%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET065+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n014.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 00:16:57 EDT 2022

% Result   : Theorem 21.70s 5.87s
% Output   : Proof 48.16s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET065+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.11/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n014.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jul 11 00:02:19 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.76/0.99  Prover 0: Preprocessing ...
% 3.28/1.39  Prover 0: Warning: ignoring some quantifiers
% 3.28/1.42  Prover 0: Constructing countermodel ...
% 6.50/2.11  Prover 0: gave up
% 6.50/2.11  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 6.76/2.17  Prover 1: Preprocessing ...
% 7.44/2.32  Prover 1: Warning: ignoring some quantifiers
% 7.44/2.33  Prover 1: Constructing countermodel ...
% 19.01/5.29  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 19.46/5.35  Prover 2: Preprocessing ...
% 20.07/5.52  Prover 2: Warning: ignoring some quantifiers
% 20.07/5.52  Prover 2: Constructing countermodel ...
% 21.34/5.87  Prover 2: proved (579ms)
% 21.70/5.87  Prover 1: stopped
% 21.70/5.87  
% 21.70/5.87  No countermodel exists, formula is valid
% 21.70/5.87  % SZS status Theorem for theBenchmark
% 21.70/5.87  
% 21.70/5.87  Generating proof ... Warning: ignoring some quantifiers
% 47.20/17.81  found it (size 149)
% 47.20/17.81  
% 47.20/17.81  % SZS output start Proof for theBenchmark
% 47.20/17.81  Assumed formulas after preprocessing and simplification: 
% 47.20/17.81  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v2 = 0) & function(v3) = 0 & inductive(v4) = 0 & cross_product(v0, universal_class) = v1 & cross_product(universal_class, universal_class) = v0 & subclass(successor_relation, v0) = 0 & subclass(element_relation, v0) = 0 & member(v4, universal_class) = 0 & member(null_class, universal_class) = v2 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (flip(v8) = v11) |  ~ (ordered_pair(v9, v7) = v10) |  ~ (ordered_pair(v5, v6) = v9) |  ~ (member(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (( ~ (v15 = 0) & ordered_pair(v13, v7) = v14 & ordered_pair(v6, v5) = v13 & member(v14, v8) = v15) | ( ~ (v13 = 0) & member(v10, v1) = v13))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (rotate(v5) = v11) |  ~ (ordered_pair(v9, v8) = v10) |  ~ (ordered_pair(v6, v7) = v9) |  ~ (member(v10, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : (( ~ (v15 = 0) & ordered_pair(v13, v6) = v14 & ordered_pair(v7, v8) = v13 & member(v14, v5) = v15) | ( ~ (v13 = 0) & member(v10, v1) = v13))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (image(v6, v10) = v11) |  ~ (image(v5, v9) = v10) |  ~ (singleton(v7) = v9) |  ~ (member(v8, v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : ((v13 = 0 & v12 = 0 & member(v7, universal_class) = 0) | ( ~ (v15 = 0) & compose(v6, v5) = v14 & ordered_pair(v7, v8) = v13 & member(v13, v14) = v15))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (compose(v6, v5) = v10) |  ~ (ordered_pair(v7, v8) = v9) |  ~ (member(v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (( ~ (v15 = 0) & image(v6, v13) = v14 & image(v5, v12) = v13 & singleton(v7) = v12 & member(v8, v14) = v15) | ( ~ (v12 = 0) & member(v7, universal_class) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (cross_product(v7, v8) = v10) |  ~ (ordered_pair(v5, v6) = v9) |  ~ (member(v9, v10) = v11) |  ? [v12] : (( ~ (v12 = 0) & member(v6, v8) = v12) | ( ~ (v12 = 0) & member(v5, v7) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (image(v6, v10) = v11) |  ~ (image(v5, v9) = v10) |  ~ (singleton(v7) = v9) |  ~ (member(v8, v11) = 0) |  ? [v12] :  ? [v13] :  ? [v14] : ((v14 = 0 & compose(v6, v5) = v13 & ordered_pair(v7, v8) = v12 & member(v12, v13) = 0) | ( ~ (v12 = 0) & member(v7, universal_class) = v12))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (flip(v8) = v11) |  ~ (ordered_pair(v9, v7) = v10) |  ~ (ordered_pair(v5, v6) = v9) |  ~ (member(v10, v11) = 0) |  ? [v12] :  ? [v13] : (ordered_pair(v12, v7) = v13 & ordered_pair(v6, v5) = v12 & member(v13, v8) = 0 & member(v10, v1) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (rotate(v5) = v11) |  ~ (ordered_pair(v9, v8) = v10) |  ~ (ordered_pair(v6, v7) = v9) |  ~ (member(v10, v11) = 0) |  ? [v12] :  ? [v13] : (ordered_pair(v12, v6) = v13 & ordered_pair(v7, v8) = v12 & member(v13, v5) = 0 & member(v10, v1) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (ordered_pair(v9, v7) = v10) |  ~ (ordered_pair(v6, v5) = v9) |  ~ (member(v10, v8) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (ordered_pair(v12, v7) = v13 & ordered_pair(v5, v6) = v12 & ((v14 = 0 & v11 = 0 & member(v13, v1) = 0) | ( ~ (v15 = 0) & flip(v8) = v14 & member(v13, v14) = v15)))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (ordered_pair(v9, v6) = v10) |  ~ (ordered_pair(v7, v8) = v9) |  ~ (member(v10, v5) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (ordered_pair(v12, v8) = v13 & ordered_pair(v6, v7) = v12 & ((v14 = 0 & v11 = 0 & member(v13, v1) = 0) | ( ~ (v15 = 0) & rotate(v5) = v14 & member(v13, v14) = v15)))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (compose(v6, v5) = v10) |  ~ (ordered_pair(v7, v8) = v9) |  ~ (member(v9, v10) = 0) |  ? [v11] :  ? [v12] :  ? [v13] : (image(v6, v12) = v13 & image(v5, v11) = v12 & singleton(v7) = v11 & member(v8, v13) = 0 & member(v7, universal_class) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (cross_product(v7, v8) = v10) |  ~ (ordered_pair(v5, v6) = v9) |  ~ (member(v9, v10) = 0) | (member(v6, v8) = 0 & member(v5, v7) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (ordered_pair(v9, v7) = v10) |  ~ (ordered_pair(v6, v5) = v9) |  ~ (member(v10, v8) = 0) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (ordered_pair(v11, v7) = v12 & ordered_pair(v5, v6) = v11 & ((v14 = 0 & flip(v8) = v13 & member(v12, v13) = 0) | ( ~ (v13 = 0) & member(v12, v1) = v13)))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (ordered_pair(v9, v6) = v10) |  ~ (ordered_pair(v7, v8) = v9) |  ~ (member(v10, v5) = 0) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (ordered_pair(v11, v8) = v12 & ordered_pair(v6, v7) = v11 & ((v14 = 0 & rotate(v5) = v13 & member(v12, v13) = 0) | ( ~ (v13 = 0) & member(v12, v1) = v13)))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (union(v5, v6) = v8) |  ~ (member(v7, v8) = v9) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) &  ~ (v10 = 0) & member(v7, v6) = v11 & member(v7, v5) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (intersection(v5, v6) = v8) |  ~ (member(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & member(v7, v6) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (sum_class(v6) = v7) |  ~ (member(v9, v6) = 0) |  ~ (member(v5, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & member(v5, v9) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v8 = 0 |  ~ (sum_class(v6) = v7) |  ~ (member(v5, v9) = 0) |  ~ (member(v5, v7) = v8) |  ? [v10] : ( ~ (v10 = 0) & member(v9, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v6 = v5 |  ~ (restrict(v9, v8, v7) = v6) |  ~ (restrict(v9, v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection(v6, v8) = v9) |  ~ (cross_product(v5, v7) = v8) | restrict(v6, v5, v7) = v9) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = null_class |  ~ (restrict(v5, v7, universal_class) = v8) |  ~ (singleton(v6) = v7) |  ? [v9] :  ? [v10] : ((v10 = 0 & domain_of(v5) = v9 & member(v6, v9) = 0) | ( ~ (v9 = 0) & member(v6, universal_class) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (power_class(v6) = v7) |  ~ (member(v5, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & subclass(v5, v6) = v9) | ( ~ (v9 = 0) & member(v5, universal_class) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (domain_of(v5) = v7) |  ~ (member(v6, v7) = v8) |  ? [v9] :  ? [v10] : ((v10 = null_class & restrict(v5, v9, universal_class) = null_class & singleton(v6) = v9) | ( ~ (v9 = 0) & member(v6, universal_class) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (complement(v5) = v7) |  ~ (member(v6, v7) = v8) |  ? [v9] : ((v9 = 0 & member(v6, v5) = 0) | ( ~ (v9 = 0) & member(v6, universal_class) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unordered_pair(v6, v5) = v7) |  ~ (member(v5, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & member(v5, universal_class) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unordered_pair(v5, v6) = v7) |  ~ (member(v5, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & member(v5, universal_class) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (subclass(v5, v6) = 0) |  ~ (member(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v5 | v6 = v5 |  ~ (unordered_pair(v6, v7) = v8) |  ~ (member(v5, v8) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (apply(v8, v7) = v6) |  ~ (apply(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (disjoint(v8, v7) = v6) |  ~ (disjoint(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (compose(v8, v7) = v6) |  ~ (compose(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (image(v8, v7) = v6) |  ~ (image(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (union(v8, v7) = v6) |  ~ (union(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection(v8, v7) = v6) |  ~ (intersection(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (cross_product(v8, v7) = v6) |  ~ (cross_product(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (ordered_pair(v8, v7) = v6) |  ~ (ordered_pair(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (unordered_pair(v8, v7) = v6) |  ~ (unordered_pair(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (subclass(v8, v7) = v6) |  ~ (subclass(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (member(v8, v7) = v6) |  ~ (member(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (image(v5, v7) = v8) |  ~ (singleton(v6) = v7) |  ? [v9] : (apply(v5, v6) = v9 & sum_class(v8) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v5, v6) = v8) |  ~ (member(v7, v8) = 0) |  ? [v9] : ((v9 = 0 & member(v7, v6) = 0) | (v9 = 0 & member(v7, v5) = 0))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (restrict(v6, v5, v7) = v8) |  ? [v9] : (intersection(v6, v9) = v8 & cross_product(v5, v7) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (restrict(v5, v7, universal_class) = v8) |  ~ (singleton(v6) = v7) |  ? [v9] :  ? [v10] : ((v9 = 0 &  ~ (v8 = null_class) & member(v6, universal_class) = 0) | ( ~ (v10 = 0) & domain_of(v5) = v9 & member(v6, v9) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v5, v6) = v8) |  ~ (member(v7, v8) = 0) | (member(v7, v6) = 0 & member(v7, v5) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (cross_product(v5, v6) = v8) |  ~ (member(v7, v8) = 0) |  ? [v9] :  ? [v10] : (first(v7) = v9 & second(v7) = v10 & ordered_pair(v9, v10) = v7)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (singleton(v6) = v7) |  ~ (unordered_pair(v5, v7) = v8) |  ? [v9] :  ? [v10] : (ordered_pair(v5, v6) = v9 & singleton(v5) = v10 & unordered_pair(v10, v8) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (unordered_pair(v6, v7) = v8) |  ~ (member(v5, v8) = 0) | member(v5, universal_class) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (disjoint(v5, v6) = v7) |  ? [v8] : (member(v8, v6) = 0 & member(v8, v5) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (subclass(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (member(v6, v5) = v7) |  ? [v8] :  ? [v9] : ((v9 = 0 & complement(v5) = v8 & member(v6, v8) = 0) | ( ~ (v8 = 0) & member(v6, universal_class) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (function(v7) = v6) |  ~ (function(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (power_class(v7) = v6) |  ~ (power_class(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (sum_class(v7) = v6) |  ~ (sum_class(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (inductive(v7) = v6) |  ~ (inductive(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (range_of(v7) = v6) |  ~ (range_of(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (inverse(v7) = v6) |  ~ (inverse(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (successor(v7) = v6) |  ~ (successor(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (flip(v7) = v6) |  ~ (flip(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (rotate(v7) = v6) |  ~ (rotate(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (domain_of(v7) = v6) |  ~ (domain_of(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (complement(v7) = v6) |  ~ (complement(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (first(v7) = v6) |  ~ (first(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (second(v7) = v6) |  ~ (second(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (singleton(v7) = v6) |  ~ (singleton(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = 0 |  ~ (ordered_pair(v7, v7) = v5) |  ~ (member(v5, identity_relation) = v6) |  ? [v8] : ( ~ (v8 = 0) & member(v7, universal_class) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = 0 |  ~ (member(v7, universal_class) = 0) |  ~ (member(v5, identity_relation) = v6) |  ? [v8] : ( ~ (v8 = v5) & ordered_pair(v7, v7) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (apply(v5, v6) = v7) |  ? [v8] :  ? [v9] : (sum_class(v9) = v7 & image(v5, v8) = v9 & singleton(v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (disjoint(v5, v6) = 