TSTP Solution File: SET020+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 00:16:12 EDT 2022
% Result : Theorem 4.21s 1.64s
% Output : Proof 6.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SET020+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n024.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 : Mon Jul 11 01:26:13 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.58/0.58 ____ _
% 0.58/0.58 ___ / __ \_____(_)___ ________ __________
% 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.58/0.58
% 0.58/0.58 A Theorem Prover for First-Order Logic
% 0.58/0.59 (ePrincess v.1.0)
% 0.58/0.59
% 0.58/0.59 (c) Philipp Rümmer, 2009-2015
% 0.58/0.59 (c) Peter Backeman, 2014-2015
% 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.59 Bug reports to peter@backeman.se
% 0.58/0.59
% 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.59
% 0.58/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.66 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.88/1.02 Prover 0: Preprocessing ...
% 3.30/1.45 Prover 0: Warning: ignoring some quantifiers
% 3.68/1.49 Prover 0: Constructing countermodel ...
% 4.21/1.64 Prover 0: proved (975ms)
% 4.21/1.64
% 4.21/1.64 No countermodel exists, formula is valid
% 4.21/1.64 % SZS status Theorem for theBenchmark
% 4.21/1.64
% 4.21/1.64 Generating proof ... Warning: ignoring some quantifiers
% 5.94/1.99 found it (size 11)
% 5.94/1.99
% 5.94/1.99 % SZS output start Proof for theBenchmark
% 5.94/2.00 Assumed formulas after preprocessing and simplification:
% 5.94/2.00 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (first(v4) = v5 & second(v4) = v6 & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & ordered_pair(v2, v3) = v4 & function(v7) & inductive(v8) & member(v8, universal_class) & member(v3, universal_class) & member(v2, universal_class) & subclass(successor_relation, v0) & subclass(element_relation, v0) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (image(v10, v15) = v16) | ~ (image(v9, v14) = v15) | ~ (ordered_pair(v11, v12) = v13) | ~ (singleton(v11) = v14) | member(v12, v16) | ? [v17] : (compose(v10, v9) = v17 & ~ member(v13, v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (image(v10, v15) = v16) | ~ (image(v9, v14) = v15) | ~ (ordered_pair(v11, v12) = v13) | ~ (singleton(v11) = v14) | member(v11, universal_class) | ? [v17] : (compose(v10, v9) = v17 & ~ member(v13, v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (image(v10, v14) = v15) | ~ (image(v9, v13) = v14) | ~ (ordered_pair(v11, v12) = v16) | ~ (singleton(v11) = v13) | ~ member(v12, v15) | ~ member(v11, universal_class) | ? [v17] : (compose(v10, v9) = v17 & member(v16, v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v11 | ~ (first(v11) = v13) | ~ (second(v11) = v14) | ~ (cross_product(v9, v10) = v12) | ~ (ordered_pair(v13, v14) = v15) | ~ member(v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (flip(v12) = v15) | ~ (ordered_pair(v13, v11) = v14) | ~ (ordered_pair(v10, v9) = v13) | ~ member(v14, v12) | ? [v16] : ? [v17] : (ordered_pair(v16, v11) = v17 & ordered_pair(v9, v10) = v16 & ( ~ member(v17, v1) | member(v17, v15)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (flip(v12) = v15) | ~ (ordered_pair(v13, v11) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ member(v14, v15) | member(v14, v1)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (flip(v12) = v15) | ~ (ordered_pair(v13, v11) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ member(v14, v15) | ? [v16] : ? [v17] : (ordered_pair(v16, v11) = v17 & ordered_pair(v10, v9) = v16 & member(v17, v12))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (flip(v12) = v15) | ~ (ordered_pair(v13, v11) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ member(v14, v1) | member(v14, v15) | ? [v16] : ? [v17] : (ordered_pair(v16, v11) = v17 & ordered_pair(v10, v9) = v16 & ~ member(v17, v12))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (flip(v12) = v13) | ~ (ordered_pair(v14, v11) = v15) | ~ (ordered_pair(v10, v9) = v14) | ? [v16] : ? [v17] : (ordered_pair(v16, v11) = v17 & ordered_pair(v9, v10) = v16 & ( ~ member(v17, v13) | (member(v17, v1) & member(v15, v12))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (rotate(v9) = v15) | ~ (ordered_pair(v13, v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ member(v14, v15) | member(v14, v1)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (rotate(v9) = v15) | ~ (ordered_pair(v13, v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ member(v14, v15) | ? [v16] : ? [v17] : (ordered_pair(v16, v10) = v17 & ordered_pair(v11, v12) = v16 & member(v17, v9))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (rotate(v9) = v15) | ~ (ordered_pair(v13, v12) = v14) | ~ (ordered_pair(v10, v11) = v13) | ~ member(v14, v1) | member(v14, v15) | ? [v16] : ? [v17] : (ordered_pair(v16, v10) = v17 & ordered_pair(v11, v12) = v16 & ~ member(v17, v9))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (rotate(v9) = v15) | ~ (ordered_pair(v13, v10) = v14) | ~ (ordered_pair(v11, v12) = v13) | ~ member(v14, v9) | ? [v16] : ? [v17] : (ordered_pair(v16, v12) = v17 & ordered_pair(v10, v11) = v16 & ( ~ member(v17, v1) | member(v17, v15)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (rotate(v9) = v13) | ~ (ordered_pair(v14, v10) = v15) | ~ (ordered_pair(v11, v12) = v14) | ? [v16] : ? [v17] : (ordered_pair(v16, v12) = v17 & ordered_pair(v10, v11) = v16 & ( ~ member(v17, v13) | (member(v17, v1) & member(v15, v9))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose(v10, v9) = v14) | ~ (ordered_pair(v11, v12) = v13) | ~ member(v13, v14) | member(v11, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose(v10, v9) = v14) | ~ (ordered_pair(v11, v12) = v13) | ~ member(v13, v14) | ? [v15] : ? [v16] : ? [v17] : (image(v10, v16) = v17 & image(v9, v15) = v16 & singleton(v11) = v15 & member(v12, v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (compose(v10, v9) = v14) | ~ (ordered_pair(v11, v12) = v13) | ~ member(v11, universal_class) | member(v13, v14) | ? [v15] : ? [v16] : ? [v17] : (image(v10, v16) = v17 & image(v9, v15) = v16 & singleton(v11) = v15 & ~ member(v12, v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cross_product(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ member(v13, v14) | member(v10, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cross_product(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ member(v13, v14) | member(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cross_product(v11, v12) = v14) | ~ (ordered_pair(v9, v10) = v13) | ~ member(v10, v12) | ~ member(v9, v11) | member(v13, v14)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (singleton(v10) = v12) | ~ (singleton(v9) = v11) | ~ (unordered_pair(v11, v13) = v14) | ~ (unordered_pair(v9, v12) = v13) | ordered_pair(v9, v10) = v14) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (restrict(v13, v12, v11) = v10) | ~ (restrict(v13, v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (intersection(v10, v12) = v13) | ~ (cross_product(v9, v11) = v12) | restrict(v10, v9, v11) = v13) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = null_class | ~ (restrict(v9, v11, universal_class) = v12) | ~ (singleton(v10) = v11) | ~ member(v10, universal_class) | ? [v13] : (domain_of(v9) = v13 & member(v10, v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = v9 | v10 = v9 | ~ (unordered_pair(v10, v11) = v12) | ~ member(v9, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (apply(v12, v11) = v10) | ~ (apply(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (compose(v12, v11) = v10) | ~ (compose(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (image(v12, v11) = v10) | ~ (image(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (union(v12, v11) = v10) | ~ (union(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (intersection(v12, v11) = v10) | ~ (intersection(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cross_product(v12, v11) = v10) | ~ (cross_product(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (ordered_pair(v12, v11) = v10) | ~ (ordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (unordered_pair(v12, v11) = v10) | ~ (unordered_pair(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (sum_class(v10) = v11) | ~ member(v12, v10) | ~ member(v9, v12) | member(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (image(v9, v11) = v12) | ~ (singleton(v10) = v11) | ? [v13] : (apply(v9, v10) = v13 & sum_class(v12) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v9, v10) = v12) | ~ member(v11, v12) | member(v11, v10) | member(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v9, v10) = v12) | ~ member(v11, v10) | member(v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (union(v9, v10) = v12) | ~ member(v11, v9) | member(v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (restrict(v10, v9, v11) = v12) | ? [v13] : (intersection(v10, v13) = v12 & cross_product(v9, v11) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (restrict(v9, v11, universal_class) = v12) | ~ (singleton(v10) = v11) | member(v10, universal_class) | ? [v13] : (domain_of(v9) = v13 & ~ member(v10, v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v9, v10) = v12) | ~ member(v11, v12) | member(v11, v10)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v9, v10) = v12) | ~ member(v11, v12) | member(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (intersection(v9, v10) = v12) | ~ member(v11, v10) | ~ member(v11, v9) | member(v11, v12)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unordered_pair(v10, v11) = v12) | ~ member(v9, v12) | member(v9, universal_class)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (power_class(v11) = v10) | ~ (power_class(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (sum_class(v11) = v10) | ~ (sum_class(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (range_of(v11) = v10) | ~ (range_of(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (inverse(v11) = v10) | ~ (inverse(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (successor(v11) = v10) | ~ (successor(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (flip(v11) = v10) | ~ (flip(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (rotate(v11) = v10) | ~ (rotate(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (domain_of(v11) = v10) | ~ (domain_of(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (complement(v11) = v10) | ~ (complement(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (first(v11) = v10) | ~ (first(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (second(v11) = v10) | ~ (second(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singleton(v11) = v10) | ~ (singleton(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (apply(v9, v10) = v11) | ? [v12] : ? [v13] : (sum_class(v13) = v11 & image(v9, v12) = v13 & singleton(v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (compose(v10, v9) = v11) | subclass(v11, v0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (compose(v9, v10) = v11) | ~ (inverse(v9) = v10) | ~ function(v9) | subclass(v11, identity_relation)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (compose(v9, v10) = v11) | ~ (inverse(v9) = v10) | ~ function(v9) | subclass(v9, v0)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (compose(v9, v10) = v11) | ~ (inverse(v9) = v10) | ~ subclass(v11, identity_relation) | ~ subclass(v9, v0) | function(v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (power_class(v10) = v11) | ~ member(v9, v11) | member(v9, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (power_class(v10) = v11) | ~ member(v9, v11) | subclass(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (power_class(v10) = v11) | ~ member(v9, universal_class) | ~ subclass(v9, v10) | member(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (sum_class(v10) = v11) | ~ member(v9, v11) | ? [v12] : (member(v12, v10) & member(v9, v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (image(v10, v9) = v11) | ~ function(v10) | ~ member(v9, universal_class) | member(v11, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (image(v10, v9) = v11) | ? [v12] : (range_of(v12) = v11 & restrict(v10, v9, universal_class) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v9, v10) = v11) | ~ (singleton(v9) = v10) | successor(v9) = v11) & ! [v9] : ! [v10] : ! [v11] : ( ~ (restrict(v10, v9, universal_class) = v11) | ? [v12] : (image(v10, v9) = v12 & range_of(v11) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (restrict(v9, v11, universal_class) = null_class) | ~ (singleton(v10) = v11) | ? [v12] : (domain_of(v9) = v12 & ~ member(v10, v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (complement(v9) = v11) | ~ member(v10, v11) | ~ member(v10, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (complement(v9) = v11) | ~ member(v10, v11) | member(v10, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (complement(v9) = v11) | ~ member(v10, universal_class) | member(v10, v11) | member(v10, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, successor_relation) | successor(v9) = v10) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, successor_relation) | member(v10, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, successor_relation) | member(v9, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, element_relation) | member(v10, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v11, element_relation) | member(v9, v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v10, universal_class) | ~ member(v9, v10) | member(v11, element_relation)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v10, universal_class) | ~ member(v9, universal_class) | member(v11, successor_relation) | ? [v12] : ( ~ (v12 = v10) & successor(v9) = v12)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ~ member(v10, universal_class) | ~ member(v9, universal_class) | (first(v11) = v9 & second(v11) = v10)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ordered_pair(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (singleton(v10) = v13 & singleton(v9) = v12 & unordered_pair(v12, v14) = v11 & unordered_pair(v9, v13) = v14)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v10, v9) = v11) | ~ member(v9, universal_class) | member(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ~ member(v9, universal_class) | member(v9, v11)) & ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | member(v11, universal_class)) & ! [v9] : ! [v10] : ! [v11] : ( ~ disjoint(v9, v10) | ~ member(v11, v10) | ~ member(v11, v9)) & ! [v9] : ! [v10] : ! [v11] : ( ~ member(v11, v9) | ~ subclass(v9, v10) | member(v11, v10)) & ! [v9] : ! [v10] : (v10 = v9 | ~ subclass(v10, v9) | ~ subclass(v9, v10)) & ! [v9] : ! [v10] : (v9 = null_class | ~ (apply(v7, v9) = v10) | ~ member(v9, universal_class) | member(v10, v9)) & ! [v9] : ! [v10] : ( ~ (power_class(v9) = v10) | ~ member(v9, universal_class) | member(v10, universal_class)) & ! [v9] : ! [v10] : ( ~ (sum_class(v9) = v10) | ~ member(v9, universal_class) | member(v10, universal_class)) & ! [v9] : ! [v10] : ( ~ (image(successor_relation, v9) = v10) | ~ inductive(v9) | member(null_class, v9)) & ! [v9] : ! [v10] : ( ~ (image(successor_relation, v9) = v10) | ~ inductive(v9) | subclass(v10, v9)) & ! [v9] : ! [v10] : ( ~ (image(successor_relation, v9) = v10) | ~ member(null_class, v9) | ~ subclass(v10, v9) | inductive(v9)) & ! [v9] : ! [v10] : ( ~ (range_of(v9) = v10) | ? [v11] : (inverse(v9) = v11 & domain_of(v11) = v10)) & ! [v9] : ! [v10] : ( ~ (inverse(v9) = v10) | ? [v11] : ? [v12] : (flip(v11) = v12 & domain_of(v12) = v10 & cross_product(v9, universal_class) = v11)) & ! [v9] : ! [v10] : ( ~ (inverse(v9) = v10) | ? [v11] : (range_of(v9) = v11 & domain_of(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (successor(v9) = v10) | ? [v11] : (union(v9, v11) = v10 & singleton(v9) = v11)) & ! [v9] : ! [v10] : ( ~ (flip(v9) = v10) | subclass(v10, v1)) & ! [v9] : ! [v10] : ( ~ (rotate(v9) = v10) | subclass(v10, v1)) & ! [v9] : ! [v10] : ( ~ (cross_product(v9, universal_class) = v10) | ? [v11] : ? [v12] : (inverse(v9) = v11 & flip(v10) = v12 & domain_of(v12) = v11)) & ! [v9] : ! [v10] : ( ~ (ordered_pair(v10, v10) = v9) | ~ member(v10, universal_class) | member(v9, identity_relation)) & ! [v9] : ! [v10] : ( ~ (singleton(v9) = v10) | unordered_pair(v9, v9) = v10) & ! [v9] : ! [v10] : ( ~ (unordered_pair(v9, v9) = v10) | singleton(v9) = v10) & ! [v9] : ( ~ inductive(v9) | subclass(v8, v9)) & ! [v9] : ( ~ member(v9, identity_relation) | ? [v10] : (ordered_pair(v10, v10) = v9 & member(v10, universal_class))) & ! [v9] : ~ member(v9, null_class) & ? [v9] : ? [v10] : (disjoint(v9, v10) | ? [v11] : (member(v11, v10) & member(v11, v9))) & ? [v9] : ? [v10] : (subclass(v9, v10) | ? [v11] : (member(v11, v9) & ~ member(v11, v10))) & ? [v9] : (v9 = null_class | ? [v10] : (disjoint(v10, v9) & member(v10, v9) & member(v10, universal_class))) & ? [v9] : subclass(v9, v9) & ? [v9] : subclass(v9, universal_class) & ( ~ (v6 = v3) | ~ (v5 = v2)))
% 5.94/2.06 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 yields:
% 5.94/2.06 | (1) first(all_0_4_4) = all_0_3_3 & second(all_0_4_4) = all_0_2_2 & cross_product(all_0_8_8, universal_class) = all_0_7_7 & cross_product(universal_class, universal_class) = all_0_8_8 & ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4 & function(all_0_1_1) & inductive(all_0_0_0) & member(all_0_0_0, universal_class) & member(all_0_5_5, universal_class) & member(all_0_6_6, universal_class) & subclass(successor_relation, all_0_8_8) & subclass(element_relation, all_0_8_8) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v3, v7) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (ordered_pair(v2, v3) = v7) | ~ (singleton(v2) = v4) | ~ member(v3, v6) | ~ member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & member(v7, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (first(v2) = v4) | ~ (second(v2) = v5) | ~ (cross_product(v0, v1) = v3) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ member(v5, v3) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, all_0_7_7) | member(v8, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | member(v5, all_0_7_7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, all_0_7_7) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & ~ member(v8, v3))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v4) | ~ (ordered_pair(v5, v2) = v6) | ~ (ordered_pair(v1, v0) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_7_7) & member(v6, v3))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | member(v5, all_0_7_7)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, all_0_7_7) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & ~ member(v8, v0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v5, v0) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, all_0_7_7) | member(v8, v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v4) | ~ (ordered_pair(v5, v1) = v6) | ~ (ordered_pair(v2, v3) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_7_7) & member(v6, v0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | member(v2, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v2, universal_class) | member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & ~ member(v3, v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v1, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v1, v3) | ~ member(v0, v2) | member(v4, v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (unordered_pair(v2, v4) = v5) | ~ (unordered_pair(v0, v3) = v4) | ordered_pair(v0, v1) = v5) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = null_class | ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ~ member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & member(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum_class(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & ~ member(v1, v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_8_8)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v2, identity_relation)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v0, all_0_8_8)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ subclass(v2, identity_relation) | ~ subclass(v0, all_0_8_8) | function(v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | member(v0, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | subclass(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, universal_class) | ~ subclass(v0, v1) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ~ function(v1) | ~ member(v0, universal_class) | member(v2, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2) & ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v0, v2, universal_class) = null_class) | ~ (singleton(v1) = v2) | ? [v3] : (domain_of(v0) = v3 & ~ member(v1, v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | ~ member(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | member(v1, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, universal_class) | member(v1, v2) | member(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | successor(v0) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v1, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v0, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v1, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, v1) | member(v2, element_relation)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | member(v2, successor_relation) | ? [v3] : ( ~ (v3 = v1) & successor(v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | (first(v2) = v0 & second(v2) = v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) = v5)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class)) & ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ member(v2, v1) | ~ member(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subclass(v0, v1) | member(v2, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ subclass(v1, v0) | ~ subclass(v0, v1)) & ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ member(v0, universal_class) | member(v1, v0)) & ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class)) & ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | member(null_class, v0)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | subclass(v1, v0)) & ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ member(null_class, v0) | ~ subclass(v1, v0) | inductive(v0)) & ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1)) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2)) & ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2)) & ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_7_7)) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_7_7)) & ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2)) & ! [v0] : ! [v1] : ( ~ (ordered_pair(v1, v1) = v0) | ~ member(v1, universal_class) | member(v0, identity_relation)) & ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) & ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) & ! [v0] : ( ~ inductive(v0) | subclass(all_0_0_0, v0)) & ! [v0] : ( ~ member(v0, identity_relation) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class))) & ! [v0] : ~ member(v0, null_class) & ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0))) & ? [v0] : ? [v1] : (subclass(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1))) & ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) & member(v1, v0) & member(v1, universal_class))) & ? [v0] : subclass(v0, v0) & ? [v0] : subclass(v0, universal_class) & ( ~ (all_0_2_2 = all_0_5_5) | ~ (all_0_3_3 = all_0_6_6))
