TSTP Solution File: SET072+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SET072+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n011.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 00:17:04 EDT 2022
% Result : Theorem 4.33s 1.63s
% Output : Proof 6.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET072+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 01:08:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.61 ____ _
% 0.60/0.61 ___ / __ \_____(_)___ ________ __________
% 0.60/0.61 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.61 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.60/0.61 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.60/0.61
% 0.60/0.61 A Theorem Prover for First-Order Logic
% 0.60/0.61 (ePrincess v.1.0)
% 0.60/0.61
% 0.60/0.61 (c) Philipp Rümmer, 2009-2015
% 0.60/0.61 (c) Peter Backeman, 2014-2015
% 0.60/0.61 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.61 Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.61 Bug reports to peter@backeman.se
% 0.60/0.61
% 0.60/0.61 For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.61
% 0.65/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.78/1.01 Prover 0: Preprocessing ...
% 3.50/1.45 Prover 0: Warning: ignoring some quantifiers
% 3.79/1.49 Prover 0: Constructing countermodel ...
% 4.33/1.63 Prover 0: proved (959ms)
% 4.33/1.63
% 4.33/1.63 No countermodel exists, formula is valid
% 4.33/1.63 % SZS status Theorem for theBenchmark
% 4.33/1.63
% 4.33/1.63 Generating proof ... Warning: ignoring some quantifiers
% 6.31/2.04 found it (size 16)
% 6.31/2.04
% 6.31/2.04 % SZS output start Proof for theBenchmark
% 6.31/2.04 Assumed formulas after preprocessing and simplification:
% 6.31/2.04 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v3 = v2) & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & unordered_pair(v3, v4) = v5 & unordered_pair(v2, v4) = v5 & function(v6) & inductive(v7) & member(v7, universal_class) & member(v3, universal_class) & member(v2, universal_class) & subclass(successor_relation, v0) & subclass(element_relation, v0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image(v9, v14) = v15) | ~ (image(v8, v13) = v14) | ~ (ordered_pair(v10, v11) = v12) | ~ (singleton(v10) = v13) | member(v11, v15) | ? [v16] : (compose(v9, v8) = v16 & ~ member(v12, v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image(v9, v14) = v15) | ~ (image(v8, v13) = v14) | ~ (ordered_pair(v10, v11) = v12) | ~ (singleton(v10) = v13) | member(v10, universal_class) | ? [v16] : (compose(v9, v8) = v16 & ~ member(v12, v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (image(v9, v13) = v14) | ~ (image(v8, v12) = v13) | ~ (ordered_pair(v10, v11) = v15) | ~ (singleton(v10) = v12) | ~ member(v11, v14) | ~ member(v10, universal_class) | ? [v16] : (compose(v9, v8) = v16 & member(v15, v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v10 | ~ (first(v10) = v12) | ~ (second(v10) = v13) | ~ (cross_product(v8, v9) = v11) | ~ (ordered_pair(v12, v13) = v14) | ~ member(v10, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (flip(v11) = v14) | ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v9, v8) = v12) | ~ member(v13, v11) | ? [v15] : ? [v16] : (ordered_pair(v15, v10) = v16 & ordered_pair(v8, v9) = v15 & ( ~ member(v16, v1) | member(v16, v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (flip(v11) = v14) | ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ member(v13, v14) | member(v13, v1)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (flip(v11) = v14) | ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ member(v13, v14) | ? [v15] : ? [v16] : (ordered_pair(v15, v10) = v16 & ordered_pair(v9, v8) = v15 & member(v16, v11))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (flip(v11) = v14) | ~ (ordered_pair(v12, v10) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ member(v13, v1) | member(v13, v14) | ? [v15] : ? [v16] : (ordered_pair(v15, v10) = v16 & ordered_pair(v9, v8) = v15 & ~ member(v16, v11))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (flip(v11) = v12) | ~ (ordered_pair(v13, v10) = v14) | ~ (ordered_pair(v9, v8) = v13) | ? [v15] : ? [v16] : (ordered_pair(v15, v10) = v16 & ordered_pair(v8, v9) = v15 & ( ~ member(v16, v12) | (member(v16, v1) & member(v14, v11))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (rotate(v8) = v14) | ~ (ordered_pair(v12, v11) = v13) | ~ (ordered_pair(v9, v10) = v12) | ~ member(v13, v14) | member(v13, v1)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (rotate(v8) = v14) | ~ (ordered_pair(v12, v11) = v13) | ~ (ordered_pair(v9, v10) = v12) | ~ member(v13, v14) | ? [v15] : ? [v16] : (ordered_pair(v15, v9) = v16 & ordered_pair(v10, v11) = v15 & member(v16, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (rotate(v8) = v14) | ~ (ordered_pair(v12, v11) = v13) | ~ (ordered_pair(v9, v10) = v12) | ~ member(v13, v1) | member(v13, v14) | ? [v15] : ? [v16] : (ordered_pair(v15, v9) = v16 & ordered_pair(v10, v11) = v15 & ~ member(v16, v8))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (rotate(v8) = v14) | ~ (ordered_pair(v12, v9) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ member(v13, v8) | ? [v15] : ? [v16] : (ordered_pair(v15, v11) = v16 & ordered_pair(v9, v10) = v15 & ( ~ member(v16, v1) | member(v16, v14)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (rotate(v8) = v12) | ~ (ordered_pair(v13, v9) = v14) | ~ (ordered_pair(v10, v11) = v13) | ? [v15] : ? [v16] : (ordered_pair(v15, v11) = v16 & ordered_pair(v9, v10) = v15 & ( ~ member(v16, v12) | (member(v16, v1) & member(v14, v8))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose(v9, v8) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ member(v12, v13) | member(v10, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose(v9, v8) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ member(v12, v13) | ? [v14] : ? [v15] : ? [v16] : (image(v9, v15) = v16 & image(v8, v14) = v15 & singleton(v10) = v14 & member(v11, v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (compose(v9, v8) = v13) | ~ (ordered_pair(v10, v11) = v12) | ~ member(v10, universal_class) | member(v12, v13) | ? [v14] : ? [v15] : ? [v16] : (image(v9, v15) = v16 & image(v8, v14) = v15 & singleton(v10) = v14 & ~ member(v11, v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cross_product(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ member(v12, v13) | member(v9, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cross_product(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ member(v12, v13) | member(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cross_product(v10, v11) = v13) | ~ (ordered_pair(v8, v9) = v12) | ~ member(v9, v11) | ~ member(v8, v10) | member(v12, v13)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (singleton(v9) = v11) | ~ (singleton(v8) = v10) | ~ (unordered_pair(v10, v12) = v13) | ~ (unordered_pair(v8, v11) = v12) | ordered_pair(v8, 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) | ~ member(v9, universal_class) | ? [v12] : (domain_of(v8) = v12 & member(v9, v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = v8 | v9 = v8 | ~ (unordered_pair(v9, v10) = v11) | ~ member(v8, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (apply(v11, v10) = v9) | ~ (apply(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] : ( ~ (sum_class(v9) = v10) | ~ member(v11, v9) | ~ member(v8, v11) | member(v8, v10)) & ! [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) | member(v10, v9) | member(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v8, v9) = v11) | ~ member(v10, v9) | member(v10, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (union(v8, v9) = v11) | ~ member(v10, v8) | member(v10, v11)) & ! [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) | member(v9, universal_class) | ? [v12] : (domain_of(v8) = v12 & ~ member(v9, v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ member(v10, v11) | member(v10, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ member(v10, v11) | member(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (intersection(v8, v9) = v11) | ~ member(v10, v9) | ~ member(v10, v8) | member(v10, v11)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unordered_pair(v9, v10) = v11) | ~ member(v8, v11) | member(v8, universal_class)) & ! [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 | ~ (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] : ( ~ (apply(v8, v9) = v10) | ? [v11] : ? [v12] : (sum_class(v12) = v10 & image(v8, v11) = v12 & singleton(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (compose(v9, v8) = v10) | subclass(v10, v0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (compose(v8, v9) = v10) | ~ (inverse(v8) = v9) | ~ function(v8) | subclass(v10, identity_relation)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (compose(v8, v9) = v10) | ~ (inverse(v8) = v9) | ~ function(v8) | subclass(v8, v0)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (compose(v8, v9) = v10) | ~ (inverse(v8) = v9) | ~ subclass(v10, identity_relation) | ~ subclass(v8, v0) | function(v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_class(v9) = v10) | ~ member(v8, v10) | member(v8, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_class(v9) = v10) | ~ member(v8, v10) | subclass(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (power_class(v9) = v10) | ~ member(v8, universal_class) | ~ subclass(v8, v9) | member(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (sum_class(v9) = v10) | ~ member(v8, v10) | ? [v11] : (member(v11, v9) & member(v8, v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (image(v9, v8) = v10) | ~ function(v9) | ~ member(v8, universal_class) | member(v10, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (image(v9, v8) = v10) | ? [v11] : (range_of(v11) = v10 & restrict(v9, v8, universal_class) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (union(v8, v9) = v10) | ~ (singleton(v8) = v9) | successor(v8) = v10) & ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v9, v8, universal_class) = v10) | ? [v11] : (image(v9, v8) = v11 & range_of(v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (restrict(v8, v10, universal_class) = null_class) | ~ (singleton(v9) = v10) | ? [v11] : (domain_of(v8) = v11 & ~ member(v9, v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (complement(v8) = v10) | ~ member(v9, v10) | ~ member(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (complement(v8) = v10) | ~ member(v9, v10) | member(v9, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (complement(v8) = v10) | ~ member(v9, universal_class) | member(v9, v10) | member(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v10, successor_relation) | successor(v8) = v9) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v10, successor_relation) | member(v9, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v10, successor_relation) | member(v8, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v10, element_relation) | member(v9, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v10, element_relation) | member(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v9, universal_class) | ~ member(v8, v9) | member(v10, element_relation)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v9, universal_class) | ~ member(v8, universal_class) | member(v10, successor_relation) | ? [v11] : ( ~ (v11 = v9) & successor(v8) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) | ~ member(v9, universal_class) | ~ member(v8, universal_class) | (first(v10) = v8 & second(v10) = v9)) & ! [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] : ( ~ (unordered_pair(v9, v8) = v10) | ~ member(v8, universal_class) | member(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | ~ member(v8, universal_class) | member(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | member(v10, universal_class)) & ! [v8] : ! [v9] : ! [v10] : ( ~ disjoint(v8, v9) | ~ member(v10, v9) | ~ member(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ member(v10, v8) | ~ subclass(v8, v9) | member(v10, v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ subclass(v9, v8) | ~ subclass(v8, v9)) & ! [v8] : ! [v9] : (v8 = null_class | ~ (apply(v6, v8) = v9) | ~ member(v8, universal_class) | member(v9, v8)) & ! [v8] : ! [v9] : ( ~ (power_class(v8) = v9) | ~ member(v8, universal_class) | member(v9, universal_class)) & ! [v8] : ! [v9] : ( ~ (sum_class(v8) = v9) | ~ member(v8, universal_class) | member(v9, universal_class)) & ! [v8] : ! [v9] : ( ~ (image(successor_relation, v8) = v9) | ~ inductive(v8) | member(null_class, v8)) & ! [v8] : ! [v9] : ( ~ (image(successor_relation, v8) = v9) | ~ inductive(v8) | subclass(v9, v8)) & ! [v8] : ! [v9] : ( ~ (image(successor_relation, v8) = v9) | ~ member(null_class, v8) | ~ subclass(v9, v8) | inductive(v8)) & ! [v8] : ! [v9] : ( ~ (range_of(v8) = v9) | ? [v10] : (inverse(v8) = v10 & domain_of(v10) = v9)) & ! [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] : (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)) & ! [v8] : ! [v9] : ( ~ (rotate(v8) = v9) | subclass(v9, v1)) & ! [v8] : ! [v9] : ( ~ (cross_product(v8, universal_class) = v9) | ? [v10] : ? [v11] : (inverse(v8) = v10 & flip(v9) = v11 & domain_of(v11) = v10)) & ! [v8] : ! [v9] : ( ~ (ordered_pair(v9, v9) = v8) | ~ member(v9, universal_class) | member(v8, identity_relation)) & ! [v8] : ! [v9] : ( ~ (singleton(v8) = v9) | unordered_pair(v8, v8) = v9) & ! [v8] : ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) & ! [v8] : ( ~ inductive(v8) | subclass(v7, v8)) & ! [v8] : ( ~ member(v8, identity_relation) | ? [v9] : (ordered_pair(v9, v9) = v8 & member(v9, universal_class))) & ! [v8] : ~ member(v8, null_class) & ? [v8] : ? [v9] : (disjoint(v8, v9) | ? [v10] : (member(v10, v9) & member(v10, v8))) & ? [v8] : ? [v9] : (subclass(v8, v9) | ? [v10] : (member(v10, v8) & ~ member(v10, v9))) & ? [v8] : (v8 = null_class | ? [v9] : (disjoint(v9, v8) & member(v9, v8) & member(v9, universal_class))) & ? [v8] : subclass(v8, v8) & ? [v8] : subclass(v8, universal_class))
% 6.66/2.12 | 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:
% 6.66/2.12 | (1) ~ (all_0_4_4 = all_0_5_5) & cross_product(all_0_7_7, universal_class) = all_0_6_6 & cross_product(universal_class, universal_class) = all_0_7_7 & unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2 & function(all_0_1_1) & inductive(all_0_0_0) & member(all_0_0_0, universal_class) & member(all_0_4_4, universal_class) & member(all_0_5_5, universal_class) & subclass(successor_relation, all_0_7_7) & subclass(element_relation, all_0_7_7) & ! [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_6_6) | 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_6_6)) & ! [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_6_6) | 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_6_6) & 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_6_6)) & ! [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_6_6) | 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_6_6) | 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_6_6) & 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_7_7)) & ! [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_7_7)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ subclass(v2, identity_relation) | ~ subclass(v0, all_0_7_7) | 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_6_6)) & ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_6_6)) & ! [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)
% 6.66/2.14 |
% 6.66/2.14 | Applying alpha-rule on (1) yields:
% 6.66/2.14 | (2) ! [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)))
% 6.66/2.14 | (3) ! [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_6_6))
% 6.66/2.14 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0))
% 6.66/2.14 | (5) ! [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))
% 6.66/2.14 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v1) | ~ member(v2, v0) | member(v2, v3))
% 6.66/2.14 | (7) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (rotate(v2) = v1) | ~ (rotate(v2) = v0))
% 6.66/2.14 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 6.66/2.15 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v0, v2))
% 6.66/2.15 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | member(v1, universal_class))
% 6.66/2.15 | (11) ? [v0] : ? [v1] : (subclass(v0, v1) | ? [v2] : (member(v2, v0) & ~ member(v2, v1)))
% 6.66/2.15 | (12) function(all_0_1_1)
% 6.66/2.15 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apply(v3, v2) = v1) | ~ (apply(v3, v2) = v0))
% 6.66/2.15 | (14) ! [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)
% 6.66/2.15 | (15) ! [v0] : ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_6_6))
% 6.66/2.15 | (16) ? [v0] : (v0 = null_class | ? [v1] : (disjoint(v1, v0) & member(v1, v0) & member(v1, universal_class)))
% 6.66/2.15 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0))
% 6.66/2.15 | (18) ! [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)))
% 6.66/2.15 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0))
% 6.66/2.15 | (20) ! [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))
% 6.66/2.15 | (21) member(all_0_4_4, universal_class)