0) |  ~ (member(v7, v6) = 0) |  ? [v8] : ( ~ (v8 = 0) & member(v7, v5) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (disjoint(v5, v6) = 0) |  ~ (member(v7, v5) = 0) |  ? [v8] : ( ~ (v8 = 0) & member(v7, v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (compose(v6, v5) = v7) | subclass(v7, v0) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (power_class(v6) = v7) |  ~ (member(v5, v7) = 0) | (subclass(v5, v6) = 0 & member(v5, universal_class) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (sum_class(v6) = v7) |  ~ (member(v5, v7) = 0) |  ? [v8] : (member(v8, v6) = 0 & member(v5, v8) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (image(v6, v5) = v7) |  ? [v8] : (range_of(v8) = v7 & restrict(v6, v5, universal_class) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (image(v6, v5) = v7) |  ? [v8] : ((v8 = 0 & member(v7, universal_class) = 0) | ( ~ (v8 = 0) & function(v6) = v8) | ( ~ (v8 = 0) & member(v5, universal_class) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (domain_of(v5) = v7) |  ~ (member(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = null_class) & restrict(v5, v8, universal_class) = v9 & singleton(v6) = v8 & member(v6, universal_class) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (restrict(v6, v5, universal_class) = v7) |  ? [v8] : (image(v6, v5) = v8 & range_of(v7) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (complement(v5) = v7) |  ~ (member(v6, v7) = 0) |  ? [v8] : ( ~ (v8 = 0) & member(v6, v5) = v8 & member(v6, universal_class) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (singleton(v6) = v9 & singleton(v5) = v8 & unordered_pair(v8, v10) = v7 & unordered_pair(v5, v9) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : ((v10 = v6 & v9 = 0 & v8 = 0 & successor(v5) = v6 & member(v6, universal_class) = 0 & member(v5, universal_class) = 0) | ( ~ (v8 = 0) & member(v7, successor_relation) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v9 = v6 & v8 = v5 & first(v7) = v5 & second(v7) = v6) | ( ~ (v8 = 0) & member(v6, universal_class) = v8) | ( ~ (v8 = 0) & member(v5, universal_class) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & member(v6, universal_class) = 0 & member(v5, v6) = 0) | ( ~ (v8 = 0) & member(v7, element_relation) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & member(v7, successor_relation) = 0) | ( ~ (v8 = v6) & successor(v5) = v8) | ( ~ (v8 = 0) & member(v6, universal_class) = v8) | ( ~ (v8 = 0) & member(v5, universal_class) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (ordered_pair(v5, v6) = v7) |  ? [v8] : ((v8 = 0 & member(v7, element_relation) = 0) | ( ~ (v8 = 0) & member(v6, universal_class) = v8) | ( ~ (v8 = 0) & member(v5, v6) = v8))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unordered_pair(v5, v6) = v7) | member(v7, universal_class) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (subclass(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v8 = 0 & v7 = 0 & member(v5, universal_class) = 0) | ( ~ (v9 = 0) & power_class(v6) = v8 & member(v5, v8) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (subclass(v5, v6) = 0) |  ~ (member(v7, v5) = 0) | member(v7, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (member(v6, v5) = v7) |  ? [v8] :  ? [v9] : ((v8 = 0 &  ~ (v7 = 0) & member(v6, universal_class) = 0) | ( ~ (v9 = 0) & complement(v5) = v8 & member(v6, v8) = v9))) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (member(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v8 = 0 & v7 = 0 & member(v6, universal_class) = 0) | ( ~ (v9 = 0) & ordered_pair(v5, v6) = v8 & member(v8, element_relation) = v9))) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (subclass(v6, v5) = 0) |  ? [v7] : ( ~ (v7 = 0) & subclass(v5, v6) = v7)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (subclass(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & subclass(v6, v5) = v7)) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (function(v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (( ~ (v9 = 0) & compose(v5, v7) = v8 & inverse(v5) = v7 & subclass(v8, identity_relation) = v9) | ( ~ (v7 = 0) & subclass(v5, v0) = v7))) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (inductive(v5) = v6) |  ? [v7] :  ? [v8] : (( ~ (v8 = 0) & image(successor_relation, v5) = v7 & subclass(v7, v5) = v8) | ( ~ (v7 = 0) & member(null_class, v5) = v7))) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (subclass(v5, v5) = v6)) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (subclass(v5, universal_class) = v6)) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (subclass(v4, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & inductive(v5) = v7)) &  ! [v5] :  ! [v6] : (v5 = null_class |  ~ (apply(v3, v5) = v6) |  ? [v7] : ((v7 = 0 & member(v6, v5) = 0) | ( ~ (v7 = 0) & member(v5, universal_class) = v7))) &  ! [v5] :  ! [v6] : ( ~ (power_class(v5) = v6) |  ? [v7] : ((v7 = 0 & member(v6, universal_class) = 0) | ( ~ (v7 = 0) & member(v5, universal_class) = v7))) &  ! [v5] :  ! [v6] : ( ~ (sum_class(v5) = v6) |  ? [v7] : ((v7 = 0 & member(v6, universal_class) = 0) | ( ~ (v7 = 0) & member(v5, universal_class) = v7))) &  ! [v5] :  ! [v6] : ( ~ (image(successor_relation, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v7 = 0 & subclass(v6, v5) = 0 & member(null_class, v5) = 0) | ( ~ (v7 = 0) & inductive(v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (image(successor_relation, v5) = v6) |  ? [v7] : ((v7 = 0 & inductive(v5) = 0) | ( ~ (v7 = 0) & subclass(v6, v5) = v7) | ( ~ (v7 = 0) & member(null_class, v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (range_of(v5) = v6) |  ? [v7] : (inverse(v5) = v7 & domain_of(v7) = v6)) &  ! [v5] :  ! [v6] : ( ~ (inverse(v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : ((v9 = 0 & v7 = 0 & compose(v5, v6) = v8 & subclass(v8, identity_relation) = 0 & subclass(v5, v0) = 0) | ( ~ (v7 = 0) & function(v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (inverse(v5) = v6) |  ? [v7] :  ? [v8] : (flip(v7) = v8 & domain_of(v8) = v6 & cross_product(v5, universal_class) = v7)) &  ! [v5] :  ! [v6] : ( ~ (inverse(v5) = v6) |  ? [v7] :  ? [v8] : ((v7 = 0 & function(v5) = 0) | ( ~ (v8 = 0) & compose(v5, v6) = v7 & subclass(v7, identity_relation) = v8) | ( ~ (v7 = 0) & subclass(v5, v0) = v7))) &  ! [v5] :  ! [v6] : ( ~ (inverse(v5) = v6) |  ? [v7] : (range_of(v5) = v7 & domain_of(v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (successor(v5) = v6) |  ? [v7] : (union(v5, v7) = v6 & singleton(v5) = v7)) &  ! [v5] :  ! [v6] : ( ~ (flip(v5) = v6) | subclass(v6, v1) = 0) &  ! [v5] :  ! [v6] : ( ~ (rotate(v5) = v6) | subclass(v6, v1) = 0) &  ! [v5] :  ! [v6] : ( ~ (cross_product(v5, universal_class) = v6) |  ? [v7] :  ? [v8] : (inverse(v5) = v7 & flip(v6) = v8 & domain_of(v8) = v7)) &  ! [v5] :  ! [v6] : ( ~ (singleton(v5) = v6) | unordered_pair(v5, v5) = v6) &  ! [v5] :  ! [v6] : ( ~ (singleton(v5) = v6) |  ? [v7] : (successor(v5) = v7 & union(v5, v6) = v7)) &  ! [v5] :  ! [v6] : ( ~ (unordered_pair(v5, v5) = v6) | singleton(v5) = v6) &  ! [v5] :  ! [v6] : ( ~ (subclass(v5, v6) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & power_class(v6) = v7 & member(v5, v7) = 0) | ( ~ (v7 = 0) & member(v5, universal_class) = v7))) &  ! [v5] :  ! [v6] : ( ~ (subclass(v5, v0) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : ((v9 = 0 & v6 = 0 & compose(v5, v7) = v8 & inverse(v5) = v7 & subclass(v8, identity_relation) = 0) | ( ~ (v7 = 0) & function(v5) = v7))) &  ! [v5] :  ! [v6] : ( ~ (member(v5, v6) = 0) |  ? [v7] :  ? [v8] : ((v8 = 0 & ordered_pair(v5, v6) = v7 & member(v7, element_relation) = 0) | ( ~ (v7 = 0) & member(v6, universal_class) = v7))) &  ! [v5] :  ! [v6] : ( ~ (member(null_class, v5) = v6) |  ? [v7] :  ? [v8] : ((v8 = 0 & v6 = 0 & image(successor_relation, v5) = v7 & subclass(v7, v5) = 0) | ( ~ (v7 = 0) & inductive(v5) = v7))) &  ! [v5] : (v5 = null_class |  ~ (member(v5, universal_class) = 0) |  ? [v6] : (apply(v3, v5) = v6 & member(v6, v5) = 0)) &  ! [v5] : ( ~ (function(v5) = 0) |  ? [v6] :  ? [v7] : (compose(v5, v6) = v7 & inverse(v5) = v6 & subclass(v7, identity_relation) = 0 & subclass(v5, v0) = 0)) &  ! [v5] : ( ~ (inductive(v5) = 0) | subclass(v4, v5) = 0) &  ! [v5] : ( ~ (inductive(v5) = 0) |  ? [v6] : (image(successor_relation, v5) = v6 & subclass(v6, v5) = 0 & member(null_class, v5) = 0)) &  ! [v5] : ( ~ (subclass(v5, v0) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : ((v6 = 0 & function(v5) = 0) | ( ~ (v8 = 0) & compose(v5, v6) = v7 & inverse(v5) = v6 & subclass(v7, identity_relation) = v8))) &  ! [v5] : ( ~ (member(v5, identity_relation) = 0) |  ? [v6] : (ordered_pair(v6, v6) = v5 & member(v6, universal_class) = 0)) &  ! [v5] :  ~ (member(v5, null_class) = 0) &  ! [v5] : ( ~ (member(v5, universal_class) = 0) |  ? [v6] : (power_class(v5) = v6 & member(v6, universal_class) = 0)) &  ! [v5] : ( ~ (member(v5, universal_class) = 0) |  ? [v6] : (sum_class(v5) = v6 & member(v6, universal_class) = 0)) &  ! [v5] : ( ~ (member(null_class, v5) = 0) |  ? [v6] :  ? [v7] : ((v6 = 0 & inductive(v5) = 0) | ( ~ (v7 = 0) & image(successor_relation, v5) = v6 & subclass(v6, v5) = v7))) &  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] : restrict(v7, v6, v5) = v8 &  ? [v5] :  ? [v6] :  ? [v7] : apply(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : disjoint(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : compose(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : image(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : union(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : intersection(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : cross_product(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : ordered_pair(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : unordered_pair(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : subclass(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : member(v6, v5) = v7 &  ? [v5] :  ? [v6] : function(v5) = v6 &  ? [v5] :  ? [v6] : power_class(v5) = v6 &  ? [v5] :  ? [v6] : sum_class(v5) = v6 &  ? [v5] :  ? [v6] : inductive(v5) = v6 &  ? [v5] :  ? [v6] : range_of(v5) = v6 &  ? [v5] :  ? [v6] : inverse(v5) = v6 &  ? [v5] :  ? [v6] : successor(v5) = v6 &  ? [v5] :  ? [v6] : flip(v5) = v6 &  ? [v5] :  ? [v6] : rotate(v5) = v6 &  ? [v5] :  ? [v6] : domain_of(v5) = v6 &  ? [v5] :  ? [v6] : complement(v5) = v6 &  ? [v5] :  ? [v6] : first(v5) = v6 &  ? [v5] :  ? [v6] : second(v5) = v6 &  ? [v5] :  ? [v6] : singleton(v5) = v6 &  ? [v5] : (v5 = null_class |  ? [v6] : (disjoint(v6, v5) = 0 & member(v6, v5) = 0 & member(v6, universal_class) = 0)))
% 47.51/17.91  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 47.51/17.91  | (1)  ~ (all_0_2_2 = 0) & function(all_0_1_1) = 0 & inductive(all_0_0_0) = 0 & cross_product(all_0_4_4, universal_class) = all_0_3_3 & cross_product(universal_class, universal_class) = all_0_4_4 & subclass(successor_relation, all_0_4_4) = 0 & subclass(element_relation, all_0_4_4) = 0 & member(all_0_0_0, universal_class) = 0 & member(null_class, universal_class) = all_0_2_2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (flip(v3) = v6) |  ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & ordered_pair(v8, v2) = v9 & ordered_pair(v1, v0) = v8 & member(v9, v3) = v10) | ( ~ (v8 = 0) & member(v5, all_0_3_3) = v8))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (rotate(v0) = v6) |  ~ (ordered_pair(v4, v3) = v5) |  ~ (ordered_pair(v1, v2) = v4) |  ~ (member(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & ordered_pair(v8, v1) = v9 & ordered_pair(v2, v3) = v8 & member(v9, v0) = v10) | ( ~ (v8 = 0) & member(v5, all_0_3_3) = v8))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (image(v1, v5) = v6) |  ~ (image(v0, v4) = v5) |  ~ (singleton(v2) = v4) |  ~ (member(v3, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : ((v8 = 0 & v7 = 0 & member(v2, universal_class) = 0) | ( ~ (v10 = 0) & compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (compose(v1, v0) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & image(v1, v8) = v9 & image(v0, v7) = v8 & singleton(v2) = v7 & member(v3, v9) = v10) | ( ~ (v7 = 0) & member(v2, universal_class) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cross_product(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & member(v1, v3) = v7) | ( ~ (v7 = 0) & member(v0, v2) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (image(v1, v5) = v6) |  ~ (image(v0, v4) = v5) |  ~ (singleton(v2) = v4) |  ~ (member(v3, v6) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : ((v9 = 0 & compose(v1, v0) = v8 & ordered_pair(v2, v3) = v7 & member(v7, v8) = 0) | ( ~ (v7 = 0) & member(v2, universal_class) = v7))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (flip(v3) = v6) |  ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v5, v6) = 0) |  ? [v7] :  ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3) = 0 & member(v5, all_0_3_3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (rotate(v0) = v6) |  ~ (ordered_pair(v4, v3) = v5) |  ~ (ordered_pair(v1, v2) = v4) |  ~ (member(v5, v6) = 0) |  ? [v7] :  ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0) = 0 & member(v5, all_0_3_3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v1, v0) = v4) |  ~ (member(v5, v3) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_3_3) = 0) | ( ~ (v10 = 0) & flip(v3) = v9 & member(v8, v9) = v10)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (ordered_pair(v4, v1) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v5, v0) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_3_3) = 0) | ( ~ (v10 = 0) & rotate(v0) = v9 & member(v8, v9) = v10)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (compose(v1, v0) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v4, v5) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8) = 0 & member(v2, universal_class) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cross_product(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v4, v5) = 0) | (member(v1, v3) = 0 & member(v0, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v1, v0) = v4) |  ~ (member(v5, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (ordered_pair(v6, v2) = v7 & ordered_pair(v0, v1) = v6 & ((v9 = 0 & flip(v3) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_3_3) = v8)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (ordered_pair(v4, v1) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v5, v0) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (ordered_pair(v6, v3) = v7 & ordered_pair(v1, v2) = v6 & ((v9 = 0 & rotate(v0) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_3_3) = v8)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (union(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum_class(v1) = v2) |  ~ (member(v4, v1) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum_class(v1) = v2) |  ~ (member(v0, v4) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (restrict(v4, v3, v2) = v1) |  ~ (restrict(v4, v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection(v1, v3) = v4) |  ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = null_class |  ~ (restrict(v0, v2, universal_class) = v3) |  ~ (singleton(v1) = v2) |  ? [v4] :  ? [v5] : ((v5 = 0 & domain_of(v0) = v4 & member(v1, v4) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (power_class(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : (( ~ (v4 = 0) & subclass(v0, v1) = v4) | ( ~ (v4 = 0) & member(v0, universal_class) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (domain_of(v0) = v2) |  ~ (member(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = null_class & restrict(v0, v4, universal_class) = null_class & singleton(v1) = v4) | ( ~ (v4 = 0) & member(v1, universal_class) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (complement(v0) = v2) |  ~ (member(v1, v2) = v3) |  ? [v4] : ((v4 = 0 & member(v1, v0) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v1, v0) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subclass(v0, v1) = 0) |  ~ (member(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (compose(v3, v2) = v1) |  ~ (compose(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (image(v3, v2) = v1) |  ~ (image(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cross_product(v3, v2) = v1) |  ~ (cross_product(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subclass(v3, v2) = v1) |  ~ (subclass(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (image(v0, v2) = v3) |  ~ (singleton(v1) = v2) |  ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) |  ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) |  ~ (singleton(v1) = v2) |  ? [v4] :  ? [v5] : ((v4 = 0 &  ~ (v3 = null_class) & member(v1, universal_class) = 0) | ( ~ (v5 = 0) & domain_of(v0) = v4 & member(v1, v4) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] :  ? [v5] : (first(v2) = v4 & second(v2) = v5 & ordered_pair(v4, v5) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (singleton(v1) = v2) |  ~ (unordered_pair(v0, v2) = v3) |  ? [v4] :  ? [v5] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & unordered_pair(v5, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subclass(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (member(v1, v0) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & complement(v0) = v3 & member(v1, v3) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_class(v2) = v1) |  ~ (power_class(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum_class(v2) = v1) |  ~ (sum_class(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (inductive(v2) = v1) |  ~ (inductive(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (range_of(v2) = v1) |  ~ (range_of(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (inverse(v2) = v1) |  ~ (inverse(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (successor(v2) = v1) |  ~ (successor(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (flip(v2) = v1) |  ~ (flip(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (rotate(v2) = v1) |  ~ (rotate(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain_of(v2) = v1) |  ~ (domain_of(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (first(v2) = v1) |  ~ (first(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (second(v2) = v1) |  ~ (second(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (ordered_pair(v2, v2) = v0) |  ~ (member(v0, identity_relation) = v1) |  ? [v3] : ( ~ (v3 = 0) & member(v2, universal_class) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (member(v2, universal_class) = 0) |  ~ (member(v0, identity_relation) = v1) |  ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(v0, v1) = v2) |  ? [v3] :  ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_4_4) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_class(v1) = v2) |  ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum_class(v1) = v2) |  ~ (member(v0, v2) = 0) |  ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (image(v1, v0) = v2) |  ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (image(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & member(v2, universal_class) = 0) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain_of(v0) = v2) |  ~ (member(v1, v2) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = null_class) & restrict(v0, v3, universal_class) = v4 & singleton(v1) = v3 & member(v1, universal_class) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) |  ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (complement(v0) = v2) |  ~ (member(v1, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = v1 & v4 = 0 & v3 = 0 & successor(v0) = v1 & member(v1, universal_class) = 0 & member(v0, universal_class) = 0) | ( ~ (v3 = 0) & member(v2, successor_relation) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = v1 & v3 = v0 & first(v2) = v0 & second(v2) = v1) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & member(v1, universal_class) = 0 & member(v0, v1) = 0) | ( ~ (v3 = 0) & member(v2, element_relation) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & member(v2, successor_relation) = 0) | ( ~ (v3 = v1) & successor(v0) = v3) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & member(v2, element_relation) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subclass(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 & v2 = 0 & member(v0, universal_class) = 0) | ( ~ (v4 = 0) & power_class(v1) = v3 & member(v0, v3) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subclass(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member(v1, v0) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v2 = 0) & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & complement(v0) = v3 & member(v1, v3) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subclass(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subclass(v0, v1) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subclass(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ (v4 = 0) & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = v4) | ( ~ (v2 = 0) & subclass(v0, all_0_4_4) = v2))) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (inductive(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & image(successor_relation, v0) = v2 & subclass(v2, v0) = v3) | ( ~ (v2 = 0) & member(null_class, v0) = v2))) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subclass(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subclass(v0, universal_class) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subclass(all_0_0_0, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & inductive(v0) = v2)) &  ! [v0] :  ! [v1] : (v0 = null_class |  ~ (apply(all_0_1_1, v0) = v1) |  ? [v2] : ((v2 = 0 & member(v1, v0) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) &  ! [v0] :  ! [v1] : ( ~ (power_class(v0) = v1) |  ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) &  ! [v0] :  ! [v1] : ( ~ (sum_class(v0) = v1) |  ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) &  ! [v0] :  ! [v1] : ( ~ (image(successor_relation, v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & subclass(v1, v0) = 0 & member(null_class, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (image(successor_relation, v0) = v1) |  ? [v2] : ((v2 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & subclass(v1, v0) = v2) | ( ~ (v2 = 0) & member(null_class, v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (range_of(v0) = v1) |  ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1)) &  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v2 = 0 & compose(v0, v1) = v3 & subclass(v3, identity_relation) = 0 & subclass(v0, all_0_4_4) = 0) | ( ~ (v2 = 0) & function(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] :  ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2)) &  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] :  ? [v3] : ((v2 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & subclass(v2, identity_relation) = v3) | ( ~ (v2 = 0) & subclass(v0, all_0_4_4) = 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_3_3) = 0) &  ! [v0] :  ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_3_3) = 0) &  ! [v0] :  ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) |  ? [v2] :  ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ? [v2] : (successor(v0) = v2 & union(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (subclass(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & power_class(v1) = v2 & member(v0, v2) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2))) &  ! [v0] :  ! [v1] : ( ~ (subclass(v0, all_0_4_4) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v1 = 0 & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = 0) | ( ~ (v2 = 0) & function(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (member(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & ordered_pair(v0, v1) = v2 & member(v2, element_relation) = 0) | ( ~ (v2 = 0) & member(v1, universal_class) = v2))) &  ! [v0] :  ! [v1] : ( ~ (member(null_class, v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v1 = 0 & image(successor_relation, v0) = v2 & subclass(v2, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2))) &  ! [v0] : (v0 = null_class |  ~ (member(v0, universal_class) = 0) |  ? [v1] : (apply(all_0_1_1, v0) = v1 & member(v1, v0) = 0)) &  ! [v0] : ( ~ (function(v0) = 0) |  ? [v1] :  ? [v2] : (compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = 0 & subclass(v0, all_0_4_4) = 0)) &  ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0) &  ! [v0] : ( ~ (inductive(v0) = 0) |  ? [v1] : (image(successor_relation, v0) = v1 & subclass(v1, v0) = 0 & member(null_class, v0) = 0)) &  ! [v0] : ( ~ (subclass(v0, all_0_4_4) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : ((v1 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3))) &  ! [v0] : ( ~ (member(v0, identity_relation) = 0) |  ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0)) &  ! [v0] :  ~ (member(v0, null_class) = 0) &  ! [v0] : ( ~ (member(v0, universal_class) = 0) |  ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0)) &  ! [v0] : ( ~ (member(v0, universal_class) = 0) |  ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0)) &  ! [v0] : ( ~ (member(null_class, v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & image(successor_relation, v0) = v1 & subclass(v1, v0) = v2))) &  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : restrict(v2, v1, v0) = v3 &  ? [v0] :  ? [v1] :  ? [v2] : apply(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : disjoint(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : compose(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : image(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : union(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : cross_product(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : ordered_pair(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : subclass(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : member(v1, v0) = v2 &  ? [v0] :  ? [v1] : function(v0) = v1 &  ? [v0] :  ? [v1] : power_class(v0) = v1 &  ? [v0] :  ? [v1] : sum_class(v0) = v1 &  ? [v0] :  ? [v1] : inductive(v0) = v1 &  ? [v0] :  ? [v1] : range_of(v0) = v1 &  ? [v0] :  ? [v1] : inverse(v0) = v1 &  ? [v0] :  ? [v1] : successor(v0) = v1 &  ? [v0] :  ? [v1] : flip(v0) = v1 &  ? [v0] :  ? [v1] : rotate(v0) = v1 &  ? [v0] :  ? [v1] : domain_of(v0) = v1 &  ? [v0] :  ? [v1] : complement(v0) = v1 &  ? [v0] :  ? [v1] : first(v0) = v1 &  ? [v0] :  ? [v1] : second(v0) = v1 &  ? [v0] :  ? [v1] : singleton(v0) = v1 &  ? [v0] : (v0 = null_class |  ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 47.84/17.95  |
% 47.84/17.95  | Applying alpha-rule on (1) yields:
% 47.84/17.95  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v0) = v3))
% 47.84/17.95  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 47.84/17.95  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (domain_of(v2) = v1) |  ~ (domain_of(v2) = v0))
