotate(v8) = v14) | ~ (ordered_pair(v12, v11) = v13) | ~ (ordered_pair(v9, v10) = v12) | ~ (member(v13, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : (( ~ (v18 = 0) & ordered_pair(v16, v9) = v17 & ordered_pair(v10, v11) = v16 & member(v17, v8) = v18) | ( ~ (v16 = 0) & member(v13, v1) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image(v9, v13) = v14) | ~ (image(v8, v12) = v13) | ~ (singleton(v10) = v12) | ~ (member(v11, v14) = v15) | ? [v16] : ? [v17] : ? [v18] : ((v16 = 0 & v15 = 0 & member(v10, universal_class) = 0) | ( ~ (v18 = 0) & compose(v9, v8) = v17 & ordered_pair(v10, v11) = v16 & member(v16, v17) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (compose(v9, v8) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ (member(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (( ~ (v18 = 0) & image(v9, v16) = v17 & image(v8, v15) = v16 & singleton(v10) = v15 & member(v11, v17) = v18) | ( ~ (v15 = 0) & member(v10, universal_class) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (cross_product(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (member(v12, v13) = v14) | ? [v15] : (( ~ (v15 = 0) & member(v9, v11) = v15) | ( ~ (v15 = 0) & member(v8, v10) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (image(v9, v13) = v14) | ~ (image(v8, v12) = v13) | ~ (singleton(v10) = v12) | ~ (member(v11, v14) = 0) | ? [v15] : ? [v16] : ? [v17] : ((v17 = 0 & compose(v9, v8) = v16 & ordered_pair(v10, v11) = v15 & member(v15, v16) = 0) | ( ~ (v15 = 0) & member(v10, universal_class) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (flip(v11) = v14) | ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (member(v13, v14) = 0) | ? [v15] : ? [v16] : (ordered_pair(v15, v10) = v16 & ordered_pair(v9, v8) = v15 & member(v16, v11) = 0 & member(v13, v1) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (rotate(v8) = v14) | ~ (ordered_pair(v12, v11) = v13) | ~ (ordered_pair(v9, v10) = v12) | ~ (member(v13, v14) = 0) | ? [v15] : ? [v16] : (ordered_pair(v15, v9) = v16 & ordered_pair(v10, v11) = v15 & member(v16, v8) = 0 & member(v13, v1) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v9, v8) = v12) | ~ (member(v13, v11) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v15, v10) = v16 & ordered_pair(v8, v9) = v15 & ((v17 = 0 & v14 = 0 & member(v16, v1) = 0) | ( ~ (v18 = 0) & flip(v11) = v17 & member(v16, v17) = v18)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (ordered_pair(v12, v9) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ (member(v13, v8) = v14) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (ordered_pair(v15, v11) = v16 & ordered_pair(v9, v10) = v15 & ((v17 = 0 & v14 = 0 & member(v16, v1) = 0) | ( ~ (v18 = 0) & rotate(v8) = v17 & member(v16, v17) = v18)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose(v9, v8) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ (member(v12, v13) = 0) | ? [v14] : ? [v15] : ? [v16] : (image(v9, v15) = v16 & image(v8, v14) = v15 & singleton(v10) = v14 & member(v11, v16) = 0 & member(v10, universal_class) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cross_product(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ (member(v12, v13) = 0) | (member(v9, v11) = 0 & member(v8, v10) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v9, v8) = v12) | ~ (member(v13, v11) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v14, v10) = v15 & ordered_pair(v8, v9) = v14 & ((v17 = 0 & flip(v11) = v16 & member(v15, v16) = 0) | ( ~ (v16 = 0) & member(v15, v1) = v16)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ordered_pair(v12, v9) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ (member(v13, v8) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (ordered_pair(v14, v11) = v15 & ordered_pair(v9, v10) = v14 & ((v17 = 0 & rotate(v8) = v16 & member(v15, v16) = 0) | ( ~ (v16 = 0) & member(v15, v1) = v16)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (union(v8, v9) = v11) | ~ (member(v10, v11) = v12) | ? [v13] : ? [v14] : ( ~ (v14 = 0) & ~ (v13 = 0) & member(v10, v9) = v14 & member(v10, v8) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (intersection(v8, v9) = v11) | ~ (member(v10, v11) = v12) | ? [v13] : (( ~ (v13 = 0) & member(v10, v9) = v13) | ( ~ (v13 = 0) & member(v10, v8) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum_class(v9) = v10) | ~ (member(v12, v9) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (sum_class(v9) = v10) | ~ (member(v8, v12) = 0) | ~ (member(v8, v10) = v11) | ? [v13] : ( ~ (v13 = 0) & member(v12, v9) = v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (restrict(v12, v11, v10) = v9) | ~ (restrict(v12, v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v9, v11) = v12) | ~ (cross_product(v8, v10) = v11) | restrict(v9, v8, v10) = v12) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = null_class | ~ (restrict(v8, v10, universal_class) = v11) | ~ (singleton(v9) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & domain_of(v8) = v12 & member(v9, v12) = 0) | ( ~ (v12 = 0) & member(v9, universal_class) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (power_class(v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & subclass(v8, v9) = v12) | ( ~ (v12 = 0) & member(v8, universal_class) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (domain_of(v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : ? [v13] : ((v13 = null_class & restrict(v8, v12, universal_class) = null_class & singleton(v9) = v12) | ( ~ (v12 = 0) & member(v9, universal_class) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (complement(v8) = v10) | ~ (member(v9, v10) = v11) | ? [v12] : ((v12 = 0 & member(v9, v8) = 0) | ( ~ (v12 = 0) & member(v9, universal_class) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v9, v8) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v8, universal_class) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unordered_pair(v8, v9) = v10) | ~ (member(v8, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v8, universal_class) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (subclass(v8, v9) = 0) | ~ (member(v10, v9) = v11) | ? [v12] : ( ~ (v12 = 0) & member(v10, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apply(v11, v10) = v9) | ~ (apply(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (disjoint(v11, v10) = v9) | ~ (disjoint(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (compose(v11, v10) = v9) | ~ (compose(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (image(v11, v10) = v9) | ~ (image(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (union(v11, v10) = v9) | ~ (union(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (intersection(v11, v10) = v9) | ~ (intersection(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cross_product(v11, v10) = v9) | ~ (cross_product(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (ordered_pair(v11, v10) = v9) | ~ (ordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unordered_pair(v11, v10) = v9) | ~ (unordered_pair(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (subclass(v11, v10) = v9) | ~ (subclass(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (member(v11, v10) = v9) | ~ (member(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (image(v8, v10) = v11) | ~ (singleton(v9) = v10) | ? [v12] : (apply(v8, v9) = v12 & sum_class(v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : ((v12 = 0 & member(v10, v9) = 0) | (v12 = 0 & member(v10, v8) = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (restrict(v9, v8, v10) = v11) | ? [v12] : (intersection(v9, v12) = v11 & cross_product(v8, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (restrict(v8, v10, universal_class) = v11) | ~ (singleton(v9) = v10) | ? [v12] : ? [v13] : ((v12 = 0 & ~ (v11 = null_class) & member(v9, universal_class) = 0) | ( ~ (v13 = 0) & domain_of(v8) = v12 & member(v9, v12) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ (member(v10, v11) = 0) | (member(v10, v9) = 0 & member(v10, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cross_product(v8, v9) = v11) | ~ (member(v10, v11) = 0) | ? [v12] : ? [v13] : (first(v10) = v12 & second(v10) = v13 & ordered_pair(v12, v13) = v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (singleton(v9) = v10) | ~ (unordered_pair(v8, v10) = v11) | ? [v12] : ? [v13] : (ordered_pair(v8, v9) = v12 & singleton(v8) = v13 & unordered_pair(v13, v11) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ~ (member(v8, v11) = 0) | member(v8, universal_class) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (disjoint(v8, v9) = v10) | ? [v11] : (member(v11, v9) = 0 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (subclass(v8, v9) = v10) | ? [v11] : ? [v12] : ( ~ (v12 = 0) & member(v11, v9) = v12 & member(v11, v8) = 0)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (member(v9, v8) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & complement(v8) = v11 & member(v9, v11) = 0) | ( ~ (v11 = 0) & member(v9, universal_class) = v11))) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (function(v10) = v9) | ~ (function(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (power_class(v10) = v9) | ~ (power_class(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (sum_class(v10) = v9) | ~ (sum_class(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (inductive(v10) = v9) | ~ (inductive(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (range_of(v10) = v9) | ~ (range_of(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (inverse(v10) = v9) | ~ (inverse(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (successor(v10) = v9) | ~ (successor(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (flip(v10) = v9) | ~ (flip(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (rotate(v10) = v9) | ~ (rotate(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (domain_of(v10) = v9) | ~ (domain_of(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (complement(v10) = v9) | ~ (complement(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (first(v10) = v9) | ~ (first(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (second(v10) = v9) | ~ (second(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singleton(v10) = v9) | ~ (singleton(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (ordered_pair(v10, v10) = v8) | ~ (member(v8, identity_relation) = v9) | ? [v11] : ( ~ (v11 = 0) & member(v10, universal_class) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (member(v10, universal_class) = 0) | ~ (member(v8, identity_relation) = v9) | ? [v11] : ( ~ (v11 = v8) & ordered_pair(v10, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (apply(v8, v9) = v10) | ? [v11] : ? [v12] : (sum_class(v12) = v10 & image(v8, v11) = v12 & singleton(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (member(v10, v9) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (disjoint(v8, v9) = 0) | ~ (member(v10, v8) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (compose(v9, v8) = v10) | subclass(v10, v0) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_class(v9) = v10) | ~ (member(v8, v10) = 0) | (subclass(v8, v9) = 0 & member(v8, universal_class) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum_class(v9) = v10) | ~ (member(v8, v10) = 0) | ? [v11] : (member(v11, v9) = 0 & member(v8, v11) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (image(v9, v8) = v10) | ? [v11] : (range_of(v11) = v10 & restrict(v9, v8, universal_class) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (image(v9, v8) = v10) | ? [v11] : ((v11 = 0 & member(v10, universal_class) = 0) | ( ~ (v11 = 0) & function(v9) = v11) | ( ~ (v11 = 0) & member(v8, universal_class) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (domain_of(v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : ? [v12] : ( ~ (v12 = null_class) & restrict(v8, v11, universal_class) = v12 & singleton(v9) = v11 & member(v9, universal_class) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v9, v8, universal_class) = v10) | ? [v11] : (image(v9, v8) = v11 & range_of(v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (complement(v8) = v10) | ~ (member(v9, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & member(v9, v8) = v11 & member(v9, universal_class) = 0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (singleton(v9) = v12 & singleton(v8) = v11 & unordered_pair(v11, v13) = v10 & unordered_pair(v8, v12) = v13)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v9 & v12 = 0 & v11 = 0 & successor(v8) = v9 & member(v9, universal_class) = 0 & member(v8, universal_class) = 0) | ( ~ (v11 = 0) & member(v10, successor_relation) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = v9 & v11 = v8 & first(v10) = v8 & second(v10) = v9) | ( ~ (v11 = 0) & member(v9, universal_class) = v11) | ( ~ (v11 = 0) & member(v8, universal_class) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & member(v9, universal_class) = 0 & member(v8, v9) = 0) | ( ~ (v11 = 0) & member(v10, element_relation) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = 0 & member(v10, successor_relation) = 0) | ( ~ (v11 = v9) & successor(v8) = v11) | ( ~ (v11 = 0) & member(v9, universal_class) = v11) | ( ~ (v11 = 0) & member(v8, universal_class) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ? [v11] : ((v11 = 0 & member(v10, element_relation) = 0) | ( ~ (v11 = 0) & member(v9, universal_class) = v11) | ( ~ (v11 = 0) & member(v8, v9) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | member(v10, universal_class) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subclass(v8, v9) = v10) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & member(v8, universal_class) = 0) | ( ~ (v12 = 0) & power_class(v9) = v11 & member(v8, v11) = v12))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (subclass(v8, v9) = 0) | ~ (member(v10, v8) = 0) | member(v10, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ( ~ (member(v9, v8) = v10) | ? [v11] : ? [v12] : ((v11 = 0 & ~ (v10 = 0) & member(v9, universal_class) = 0) | ( ~ (v12 = 0) & complement(v8) = v11 & member(v9, v11) = v12))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (member(v8, v9) = v10) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & member(v9, universal_class) = 0) | ( ~ (v12 = 0) & ordered_pair(v8, v9) = v11 & member(v11, element_relation) = v12))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subclass(v9, v8) = 0) | ? [v10] : ( ~ (v10 = 0) & subclass(v8, v9) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (subclass(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & subclass(v9, v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (function(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : (( ~ (v12 = 0) & compose(v8, v10) = v11 & inverse(v8) = v10 & subclass(v11, identity_relation) = v12) | ( ~ (v10 = 0) & subclass(v8, v0) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (inductive(v8) = v9) | ? [v10] : ? [v11] : (( ~ (v11 = 0) & image(successor_relation, v8) = v10 & subclass(v10, v8) = v11) | ( ~ (v10 = 0) & member(null_class, v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subclass(v8, v8) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subclass(v8, universal_class) = v9)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (subclass(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & inductive(v8) = v10)) & ! [v8] : ! [v9] : (v8 = null_class | ~ (apply(v6, v8) = v9) | ? [v10] : ((v10 = 0 & member(v9, v8) = 0) | ( ~ (v10 = 0) & member(v8, universal_class) = v10))) & ! [v8] : ! [v9] : ( ~ (power_class(v8) = v9) | ? [v10] : ((v10 = 0 & member(v9, universal_class) = 0) | ( ~ (v10 = 0) & member(v8, universal_class) = v10))) & ! [v8] : ! [v9] : ( ~ (sum_class(v8) = v9) | ? [v10] : ((v10 = 0 & member(v9, universal_class) = 0) | ( ~ (v10 = 0) & member(v8, universal_class) = v10))) & ! [v8] : ! [v9] : ( ~ (image(successor_relation, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & subclass(v9, v8) = 0 & member(null_class, v8) = 0) | ( ~ (v10 = 0) & inductive(v8) = v10))) & ! [v8] : ! [v9] : ( ~ (image(successor_relation, v8) = v9) | ? [v10] : ((v10 = 0 & inductive(v8) = 0) | ( ~ (v10 = 0) & subclass(v9, v8) = v10) | ( ~ (v10 = 0) & member(null_class, v8) = v10))) & ! [v8] : ! [v9] : ( ~ (range_of(v8) = v9) | ? [v10] : (inverse(v8) = v10 & domain_of(v10) = v9)) & ! [v8] : ! [v9] : ( ~ (inverse(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v10 = 0 & compose(v8, v9) = v11 & subclass(v11, identity_relation) = 0 & subclass(v8, v0) = 0) | ( ~ (v10 = 0) & function(v8) = v10))) & ! [v8] : ! [v9] : ( ~ (inverse(v8) = v9) | ? [v10] : ? [v11] : (flip(v10) = v11 & domain_of(v11) = v9 & cross_product(v8, universal_class) = v10)) & ! [v8] : ! [v9] : ( ~ (inverse(v8) = v9) | ? [v10] : ? [v11] : ((v10 = 0 & function(v8) = 0) | ( ~ (v11 = 0) & compose(v8, v9) = v10 & subclass(v10, identity_relation) = v11) | ( ~ (v10 = 0) & subclass(v8, v0) = v10))) & ! [v8] : ! [v9] : ( ~ (inverse(v8) = v9) | ? [v10] : (range_of(v8) = v10 & domain_of(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (successor(v8) = v9) | ? [v10] : (union(v8, v10) = v9 & singleton(v8) = v10)) & ! [v8] : ! [v9] : ( ~ (flip(v8) = v9) | subclass(v9, v1) = 0) & ! [v8] : ! [v9] : ( ~ (rotate(v8) = v9) | subclass(v9, v1) = 0) & ! [v8] : ! [v9] : ( ~ (cross_product(v8, universal_class) = v9) | ? [v10] : ? [v11] : (inverse(v8) = v10 & flip(v9) = v11 & domain_of(v11) = v10)) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | unordered_pair(v8, v8) = v9) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | ? [v10] : (successor(v8) = v10 & union(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) & ! [v8] : ! [v9] : ( ~ (subclass(v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & power_class(v9) = v10 & member(v8, v10) = 0) | ( ~ (v10 = 0) & member(v8, universal_class) = v10))) & ! [v8] : ! [v9] : ( ~ (subclass(v8, v0) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v9 = 0 & compose(v8, v10) = v11 & inverse(v8) = v10 & subclass(v11, identity_relation) = 0) | ( ~ (v10 = 0) & function(v8) = v10))) & ! [v8] : ! [v9] : ( ~ (member(v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & ordered_pair(v8, v9) = v10 & member(v10, element_relation) = 0) | ( ~ (v10 = 0) & member(v9, universal_class) = v10))) & ! [v8] : ! [v9] : ( ~ (member(null_class, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & image(successor_relation, v8) = v10 & subclass(v10, v8) = 0) | ( ~ (v10 = 0) & inductive(v8) = v10))) & ! [v8] : (v8 = null_class | ~ (member(v8, universal_class) = 0) | ? [v9] : (apply(v6, v8) = v9 & member(v9, v8) = 0)) & ! [v8] : ( ~ (function(v8) = 0) | ? [v9] : ? [v10] : (compose(v8, v9) = v10 & inverse(v8) = v9 & subclass(v10, identity_relation) = 0 & subclass(v8, v0) = 0)) & ! [v8] : ( ~ (inductive(v8) = 0) | subclass(v7, v8) = 0) & ! [v8] : ( ~ (inductive(v8) = 0) | ? [v9] : (image(successor_relation, v8) = v9 & subclass(v9, v8) = 0 & member(null_class, v8) = 0)) & ! [v8] : ( ~ (subclass(v8, v0) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v9 = 0 & function(v8) = 0) | ( ~ (v11 = 0) & compose(v8, v9) = v10 & inverse(v8) = v9 & subclass(v10, identity_relation) = v11))) & ! [v8] : ( ~ (member(v8, identity_relation) = 0) | ? [v9] : (ordered_pair(v9, v9) = v8 & member(v9, universal_class) = 0)) & ! [v8] : ~ (member(v8, null_class) = 0) & ! [v8] : ( ~ (member(v8, universal_class) = 0) | ? [v9] : (power_class(v8) = v9 & member(v9, universal_class) = 0)) & ! [v8] : ( ~ (member(v8, universal_class) = 0) | ? [v9] : (sum_class(v8) = v9 & member(v9, universal_class) = 0)) & ! [v8] : ( ~ (member(null_class, v8) = 0) | ? [v9] : ? [v10] : ((v9 = 0 & inductive(v8) = 0) | ( ~ (v10 = 0) & image(successor_relation, v8) = v9 & subclass(v9, v8) = v10))) & ? [v8] : ? [v9] : ? [v10] : ? [v11] : restrict(v10, v9, v8) = v11 & ? [v8] : ? [v9] : ? [v10] : apply(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : disjoint(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : compose(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : image(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : union(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : intersection(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : cross_product(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : ordered_pair(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : unordered_pair(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : subclass(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : member(v9, v8) = v10 & ? [v8] : ? [v9] : function(v8) = v9 & ? [v8] : ? [v9] : power_class(v8) = v9 & ? [v8] : ? [v9] : sum_class(v8) = v9 & ? [v8] : ? [v9] : inductive(v8) = v9 & ? [v8] : ? [v9] : range_of(v8) = v9 & ? [v8] : ? [v9] : inverse(v8) = v9 & ? [v8] : ? [v9] : successor(v8) = v9 & ? [v8] : ? [v9] : flip(v8) = v9 & ? [v8] : ? [v9] : rotate(v8) = v9 & ? [v8] : ? [v9] : domain_of(v8) = v9 & ? [v8] : ? [v9] : complement(v8) = v9 & ? [v8] : ? [v9] : first(v8) = v9 & ? [v8] : ? [v9] : second(v8) = v9 & ? [v8] : ? [v9] : singleton(v8) = v9 & ? [v8] : (v8 = null_class | ? [v9] : (disjoint(v9, v8) = 0 & member(v9, v8) = 0 & member(v9, universal_class) = 0)))
% 24.54/6.42 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 24.54/6.42 | (1) ~ (all_0_2_2 = 0) & function(all_0_1_1) = 0 & inductive(all_0_0_0) = 0 & cross_product(all_0_7_7, universal_class) = all_0_6_6 & cross_product(universal_class, universal_class) = all_0_7_7 & singleton(all_0_5_5) = all_0_3_3 & subclass(all_0_3_3, all_0_4_4) = all_0_2_2 & subclass(successor_relation, all_0_7_7) = 0 & subclass(element_relation, all_0_7_7) = 0 & member(all_0_0_0, universal_class) = 0 & member(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ (member(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v10 = 0) & ordered_pair(v8, v2) = v9 & ordered_pair(v1, v0) = v8 & member(v9, v3) = v10) | ( ~ (v8 = 0) & member(v5, all_0_6_6) = 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_6_6) = 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_6_6) = 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_6_6) = 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_6_6) = 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_6_6) = 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_6_6) = 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_6_6) = 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_7_7) = 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_7_7) = 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_7_7) = 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_7_7) = 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_6_6) = 0) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_6_6) = 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_7_7) = 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_7_7) = 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_7_7) = 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))
% 24.54/6.45 |
% 24.54/6.45 | Applying alpha-rule on (1) yields:
% 24.54/6.45 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 24.54/6.45 | (3) ! [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)))
% 24.54/6.45 | (4) ! [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)))
% 24.54/6.45 | (5) ! [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)))
% 24.54/6.45 | (6) ! [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))
% 24.54/6.45 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0))
% 24.54/6.45 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4))
% 24.54/6.45 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 24.54/6.45 | (10) ? [v0] : ? [v1] : ? [v2] : image(v1, v0) = v2
% 24.54/6.45 | (11) ! [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_6_6) = 0))
% 24.54/6.45 | (12) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, universal_class) = v1))
% 24.54/6.45 | (13) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 24.54/6.45 | (14) ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0)
% 24.54/6.45 | (15) ! [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))
% 24.54/6.45 | (16) ? [v0] : ? [v1] : complement(v0) = v1
% 24.54/6.45 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_7_7) = 0)
% 24.54/6.45 | (18) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2))
