ePrincess---1.0.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.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 08:47:19 EDT 2022

% Result   : Theorem 24.86s 6.67s
% Output   : Proof 32.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n016.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 01:09:54 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.63/0.62          ____       _                          
% 0.63/0.62    ___  / __ \_____(_)___  ________  __________
% 0.63/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.63/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.63/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.63/0.62  
% 0.63/0.62  A Theorem Prover for First-Order Logic
% 0.63/0.62  (ePrincess v.1.0)
% 0.63/0.62  
% 0.63/0.62  (c) Philipp Rümmer, 2009-2015
% 0.63/0.62  (c) Peter Backeman, 2014-2015
% 0.63/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.63/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.63/0.62  Bug reports to peter@backeman.se
% 0.63/0.62  
% 0.63/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.63/0.62  
% 0.63/0.63  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.68/0.71  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.61/1.19  Prover 0: Preprocessing ...
% 5.36/1.92  Prover 0: Warning: ignoring some quantifiers
% 5.36/1.96  Prover 0: Constructing countermodel ...
% 22.16/5.99  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.25/6.10  Prover 1: Preprocessing ...
% 23.60/6.32  Prover 1: Warning: ignoring some quantifiers
% 23.60/6.33  Prover 1: Constructing countermodel ...
% 24.86/6.67  Prover 1: proved (673ms)
% 24.86/6.67  Prover 0: stopped
% 24.86/6.67  
% 24.86/6.67  No countermodel exists, formula is valid
% 24.86/6.67  % SZS status Theorem for theBenchmark
% 24.86/6.67  
% 24.86/6.67  Generating proof ... Warning: ignoring some quantifiers
% 31.21/8.13  found it (size 112)
% 31.21/8.13  
% 31.21/8.13  % SZS output start Proof for theBenchmark
% 31.21/8.13  Assumed formulas after preprocessing and simplification: 
% 31.21/8.13  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v6 = 0) &  ~ (v2 = empty_set) & complements_of_subsets(v1, v2) = empty_set & element(v2, v4) = 0 & empty(v7) = 0 & empty(v5) = v6 & empty(empty_set) = 0 & powerset(v3) = v4 & powerset(v1) = v3 & powerset(empty_set) = v0 & singleton(empty_set) = v0 &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (cartesian_product2(v10, v11) = v13) |  ~ (ordered_pair(v8, v9) = v12) |  ~ (in(v12, v13) = v14) |  ? [v15] :  ? [v16] : (in(v9, v11) = v16 & in(v8, v10) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (cartesian_product2(v9, v11) = v13) |  ~ (cartesian_product2(v8, v10) = v12) |  ~ (subset(v12, v13) = v14) |  ? [v15] :  ? [v16] : (subset(v10, v11) = v16 & subset(v8, v9) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = 0 |  ~ (cartesian_product2(v8, v9) = v10) |  ~ (ordered_pair(v13, v14) = v11) |  ~ (in(v11, v10) = v12) |  ? [v15] :  ? [v16] : (in(v14, v9) = v16 & in(v13, v8) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (complements_of_subsets(v8, v9) = v12) |  ~ (element(v12, v11) = v13) |  ~ (powerset(v10) = v11) |  ~ (powerset(v8) = v10) |  ? [v14] : ( ~ (v14 = 0) & element(v9, v11) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (set_difference(v9, v11) = v12) |  ~ (singleton(v10) = v11) |  ~ (subset(v8, v12) = v13) |  ? [v14] :  ? [v15] : (subset(v8, v9) = v14 & in(v10, v8) = v15 & ( ~ (v14 = 0) | v15 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (set_difference(v9, v10) = v12) |  ~ (set_difference(v8, v10) = v11) |  ~ (subset(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (subset(v11, v12) = v13) |  ~ (set_intersection2(v9, v10) = v12) |  ~ (set_intersection2(v8, v10) = v11) |  ? [v14] : ( ~ (v14 = 0) & subset(v8, v9) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (cartesian_product2(v10, v11) = v13) |  ~ (ordered_pair(v8, v9) = v12) |  ~ (in(v12, v13) = 0) | (in(v9, v11) = 0 & in(v8, v10) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (cartesian_product2(v9, v10) = v12) |  ~ (cartesian_product2(v8, v10) = v11) |  ~ (subset(v11, v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : (cartesian_product2(v10, v9) = v16 & cartesian_product2(v10, v8) = v15 & subset(v15, v16) = v17 & subset(v8, v9) = v14 & ( ~ (v14 = 0) | (v17 = 0 & v13 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset_complement(v8, v9) = v11) |  ~ (element(v11, v10) = v12) |  ~ (powerset(v8) = v10) |  ? [v13] : ( ~ (v13 = 0) & element(v9, v10) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (element(v9, v11) = 0) |  ~ (element(v8, v10) = v12) |  ~ (powerset(v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & in(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (element(v9, v10) = 0) |  ~ (powerset(v8) = v10) |  ~ (in(v11, v8) = v12) |  ? [v13] : ( ~ (v13 = 0) & in(v11, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v11, v10) = v12) |  ~ (unordered_pair(v8, v9) = v11) |  ? [v13] :  ? [v14] : (in(v9, v10) = v14 & in(v8, v10) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v11, v9) = v12) |  ~ (set_union2(v8, v10) = v11) |  ? [v13] :  ? [v14] : (subset(v10, v9) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v8, v11) = v12) |  ~ (set_intersection2(v9, v10) = v11) |  ? [v13] :  ? [v14] : (subset(v8, v10) = v14 & subset(v8, v9) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (set_union2(v8, v9) = v10) |  ~ (in(v11, v8) = v12) |  ? [v13] :  ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | v14 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v9 |  ~ (ordered_pair(v10, v11) = v12) |  ~ (ordered_pair(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = v8 | v10 = v8 |  ~ (unordered_pair(v10, v11) = v12) |  ~ (unordered_pair(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v11 = 0 |  ~ (union(v8) = v9) |  ~ (in(v10, v12) = 0) |  ~ (in(v10, v9) = v11) |  ? [v13] : ( ~ (v13 = 0) & in(v12, v8) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v10 = v8 |  ~ (ordered_pair(v10, v11) = v12) |  ~ (ordered_pair(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (set_difference(v8, v9) = v10) |  ~ (in(v11, v8) = v12) |  ? [v13] :  ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v12 = 0 &  ~ (v14 = 0))))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (singleton(v8) = v11) |  ~ (unordered_pair(v10, v11) = v12) |  ~ (unordered_pair(v8, v9) = v10) | ordered_pair(v8, v9) = v12) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (set_intersection2(v8, v9) = v10) |  ~ (in(v11, v8) = v12) |  ? [v13] :  ? [v14] : (in(v11, v10) = v13 & in(v11, v9) = v14 & ( ~ (v13 = 0) | (v14 = 0 & v12 = 0)))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (set_union2(v8, v9) = v10) |  ~ (in(v11, v8) = v12) |  ? [v13] :  ? [v14] : (in(v11, v10) = v14 & in(v11, v9) = v13 & (v14 = 0 | ( ~ (v13 = 0) &  ~ (v12 = 0))))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v9 | v11 = v8 |  ~ (unordered_pair(v8, v9) = v10) |  ~ (in(v11, v10) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v9 |  ~ (subset_complement(v8, v10) = v11) |  ~ (subset_complement(v8, v9) = v10) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & element(v9, v12) = v13 & powerset(v8) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v9 |  ~ (set_difference(v9, v8) = v10) |  ~ (set_union2(v8, v10) = v11) |  ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v9 |  ~ (singleton(v8) = v10) |  ~ (set_union2(v10, v9) = v11) |  ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (set_difference(v8, v10) = v11) |  ~ (singleton(v9) = v10) | in(v9, v8) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (disjoint(v10, v9) = v11) |  ~ (singleton(v8) = v10) | in(v8, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (disjoint(v9, v10) = 0) |  ~ (disjoint(v8, v10) = v11) |  ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (set_difference(v8, v9) = v10) |  ~ (subset(v10, v8) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (union(v9) = v10) |  ~ (subset(v8, v10) = v11) |  ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (element(v8, v10) = v11) |  ~ (powerset(v9) = v10) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & in(v12, v9) = v13 & in(v12, v8) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (element(v8, v10) = v11) |  ~ (powerset(v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & subset(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (powerset(v8) = v9) |  ~ (subset(v10, v8) = v11) |  ? [v12] : ( ~ (v12 = 0) & in(v10, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (singleton(v8) = v10) |  ~ (subset(v10, v9) = v11) |  ? [v12] : ( ~ (v12 = 0) & in(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v10, v8) = v11) |  ~ (set_intersection2(v8, v9) = v10)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v8, v10) = v11) |  ~ (subset(v8, v9) = 0) |  ? [v12] : ( ~ (v12 = 0) & subset(v9, v10) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v8, v10) = v11) |  ~ (set_union2(v8, v9) = v10)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (unordered_pair(v8, v9) = v10) |  ~ (in(v9, v10) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (unordered_pair(v8, v9) = v10) |  ~ (in(v8, v10) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v10 = v9 |  ~ (singleton(v8) = v11) |  ~ (unordered_pair(v9, v10) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (are_equipotent(v11, v10) = v9) |  ~ (are_equipotent(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (complements_of_subsets(v11, v10) = v9) |  ~ (complements_of_subsets(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (disjoint(v11, v10) = v9) |  ~ (disjoint(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (subset_complement(v11, v10) = v9) |  ~ (subset_complement(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (set_difference(v11, v10) = v9) |  ~ (set_difference(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (cartesian_product2(v11, v10) = v9) |  ~ (cartesian_product2(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (ordered_pair(v11, v10) = v9) |  ~ (ordered_pair(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (element(v11, v10) = v9) |  ~ (element(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (singleton(v9) = v11) |  ~ (singleton(v8) = v10) |  ~ (subset(v10, v11) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (singleton(v8) = v11) |  ~ (unordered_pair(v9, v10) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (subset(v11, v10) = v9) |  ~ (subset(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (set_intersection2(v11, v10) = v9) |  ~ (set_intersection2(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (set_union2(v11, v10) = v9) |  ~ (set_union2(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (unordered_pair(v11, v10) = v9) |  ~ (unordered_pair(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (proper_subset(v11, v10) = v9) |  ~ (proper_subset(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (in(v11, v10) = v9) |  ~ (in(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v10, v9) = v11) |  ~ (set_union2(v8, v9) = v10) | set_difference(v8, v9) = v11) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v9, v8) = v10) |  ~ (set_union2(v8, v10) = v11) | set_union2(v8, v9) = v11) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v8, v10) = v11) |  ~ (set_difference(v8, v9) = v10) | set_intersection2(v8, v9) = v11) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v8, v9) = v10) |  ~ (in(v11, v8) = 0) |  ? [v12] :  ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & (v13 = 0 | v12 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (cartesian_product2(v8, v9) = v10) |  ~ (in(v11, v10) = 0) |  ? [v12] :  ? [v13] : (ordered_pair(v12, v13) = v11 & in(v13, v9) = 0 & in(v12, v8) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (element(v11, v10) = 0) |  ~ (element(v9, v10) = 0) |  ~ (powerset(v8) = v10) |  ? [v12] :  ? [v13] :  ? [v14] : (disjoint(v9, v11) = v12 & subset_complement(v8, v11) = v13 & subset(v9, v13) = v14 & ( ~ (v14 = 0) | v12 = 0) & ( ~ (v12 = 0) | v14 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (element(v10, v11) = 0) |  ~ (powerset(v8) = v11) |  ~ (in(v9, v10) = 0) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & subset_complement(v8, v10) = v12 & in(v9, v12) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (element(v9, v11) = 0) |  ~ (powerset(v10) = v11) |  ~ (powerset(v8) = v10) |  ? [v12] : (complements_of_subsets(v8, v12) = v9 & complements_of_subsets(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (element(v9, v11) = 0) |  ~ (powerset(v10) = v11) |  ~ (powerset(v8) = v10) |  ? [v12] : (complements_of_subsets(v8, v9) = v12 &  ! [v13] : (v13 = v12 |  ~ (element(v13, v11) = 0) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] : (subset_complement(v8, v14) = v16 & element(v14, v10) = 0 & in(v16, v9) = v17 & in(v14, v13) = v15 & ( ~ (v17 = 0) |  ~ (v15 = 0)) & (v17 = 0 | v15 = 0))) &  ! [v13] : ( ~ (element(v13, v10) = 0) |  ~ (element(v12, v11) = 0) |  ? [v14] :  ? [v15] :  ? [v16] : (subset_complement(v8, v13) = v15 & in(v15, v9) = v16 & in(v13, v12) = v14 & ( ~ (v16 = 0) | v14 = 0) & ( ~ (v14 = 0) | v16 = 0))))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (element(v9, v11) = 0) |  ~ (powerset(v10) = v11) |  ~ (in(v8, v9) = 0) |  ? [v12] : ( ~ (v12 = 0) & empty(v10) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (subset(v11, v10) = 0) |  ~ (unordered_pair(v8, v9) = v11) | (in(v9, v10) = 0 & in(v8, v10) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) |  ~ (in(v11, v10) = 0) |  ? [v12] : ( ~ (v12 = 0) & disjoint(v8, v9) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_intersection2(v8, v9) = v10) |  ~ (in(v11, v8) = 0) |  ? [v12] :  ? [v13] : (in(v11, v10) = v13 & in(v11, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (set_difference(v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0) | v15 = 0) & (v13 = 0 | (v14 = 0 &  ~ (v15 = 0))))) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (cartesian_product2(v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (in(v12, v8) = v13 & ( ~ (v13 = 0) |  ! [v19] :  ! [v20] : ( ~ (ordered_pair(v19, v20) = v12) |  ? [v21] :  ? [v22] : (in(v20, v10) = v22 & in(v19, v9) = v21 & ( ~ (v22 = 0) |  ~ (v21 = 0))))) & (v13 = 0 | (v18 = v12 & v17 = 0 & v16 = 0 & ordered_pair(v14, v15) = v12 & in(v15, v10) = 0 & in(v14, v9) = 0)))) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (set_intersection2(v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v15 = 0) |  ~ (v14 = 0) |  ~ (v13 = 0)) & (v13 = 0 | (v15 = 0 & v14 = 0)))) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (set_union2(v9, v10) = v11) |  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (in(v12, v10) = v15 & in(v12, v9) = v14 & in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v15 = 0) &  ~ (v14 = 0))) & (v15 = 0 | v14 = 0 | v13 = 0))) &  ? [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = v8 |  ~ (unordered_pair(v9, v10) = v11) |  ? [v12] :  ? [v13] : (in(v12, v8) = v13 & ( ~ (v13 = 0) | ( ~ (v12 = v10) &  ~ (v12 = v9))) & (v13 = 0 | v12 = v10 | v12 = v9))) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v9 |  ~ (set_union2(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v8 | v8 = empty_set |  ~ (singleton(v9) = v10) |  ~ (subset(v8, v10) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (singleton(v8) = v9) |  ~ (in(v10, v9) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (set_intersection2(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = empty_set |  ~ (set_difference(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = empty_set |  ~ (set_intersection2(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & disjoint(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = v8 |  ~ (proper_subset(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (disjoint(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = v8) & set_difference(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (disjoint(v8, v9) = v10) |  ? [v11] : (in(v11, v9) = 0 & in(v11, v8) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (element(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & in(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (singleton(v9) = v8) |  ~ (subset(v8, v8) = v10)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (singleton(v8) = v9) |  ~ (subset(empty_set, v9) = v10)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (singleton(v8) = v9) |  ~ (in(v8, v9) = v10)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v8, v9) = v10) |  ? [v11] :  ? [v12] : ( ~ (v12 = 0) & in(v11, v9) = v12 & in(v11, v8) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (union(v10) = v9) |  ~ (union(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (empty(v10) = v9) |  ~ (empty(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (powerset(v10) = v9) |  ~ (powerset(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v9 = v8 |  ~ (singleton(v10) = v9) |  ~ (singleton(v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] : (v8 = empty_set |  ~ (element(v10, v9) = 0) |  ~ (powerset(v8) = v9) |  ? [v11] : (subset_complement(v8, v10) = v11 &  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (in(v12, v11) = v13) |  ? [v14] :  ? [v15] : (element(v12, v8) = v14 & in(v12, v10) = v15 & ( ~ (v14 = 0) | v15 = 0))))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (disjoint(v10, v9) = 0) |  ~ (singleton(v8) = v10) |  ? [v11] : ( ~ (v11 = 0) & in(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (disjoint(v8, v9) = 0) |  ~ (in(v10, v8) = 0) |  ? [v11] : ( ~ (v11 = 0) & in(v10, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v8, v10) = v8) |  ~ (singleton(v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & in(v9, v8) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v8) = v9) |  ~ (in(v10, v9) = 0) |  ? [v11] : (in(v11, v8) = 0 & in(v10, v11) = 0)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (ordered_pair(v8, v9) = v10) |  ? [v11] : ( ~ (v11 = 0) & empty(v10) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (element(v9, v10) = 0) |  ~ (powerset(v8) = v10) |  ? [v11] : (subset_complement(v8, v9) = v11 & set_difference(v8, v9) = v11)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (element(v9, v8) = v10) |  ? [v11] :  ? [v12] : (empty(v8) = v11 & in(v9, v8) = v12 & (v11 = 0 | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (element(v8, v10) = 0) |  ~ (powerset(v9) = v10) | subset(v8, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (empty(v9) = v10) |  ~ (empty(v8) = 0) |  ? [v11] : (element(v9, v8) = v11 & ( ~ (v11 = 0) | v10 = 0) & ( ~ (v10 = 0) | v11 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (powerset(v8) = v9) |  ~ (subset(v10, v8) = 0) | in(v10, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (singleton(v8) = v10) |  ~ (subset(v10, v9) = 0) | in(v8, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (subset(v8, v9) = 0) |  ~ (in(v10, v8) = 0) | in(v10, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) | set_intersection2(v9, v8) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & in(v11, v10) = 0) | (v11 = 0 & disjoint(v8, v9) = 0))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v9, v8) = v10) |  ? [v11] :  ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v8, v9) = v10) | set_union2(v9, v8) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v8, v9) = v10) |  ? [v11] :  ? [v12] : (empty(v10) = v12 & empty(v8) = v11 & ( ~ (v12 = 0) | v11 = 0))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unordered_pair(v8, v9) = v10) | unordered_pair(v9, v8) = v10) &  ? [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (union(v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] :  ? [v15] : (in(v11, v8) = v12 & ( ~ (v12 = 0) |  ! [v16] : ( ~ (in(v11, v16) = 0) |  ? [v17] : ( ~ (v17 = 0) & in(v16, v9) = v17))) & (v12 = 0 | (v15 = 0 & v14 = 0 & in(v13, v9) = 0 & in(v11, v13) = 0)))) &  ? [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (powerset(v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] : (subset(v11, v9) = v13 & in(v11, v8) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)) & (v13 = 0 | v12 = 0))) &  ? [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (singleton(v9) = v10) |  ? [v11] :  ? [v12] : (in(v11, v8) = v12 & ( ~ (v12 = 0) |  ~ (v11 = v9)) & (v12 = 0 | v11 = v9))) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_difference(v8, empty_set) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (empty(v9) = 0) |  ~ (empty(v8) = 0)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (subset(v8, v9) = 0) |  ? [v10] : ( ~ (v10 = 0) & subset(v9, v8) = v10)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_intersection2(v8, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v8, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v8, empty_set) = v9)) &  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_difference(empty_set, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_intersection2(v8, empty_set) = v9)) &  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (empty(v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] : ( ~ (v12 = 0) & element(v11, v10) = 0 & empty(v11) = v12 & powerset(v8) = v10)) &  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v8, v8) = v9)) &  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(empty_set, v8) = v9)) &  ! [v8] :  ! [v9] : ( ~ (disjoint(v8, v9) = 0) | disjoint(v9, v8) = 0) &  ! [v8] :  ! [v9] : ( ~ (disjoint(v8, v9) = 0) | set_difference(v8, v9) = v8) &  ! [v8] :  ! [v9] : ( ~ (set_difference(v8, v9) = empty_set) | subset(v8, v9) = 0) &  ! [v8] :  ! [v9] : ( ~ (element(v8, v9) = 0) |  ? [v10] :  ? [v11] : (empty(v9) = v10 & in(v8, v9) = v11 & (v11 = 0 | v10 = 0))) &  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) | union(v9) = v8) &  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) &  ! [v8] :  ! [v9] : ( ~ (powerset(v8) = v9) |  ? [v10] : (element(v10, v9) = 0 & empty(v10) = 0)) &  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v8, v9) = empty_set) | disjoint(v8, v9) = 0) &  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v8, v8) = v9) | singleton(v8) = v9) &  ! [v8] :  ! [v9] : ( ~ (proper_subset(v9, v8) = 0) |  ? [v10] : ( ~ (v10 = 0) & subset(v8, v9) = v10)) &  ! [v8] :  ! [v9] : ( ~ (proper_subset(v8, v9) = 0) | subset(v8, v9) = 0) &  ! [v8] :  ! [v9] : ( ~ (proper_subset(v8, v9) = 0) |  ? [v10] : ( ~ (v10 = 0) & proper_subset(v9, v8) = v10)) &  ! [v8] :  ! [v9] : ( ~ (in(v8, v9) = 0) |  ? [v10] : ( ~ (v10 = 0) & empty(v9) = v10)) &  ! [v8] :  ! [v9] : ( ~ (in(v8, v9) = 0) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) &  ! [v8] : (v8 = empty_set |  ~ (empty(v8) = 0)) &  ! [v8] : (v8 = empty_set |  ~ (subset(v8, empty_set) = 0)) &  ! [v8] :  ~ (singleton(v8) = empty_set) &  ! [v8] :  ~ (proper_subset(v8, v8) = 0) &  ! [v8] :  ~ (in(v8, empty_set) = 0) &  ? [v8] :  ? [v9] : (v9 = v8 |  ? [v10] :  ? [v11] :  ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v12 = 0) |  ~ (v11 = 0)) & (v12 = 0 | v11 = 0))) &  ? [v8] :  ? [v9] : element(v9, v8) = 0 &  ? [v8] :  ? [v9] : (in(v8, v9) = 0 &  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (powerset(v10) = v11) |  ~ (in(v11, v9) = v12) |  ? [v13] : ( ~ (v13 = 0) & in(v10, v9) = v13)) &  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (are_equipotent(v10, v9) = v11) |  ? [v12] :  ? [v13] : (subset(v10, v9) = v12 & in(v10, v9) = v13 & ( ~ (v12 = 0) | v13 = 0))) &  ! [v10] :  ! [v11] : ( ~ (subset(v11, v10) = 0) |  ? [v12] :  ? [v13] : (in(v11, v9) = v13 & in(v10, v9) = v12 & ( ~ (v12 = 0) | v13 = 0)))) &  ? [v8] :  ? [v9] : (in(v8, v9) = 0 &  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (are_equipotent(v10, v9) = v11) |  ? [v12] :  ? [v13] : (subset(v10, v9) = v12 & in(v10, v9) = v13 & ( ~ (v12 = 0) | v13 = 0))) &  ! [v10] :  ! [v11] : ( ~ (subset(v11, v10) = 0) |  ? [v12] :  ? [v13] : (in(v11, v9) = v13 & in(v10, v9) = v12 & ( ~ (v12 = 0) | v13 = 0))) &  ! [v10] : ( ~ (in(v10, v9) = 0) |  ? [v11] : (in(v11, v9) = 0 &  ! [v12] : ( ~ (subset(v12, v10) = 0) | in(v12, v11) = 0)))) &  ? [v8] : (v8 = empty_set |  ? [v9] : in(v9, v8) = 0))
% 31.54/8.20  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 31.54/8.20  | (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_5_5 = empty_set) & complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set & element(all_0_5_5, all_0_3_3) = 0 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & powerset(all_0_4_4) = all_0_3_3 & powerset(all_0_6_6) = all_0_4_4 & powerset(empty_set) = all_0_7_7 & singleton(empty_set) = all_0_7_7 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cartesian_product2(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = v6) |  ? [v7] :  ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cartesian_product2(v1, v3) = v5) |  ~ (cartesian_product2(v0, v2) = v4) |  ~ (subset(v4, v5) = v6) |  ? [v7] :  ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = 0 |  ~ (cartesian_product2(v0, v1) = v2) |  ~ (ordered_pair(v5, v6) = v3) |  ~ (in(v3, v2) = v4) |  ? [v7] :  ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (complements_of_subsets(v0, v1) = v4) |  ~ (element(v4, v3) = v5) |  ~ (powerset(v2) = v3) |  ~ (powerset(v0) = v2) |  ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (set_difference(v1, v3) = v4) |  ~ (singleton(v2) = v3) |  ~ (subset(v0, v4) = v5) |  ? [v6] :  ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ (subset(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (subset(v3, v4) = v5) |  ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) |  ~ (cartesian_product2(v0, v2) = v3) |  ~ (subset(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset_complement(v0, v1) = v3) |  ~ (element(v3, v2) = v4) |  ~ (powerset(v0) = v2) |  ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (element(v1, v3) = 0) |  ~ (element(v0, v2) = v4) |  ~ (powerset(v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v2) = v4) |  ~ (unordered_pair(v0, v1) = v3) |  ? [v5] :  ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v1) = v4) |  ~ (set_union2(v0, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v0, v3) = v4) |  ~ (set_intersection2(v1, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v0 | v2 = v0 |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (union(v0) = v1) |  ~ (in(v2, v4) = 0) |  ~ (in(v2, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v0 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 &  ~ (v6 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v3 = v0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v3, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (subset_complement(v0, v2) = v3) |  ~ (subset_complement(v0, v1) = v2) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v0, v2) = v3) |  ~ (singleton(v1) = v2) | in(v1, v0) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (disjoint(v2, v1) = v3) |  ~ (singleton(v0) = v2) | in(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (disjoint(v1, v2) = 0) |  ~ (disjoint(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (set_difference(v0, v1) = v2) |  ~ (subset(v2, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (union(v1) = v2) |  ~ (subset(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (element(v0, v2) = v3) |  ~ (powerset(v1) = v2) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (element(v0, v2) = v3) |  ~ (powerset(v1) = v2) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ (set_intersection2(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (set_union2(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v1, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (are_equipotent(v3, v2) = v1) |  ~ (are_equipotent(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (complements_of_subsets(v3, v2) = v1) |  ~ (complements_of_subsets(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset_complement(v3, v2) = v1) |  ~ (subset_complement(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(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 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ (subset(v2, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(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 |  ~ (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v3, v2) = 0) |  ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ? [v4] :  ? [v5] :  ? [v6] : (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v2, v3) = 0) |  ~ (powerset(v0) = v3) |  ~ (in(v1, v2) = 0) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v1, v3) = 0) |  ~ (powerset(v2) = v3) |  ~ (powerset(v0) = v2) |  ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v1, v3) = 0) |  ~ (powerset(v2) = v3) |  ~ (powerset(v0) = v2) |  ? [v4] : (complements_of_subsets(v0, v1) = v4 &  ! [v5] : (v5 = v4 |  ~ (element(v5, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) |  ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) &  ! [v5] : ( ~ (element(v5, v2) = 0) |  ~ (element(v4, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v1, v3) = 0) |  ~ (powerset(v2) = v3) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 &  ~ (v7 = 0))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (cartesian_product2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) |  ! [v11] :  ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) |  ? [v13] :  ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ? [v4] :  ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) &  ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ (subset(v0, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ (in(v2, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (proper_subset(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v1) = v0) |  ~ (subset(v0, v0) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (subset(empty_set, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (in(v0, v1) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v0 = empty_set |  ~ (element(v2, v1) = 0) |  ~ (powerset(v0) = v1) |  ? [v3] : (subset_complement(v0, v2) = v3 &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (in(v4, v3) = v5) |  ? [v6] :  ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v2, v1) = 0) |  ~ (singleton(v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v2) = v0) |  ~ (singleton(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v0, v2) = 0) |  ~ (powerset(v1) = v2) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v1) = v2) |  ~ (empty(v0) = 0) |  ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = 0) | in(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = 0) | in(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (union(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ! [v8] : ( ~ (in(v3, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (powerset(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] :  ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ~ (v3 = v1)) & (v4 = 0 | v3 = v1))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & powerset(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0) &  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] :  ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0))) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0)) &  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (proper_subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2)) &  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0)) &  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0)) &  ! [v0] :  ~ (singleton(v0) = empty_set) &  ! [v0] :  ~ (proper_subset(v0, v0) = 0) &  ! [v0] :  ~ (in(v0, empty_set) = 0) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) &  ? [v0] :  ? [v1] : element(v1, v0) = 0 &  ? [v0] :  ? [v1] : (in(v0, v1) = 0 &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (powerset(v2) = v3) |  ~ (in(v3, v1) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (are_equipotent(v2, v1) = v3) |  ? [v4] :  ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ? [v4] :  ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))) &  ? [v0] :  ? [v1] : (in(v0, v1) = 0 &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (are_equipotent(v2, v1) = v3) |  ? [v4] :  ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ? [v4] :  ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v2] : ( ~ (in(v2, v1) = 0) |  ? [v3] : (in(v3, v1) = 0 &  ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0)))) &  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 31.54/8.23  |
% 31.54/8.23  | Applying alpha-rule on (1) yields:
% 31.54/8.23  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v3, v2) = 0) |  ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ? [v4] :  ? [v5] :  ? [v6] : (disjoint(v1, v3) = v4 & subset_complement(v0, v3) = v5 & subset(v1, v5) = v6 & ( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0)))
% 31.54/8.23  | (3)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 31.54/8.23  | (4)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 31.54/8.23  | (5)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 31.54/8.23  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (disjoint(v1, v2) = 0) |  ~ (disjoint(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 31.54/8.23  | (7)  ! [v0] :  ! [v1] : ( ~ (element(v0, v1) = 0) |  ? [v2] :  ? [v3] : (empty(v1) = v2 & in(v0, v1) = v3 & (v3 = 0 | v2 = 0)))
% 31.54/8.23  | (8)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0)))
% 31.54/8.23  | (9)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (powerset(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & ( ~ (v5 = 0) |  ~ (v4 = 0)) & (v5 = 0 | v4 = 0)))
% 31.54/8.23  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.54/8.23  | (11)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 31.54/8.23  | (12) singleton(empty_set) = all_0_7_7
% 31.54/8.23  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 31.54/8.23  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 31.54/8.23  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 &  ~ (v6 = 0)))))
% 31.54/8.23  | (16)  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 31.54/8.23  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v2) = v4) |  ~ (unordered_pair(v0, v1) = v3) |  ? [v5] :  ? [v6] : (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
% 31.54/8.23  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cartesian_product2(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = v6) |  ? [v7] :  ? [v8] : (in(v1, v3) = v8 & in(v0, v2) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0))))
% 31.54/8.23  | (19)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 31.54/8.23  | (20) powerset(all_0_6_6) = all_0_4_4
% 31.54/8.23  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v0, v2) = 0) |  ~ (powerset(v1) = v2) | subset(v0, v1) = 0)
% 31.54/8.23  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 31.54/8.23  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v1, v3) = 0) |  ~ (powerset(v2) = v3) |  ~ (powerset(v0) = v2) |  ? [v4] : (complements_of_subsets(v0, v4) = v1 & complements_of_subsets(v0, v1) = v4))
% 31.54/8.23  | (24)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & element(v3, v2) = 0 & empty(v3) = v4 & powerset(v0) = v2))
% 31.54/8.23  | (25)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 31.54/8.23  | (26)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 31.54/8.23  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 31.54/8.23  | (28)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 &  ~ (v7 = 0)))))
% 31.54/8.23  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ (subset(v3, v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 31.54/8.24  | (30)  ! [v0] :  ~ (in(v0, empty_set) = 0)
% 31.54/8.24  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 31.54/8.24  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 31.54/8.24  | (33)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 31.54/8.24  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0))