% 47.84/17.95  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (complement(v0) = v2) |  ~ (member(v1, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1, universal_class) = 0))
% 47.84/17.95  | (6)  ! [v0] : ( ~ (function(v0) = 0) |  ? [v1] :  ? [v2] : (compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = 0 & subclass(v0, all_0_4_4) = 0))
% 47.84/17.95  | (7)  ! [v0] :  ! [v1] : (v0 = null_class |  ~ (apply(all_0_1_1, v0) = v1) |  ? [v2] : ((v2 = 0 & member(v1, v0) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 47.84/17.96  | (8)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subclass(all_0_0_0, v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & inductive(v0) = v2))
% 47.84/17.96  | (9)  ? [v0] :  ? [v1] : rotate(v0) = v1
% 47.84/17.96  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 47.84/17.96  | (11)  ! [v0] :  ! [v1] : ( ~ (subclass(v0, all_0_4_4) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v1 = 0 & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = 0) | ( ~ (v2 = 0) & function(v0) = v2)))
% 47.84/17.96  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : ((v5 = v1 & v4 = 0 & v3 = 0 & successor(v0) = v1 & member(v1, universal_class) = 0 & member(v0, universal_class) = 0) | ( ~ (v3 = 0) & member(v2, successor_relation) = v3)))
% 47.84/17.96  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (power_class(v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : (( ~ (v4 = 0) & subclass(v0, v1) = v4) | ( ~ (v4 = 0) & member(v0, universal_class) = v4)))
% 47.84/17.96  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v1, v0) = v4) |  ~ (member(v5, v3) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (ordered_pair(v7, v2) = v8 & ordered_pair(v0, v1) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_3_3) = 0) | ( ~ (v10 = 0) & flip(v3) = v9 & member(v8, v9) = v10))))
% 47.84/17.96  | (15)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subclass(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 47.84/17.96  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum_class(v1) = v2) |  ~ (member(v0, v4) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v4, v1) = v5))
% 47.84/17.96  | (17)  ? [v0] :  ? [v1] : range_of(v0) = v1
% 47.84/17.96  | (18)  ? [v0] :  ? [v1] : flip(v0) = v1
% 47.84/17.96  | (19)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ? [v2] : (successor(v0) = v2 & union(v0, v1) = v2))
% 47.84/17.96  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (compose(v1, v0) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & image(v1, v8) = v9 & image(v0, v7) = v8 & singleton(v2) = v7 & member(v3, v9) = v10) | ( ~ (v7 = 0) & member(v2, universal_class) = v7)))
% 47.84/17.96  | (21)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (flip(v2) = v1) |  ~ (flip(v2) = v0))
% 47.84/17.96  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v1 = v0 |  ~ (restrict(v4, v3, v2) = v1) |  ~ (restrict(v4, v3, v2) = v0))
% 47.84/17.96  | (23)  ! [v0] :  ! [v1] : ( ~ (rotate(v0) = v1) | subclass(v1, all_0_3_3) = 0)
% 47.84/17.96  | (24)  ! [v0] :  ! [v1] : ( ~ (sum_class(v0) = v1) |  ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 47.84/17.96  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v1, v0) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 47.84/17.96  | (26) cross_product(all_0_4_4, universal_class) = all_0_3_3
% 47.84/17.96  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (compose(v1, v0) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v4, v5) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (image(v1, v7) = v8 & image(v0, v6) = v7 & singleton(v2) = v6 & member(v3, v8) = 0 & member(v2, universal_class) = 0))
% 47.84/17.96  | (28)  ? [v0] : (v0 = null_class |  ? [v1] : (disjoint(v1, v0) = 0 & member(v1, v0) = 0 & member(v1, universal_class) = 0))
% 47.84/17.96  | (29)  ? [v0] :  ? [v1] :  ? [v2] : subclass(v1, v0) = v2
% 47.84/17.96  | (30)  ! [v0] :  ! [v1] : ( ~ (member(null_class, v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v1 = 0 & image(successor_relation, v0) = v2 & subclass(v2, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2)))
% 47.84/17.96  | (31)  ! [v0] :  ! [v1] : ( ~ (member(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & ordered_pair(v0, v1) = v2 & member(v2, element_relation) = 0) | ( ~ (v2 = 0) & member(v1, universal_class) = v2)))
% 47.84/17.96  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v1, v0) = v4) |  ~ (member(v5, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (ordered_pair(v6, v2) = v7 & ordered_pair(v0, v1) = v6 & ((v9 = 0 & flip(v3) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_3_3) = v8))))
% 47.84/17.96  | (33)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4)))
% 47.84/17.97  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (ordered_pair(v2, v2) = v0) |  ~ (member(v0, identity_relation) = v1) |  ? [v3] : ( ~ (v3 = 0) & member(v2, universal_class) = v3))
% 47.84/17.97  | (35)  ~ (all_0_2_2 = 0)
% 47.84/17.97  | (36)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (inductive(v0) = v1) |  ? [v2] :  ? [v3] : (( ~ (v3 = 0) & image(successor_relation, v0) = v2 & subclass(v2, v0) = v3) | ( ~ (v2 = 0) & member(null_class, v0) = v2)))
% 47.84/17.97  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (ordered_pair(v4, v1) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v5, v0) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (ordered_pair(v6, v3) = v7 & ordered_pair(v1, v2) = v6 & ((v9 = 0 & rotate(v0) = v8 & member(v7, v8) = 0) | ( ~ (v8 = 0) & member(v7, all_0_3_3) = v8))))
% 47.84/17.97  | (38)  ! [v0] : ( ~ (member(v0, universal_class) = 0) |  ? [v1] : (sum_class(v0) = v1 & member(v1, universal_class) = 0))
% 47.84/17.97  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (rotate(v0) = v6) |  ~ (ordered_pair(v4, v3) = v5) |  ~ (ordered_pair(v1, v2) = v4) |  ~ (member(v5, v6) = 0) |  ? [v7] :  ? [v8] : (ordered_pair(v7, v1) = v8 & ordered_pair(v2, v3) = v7 & member(v8, v0) = 0 & member(v5, all_0_3_3) = 0))
% 47.84/17.97  | (40)  ? [v0] :  ? [v1] : sum_class(v0) = v1
% 47.84/17.97  | (41)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (member(v3, v1) = 0 & member(v3, v0) = 0))
% 47.84/17.97  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cross_product(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & member(v1, v3) = v7) | ( ~ (v7 = 0) & member(v0, v2) = v7)))
% 47.84/17.97  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = 0) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 47.84/17.97  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = null_class |  ~ (restrict(v0, v2, universal_class) = v3) |  ~ (singleton(v1) = v2) |  ? [v4] :  ? [v5] : ((v5 = 0 & domain_of(v0) = v4 & member(v1, v4) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4)))
% 47.84/17.97  | (45)  ? [v0] :  ? [v1] : first(v0) = v1
% 47.84/17.97  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = v1 & v3 = v0 & first(v2) = v0 & second(v2) = v1) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3)))
% 47.84/17.97  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (restrict(v1, v0, v2) = v3) |  ? [v4] : (intersection(v1, v4) = v3 & cross_product(v0, v2) = v4))
% 47.84/17.97  | (48)  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 47.84/17.97  | (49)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 47.84/17.97  | (50)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (range_of(v2) = v1) |  ~ (range_of(v2) = v0))
% 47.84/17.97  | (51) cross_product(universal_class, universal_class) = all_0_4_4
% 47.84/17.97  | (52)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (compose(v1, v0) = v2) | subclass(v2, all_0_4_4) = 0)
% 47.84/17.97  | (53)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (domain_of(v0) = v2) |  ~ (member(v1, v2) = 0) |  ? [v3] :  ? [v4] : ( ~ (v4 = null_class) & restrict(v0, v3, universal_class) = v4 & singleton(v1) = v3 & member(v1, universal_class) = 0))
% 47.84/17.97  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cross_product(v3, v2) = v1) |  ~ (cross_product(v3, v2) = v0))
% 47.84/17.97  | (55)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (function(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (( ~ (v4 = 0) & compose(v0, v2) = v3 & inverse(v0) = v2 & subclass(v3, identity_relation) = v4) | ( ~ (v2 = 0) & subclass(v0, all_0_4_4) = v2)))
% 47.84/17.98  | (56)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subclass(v0, v0) = v1))
% 47.84/17.98  | (57)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (function(v2) = v1) |  ~ (function(v2) = v0))
% 47.84/17.98  | (58)  ! [v0] : ( ~ (member(null_class, v0) = 0) |  ? [v1] :  ? [v2] : ((v1 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & image(successor_relation, v0) = v1 & subclass(v1, v0) = v2)))
% 47.84/17.98  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (complement(v0) = v2) |  ~ (member(v1, v2) = v3) |  ? [v4] : ((v4 = 0 & member(v1, v0) = 0) | ( ~ (v4 = 0) & member(v1, universal_class) = v4)))
% 47.84/17.98  | (60)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (inverse(v2) = v1) |  ~ (inverse(v2) = v0))
% 47.84/17.98  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (domain_of(v0) = v2) |  ~ (member(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = null_class & restrict(v0, v4, universal_class) = null_class & singleton(v1) = v4) | ( ~ (v4 = 0) & member(v1, universal_class) = v4)))
% 48.16/17.98  | (62)  ! [v0] :  ! [v1] : ( ~ (successor(v0) = v1) |  ? [v2] : (union(v0, v2) = v1 & singleton(v0) = v2))
% 48.16/17.98  | (63)  ? [v0] :  ? [v1] : domain_of(v0) = v1
% 48.16/17.98  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = 0 |  ~ (member(v2, universal_class) = 0) |  ~ (member(v0, identity_relation) = v1) |  ? [v3] : ( ~ (v3 = v0) & ordered_pair(v2, v2) = v3))
% 48.16/17.98  | (65)  ! [v0] :  ! [v1] : ( ~ (power_class(v0) = v1) |  ? [v2] : ((v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 48.16/17.98  | (66)  ! [v0] : ( ~ (member(v0, identity_relation) = 0) |  ? [v1] : (ordered_pair(v1, v1) = v0 & member(v1, universal_class) = 0))
% 48.16/17.98  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (sum_class(v1) = v2) |  ~ (member(v4, v1) = 0) |  ~ (member(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & member(v0, v4) = v5))
% 48.16/17.98  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (second(v2) = v1) |  ~ (second(v2) = v0))
% 48.16/17.98  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (flip(v3) = v6) |  ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v5, v6) = 0) |  ? [v7] :  ? [v8] : (ordered_pair(v7, v2) = v8 & ordered_pair(v1, v0) = v7 & member(v8, v3) = 0 & member(v5, all_0_3_3) = 0))
% 48.16/17.98  | (70)  ? [v0] :  ? [v1] :  ? [v2] : member(v1, v0) = v2
% 48.16/17.98  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0) | member(v0, universal_class) = 0)
% 48.16/17.98  | (72)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 48.16/17.98  | (73)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & v3 = 0 & member(v1, universal_class) = 0 & member(v0, v1) = 0) | ( ~ (v3 = 0) & member(v2, element_relation) = v3)))
% 48.16/17.98  | (74)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (power_class(v1) = v2) |  ~ (member(v0, v2) = 0) | (subclass(v0, v1) = 0 & member(v0, universal_class) = 0))
% 48.16/17.98  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (image(v3, v2) = v1) |  ~ (image(v3, v2) = v0))
% 48.16/17.98  | (76)  ! [v0] :  ! [v1] : ( ~ (image(successor_relation, v0) = v1) |  ? [v2] :  ? [v3] : ((v3 = 0 & v2 = 0 & subclass(v1, v0) = 0 & member(null_class, v0) = 0) | ( ~ (v2 = 0) & inductive(v0) = v2)))
% 48.16/17.98  | (77)  ? [v0] :  ? [v1] :  ? [v2] : ordered_pair(v1, v0) = v2
% 48.16/17.98  | (78)  ? [v0] :  ? [v1] :  ? [v2] : apply(v1, v0) = v2
% 48.16/17.98  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (rotate(v0) = v6) |  ~ (ordered_pair(v4, v3) = v5) |  ~ (ordered_pair(v1, v2) = v4) |  ~ (member(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & ordered_pair(v8, v1) = v9 & ordered_pair(v2, v3) = v8 & member(v9, v0) = v10) | ( ~ (v8 = 0) & member(v5, all_0_3_3) = v8)))
% 48.16/17.98  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subclass(v3, v2) = v1) |  ~ (subclass(v3, v2) = v0))
% 48.16/17.98  | (81)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (power_class(v2) = v1) |  ~ (power_class(v2) = v0))
% 48.16/17.98  | (82)  ! [v0] :  ! [v1] : ( ~ (image(successor_relation, v0) = v1) |  ? [v2] : ((v2 = 0 & inductive(v0) = 0) | ( ~ (v2 = 0) & subclass(v1, v0) = v2) | ( ~ (v2 = 0) & member(null_class, v0) = v2)))
% 48.16/17.98  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 48.16/17.98  | (84)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (successor(v2) = v1) |  ~ (successor(v2) = v0))
% 48.16/17.98  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apply(v3, v2) = v1) |  ~ (apply(v3, v2) = v0))
% 48.16/17.98  | (86)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (ordered_pair(v4, v1) = v5) |  ~ (ordered_pair(v2, v3) = v4) |  ~ (member(v5, v0) = v6) |  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (ordered_pair(v7, v3) = v8 & ordered_pair(v1, v2) = v7 & ((v9 = 0 & v6 = 0 & member(v8, all_0_3_3) = 0) | ( ~ (v10 = 0) & rotate(v0) = v9 & member(v8, v9) = v10))))
% 48.16/17.98  | (87)  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v4 = 0 & v2 = 0 & compose(v0, v1) = v3 & subclass(v3, identity_relation) = 0 & subclass(v0, all_0_4_4) = 0) | ( ~ (v2 = 0) & function(v0) = v2)))