% 24.54/6.45 | (19) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0))
% 24.54/6.45 | (20) member(all_0_0_0, universal_class) = 0
% 24.54/6.45 | (21) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_6_6) = 0)
% 24.54/6.45 | (22) ! [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)))
% 24.54/6.45 | (23) singleton(all_0_5_5) = all_0_3_3
% 24.54/6.45 | (24) ! [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)))
% 24.54/6.45 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 24.54/6.45 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 24.54/6.45 | (27) subclass(successor_relation, all_0_7_7) = 0
% 24.54/6.45 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0))
% 24.54/6.45 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 24.54/6.45 | (30) ! [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_6_6) = v8)))
% 24.54/6.45 | (31) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2))
% 24.54/6.45 | (32) ? [v0] : ? [v1] : inductive(v0) = v1
% 24.54/6.45 | (33) ! [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))
% 24.54/6.45 | (34) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_6_6) = 0)
% 24.54/6.45 | (35) ! [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_6_6) = v8)))
% 24.54/6.46 | (36) ! [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_6_6) = 0))
% 24.54/6.46 | (37) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (disjoint(v0, v1) = v2) | ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 24.54/6.46 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 24.54/6.46 | (39) member(all_0_5_5, all_0_4_4) = 0
% 24.54/6.46 | (40) ! [v0] : ( ~ (function(v0) = 0) | ? [v1] : ? [v2] : (compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = 0 & subclass(v0, all_0_7_7) = 0))
% 24.54/6.46 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 24.54/6.46 | (42) ? [v0] : ? [v1] : rotate(v0) = v1
% 24.54/6.46 | (43) ! [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)))
% 24.54/6.46 | (44) ! [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)))
% 24.54/6.46 | (45) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(v0, v0) = v1))
% 24.54/6.46 | (46) ! [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)))
% 24.54/6.46 | (47) ! [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)))
% 24.54/6.46 | (48) ? [v0] : ? [v1] : ? [v2] : disjoint(v1, v0) = v2
% 24.54/6.46 | (49) ! [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))
% 24.54/6.46 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 24.54/6.46 | (51) ! [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)))
% 24.54/6.46 | (52) ! [v0] : ! [v1] : (v1 = 0 | ~ (subclass(all_0_0_0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & inductive(v0) = v2))
% 24.54/6.46 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0))
% 24.54/6.46 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3))
% 24.54/6.46 | (55) cross_product(all_0_7_7, universal_class) = all_0_6_6
% 24.54/6.46 | (56) ! [v0] : ( ~ (member(v0, identity_relation) = 0) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0))
% 24.54/6.46 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0)
% 24.54/6.46 | (58) ! [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)))
% 24.54/6.46 | (59) ? [v0] : ? [v1] : singleton(v0) = v1
% 24.54/6.46 | (60) ! [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))
% 24.54/6.46 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 24.54/6.46 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 24.54/6.46 | (63) ? [v0] : ? [v1] : ? [v2] : ? [v3] : restrict(v2, v1, v0) = v3
% 24.54/6.46 | (64) ! [v0] : ( ~ (member(null_class, v0) = 0) | ? [v1] : ? [v2] : ((v1 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & image(successor_relation, v0) = v1 & subclass(v1, v0) = v2)))
% 24.54/6.46 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 24.54/6.46 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 24.54/6.46 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 24.54/6.46 | (68) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 24.54/6.46 | (69) ? [v0] : ? [v1] : ? [v2] : subclass(v1, v0) = v2
% 24.54/6.46 | (70) ! [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)))
% 24.54/6.46 | (71) ! [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_6_6) = 0) | ( ~ (v10 = 0) & flip(v3) = v9 & member(v8, v9) = v10))))
% 24.54/6.46 | (72) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0))
% 24.54/6.46 | (73) ? [v0] : ? [v1] : ? [v2] : cross_product(v1, v0) = v2
% 24.54/6.46 | (74) ! [v0] : ! [v1] : ! [v2] : ( ~ (disjoint(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3))
% 24.54/6.46 | (75) ! [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)))
% 24.54/6.46 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0))
% 24.54/6.46 | (77) ? [v0] : ? [v1] : sum_class(v0) = v1