% 6.66/2.15 | (22) ! [v0] : ! [v1] : ( ~ (range_of(v0) = v1) | ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 6.66/2.15 | (23) ! [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)))
% 6.66/2.15 | (24) cross_product(universal_class, universal_class) = all_0_7_7
% 6.66/2.15 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v0) | member(v2, v3))
% 6.66/2.15 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0))
% 6.66/2.15 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ subclass(v2, identity_relation) | ~ subclass(v0, all_0_7_7) | function(v0))
% 6.66/2.15 | (28) ! [v0] : ! [v1] : ( ~ (ordered_pair(v1, v1) = v0) | ~ member(v1, universal_class) | member(v0, identity_relation))
% 6.66/2.15 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v0))
% 6.66/2.15 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0))
% 6.66/2.15 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v2, identity_relation))
% 6.66/2.15 | (32) ! [v0] : ! [v1] : ! [v2] : ( ~ disjoint(v0, v1) | ~ member(v2, v1) | ~ member(v2, v0))
% 6.66/2.15 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3))
% 6.66/2.15 | (34) ? [v0] : subclass(v0, v0)
% 6.66/2.15 | (35) ! [v0] : ! [v1] : ( ~ (sum_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class))
% 6.66/2.15 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, universal_class) | ~ subclass(v0, v1) | member(v0, v2))
% 6.66/2.15 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0))
% 6.66/2.15 | (38) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2))
% 6.66/2.15 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, v2) | ~ member(v1, v0))
% 6.66/2.15 | (40) ! [v0] : ~ member(v0, null_class)
% 6.66/2.15 | (41) ? [v0] : subclass(v0, universal_class)
% 6.66/2.16 | (42) ! [v0] : ( ~ member(v0, identity_relation) | ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class)))
% 6.66/2.16 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | member(v0, universal_class))
% 6.66/2.16 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v0, v2, universal_class) = null_class) | ~ (singleton(v1) = v2) | ? [v3] : (domain_of(v0) = v3 & ~ member(v1, v3)))
% 6.66/2.16 | (45) subclass(successor_relation, all_0_7_7)
% 6.66/2.16 | (46) ! [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)))
% 6.66/2.16 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (image(v0, v2) = v3) | ~ (singleton(v1) = v2) | ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 6.66/2.16 | (48) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class))
% 6.66/2.16 | (49) ! [v0] : ! [v1] : (v0 = null_class | ~ (apply(all_0_1_1, v0) = v1) | ~ member(v0, universal_class) | member(v1, v0))
% 6.66/2.16 | (50) ! [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)))
% 6.66/2.16 | (51) ! [v0] : ! [v1] : ( ~ (inverse(v0) = v1) | ? [v2] : ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2))
% 6.66/2.16 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v0, v1))
% 6.66/2.16 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0))
% 6.66/2.16 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v1) | member(v2, v3))
% 6.66/2.16 | (55) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | subclass(v1, v0))
% 6.66/2.16 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (complement(v0) = v2) | ~ member(v1, universal_class) | member(v1, v2) | member(v1, v0))
% 6.66/2.16 | (57) ! [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_6_6) & member(v6, v3)))))
% 6.66/2.16 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cross_product(v2, v3) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v4, v5) | member(v1, v3))
% 6.66/2.16 | (59) ! [v0] : ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 6.66/2.16 | (60) ! [v0] : ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 6.66/2.16 | (61) subclass(element_relation, all_0_7_7)
% 6.66/2.16 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (intersection(v1, v3) = v4) | ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 6.66/2.16 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | ~ member(v0, universal_class) | member(v0, v2))
% 6.66/2.16 | (64) cross_product(all_0_7_7, universal_class) = all_0_6_6
% 6.66/2.16 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) | ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4))
% 6.66/2.16 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) | ~ member(v0, v3) | member(v0, universal_class))