% 48.16/17.98  | (88)  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] :  ? [v3] : ((v2 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & subclass(v2, identity_relation) = v3) | ( ~ (v2 = 0) & subclass(v0, all_0_4_4) = v2)))
% 48.16/17.98  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (image(v1, v5) = v6) |  ~ (image(v0, v4) = v5) |  ~ (singleton(v2) = v4) |  ~ (member(v3, v6) = 0) |  ? [v7] :  ? [v8] :  ? [v9] : ((v9 = 0 & compose(v1, v0) = v8 & ordered_pair(v2, v3) = v7 & member(v7, v8) = 0) | ( ~ (v7 = 0) & member(v2, universal_class) = v7)))
% 48.16/17.98  | (90)  ! [v0] : (v0 = null_class |  ~ (member(v0, universal_class) = 0) |  ? [v1] : (apply(all_0_1_1, v0) = v1 & member(v1, v0) = 0))
% 48.16/17.98  | (91)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0)))
% 48.16/17.98  | (92)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (rotate(v2) = v1) |  ~ (rotate(v2) = v0))
% 48.16/17.99  | (93)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & member(v2, successor_relation) = 0) | ( ~ (v3 = v1) & successor(v0) = v3) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3)))
% 48.16/17.99  | (94) member(null_class, universal_class) = all_0_2_2
% 48.16/17.99  | (95)  ? [v0] :  ? [v1] : successor(v0) = v1
% 48.16/17.99  | (96) function(all_0_1_1) = 0
% 48.16/17.99  | (97)  ! [v0] : ( ~ (inductive(v0) = 0) | subclass(all_0_0_0, v0) = 0)
% 48.16/17.99  | (98)  ! [v0] : ( ~ (member(v0, universal_class) = 0) |  ? [v1] : (power_class(v0) = v1 & member(v1, universal_class) = 0))
% 48.16/17.99  | (99)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : restrict(v2, v1, v0) = v3
% 48.16/17.99  | (100)  ? [v0] :  ? [v1] :  ? [v2] : union(v1, v0) = v2
% 48.16/17.99  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (flip(v3) = v6) |  ~ (ordered_pair(v4, v2) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v5, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : (( ~ (v10 = 0) & ordered_pair(v8, v2) = v9 & ordered_pair(v1, v0) = v8 & member(v9, v3) = v10) | ( ~ (v8 = 0) & member(v5, all_0_3_3) = v8)))
% 48.16/17.99  | (102)  ? [v0] :  ? [v1] : inductive(v0) = v1
% 48.16/17.99  | (103)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (apply(v0, v1) = v2) |  ? [v3] :  ? [v4] : (sum_class(v4) = v2 & image(v0, v3) = v4 & singleton(v1) = v3))
% 48.16/17.99  | (104)  ? [v0] :  ? [v1] :  ? [v2] : disjoint(v1, v0) = v2
% 48.16/17.99  | (105)  ! [v0] :  ! [v1] : ( ~ (range_of(v0) = v1) |  ? [v2] : (inverse(v0) = v2 & domain_of(v2) = v1))
% 48.16/17.99  | (106)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection(v1, v3) = v4) |  ~ (cross_product(v0, v2) = v3) | restrict(v1, v0, v2) = v4)
% 48.16/17.99  | (107)  ? [v0] :  ? [v1] : complement(v0) = v1
% 48.16/17.99  | (108)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (member(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v0, universal_class) = v4))
% 48.16/17.99  | (109)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subclass(v0, v1) = 0) |  ~ (member(v2, v0) = 0) | member(v2, v1) = 0)
% 48.16/17.99  | (110)  ! [v0] : ( ~ (subclass(v0, all_0_4_4) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : ((v1 = 0 & function(v0) = 0) | ( ~ (v3 = 0) & compose(v0, v1) = v2 & inverse(v0) = v1 & subclass(v2, identity_relation) = v3)))
% 48.16/17.99  | (111)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (restrict(v0, v2, universal_class) = v3) |  ~ (singleton(v1) = v2) |  ? [v4] :  ? [v5] : ((v4 = 0 &  ~ (v3 = null_class) & member(v1, universal_class) = 0) | ( ~ (v5 = 0) & domain_of(v0) = v4 & member(v1, v4) = v5)))
% 48.16/17.99  | (112)  ? [v0] :  ? [v1] : function(v0) = v1
% 48.16/17.99  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cross_product(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (member(v4, v5) = 0) | (member(v1, v3) = 0 & member(v0, v2) = 0))
% 48.16/17.99  | (114)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (first(v2) = v1) |  ~ (first(v2) = v0))
% 48.16/17.99  | (115)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (union(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5))
% 48.16/17.99  | (116)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection(v0, v1) = v3) |  ~ (member(v2, v3) = v4) |  ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5)))
% 48.16/17.99  | (117)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subclass(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 & v2 = 0 & member(v0, universal_class) = 0) | ( ~ (v4 = 0) & power_class(v1) = v3 & member(v0, v3) = v4)))
% 48.16/17.99  | (118)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member(v1, v0) = v2) |  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v2 = 0) & member(v1, universal_class) = 0) | ( ~ (v4 = 0) & complement(v0) = v3 & member(v1, v3) = v4)))
% 48.16/17.99  | (119)  ? [v0] :  ? [v1] :  ? [v2] : intersection(v1, v0) = v2
% 48.16/17.99  | (120)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (inductive(v2) = v1) |  ~ (inductive(v2) = v0))
% 48.16/17.99  | (121)  ? [v0] :  ? [v1] : second(v0) = v1
% 48.16/17.99  | (122)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (image(v1, v0) = v2) |  ? [v3] : (range_of(v3) = v2 & restrict(v1, v0, universal_class) = v3))
% 48.16/17.99  | (123)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subclass(v0, v1) = 0) |  ~ (member(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 48.16/17.99  | (124)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (compose(v3, v2) = v1) |  ~ (compose(v3, v2) = v0))
% 48.16/17.99  | (125) inductive(all_0_0_0) = 0
% 48.16/17.99  | (126)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v0 | v1 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ~ (member(v0, v3) = 0))
% 48.16/17.99  | (127) subclass(successor_relation, all_0_4_4) = 0
% 48.16/17.99  | (128)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (restrict(v1, v0, universal_class) = v2) |  ? [v3] : (image(v1, v0) = v3 & range_of(v2) = v3))
% 48.16/17.99  | (129)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 48.16/17.99  | (130)  ! [v0] :  ! [v1] : ( ~ (flip(v0) = v1) | subclass(v1, all_0_3_3) = 0)
% 48.16/17.99  | (131)  ! [v0] :  ! [v1] : ( ~ (cross_product(v0, universal_class) = v1) |  ? [v2] :  ? [v3] : (inverse(v0) = v2 & flip(v1) = v3 & domain_of(v3) = v2))
% 48.16/17.99  | (132)  ? [v0] :  ? [v1] :  ? [v2] : unordered_pair(v1, v0) = v2
% 48.16/17.99  | (133)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 48.16/17.99  | (134)  ? [v0] :  ? [v1] : inverse(v0) = v1
% 48.16/17.99  | (135)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (singleton(v1) = v2) |  ~ (unordered_pair(v0, v2) = v3) |  ? [v4] :  ? [v5] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 & unordered_pair(v5, v3) = v4))
% 48.16/17.99  | (136)  ! [v0] :  ~ (member(v0, null_class) = 0)
% 48.16/17.99  | (137) member(all_0_0_0, universal_class) = 0
% 48.16/17.99  | (138)  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] : (range_of(v0) = v2 & domain_of(v1) = v2))
% 48.16/17.99  | (139)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subclass(v0, universal_class) = v1))
% 48.16/17.99  | (140)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (member(v1, v0) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & complement(v0) = v3 & member(v1, v3) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3)))
% 48.16/17.99  | (141)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cross_product(v0, v1) = v3) |  ~ (member(v2, v3) = 0) |  ? [v4] :  ? [v5] : (first(v2) = v4 & second(v2) = v5 & ordered_pair(v4, v5) = v2))
% 48.16/17.99  | (142)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subclass(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subclass(v0, v1) = v2))
% 48.16/17.99  | (143)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (image(v0, v2) = v3) |  ~ (singleton(v1) = v2) |  ? [v4] : (apply(v0, v1) = v4 & sum_class(v3) = v4))
% 48.16/18.00  | (144)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & member(v2, element_relation) = 0) | ( ~ (v3 = 0) & member(v1, universal_class) = v3) | ( ~ (v3 = 0) & member(v0, v1) = v3)))
% 48.16/18.00  | (145)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (complement(v2) = v1) |  ~ (complement(v2) = v0))
% 48.16/18.00  | (146)  ? [v0] :  ? [v1] :  ? [v2] : compose(v1, v0) = v2
% 48.16/18.00  | (147)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 48.16/18.00  | (148)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (member(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & member(v2, v1) = v3))
% 48.16/18.00  | (149)  ? [v0] :  ? [v1] : power_class(v0) = v1
% 48.16/18.00  | (150)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (sum_class(v1) = v2) |  ~ (member(v0, v2) = 0) |  ? [v3] : (member(v3, v1) = 0 & member(v0, v3) = 0))
% 48.16/18.00  | (151)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (image(v1, v5) = v6) |  ~ (image(v0, v4) = v5) |  ~ (singleton(v2) = v4) |  ~ (member(v3, v6) = v7) |  ? [v8] :  ? [v9] :  ? [v10] : ((v8 = 0 & v7 = 0 & member(v2, universal_class) = 0) | ( ~ (v10 = 0) & compose(v1, v0) = v9 & ordered_pair(v2, v3) = v8 & member(v8, v9) = v10)))
% 48.16/18.00  | (152)  ! [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))
% 48.16/18.00  | (153) subclass(element_relation, all_0_4_4) = 0
% 48.16/18.00  | (154)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (image(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & member(v2, universal_class) = 0) | ( ~ (v3 = 0) & function(v1) = v3) | ( ~ (v3 = 0) & member(v0, universal_class) = v3)))
% 48.16/18.00  | (155)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (sum_class(v2) = v1) |  ~ (sum_class(v2) = v0))
% 48.16/18.00  | (156)  ? [v0] :  ? [v1] :  ? [v2] : cross_product(v1, v0) = v2
% 48.16/18.00  | (157)  ! [v0] : ( ~ (inductive(v0) = 0) |  ? [v1] : (image(successor_relation, v0) = v1 & subclass(v1, v0) = 0 & member(null_class, v0) = 0))
% 48.16/18.00  | (158)  ! [v0] :  ! [v1] : ( ~ (subclass(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & power_class(v1) = v2 & member(v0, v2) = 0) | ( ~ (v2 = 0) & member(v0, universal_class) = v2)))
% 48.16/18.00  | (159)  ? [v0] :  ? [v1] :  ? [v2] : image(v1, v0) = v2
% 48.16/18.00  | (160)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subclass(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subclass(v1, v0) = v2))
% 48.16/18.00  | (161)  ! [v0] :  ! [v1] : ( ~ (inverse(v0) = v1) |  ? [v2] :  ? [v3] : (flip(v2) = v3 & domain_of(v3) = v1 & cross_product(v0, universal_class) = v2))
% 48.16/18.00  | (162)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | member(v2, universal_class) = 0)
% 48.16/18.00  | (163)  ? [v0] :  ? [v1] : singleton(v0) = v1
% 48.16/18.00  |
% 48.16/18.00  | Instantiating formula (157) with all_0_0_0 and discharging atoms inductive(all_0_0_0) = 0, yields:
% 48.16/18.00  | (164)  ? [v0] : (image(successor_relation, all_0_0_0) = v0 & subclass(v0, all_0_0_0) = 0 & member(null_class, all_0_0_0) = 0)
% 48.16/18.00  |
% 48.16/18.00  | Instantiating formula (118) with 0, all_0_0_0, universal_class and discharging atoms member(all_0_0_0, universal_class) = 0, yields:
% 48.16/18.00  | (165)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & complement(universal_class) = v0 & member(all_0_0_0, v0) = v1)
% 48.16/18.00  |
% 48.16/18.00  | Instantiating formula (140) with all_0_2_2, null_class, universal_class and discharging atoms member(null_class, universal_class) = all_0_2_2, yields:
% 48.16/18.00  | (166) all_0_2_2 = 0 |  ? [v0] :  ? [v1] : ((v1 = 0 & complement(universal_class) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.00  |
% 48.16/18.00  | Instantiating formula (118) with all_0_2_2, null_class, universal_class and discharging atoms member(null_class, universal_class) = all_0_2_2, yields:
% 48.16/18.00  | (167)  ? [v0] :  ? [v1] : ((v0 = 0 &  ~ (all_0_2_2 = 0) & member(null_class, universal_class) = 0) | ( ~ (v1 = 0) & complement(universal_class) = v0 & member(null_class, v0) = v1))
% 48.16/18.00  |
% 48.16/18.00  | Instantiating (165) with all_68_0_80, all_68_1_81 yields:
% 48.16/18.00  | (168)  ~ (all_68_0_80 = 0) & complement(universal_class) = all_68_1_81 & member(all_0_0_0, all_68_1_81) = all_68_0_80
% 48.16/18.00  |
% 48.16/18.00  | Applying alpha-rule on (168) yields:
% 48.16/18.00  | (169)  ~ (all_68_0_80 = 0)
% 48.16/18.00  | (170) complement(universal_class) = all_68_1_81
% 48.16/18.00  | (171) member(all_0_0_0, all_68_1_81) = all_68_0_80
% 48.16/18.00  |
% 48.16/18.00  | Instantiating (167) with all_72_0_83, all_72_1_84 yields:
% 48.16/18.00  | (172) (all_72_1_84 = 0 &  ~ (all_0_2_2 = 0) & member(null_class, universal_class) = 0) | ( ~ (all_72_0_83 = 0) & complement(universal_class) = all_72_1_84 & member(null_class, all_72_1_84) = all_72_0_83)
% 48.16/18.00  |
% 48.16/18.00  | Instantiating (164) with all_76_0_92 yields:
% 48.16/18.00  | (173) image(successor_relation, all_0_0_0) = all_76_0_92 & subclass(all_76_0_92, all_0_0_0) = 0 & member(null_class, all_0_0_0) = 0
% 48.16/18.00  |
% 48.16/18.00  | Applying alpha-rule on (173) yields:
% 48.16/18.00  | (174) image(successor_relation, all_0_0_0) = all_76_0_92
% 48.16/18.00  | (175) subclass(all_76_0_92, all_0_0_0) = 0
% 48.16/18.00  | (176) member(null_class, all_0_0_0) = 0
% 48.16/18.00  |
% 48.16/18.00  +-Applying beta-rule and splitting (166), into two cases.