% 24.54/6.46 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0))
% 24.54/6.46 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0))
% 24.54/6.46 | (80) ! [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))
% 24.54/6.47 | (81) ! [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)))
% 24.54/6.47 | (82) ! [v0] : ( ~ (member(v0, universal_class) = 0) | ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0))
% 24.54/6.47 | (83) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | ? [v2] : (successor(v0) = v2 & union(v0, v1) = v2))
% 24.54/6.47 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 24.54/6.47 | (85) ! [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_6_6) = 0) | ( ~ (v10 = 0) & rotate(v0) = v9 & member(v8, v9) = v10))))
% 24.54/6.47 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0)
% 24.54/6.47 | (87) ? [v0] : ? [v1] : first(v0) = v1
% 24.54/6.47 | (88) ! [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)))
% 24.54/6.47 | (89) ! [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)))
% 24.54/6.47 | (90) ! [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_7_7) = v2)))
% 24.54/6.47 | (91) cross_product(universal_class, universal_class) = all_0_7_7
% 24.54/6.47 | (92) ! [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)))
% 24.54/6.47 | (93) ! [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)))
% 24.54/6.47 | (94) ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 24.54/6.47 | (95) ! [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_7_7) = 0) | ( ~ (v2 = 0) & function(v0) = v2)))
% 24.54/6.47 | (96) ? [v0] : ? [v1] : domain_of(v0) = v1
% 24.54/6.47 | (97) ? [v0] : ? [v1] : power_class(v0) = v1
% 24.54/6.47 | (98) ? [v0] : ? [v1] : ? [v2] : compose(v1, v0) = v2
% 24.54/6.47 | (99) function(all_0_1_1) = 0
% 24.54/6.47 | (100) ! [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_6_6) = v8))))
% 24.54/6.47 | (101) ? [v0] : ? [v1] : function(v0) = v1
% 24.54/6.47 | (102) ? [v0] : ? [v1] : successor(v0) = v1
% 24.54/6.47 | (103) ! [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)))
% 24.54/6.47 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 24.54/6.47 | (105) ! [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))
% 24.54/6.47 | (106) ? [v0] : ? [v1] : inverse(v0) = v1
% 24.54/6.47 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0))
% 24.54/6.47 | (108) ! [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)))
% 24.54/6.47 | (109) subclass(element_relation, all_0_7_7) = 0
% 24.54/6.47 | (110) ! [v0] : ~ (member(v0, null_class) = 0)
% 24.54/6.47 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0))
% 24.54/6.47 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0))
% 24.54/6.47 | (113) ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 24.54/6.47 | (114) ? [v0] : ? [v1] : ? [v2] : member(v1, v0) = v2
% 24.54/6.47 | (115) ! [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_6_6) = v8))))
% 24.54/6.47 | (116) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 24.54/6.47 | (117) ! [v0] : (v0 = null_class | ~ (member(v0, universal_class) = 0) | ? [v1] : (apply(all_0_1_1, v0) = v1 & member(v1, v0) = 0))
% 24.54/6.47 | (118) ? [v0] : ? [v1] : range_of(v0) = v1
% 24.54/6.47 | (119) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0))
% 24.54/6.47 | (120) ? [v0] : ? [v1] : second(v0) = v1
% 24.54/6.47 | (121) ? [v0] : ? [v1] : ? [v2] : intersection(v1, v0) = v2
% 24.54/6.47 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (ordered_pair(v2, v2) = v0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = 0) & member(v2, universal_class) = v3))
% 24.54/6.47 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 24.54/6.47 | (124) ! [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)))
% 24.54/6.47 | (125) ! [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)))
% 24.54/6.47 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0))
% 24.54/6.47 | (127) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (member(v2, universal_class) = 0) | ~ (member(v0, identity_relation) = v1) | ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3))
% 24.54/6.47 | (128) ! [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)))
% 24.54/6.48 | (129) ! [v0] : ( ~ (inductive(v0) = 0) | ? [v1] : (image(successor_relation, v0) = v1 & subclass(v1, v0) = 0 & member(null_class, v0) = 0))
% 24.54/6.48 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0))
% 24.54/6.48 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 24.54/6.48 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ (member(v0, v2) = 0) | ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 24.54/6.48 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0))
% 24.54/6.48 | (134) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 24.54/6.48 | (135) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 24.54/6.48 | (136) ? [v0] : ? [v1] : ? [v2] : apply(v1, v0) = v2