% 6.66/2.16 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (rotate(v0) = v6) | ~ (ordered_pair(v4, v3) = v5) | ~ (ordered_pair(v1, v2) = v4) | ~ member(v5, all_0_6_6) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & ~ member(v8, v0)))
% 6.66/2.17 | (68) ! [v0] : ( ~ inductive(v0) | subclass(all_0_0_0, v0))
% 6.66/2.17 | (69) ! [v0] : ! [v1] : ! [v2] : ( ~ (apply(v0, v1) = v2) | ? [v3] : ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3))
% 6.66/2.17 | (70) ~ (all_0_4_4 = all_0_5_5)
% 6.66/2.17 | (71) ! [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)))
% 6.66/2.17 | (72) member(all_0_5_5, universal_class)
% 6.66/2.17 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (power_class(v1) = v2) | ~ member(v0, v2) | subclass(v0, v1))
% 6.66/2.17 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3, v2) = v0))
% 6.66/2.17 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ~ function(v1) | ~ member(v0, universal_class) | member(v2, universal_class))
% 6.66/2.17 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (intersection(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1))
% 6.66/2.17 | (77) ! [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_6_6))
% 6.66/2.17 | (78) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ member(null_class, v0) | ~ subclass(v1, v0) | inductive(v0))
% 6.66/2.17 | (79) ! [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)))
% 6.66/2.17 | (80) ! [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))
% 6.66/2.17 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0))
% 6.66/2.17 | (82) ! [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))
% 6.66/2.17 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_7_7))
% 6.66/2.17 | (84) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (flip(v2) = v1) | ~ (flip(v2) = v0))
% 6.66/2.17 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (compose(v1, v0) = v5) | ~ (ordered_pair(v2, v3) = v4) | ~ member(v4, v5) | member(v2, universal_class))
% 6.66/2.17 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (union(v0, v1) = v3) | ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 6.66/2.17 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ (union(v0, v1) = v2) | ~ (singleton(v0) = v1) | successor(v0) = v2)
% 6.66/2.17 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (sum_class(v1) = v2) | ~ member(v0, v2) | ? [v3] : (member(v3, v1) & member(v0, v3)))
% 6.66/2.17 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v0, universal_class))
% 6.66/2.17 | (90) ! [v0] : ! [v1] : (v1 = v0 | ~ subclass(v1, v0) | ~ subclass(v0, v1))
% 6.66/2.17 | (91) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (complement(v2) = v1) | ~ (complement(v2) = v0))
% 6.66/2.17 | (92) member(all_0_0_0, universal_class)
% 6.66/2.17 | (93) ! [v0] : ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) | ? [v2] : ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 6.66/2.17 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (sum_class(v1) = v2) | ~ member(v3, v1) | ~ member(v0, v3) | member(v0, v2))
% 6.66/2.17 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (image(v1, v0) = v2) | ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3))
% 6.66/2.17 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ member(v2, v0) | ~ subclass(v0, v1) | member(v2, v1))
% 6.66/2.17 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) | ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 6.66/2.17 | (98) ! [v0] : ! [v1] : ( ~ (image(successor_relation, v0) = v1) | ~ inductive(v0) | member(null_class, v0))
% 6.66/2.17 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0))
% 6.66/2.17 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | member(v1, universal_class))
% 6.66/2.17 | (101) ! [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)))
% 6.66/2.18 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0))
% 6.66/2.18 | (103) unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2
% 6.66/2.18 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, v1) | member(v2, element_relation))
% 6.66/2.18 | (105) ! [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_6_6) | member(v8, v6))))
% 6.66/2.18 | (106) inductive(all_0_0_0)
% 6.66/2.18 | (107) ! [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)))