% 48.16/18.00  |-Branch one:
% 48.16/18.00  | (177) all_0_2_2 = 0
% 48.16/18.00  |
% 48.16/18.00  	| Equations (177) can reduce 35 to:
% 48.16/18.00  	| (178) $false
% 48.16/18.00  	|
% 48.16/18.00  	|-The branch is then unsatisfiable
% 48.16/18.00  |-Branch two:
% 48.16/18.00  | (35)  ~ (all_0_2_2 = 0)
% 48.16/18.00  | (180)  ? [v0] :  ? [v1] : ((v1 = 0 & complement(universal_class) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.00  |
% 48.16/18.00  	| Instantiating (180) with all_96_0_112, all_96_1_113 yields:
% 48.16/18.00  	| (181) (all_96_0_112 = 0 & complement(universal_class) = all_96_1_113 & member(null_class, all_96_1_113) = 0) | ( ~ (all_96_1_113 = 0) & member(null_class, universal_class) = all_96_1_113)
% 48.16/18.00  	|
% 48.16/18.00  	+-Applying beta-rule and splitting (172), into two cases.
% 48.16/18.00  	|-Branch one:
% 48.16/18.00  	| (182) all_72_1_84 = 0 &  ~ (all_0_2_2 = 0) & member(null_class, universal_class) = 0
% 48.16/18.00  	|
% 48.16/18.00  		| Applying alpha-rule on (182) yields:
% 48.16/18.00  		| (183) all_72_1_84 = 0
% 48.16/18.00  		| (35)  ~ (all_0_2_2 = 0)
% 48.16/18.00  		| (185) member(null_class, universal_class) = 0
% 48.16/18.00  		|
% 48.16/18.00  		| Instantiating formula (10) with null_class, universal_class, 0, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_0_2_2, member(null_class, universal_class) = 0, yields:
% 48.16/18.00  		| (177) all_0_2_2 = 0
% 48.16/18.00  		|
% 48.16/18.00  		| Equations (177) can reduce 35 to:
% 48.16/18.00  		| (178) $false
% 48.16/18.00  		|
% 48.16/18.00  		|-The branch is then unsatisfiable
% 48.16/18.00  	|-Branch two:
% 48.16/18.00  	| (188)  ~ (all_72_0_83 = 0) & complement(universal_class) = all_72_1_84 & member(null_class, all_72_1_84) = all_72_0_83
% 48.16/18.00  	|
% 48.16/18.00  		| Applying alpha-rule on (188) yields:
% 48.16/18.00  		| (189)  ~ (all_72_0_83 = 0)
% 48.16/18.00  		| (190) complement(universal_class) = all_72_1_84
% 48.16/18.00  		| (191) member(null_class, all_72_1_84) = all_72_0_83
% 48.16/18.00  		|
% 48.16/18.00  		+-Applying beta-rule and splitting (181), into two cases.
% 48.16/18.00  		|-Branch one:
% 48.16/18.00  		| (192) all_96_0_112 = 0 & complement(universal_class) = all_96_1_113 & member(null_class, all_96_1_113) = 0
% 48.16/18.00  		|
% 48.16/18.00  			| Applying alpha-rule on (192) yields:
% 48.16/18.00  			| (193) all_96_0_112 = 0
% 48.16/18.00  			| (194) complement(universal_class) = all_96_1_113
% 48.16/18.00  			| (195) member(null_class, all_96_1_113) = 0
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (145) with universal_class, all_72_1_84, all_96_1_113 and discharging atoms complement(universal_class) = all_96_1_113, complement(universal_class) = all_72_1_84, yields:
% 48.16/18.01  			| (196) all_96_1_113 = all_72_1_84
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (145) with universal_class, all_68_1_81, all_96_1_113 and discharging atoms complement(universal_class) = all_96_1_113, complement(universal_class) = all_68_1_81, yields:
% 48.16/18.01  			| (197) all_96_1_113 = all_68_1_81
% 48.16/18.01  			|
% 48.16/18.01  			| Combining equations (197,196) yields a new equation:
% 48.16/18.01  			| (198) all_72_1_84 = all_68_1_81
% 48.16/18.01  			|
% 48.16/18.01  			| Combining equations (198,196) yields a new equation:
% 48.16/18.01  			| (197) all_96_1_113 = all_68_1_81
% 48.16/18.01  			|
% 48.16/18.01  			| From (197) and (195) follows:
% 48.16/18.01  			| (200) member(null_class, all_68_1_81) = 0
% 48.16/18.01  			|
% 48.16/18.01  			| From (198) and (191) follows:
% 48.16/18.01  			| (201) member(null_class, all_68_1_81) = all_72_0_83
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (10) with null_class, all_68_1_81, 0, all_72_0_83 and discharging atoms member(null_class, all_68_1_81) = all_72_0_83, member(null_class, all_68_1_81) = 0, yields:
% 48.16/18.01  			| (202) all_72_0_83 = 0
% 48.16/18.01  			|
% 48.16/18.01  			| Equations (202) can reduce 189 to:
% 48.16/18.01  			| (178) $false
% 48.16/18.01  			|
% 48.16/18.01  			|-The branch is then unsatisfiable
% 48.16/18.01  		|-Branch two:
% 48.16/18.01  		| (204)  ~ (all_96_1_113 = 0) & member(null_class, universal_class) = all_96_1_113
% 48.16/18.01  		|
% 48.16/18.01  			| Applying alpha-rule on (204) yields:
% 48.16/18.01  			| (205)  ~ (all_96_1_113 = 0)
% 48.16/18.01  			| (206) member(null_class, universal_class) = all_96_1_113
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (145) with universal_class, all_68_1_81, all_72_1_84 and discharging atoms complement(universal_class) = all_72_1_84, complement(universal_class) = all_68_1_81, yields:
% 48.16/18.01  			| (198) all_72_1_84 = all_68_1_81
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (10) with null_class, universal_class, all_96_1_113, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_96_1_113, member(null_class, universal_class) = all_0_2_2, yields:
% 48.16/18.01  			| (208) all_96_1_113 = all_0_2_2
% 48.16/18.01  			|
% 48.16/18.01  			| Equations (208) can reduce 205 to:
% 48.16/18.01  			| (35)  ~ (all_0_2_2 = 0)
% 48.16/18.01  			|
% 48.16/18.01  			| From (198) and (191) follows:
% 48.16/18.01  			| (201) member(null_class, all_68_1_81) = all_72_0_83
% 48.16/18.01  			|
% 48.16/18.01  			| From (208) and (206) follows:
% 48.16/18.01  			| (94) member(null_class, universal_class) = all_0_2_2
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (140) with all_68_0_80, all_0_0_0, all_68_1_81 and discharging atoms member(all_0_0_0, all_68_1_81) = all_68_0_80, yields:
% 48.16/18.01  			| (212) all_68_0_80 = 0 |  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_68_1_81) = v0 & member(all_0_0_0, v0) = 0) | ( ~ (v0 = 0) & member(all_0_0_0, universal_class) = v0))
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (140) with all_72_0_83, null_class, all_68_1_81 and discharging atoms member(null_class, all_68_1_81) = all_72_0_83, yields:
% 48.16/18.01  			| (213) all_72_0_83 = 0 |  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_68_1_81) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (118) with all_72_0_83, null_class, all_68_1_81 and discharging atoms member(null_class, all_68_1_81) = all_72_0_83, yields:
% 48.16/18.01  			| (214)  ? [v0] :  ? [v1] : ((v0 = 0 &  ~ (all_72_0_83 = 0) & member(null_class, universal_class) = 0) | ( ~ (v1 = 0) & complement(all_68_1_81) = v0 & member(null_class, v0) = v1))
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (31) with all_0_0_0, null_class and discharging atoms member(null_class, all_0_0_0) = 0, yields:
% 48.16/18.01  			| (215)  ? [v0] :  ? [v1] : ((v1 = 0 & ordered_pair(null_class, all_0_0_0) = v0 & member(v0, element_relation) = 0) | ( ~ (v0 = 0) & member(all_0_0_0, universal_class) = v0))
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating formula (118) with 0, null_class, all_0_0_0 and discharging atoms member(null_class, all_0_0_0) = 0, yields:
% 48.16/18.01  			| (216)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & complement(all_0_0_0) = v0 & member(null_class, v0) = v1)
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating (214) with all_154_0_164, all_154_1_165 yields:
% 48.16/18.01  			| (217) (all_154_1_165 = 0 &  ~ (all_72_0_83 = 0) & member(null_class, universal_class) = 0) | ( ~ (all_154_0_164 = 0) & complement(all_68_1_81) = all_154_1_165 & member(null_class, all_154_1_165) = all_154_0_164)
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating (216) with all_161_0_173, all_161_1_174 yields:
% 48.16/18.01  			| (218)  ~ (all_161_0_173 = 0) & complement(all_0_0_0) = all_161_1_174 & member(null_class, all_161_1_174) = all_161_0_173
% 48.16/18.01  			|
% 48.16/18.01  			| Applying alpha-rule on (218) yields:
% 48.16/18.01  			| (219)  ~ (all_161_0_173 = 0)
% 48.16/18.01  			| (220) complement(all_0_0_0) = all_161_1_174
% 48.16/18.01  			| (221) member(null_class, all_161_1_174) = all_161_0_173
% 48.16/18.01  			|
% 48.16/18.01  			| Instantiating (215) with all_168_0_180, all_168_1_181 yields:
% 48.16/18.01  			| (222) (all_168_0_180 = 0 & ordered_pair(null_class, all_0_0_0) = all_168_1_181 & member(all_168_1_181, element_relation) = 0) | ( ~ (all_168_1_181 = 0) & member(all_0_0_0, universal_class) = all_168_1_181)
% 48.16/18.01  			|
% 48.16/18.01  			+-Applying beta-rule and splitting (222), into two cases.
% 48.16/18.01  			|-Branch one:
% 48.16/18.01  			| (223) all_168_0_180 = 0 & ordered_pair(null_class, all_0_0_0) = all_168_1_181 & member(all_168_1_181, element_relation) = 0
% 48.16/18.01  			|
% 48.16/18.01  				| Applying alpha-rule on (223) yields:
% 48.16/18.01  				| (224) all_168_0_180 = 0
% 48.16/18.01  				| (225) ordered_pair(null_class, all_0_0_0) = all_168_1_181
% 48.16/18.01  				| (226) member(all_168_1_181, element_relation) = 0
% 48.16/18.01  				|
% 48.16/18.01  				+-Applying beta-rule and splitting (212), into two cases.
% 48.16/18.01  				|-Branch one:
% 48.16/18.01  				| (227) all_68_0_80 = 0
% 48.16/18.01  				|
% 48.16/18.01  					| Equations (227) can reduce 169 to:
% 48.16/18.01  					| (178) $false
% 48.16/18.01  					|
% 48.16/18.01  					|-The branch is then unsatisfiable
% 48.16/18.01  				|-Branch two:
% 48.16/18.01  				| (169)  ~ (all_68_0_80 = 0)
% 48.16/18.01  				| (230)  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_68_1_81) = v0 & member(all_0_0_0, v0) = 0) | ( ~ (v0 = 0) & member(all_0_0_0, universal_class) = v0))
% 48.16/18.01  				|
% 48.16/18.01  					| Instantiating (230) with all_206_0_197, all_206_1_198 yields:
% 48.16/18.01  					| (231) (all_206_0_197 = 0 & complement(all_68_1_81) = all_206_1_198 & member(all_0_0_0, all_206_1_198) = 0) | ( ~ (all_206_1_198 = 0) & member(all_0_0_0, universal_class) = all_206_1_198)
% 48.16/18.01  					|
% 48.16/18.01  					+-Applying beta-rule and splitting (231), into two cases.
% 48.16/18.01  					|-Branch one:
% 48.16/18.01  					| (232) all_206_0_197 = 0 & complement(all_68_1_81) = all_206_1_198 & member(all_0_0_0, all_206_1_198) = 0
% 48.16/18.01  					|
% 48.16/18.01  						| Applying alpha-rule on (232) yields:
% 48.16/18.01  						| (233) all_206_0_197 = 0
% 48.16/18.01  						| (234) complement(all_68_1_81) = all_206_1_198
% 48.16/18.01  						| (235) member(all_0_0_0, all_206_1_198) = 0
% 48.16/18.01  						|
% 48.16/18.01  						+-Applying beta-rule and splitting (213), into two cases.