% 6.41/2.09 |
% 6.41/2.09 | Applying alpha-rule on (1) yields:
% 6.41/2.09 | (2) function(all_0_1_1)
% 6.41/2.10 | (3) cross_product(universal_class, universal_class) = all_0_8_8
% 6.41/2.10 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3))
% 6.41/2.10 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class))
% 6.41/2.10 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ~ function(v1) | ~ member(v0, universal_class) | member(v2, universal_class))
% 6.41/2.10 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v0, v1))
% 6.41/2.10 | (8) ! [v0] : ( ~ member(v0, identity_relation) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class)))
% 6.41/2.10 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v1, universal_class))
% 6.41/2.10 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, all_0_7_7) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & ~ member(v8, v0)))
% 6.41/2.10 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v2, universal_class) | member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & ~ member(v3, v8)))
% 6.41/2.10 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | ~ member(v1, v0))
% 6.41/2.10 | (13) ? [v0] : subclass(v0, universal_class)
% 6.41/2.10 | (14) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0))
% 6.41/2.10 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4))
% 6.41/2.10 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3))
% 6.41/2.10 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | member(v2, successor_relation) | ? [v3] : ( ~ (v3 = v1) & successor(v0) = v3))
% 6.41/2.10 | (18) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, universal_class) | member(v1, v2) | member(v1, v0))
% 6.41/2.10 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & ~ member(v1, v4)))
% 6.41/2.10 | (20) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, universal_class) | ~ subclass(v0, v1) | member(v0, v2))
% 6.41/2.10 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 6.41/2.10 | (22) ! [v0] : ( ~ inductive(v0) | subclass(all_0_0_0, v0))
% 6.41/2.10 | (23) ? [v0] : ? [v1] : (subclass(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 6.41/2.10 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v3, v7) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8)))
% 6.41/2.10 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3))
% 6.41/2.10 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.41/2.10 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 6.41/2.10 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0))
% 6.41/2.10 | (29) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ member(v2, v1) | ~ member(v2, v0))
% 6.41/2.10 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0))
% 6.41/2.10 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | member(v5, all_0_7_7))
% 6.41/2.10 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.41/2.10 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subclass(v0, v1) | member(v2, v1))
% 6.41/2.10 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ (unordered_pair(v2, v4) = v5) | ~ (unordered_pair(v0, v3) = v4) | ordered_pair(v0, v1) = v5)
% 6.41/2.10 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.41/2.10 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3))
% 6.41/2.10 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ subclass(v2, identity_relation) | ~ subclass(v0, all_0_8_8) | function(v0))
% 6.41/2.10 | (38) ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class))
% 6.41/2.10 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0))
% 6.41/2.10 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3)))
% 6.41/2.10 | (41) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v0, universal_class))
% 6.41/2.10 | (42) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_7_7))
% 6.41/2.10 | (43) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0))
% 6.41/2.10 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | member(v5, all_0_7_7))
% 6.41/2.10 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v1, universal_class))
% 6.41/2.10 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = null_class | ~ (restrict(v0, v2, universal_class) = v3) | ~ (singleton(v1) = v2) | ~ member(v1, universal_class) | ? [v4] : (domain_of(v0) = v4 & member(v1, v4)))