% 24.54/6.48 | (137) ! [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)))
% 24.54/6.48 | (138) ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v0, v1) = v2))
% 24.54/6.48 | (139) ? [v0] : ? [v1] : ? [v2] : unordered_pair(v1, v0) = v2
% 24.54/6.48 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 24.54/6.48 | (141) ! [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_7_7) = v2)))
% 24.54/6.48 | (142) ? [v0] : ? [v1] : ? [v2] : union(v1, v0) = v2
% 24.54/6.48 | (143) ! [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)))
% 24.54/6.48 | (144) ! [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)))
% 24.54/6.48 | (145) ? [v0] : ? [v1] : flip(v0) = v1
% 24.54/6.48 | (146) ! [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))
% 24.54/6.48 | (147) ! [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)))
% 24.54/6.48 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 24.54/6.48 | (149) ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2))
% 24.54/6.48 | (150) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 24.54/6.48 | (151) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0))
% 24.54/6.48 | (152) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0))
% 24.54/6.48 | (153) ~ (all_0_2_2 = 0)
% 24.54/6.48 | (154) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0))
% 24.54/6.48 | (155) inductive(all_0_0_0) = 0
% 24.54/6.48 | (156) ! [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)))
% 24.54/6.48 | (157) ? [v0] : ? [v1] : ? [v2] : ordered_pair(v1, v0) = v2
% 24.54/6.48 | (158) ! [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))
% 24.54/6.48 | (159) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 24.54/6.48 | (160) ! [v0] : ! [v1] : ( ~ (subclass(v0, all_0_7_7) = 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)))
% 24.54/6.48 | (161) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (function(v2) = v1) | ~ (function(v2) = v0))
% 24.54/6.48 | (162) ! [v0] : ( ~ (subclass(v0, all_0_7_7) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v1 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3)))
% 25.04/6.48 | (163) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3))
% 25.04/6.48 | (164) ! [v0] : ! [v1] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2))
% 25.04/6.48 | (165) subclass(all_0_3_3, all_0_4_4) = all_0_2_2
% 25.04/6.48 |
% 25.04/6.48 | Instantiating formula (135) with all_0_3_3, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_3_3, yields:
% 25.04/6.48 | (166) unordered_pair(all_0_5_5, all_0_5_5) = all_0_3_3
% 25.04/6.48 |
% 25.04/6.48 | Instantiating formula (29) with all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms subclass(all_0_3_3, all_0_4_4) = all_0_2_2, yields:
% 25.04/6.48 | (167) all_0_2_2 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = 0 & member(v0, all_0_4_4) = v1)
% 25.04/6.48 |
% 25.04/6.48 +-Applying beta-rule and splitting (167), into two cases.
% 25.04/6.48 |-Branch one:
% 25.04/6.48 | (168) all_0_2_2 = 0
% 25.04/6.48 |
% 25.04/6.48 | Equations (168) can reduce 153 to:
% 25.04/6.48 | (169) $false
% 25.04/6.48 |
% 25.04/6.48 |-The branch is then unsatisfiable
% 25.04/6.48 |-Branch two:
% 25.04/6.48 | (153) ~ (all_0_2_2 = 0)
% 25.04/6.48 | (171) ? [v0] : ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = 0 & member(v0, all_0_4_4) = v1)
% 25.04/6.48 |
% 25.04/6.48 | Instantiating (171) with all_101_0_118, all_101_1_119 yields:
% 25.04/6.48 | (172) ~ (all_101_0_118 = 0) & member(all_101_1_119, all_0_3_3) = 0 & member(all_101_1_119, all_0_4_4) = all_101_0_118
% 25.04/6.48 |
% 25.04/6.48 | Applying alpha-rule on (172) yields:
% 25.04/6.48 | (173) ~ (all_101_0_118 = 0)
% 25.04/6.48 | (174) member(all_101_1_119, all_0_3_3) = 0
% 25.04/6.48 | (175) member(all_101_1_119, all_0_4_4) = all_101_0_118
% 25.04/6.48 |
% 25.04/6.48 | Instantiating formula (28) with all_0_3_3, all_0_5_5, all_0_5_5, all_101_1_119 and discharging atoms unordered_pair(all_0_5_5, all_0_5_5) = all_0_3_3, member(all_101_1_119, all_0_3_3) = 0, yields:
% 25.04/6.48 | (176) all_101_1_119 = all_0_5_5
% 25.04/6.48 |
% 25.04/6.49 | From (176) and (175) follows:
% 25.04/6.49 | (177) member(all_0_5_5, all_0_4_4) = all_101_0_118
% 25.04/6.49 |
% 25.04/6.49 | Instantiating formula (130) with all_0_5_5, all_0_4_4, all_101_0_118, 0 and discharging atoms member(all_0_5_5, all_0_4_4) = all_101_0_118, member(all_0_5_5, all_0_4_4) = 0, yields:
% 25.04/6.49 | (178) all_101_0_118 = 0
% 25.04/6.49 |
% 25.04/6.49 | Equations (178) can reduce 173 to:
% 25.04/6.49 | (169) $false
% 25.04/6.49 |
% 25.04/6.49 |-The branch is then unsatisfiable
% 25.04/6.49 % SZS output end Proof for theBenchmark
% 25.04/6.49
% 25.04/6.49 5891ms
%------------------------------------------------------------------------------