% 48.16/18.01  						|-Branch one:
% 48.16/18.01  						| (202) all_72_0_83 = 0
% 48.16/18.01  						|
% 48.16/18.01  							| Equations (202) can reduce 189 to:
% 48.16/18.01  							| (178) $false
% 48.16/18.01  							|
% 48.16/18.01  							|-The branch is then unsatisfiable
% 48.16/18.01  						|-Branch two:
% 48.16/18.01  						| (189)  ~ (all_72_0_83 = 0)
% 48.16/18.01  						| (239)  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_68_1_81) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.01  						|
% 48.16/18.01  							| Instantiating (239) with all_222_0_201, all_222_1_202 yields:
% 48.16/18.01  							| (240) (all_222_0_201 = 0 & complement(all_68_1_81) = all_222_1_202 & member(null_class, all_222_1_202) = 0) | ( ~ (all_222_1_202 = 0) & member(null_class, universal_class) = all_222_1_202)
% 48.16/18.01  							|
% 48.16/18.01  							+-Applying beta-rule and splitting (217), into two cases.
% 48.16/18.01  							|-Branch one:
% 48.16/18.01  							| (241) all_154_1_165 = 0 &  ~ (all_72_0_83 = 0) & member(null_class, universal_class) = 0
% 48.16/18.01  							|
% 48.16/18.01  								| Applying alpha-rule on (241) yields:
% 48.16/18.01  								| (242) all_154_1_165 = 0
% 48.16/18.01  								| (189)  ~ (all_72_0_83 = 0)
% 48.16/18.01  								| (185) member(null_class, universal_class) = 0
% 48.16/18.01  								|
% 48.16/18.01  								| Instantiating formula (10) with null_class, universal_class, 0, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_0_2_2, member(null_class, universal_class) = 0, yields:
% 48.16/18.01  								| (177) all_0_2_2 = 0
% 48.16/18.01  								|
% 48.16/18.01  								| Equations (177) can reduce 35 to:
% 48.16/18.01  								| (178) $false
% 48.16/18.01  								|
% 48.16/18.01  								|-The branch is then unsatisfiable
% 48.16/18.01  							|-Branch two:
% 48.16/18.01  							| (247)  ~ (all_154_0_164 = 0) & complement(all_68_1_81) = all_154_1_165 & member(null_class, all_154_1_165) = all_154_0_164
% 48.16/18.01  							|
% 48.16/18.01  								| Applying alpha-rule on (247) yields:
% 48.16/18.01  								| (248)  ~ (all_154_0_164 = 0)
% 48.16/18.01  								| (249) complement(all_68_1_81) = all_154_1_165
% 48.16/18.01  								| (250) member(null_class, all_154_1_165) = all_154_0_164
% 48.16/18.01  								|
% 48.16/18.01  								| Instantiating formula (145) with all_68_1_81, all_154_1_165, all_206_1_198 and discharging atoms complement(all_68_1_81) = all_206_1_198, complement(all_68_1_81) = all_154_1_165, yields:
% 48.16/18.01  								| (251) all_206_1_198 = all_154_1_165
% 48.16/18.01  								|
% 48.16/18.01  								| From (251) and (234) follows:
% 48.16/18.01  								| (249) complement(all_68_1_81) = all_154_1_165
% 48.16/18.01  								|
% 48.16/18.01  								| From (251) and (235) follows:
% 48.16/18.01  								| (253) member(all_0_0_0, all_154_1_165) = 0
% 48.16/18.01  								|
% 48.16/18.01  								+-Applying beta-rule and splitting (240), into two cases.
% 48.16/18.01  								|-Branch one:
% 48.16/18.01  								| (254) all_222_0_201 = 0 & complement(all_68_1_81) = all_222_1_202 & member(null_class, all_222_1_202) = 0
% 48.16/18.01  								|
% 48.16/18.01  									| Applying alpha-rule on (254) yields:
% 48.16/18.01  									| (255) all_222_0_201 = 0
% 48.16/18.01  									| (256) complement(all_68_1_81) = all_222_1_202
% 48.16/18.01  									| (257) member(null_class, all_222_1_202) = 0
% 48.16/18.01  									|
% 48.16/18.01  									| Instantiating formula (145) with all_68_1_81, all_222_1_202, all_154_1_165 and discharging atoms complement(all_68_1_81) = all_222_1_202, complement(all_68_1_81) = all_154_1_165, yields:
% 48.16/18.01  									| (258) all_222_1_202 = all_154_1_165
% 48.16/18.01  									|
% 48.16/18.01  									| From (258) and (257) follows:
% 48.16/18.01  									| (259) member(null_class, all_154_1_165) = 0
% 48.16/18.01  									|
% 48.16/18.01  									| Instantiating formula (10) with null_class, all_154_1_165, 0, all_154_0_164 and discharging atoms member(null_class, all_154_1_165) = all_154_0_164, member(null_class, all_154_1_165) = 0, yields:
% 48.16/18.01  									| (260) all_154_0_164 = 0
% 48.16/18.01  									|
% 48.16/18.01  									| Equations (260) can reduce 248 to:
% 48.16/18.01  									| (178) $false
% 48.16/18.01  									|
% 48.16/18.01  									|-The branch is then unsatisfiable
% 48.16/18.01  								|-Branch two:
% 48.16/18.01  								| (262)  ~ (all_222_1_202 = 0) & member(null_class, universal_class) = all_222_1_202
% 48.16/18.01  								|
% 48.16/18.01  									| Applying alpha-rule on (262) yields:
% 48.16/18.01  									| (263)  ~ (all_222_1_202 = 0)
% 48.16/18.02  									| (264) member(null_class, universal_class) = all_222_1_202
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (10) with null_class, universal_class, all_222_1_202, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_222_1_202, member(null_class, universal_class) = all_0_2_2, yields:
% 48.16/18.02  									| (265) all_222_1_202 = all_0_2_2
% 48.16/18.02  									|
% 48.16/18.02  									| Equations (265) can reduce 263 to:
% 48.16/18.02  									| (35)  ~ (all_0_2_2 = 0)
% 48.16/18.02  									|
% 48.16/18.02  									| From (265) and (264) follows:
% 48.16/18.02  									| (94) member(null_class, universal_class) = all_0_2_2
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (109) with all_168_1_181, all_0_4_4, element_relation and discharging atoms subclass(element_relation, all_0_4_4) = 0, member(all_168_1_181, element_relation) = 0, yields:
% 48.16/18.02  									| (268) member(all_168_1_181, all_0_4_4) = 0
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (118) with 0, all_0_0_0, all_154_1_165 and discharging atoms member(all_0_0_0, all_154_1_165) = 0, yields:
% 48.16/18.02  									| (269)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & complement(all_154_1_165) = v0 & member(all_0_0_0, v0) = v1)
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (59) with all_161_0_173, all_161_1_174, null_class, all_0_0_0 and discharging atoms complement(all_0_0_0) = all_161_1_174, member(null_class, all_161_1_174) = all_161_0_173, yields:
% 48.16/18.02  									| (270) all_161_0_173 = 0 |  ? [v0] : ((v0 = 0 & member(null_class, all_0_0_0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (140) with all_161_0_173, null_class, all_161_1_174 and discharging atoms member(null_class, all_161_1_174) = all_161_0_173, yields:
% 48.16/18.02  									| (271) all_161_0_173 = 0 |  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_161_1_174) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (118) with all_161_0_173, null_class, all_161_1_174 and discharging atoms member(null_class, all_161_1_174) = all_161_0_173, yields:
% 48.16/18.02  									| (272)  ? [v0] :  ? [v1] : ((v0 = 0 &  ~ (all_161_0_173 = 0) & member(null_class, universal_class) = 0) | ( ~ (v1 = 0) & complement(all_161_1_174) = v0 & member(null_class, v0) = v1))
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (140) with all_154_0_164, null_class, all_154_1_165 and discharging atoms member(null_class, all_154_1_165) = all_154_0_164, yields:
% 48.16/18.02  									| (273) all_154_0_164 = 0 |  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_154_1_165) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating formula (118) with all_154_0_164, null_class, all_154_1_165 and discharging atoms member(null_class, all_154_1_165) = all_154_0_164, yields:
% 48.16/18.02  									| (274)  ? [v0] :  ? [v1] : ((v0 = 0 &  ~ (all_154_0_164 = 0) & member(null_class, universal_class) = 0) | ( ~ (v1 = 0) & complement(all_154_1_165) = v0 & member(null_class, v0) = v1))
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating (274) with all_290_0_256, all_290_1_257 yields:
% 48.16/18.02  									| (275) (all_290_1_257 = 0 &  ~ (all_154_0_164 = 0) & member(null_class, universal_class) = 0) | ( ~ (all_290_0_256 = 0) & complement(all_154_1_165) = all_290_1_257 & member(null_class, all_290_1_257) = all_290_0_256)
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating (269) with all_317_0_292, all_317_1_293 yields:
% 48.16/18.02  									| (276)  ~ (all_317_0_292 = 0) & complement(all_154_1_165) = all_317_1_293 & member(all_0_0_0, all_317_1_293) = all_317_0_292
% 48.16/18.02  									|
% 48.16/18.02  									| Applying alpha-rule on (276) yields:
% 48.16/18.02  									| (277)  ~ (all_317_0_292 = 0)
% 48.16/18.02  									| (278) complement(all_154_1_165) = all_317_1_293
% 48.16/18.02  									| (279) member(all_0_0_0, all_317_1_293) = all_317_0_292
% 48.16/18.02  									|
% 48.16/18.02  									| Instantiating (272) with all_337_0_325, all_337_1_326 yields:
% 48.16/18.02  									| (280) (all_337_1_326 = 0 &  ~ (all_161_0_173 = 0) & member(null_class, universal_class) = 0) | ( ~ (all_337_0_325 = 0) & complement(all_161_1_174) = all_337_1_326 & member(null_class, all_337_1_326) = all_337_0_325)
% 48.16/18.02  									|
% 48.16/18.02  									+-Applying beta-rule and splitting (275), into two cases.
% 48.16/18.02  									|-Branch one:
% 48.16/18.02  									| (281) all_290_1_257 = 0 &  ~ (all_154_0_164 = 0) & member(null_class, universal_class) = 0
% 48.16/18.02  									|
% 48.16/18.02  										| Applying alpha-rule on (281) yields:
% 48.16/18.02  										| (282) all_290_1_257 = 0
% 48.16/18.02  										| (248)  ~ (all_154_0_164 = 0)
% 48.16/18.02  										| (185) member(null_class, universal_class) = 0
% 48.16/18.02  										|
% 48.16/18.02  										| Instantiating formula (10) with null_class, universal_class, 0, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_0_2_2, member(null_class, universal_class) = 0, yields:
% 48.16/18.02  										| (177) all_0_2_2 = 0
% 48.16/18.02  										|
% 48.16/18.02  										| Equations (177) can reduce 35 to:
% 48.16/18.02  										| (178) $false
% 48.16/18.02  										|
% 48.16/18.02  										|-The branch is then unsatisfiable
% 48.16/18.02  									|-Branch two:
% 48.16/18.02  									| (287)  ~ (all_290_0_256 = 0) & complement(all_154_1_165) = all_290_1_257 & member(null_class, all_290_1_257) = all_290_0_256
% 48.16/18.02  									|
% 48.16/18.02  										| Applying alpha-rule on (287) yields:
% 48.16/18.02  										| (288)  ~ (all_290_0_256 = 0)
% 48.16/18.02  										| (289) complement(all_154_1_165) = all_290_1_257
% 48.16/18.02  										| (290) member(null_class, all_290_1_257) = all_290_0_256
% 48.16/18.02  										|
% 48.16/18.02  										+-Applying beta-rule and splitting (273), into two cases.
% 48.16/18.02  										|-Branch one:
% 48.16/18.02  										| (260) all_154_0_164 = 0
% 48.16/18.02  										|
% 48.16/18.02  											| Equations (260) can reduce 248 to:
% 48.16/18.02  											| (178) $false
% 48.16/18.02  											|
% 48.16/18.02  											|-The branch is then unsatisfiable
% 48.16/18.02  										|-Branch two:
% 48.16/18.02  										| (248)  ~ (all_154_0_164 = 0)
% 48.16/18.02  										| (294)  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_154_1_165) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.02  										|
% 48.16/18.02  											| Instantiating (294) with all_388_0_377, all_388_1_378 yields:
% 48.16/18.02  											| (295) (all_388_0_377 = 0 & complement(all_154_1_165) = all_388_1_378 & member(null_class, all_388_1_378) = 0) | ( ~ (all_388_1_378 = 0) & member(null_class, universal_class) = all_388_1_378)
% 48.16/18.02  											|
% 48.16/18.02  											+-Applying beta-rule and splitting (270), into two cases.