% 6.41/2.10 | (47) ! [v0] : ~ member(v0, null_class)
% 6.41/2.10 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 6.41/2.10 | (49) ? [v0] : subclass(v0, v0)
% 6.41/2.10 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | subclass(v0, v1))
% 6.41/2.10 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0))
% 6.41/2.10 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | ? [v6] : ? [v7] : ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8)))
% 6.47/2.10 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 6.47/2.11 | (54) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | subclass(v1, v0))
% 6.47/2.11 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | (first(v2) = v0 & second(v2) = v1))
% 6.47/2.11 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v4) | ~ (ordered_pair(v5, v1) = v6) | ~ (ordered_pair(v2, v3) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_7_7) & member(v6, v0)))))
% 6.47/2.11 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v0, v2, universal_class) = null_class) | ~ (singleton(v1) = v2) | ? [v3] : (domain_of(v0) = v3 & ~ member(v1, v3)))
% 6.47/2.11 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | successor(v0) = v1)
% 6.47/2.11 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3)))
% 6.47/2.11 | (60) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2))
% 6.47/2.11 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 6.47/2.11 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v1, v3) | ~ member(v0, v2) | member(v4, v5))
% 6.47/2.11 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 6.47/2.11 | (64) ! [v0] : ! [v1] : ( ~ (ordered_pair(v1, v1) = v0) | ~ member(v1, universal_class) | member(v0, identity_relation))
% 6.47/2.11 | (65) ! [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))
% 6.47/2.11 | (66) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 6.48/2.11 | (67) ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4
% 6.48/2.11 | (68) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 6.48/2.11 | (69) member(all_0_6_6, universal_class)
% 6.48/2.11 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v1, v3))
% 6.48/2.11 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v6) = v7) | ~ (image(v0, v5) = v6) | ~ (ordered_pair(v2, v3) = v4) | ~ (singleton(v2) = v5) | member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & ~ member(v4, v8)))
% 6.48/2.11 | (72) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) & member(v1, v0) & member(v1, universal_class)))
% 6.48/2.11 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ member(v0, universal_class) | member(v0, v2))
% 6.48/2.11 | (74) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 6.48/2.11 | (75) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 6.48/2.11 | (76) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | member(v1, universal_class))
% 6.48/2.11 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = v2 | ~ (first(v2) = v4) | ~ (second(v2) = v5) | ~ (cross_product(v0, v1) = v3) | ~ (ordered_pair(v4, v5) = v6) | ~ member(v2, v3))
% 6.48/2.11 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v1) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v5, v0) | ? [v7] : ? [v8] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ( ~ member(v8, all_0_7_7) | member(v8, v6))))
% 6.48/2.11 | (79) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 6.48/2.11 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v0, all_0_8_8))
% 6.48/2.11 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, all_0_7_7) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & ~ member(v8, v3)))
% 6.48/2.11 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0))
% 6.48/2.11 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (image(v1, v5) = v6) | ~ (image(v0, v4) = v5) | ~ (ordered_pair(v2, v3) = v7) | ~ (singleton(v2) = v4) | ~ member(v3, v6) | ~ member(v2, universal_class) | ? [v8] : (compose(v1, v0) = v8 & member(v7, v8)))
% 6.48/2.11 | (84) ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ member(v0, universal_class) | member(v1, v0))
% 6.48/2.11 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum_class(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2))
% 6.48/2.11 | (86) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ member(null_class, v0) | ~ subclass(v1, v0) | inductive(v0))
% 6.48/2.11 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.48/2.11 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | member(v0, universal_class))
% 6.48/2.11 | (89) cross_product(all_0_8_8, universal_class) = all_0_7_7