% 6.66/2.18 | (108) ! [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_6_6) & member(v6, v0)))))
% 6.66/2.18 | (109) ! [v0] : ! [v1] : ( ~ (power_class(v0) = v1) | ~ member(v0, universal_class) | member(v1, universal_class))
% 6.66/2.18 | (110) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0))
% 6.66/2.18 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ~ member(v0, universal_class) | member(v0, v2))
% 6.66/2.18 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, element_relation) | member(v1, universal_class))
% 6.66/2.18 | (113) ? [v0] : ? [v1] : (disjoint(v0, v1) | ? [v2] : (member(v2, v1) & member(v2, v0)))
% 6.66/2.18 | (114) unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2
% 6.66/2.18 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) = v0))
% 6.66/2.18 | (116) ! [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_6_6) | member(v8, v6))))
% 6.66/2.18 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (flip(v3) = v6) | ~ (ordered_pair(v4, v2) = v5) | ~ (ordered_pair(v0, v1) = v4) | ~ member(v5, all_0_6_6) | member(v5, v6) | ? [v7] : ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & ~ member(v8, v3)))
% 6.66/2.18 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~ (compose(v3, v2) = v0))
% 6.66/2.18 | (119) ! [v0] : ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_6_6))
% 6.66/2.18 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (compose(v0, v1) = v2) | ~ (inverse(v0) = v1) | ~ function(v0) | subclass(v0, all_0_7_7))
% 6.66/2.18 | (121) ! [v0] : ! [v1] : ( ~ (successor(v0) = v1) | ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2))
% 6.66/2.18 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v1, universal_class) | ~ member(v0, universal_class) | (first(v2) = v0 & second(v2) = v1))
% 6.66/2.18 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (inverse(v2) = v1) | ~ (inverse(v2) = v0))
% 6.66/2.18 | (124) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (power_class(v2) = v1) | ~ (power_class(v2) = v0))
% 6.66/2.18 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) | ~ member(v2, successor_relation) | successor(v0) = v1)
% 6.66/2.18 |
% 6.96/2.18 | Instantiating formula (111) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_0_4_4, universal_class), yields:
% 6.96/2.18 | (126) member(all_0_4_4, all_0_2_2)
% 6.96/2.18 |
% 6.96/2.18 | Instantiating formula (111) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2, member(all_0_5_5, universal_class), yields:
% 6.96/2.18 | (127) member(all_0_5_5, all_0_2_2)
% 6.96/2.18 |
% 6.96/2.18 | Instantiating formula (33) with all_0_2_2, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2, member(all_0_4_4, all_0_2_2), yields:
% 6.96/2.18 | (128) all_0_3_3 = all_0_4_4 | all_0_4_4 = all_0_5_5
% 6.96/2.18 |
% 6.96/2.18 | Instantiating formula (33) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, member(all_0_5_5, all_0_2_2), yields:
% 6.96/2.18 | (129) all_0_3_3 = all_0_5_5 | all_0_4_4 = all_0_5_5
% 6.96/2.18 |
% 6.96/2.18 +-Applying beta-rule and splitting (129), into two cases.
% 6.96/2.18 |-Branch one:
% 6.96/2.18 | (130) all_0_3_3 = all_0_5_5
% 6.96/2.18 |
% 6.96/2.18 +-Applying beta-rule and splitting (128), into two cases.
% 6.96/2.18 |-Branch one:
% 6.96/2.18 | (131) all_0_3_3 = all_0_4_4
% 6.96/2.18 |
% 6.96/2.18 | Combining equations (131,130) yields a new equation:
% 6.96/2.18 | (132) all_0_4_4 = all_0_5_5
% 6.96/2.18 |
% 6.96/2.18 | Simplifying 132 yields:
% 6.96/2.18 | (133) all_0_4_4 = all_0_5_5
% 6.96/2.18 |
% 6.96/2.18 | Equations (133) can reduce 70 to:
% 6.96/2.18 | (134) $false
% 6.96/2.18 |
% 6.96/2.19 |-The branch is then unsatisfiable
% 6.96/2.19 |-Branch two:
% 6.96/2.19 | (135) ~ (all_0_3_3 = all_0_4_4)
% 6.96/2.19 | (133) all_0_4_4 = all_0_5_5
% 6.96/2.19 |
% 6.96/2.19 | Equations (133) can reduce 70 to:
% 6.96/2.19 | (134) $false
% 6.96/2.19 |
% 6.96/2.19 |-The branch is then unsatisfiable
% 6.96/2.19 |-Branch two:
% 6.96/2.19 | (138) ~ (all_0_3_3 = all_0_5_5)
% 6.96/2.19 | (133) all_0_4_4 = all_0_5_5
% 6.96/2.19 |
% 6.96/2.19 | Equations (133) can reduce 70 to:
% 6.96/2.19 | (134) $false
% 6.96/2.19 |
% 6.96/2.19 |-The branch is then unsatisfiable
% 6.96/2.19 % SZS output end Proof for theBenchmark
% 6.96/2.19
% 6.96/2.19 1560ms
%------------------------------------------------------------------------------