% 48.16/18.02  											|-Branch one:
% 48.16/18.02  											| (296) all_161_0_173 = 0
% 48.16/18.02  											|
% 48.16/18.02  												| Equations (296) can reduce 219 to:
% 48.16/18.02  												| (178) $false
% 48.16/18.02  												|
% 48.16/18.02  												|-The branch is then unsatisfiable
% 48.16/18.02  											|-Branch two:
% 48.16/18.02  											| (219)  ~ (all_161_0_173 = 0)
% 48.16/18.02  											| (299)  ? [v0] : ((v0 = 0 & member(null_class, all_0_0_0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.02  											|
% 48.16/18.02  												+-Applying beta-rule and splitting (280), into two cases.
% 48.16/18.02  												|-Branch one:
% 48.16/18.02  												| (300) all_337_1_326 = 0 &  ~ (all_161_0_173 = 0) & member(null_class, universal_class) = 0
% 48.16/18.02  												|
% 48.16/18.02  													| Applying alpha-rule on (300) yields:
% 48.16/18.02  													| (301) all_337_1_326 = 0
% 48.16/18.02  													| (219)  ~ (all_161_0_173 = 0)
% 48.16/18.02  													| (185) member(null_class, universal_class) = 0
% 48.16/18.02  													|
% 48.16/18.02  													| Instantiating formula (10) with null_class, universal_class, 0, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_0_2_2, member(null_class, universal_class) = 0, yields:
% 48.16/18.02  													| (177) all_0_2_2 = 0
% 48.16/18.02  													|
% 48.16/18.02  													| Equations (177) can reduce 35 to:
% 48.16/18.02  													| (178) $false
% 48.16/18.02  													|
% 48.16/18.02  													|-The branch is then unsatisfiable
% 48.16/18.02  												|-Branch two:
% 48.16/18.02  												| (306)  ~ (all_337_0_325 = 0) & complement(all_161_1_174) = all_337_1_326 & member(null_class, all_337_1_326) = all_337_0_325
% 48.16/18.02  												|
% 48.16/18.02  													| Applying alpha-rule on (306) yields:
% 48.16/18.02  													| (307)  ~ (all_337_0_325 = 0)
% 48.16/18.02  													| (308) complement(all_161_1_174) = all_337_1_326
% 48.16/18.02  													| (309) member(null_class, all_337_1_326) = all_337_0_325
% 48.16/18.02  													|
% 48.16/18.02  													+-Applying beta-rule and splitting (271), into two cases.
% 48.16/18.02  													|-Branch one:
% 48.16/18.02  													| (296) all_161_0_173 = 0
% 48.16/18.02  													|
% 48.16/18.02  														| Equations (296) can reduce 219 to:
% 48.16/18.02  														| (178) $false
% 48.16/18.02  														|
% 48.16/18.02  														|-The branch is then unsatisfiable
% 48.16/18.02  													|-Branch two:
% 48.16/18.02  													| (219)  ~ (all_161_0_173 = 0)
% 48.16/18.02  													| (313)  ? [v0] :  ? [v1] : ((v1 = 0 & complement(all_161_1_174) = v0 & member(null_class, v0) = 0) | ( ~ (v0 = 0) & member(null_class, universal_class) = v0))
% 48.16/18.02  													|
% 48.16/18.02  														| Instantiating (313) with all_444_0_404, all_444_1_405 yields:
% 48.16/18.02  														| (314) (all_444_0_404 = 0 & complement(all_161_1_174) = all_444_1_405 & member(null_class, all_444_1_405) = 0) | ( ~ (all_444_1_405 = 0) & member(null_class, universal_class) = all_444_1_405)
% 48.16/18.02  														|
% 48.16/18.02  														+-Applying beta-rule and splitting (314), into two cases.
% 48.16/18.02  														|-Branch one:
% 48.16/18.02  														| (315) all_444_0_404 = 0 & complement(all_161_1_174) = all_444_1_405 & member(null_class, all_444_1_405) = 0
% 48.16/18.02  														|
% 48.16/18.02  															| Applying alpha-rule on (315) yields:
% 48.16/18.02  															| (316) all_444_0_404 = 0
% 48.16/18.02  															| (317) complement(all_161_1_174) = all_444_1_405
% 48.16/18.02  															| (318) member(null_class, all_444_1_405) = 0
% 48.16/18.02  															|
% 48.16/18.02  															| Instantiating formula (145) with all_161_1_174, all_337_1_326, all_444_1_405 and discharging atoms complement(all_161_1_174) = all_444_1_405, complement(all_161_1_174) = all_337_1_326, yields:
% 48.16/18.02  															| (319) all_444_1_405 = all_337_1_326
% 48.16/18.02  															|
% 48.16/18.02  															| From (319) and (318) follows:
% 48.16/18.02  															| (320) member(null_class, all_337_1_326) = 0
% 48.16/18.02  															|
% 48.16/18.02  															| Instantiating formula (10) with null_class, all_337_1_326, 0, all_337_0_325 and discharging atoms member(null_class, all_337_1_326) = all_337_0_325, member(null_class, all_337_1_326) = 0, yields:
% 48.16/18.02  															| (321) all_337_0_325 = 0
% 48.16/18.02  															|
% 48.16/18.02  															| Equations (321) can reduce 307 to:
% 48.16/18.02  															| (178) $false
% 48.16/18.02  															|
% 48.16/18.02  															|-The branch is then unsatisfiable
% 48.16/18.02  														|-Branch two:
% 48.16/18.02  														| (323)  ~ (all_444_1_405 = 0) & member(null_class, universal_class) = all_444_1_405
% 48.16/18.02  														|
% 48.16/18.02  															| Applying alpha-rule on (323) yields:
% 48.16/18.02  															| (324)  ~ (all_444_1_405 = 0)
% 48.16/18.02  															| (325) member(null_class, universal_class) = all_444_1_405
% 48.16/18.02  															|
% 48.16/18.02  															| Instantiating formula (145) with all_154_1_165, all_290_1_257, all_317_1_293 and discharging atoms complement(all_154_1_165) = all_317_1_293, complement(all_154_1_165) = all_290_1_257, yields:
% 48.16/18.02  															| (326) all_317_1_293 = all_290_1_257
% 48.16/18.02  															|
% 48.16/18.02  															| Instantiating formula (10) with null_class, universal_class, all_444_1_405, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_444_1_405, member(null_class, universal_class) = all_0_2_2, yields:
% 48.16/18.02  															| (327) all_444_1_405 = all_0_2_2
% 48.16/18.02  															|
% 48.16/18.02  															| From (326) and (278) follows:
% 48.16/18.02  															| (289) complement(all_154_1_165) = all_290_1_257
% 48.16/18.02  															|
% 48.16/18.02  															| From (327) and (325) follows:
% 48.16/18.02  															| (94) member(null_class, universal_class) = all_0_2_2
% 48.16/18.02  															|
% 48.16/18.02  															+-Applying beta-rule and splitting (295), into two cases.
% 48.16/18.02  															|-Branch one:
% 48.16/18.02  															| (330) all_388_0_377 = 0 & complement(all_154_1_165) = all_388_1_378 & member(null_class, all_388_1_378) = 0
% 48.16/18.02  															|
% 48.16/18.02  																| Applying alpha-rule on (330) yields:
% 48.16/18.02  																| (331) all_388_0_377 = 0
% 48.16/18.02  																| (332) complement(all_154_1_165) = all_388_1_378
% 48.16/18.02  																| (333) member(null_class, all_388_1_378) = 0
% 48.16/18.02  																|
% 48.16/18.02  																| Instantiating formula (145) with all_154_1_165, all_388_1_378, all_290_1_257 and discharging atoms complement(all_154_1_165) = all_388_1_378, complement(all_154_1_165) = all_290_1_257, yields:
% 48.16/18.02  																| (334) all_388_1_378 = all_290_1_257
% 48.16/18.02  																|
% 48.16/18.02  																| From (334) and (333) follows:
% 48.16/18.02  																| (335) member(null_class, all_290_1_257) = 0
% 48.16/18.02  																|
% 48.16/18.02  																| Instantiating formula (10) with null_class, all_290_1_257, 0, all_290_0_256 and discharging atoms member(null_class, all_290_1_257) = all_290_0_256, member(null_class, all_290_1_257) = 0, yields:
% 48.16/18.02  																| (336) all_290_0_256 = 0
% 48.16/18.02  																|
% 48.16/18.02  																| Equations (336) can reduce 288 to:
% 48.16/18.02  																| (178) $false
% 48.16/18.02  																|
% 48.16/18.02  																|-The branch is then unsatisfiable
% 48.16/18.02  															|-Branch two:
% 48.16/18.02  															| (338)  ~ (all_388_1_378 = 0) & member(null_class, universal_class) = all_388_1_378
% 48.16/18.02  															|
% 48.16/18.02  																| Applying alpha-rule on (338) yields:
% 48.16/18.03  																| (339)  ~ (all_388_1_378 = 0)
% 48.16/18.03  																| (340) member(null_class, universal_class) = all_388_1_378
% 48.16/18.03  																|
% 48.16/18.03  																| Instantiating formula (10) with null_class, universal_class, all_388_1_378, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_388_1_378, member(null_class, universal_class) = all_0_2_2, yields:
% 48.16/18.03  																| (341) all_388_1_378 = all_0_2_2
% 48.16/18.03  																|
% 48.16/18.03  																| Equations (341) can reduce 339 to:
% 48.16/18.03  																| (35)  ~ (all_0_2_2 = 0)
% 48.16/18.03  																|
% 48.16/18.03  																| From (341) and (340) follows:
% 48.16/18.03  																| (94) member(null_class, universal_class) = all_0_2_2
% 48.16/18.03  																|
% 48.16/18.03  																| Instantiating formula (113) with all_0_4_4, all_168_1_181, universal_class, universal_class, all_0_0_0, null_class and discharging atoms cross_product(universal_class, universal_class) = all_0_4_4, ordered_pair(null_class, all_0_0_0) = all_168_1_181, member(all_168_1_181, all_0_4_4) = 0, yields:
% 48.16/18.03  																| (344) member(all_0_0_0, universal_class) = 0 & member(null_class, universal_class) = 0
% 48.16/18.03  																|
% 48.16/18.03  																| Applying alpha-rule on (344) yields:
% 48.16/18.03  																| (137) member(all_0_0_0, universal_class) = 0
% 48.16/18.03  																| (185) member(null_class, universal_class) = 0
% 48.16/18.03  																|
% 48.16/18.03  																| Instantiating formula (10) with null_class, universal_class, 0, all_0_2_2 and discharging atoms member(null_class, universal_class) = all_0_2_2, member(null_class, universal_class) = 0, yields:
% 48.16/18.03  																| (177) all_0_2_2 = 0
% 48.16/18.03  																|
% 48.16/18.03  																| Equations (177) can reduce 35 to:
% 48.16/18.03  																| (178) $false
% 48.16/18.03  																|
% 48.16/18.03  																|-The branch is then unsatisfiable
% 48.16/18.03  					|-Branch two:
% 48.16/18.03  					| (349)  ~ (all_206_1_198 = 0) & member(all_0_0_0, universal_class) = all_206_1_198
% 48.16/18.03  					|
% 48.16/18.03  						| Applying alpha-rule on (349) yields:
% 48.16/18.03  						| (350)  ~ (all_206_1_198 = 0)
% 48.16/18.03  						| (351) member(all_0_0_0, universal_class) = all_206_1_198
% 48.16/18.03  						|
% 48.16/18.03  						| Instantiating formula (10) with all_0_0_0, universal_class, all_206_1_198, 0 and discharging atoms member(all_0_0_0, universal_class) = all_206_1_198, member(all_0_0_0, universal_class) = 0, yields:
% 48.16/18.03  						| (352) all_206_1_198 = 0
% 48.16/18.03  						|
% 48.16/18.03  						| Equations (352) can reduce 350 to:
% 48.16/18.03  						| (178) $false
% 48.16/18.03  						|
% 48.16/18.03  						|-The branch is then unsatisfiable
% 48.16/18.03  			|-Branch two:
% 48.16/18.03  			| (354)  ~ (all_168_1_181 = 0) & member(all_0_0_0, universal_class) = all_168_1_181
% 48.16/18.03  			|
% 48.16/18.03  				| Applying alpha-rule on (354) yields:
% 48.16/18.03  				| (355)  ~ (all_168_1_181 = 0)
% 48.16/18.03  				| (356) member(all_0_0_0, universal_class) = all_168_1_181
% 48.16/18.03  				|
% 48.16/18.03  				| Instantiating formula (10) with all_0_0_0, universal_class, all_168_1_181, 0 and discharging atoms member(all_0_0_0, universal_class) = all_168_1_181, member(all_0_0_0, universal_class) = 0, yields:
% 48.16/18.03  				| (357) all_168_1_181 = 0
% 48.16/18.03  				|
% 48.16/18.03  				| Equations (357) can reduce 355 to:
% 48.16/18.03  				| (178) $false
% 48.16/18.03  				|
% 48.16/18.03  				|-The branch is then unsatisfiable
% 48.16/18.03  % SZS output end Proof for theBenchmark
% 48.16/18.03  
% 48.16/18.03  17434ms
%------------------------------------------------------------------------------