% 6.48/2.11 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 6.48/2.11 | (91) subclass(element_relation, all_0_8_8)
% 6.48/2.11 | (92) ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2))
% 6.48/2.11 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v1, v0) = v4) | ~ member(v5, v3) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, all_0_7_7) | member(v8, v6))))
% 6.48/2.11 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0))
% 6.48/2.11 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1))
% 6.48/2.11 | (96) member(all_0_5_5, universal_class)
% 6.48/2.11 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2)
% 6.48/2.11 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | ~ member(v0, universal_class) | member(v0, v2))
% 6.48/2.11 | (99) ~ (all_0_2_2 = all_0_5_5) | ~ (all_0_3_3 = all_0_6_6)
% 6.48/2.11 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 6.48/2.11 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 6.48/2.11 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3))
% 6.48/2.11 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, v1) | member(v2, element_relation))
% 6.48/2.11 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v0, v2))
% 6.48/2.11 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_8_8))
% 6.48/2.11 | (106) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0)))
% 6.48/2.11 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v4) | ~ (ordered_pair(v5, v2) = v6) | ~ (ordered_pair(v1, v0) = v5) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ( ~ member(v8, v4) | (member(v8, all_0_7_7) & member(v6, v3)))))
% 6.48/2.12 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0)))
% 6.48/2.12 | (109) member(all_0_0_0, universal_class)
% 6.48/2.12 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0))
% 6.48/2.12 | (111) first(all_0_4_4) = all_0_3_3
% 6.48/2.12 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0))
% 6.48/2.12 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v2, identity_relation))
% 6.48/2.12 | (114) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_7_7))
% 6.48/2.12 | (115) ! [v0] : ! [v1] : (v1 = v0 | ~ subclass(v1, v0) | ~ subclass(v0, v1))
% 6.48/2.12 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3))
% 6.48/2.12 | (117) subclass(successor_relation, all_0_8_8)
% 6.48/2.12 | (118) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | member(null_class, v0))
% 6.48/2.12 | (119) second(all_0_4_4) = all_0_2_2
% 6.48/2.12 | (120) ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class))
% 6.48/2.12 | (121) inductive(all_0_0_0)
% 6.48/2.12 | (122) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2))
% 6.48/2.12 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 6.48/2.12 | (124) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0))
% 6.48/2.12 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3) | member(v0, universal_class))
% 6.48/2.12 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | member(v2, universal_class))
% 6.48/2.12 |
% 6.48/2.12 | Instantiating formula (55) with all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms ordered_pair(all_0_6_6, all_0_5_5) = all_0_4_4, member(all_0_5_5, universal_class), member(all_0_6_6, universal_class), yields:
% 6.48/2.12 | (127) first(all_0_4_4) = all_0_6_6 & second(all_0_4_4) = all_0_5_5
% 6.48/2.12 |
% 6.48/2.12 | Applying alpha-rule on (127) yields:
% 6.48/2.12 | (128) first(all_0_4_4) = all_0_6_6
% 6.48/2.12 | (129) second(all_0_4_4) = all_0_5_5
% 6.48/2.12 |
% 6.48/2.12 | Instantiating formula (14) with all_0_4_4, all_0_6_6, all_0_3_3 and discharging atoms first(all_0_4_4) = all_0_3_3, first(all_0_4_4) = all_0_6_6, yields:
% 6.48/2.12 | (130) all_0_3_3 = all_0_6_6
% 6.48/2.12 |
% 6.48/2.12 | Instantiating formula (43) with all_0_4_4, all_0_5_5, all_0_2_2 and discharging atoms second(all_0_4_4) = all_0_2_2, second(all_0_4_4) = all_0_5_5, yields:
% 6.48/2.12 | (131) all_0_2_2 = all_0_5_5
% 6.48/2.12 |
% 6.48/2.12 +-Applying beta-rule and splitting (99), into two cases.
% 6.48/2.12 |-Branch one:
% 6.48/2.12 | (132) ~ (all_0_2_2 = all_0_5_5)
% 6.48/2.12 |
% 6.48/2.12 | Equations (131) can reduce 132 to:
% 6.48/2.12 | (133) $false
% 6.48/2.12 |
% 6.48/2.12 |-The branch is then unsatisfiable
% 6.48/2.12 |-Branch two:
% 6.48/2.12 | (131) all_0_2_2 = all_0_5_5
% 6.48/2.12 | (135) ~ (all_0_3_3 = all_0_6_6)
% 6.48/2.12 |
% 6.48/2.12 | Equations (130) can reduce 135 to:
% 6.48/2.12 | (133) $false
% 6.48/2.12 |
% 6.48/2.12 |-The branch is then unsatisfiable
% 6.48/2.12 % SZS output end Proof for theBenchmark
% 6.48/2.12
% 6.48/2.12 1520ms
%------------------------------------------------------------------------------