% 31.54/8.24  | (35)  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0))
% 31.54/8.24  | (36)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 31.54/8.24  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v2, v1) = 0) |  ~ (singleton(v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 31.54/8.24  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 31.54/8.24  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 31.54/8.24  | (40) empty(empty_set) = 0
% 31.54/8.24  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 31.54/8.24  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
% 31.54/8.24  | (43)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (cartesian_product2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : (in(v4, v0) = v5 & ( ~ (v5 = 0) |  ! [v11] :  ! [v12] : ( ~ (ordered_pair(v11, v12) = v4) |  ? [v13] :  ? [v14] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ (v14 = 0) |  ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0))))
% 31.54/8.24  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 31.54/8.24  | (45)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 31.54/8.24  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (cartesian_product2(v1, v3) = v5) |  ~ (cartesian_product2(v0, v2) = v4) |  ~ (subset(v4, v5) = v6) |  ? [v7] :  ? [v8] : (subset(v2, v3) = v8 & subset(v0, v1) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0))))
% 31.54/8.24  | (47)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 31.54/8.24  | (48)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 31.54/8.24  | (49)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (subset(empty_set, v1) = v2))
% 31.54/8.24  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 31.54/8.24  | (51)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v0) = v3 & in(v1, v0) = v4 & (v3 = 0 | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 31.54/8.24  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 31.54/8.24  | (53) element(all_0_5_5, all_0_3_3) = 0
% 31.54/8.24  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v0, v2) = v3) |  ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 31.54/8.24  | (55)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 31.54/8.24  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] :  ? [v5] : (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0)))
% 31.54/8.24  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 31.54/8.24  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (set_difference(v1, v3) = v4) |  ~ (singleton(v2) = v3) |  ~ (subset(v0, v4) = v5) |  ? [v6] :  ? [v7] : (subset(v0, v1) = v6 & in(v2, v0) = v7 & ( ~ (v6 = 0) | v7 = 0)))
% 31.54/8.24  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (are_equipotent(v3, v2) = v1) |  ~ (are_equipotent(v3, v2) = v0))
% 31.54/8.24  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (element(v1, v3) = 0) |  ~ (element(v0, v2) = v4) |  ~ (powerset(v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 31.54/8.24  | (61)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 31.54/8.24  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ (set_intersection2(v0, v1) = v2))
% 31.54/8.24  | (63)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 31.54/8.24  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 31.54/8.24  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4))
% 31.54/8.24  | (66) powerset(all_0_4_4) = all_0_3_3
% 31.54/8.24  | (67)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.54/8.24  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ (subset(v0, v2) = 0))
% 31.54/8.25  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v2, v3) = 0) |  ~ (powerset(v0) = v3) |  ~ (in(v1, v2) = 0) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & subset_complement(v0, v2) = v4 & in(v1, v4) = v5))
% 31.54/8.25  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 31.54/8.25  | (71)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 31.54/8.25  | (72)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) &  ~ (v4 = 0)))))
% 31.54/8.25  | (73)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 31.54/8.25  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v0, v2) = v3))
% 31.54/8.25  | (75)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (element(v0, v2) = v3) |  ~ (powerset(v1) = v2) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & in(v4, v1) = v5 & in(v4, v0) = 0))
% 31.54/8.25  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (disjoint(v2, v1) = v3) |  ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 31.54/8.25  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (cartesian_product2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] :  ? [v5] : (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0))
% 31.54/8.25  | (78)  ! [v0] :  ~ (singleton(v0) = empty_set)
% 31.54/8.25  | (79)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & ( ~ (v7 = 0) |  ~ (v6 = 0) |  ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0))))
% 31.54/8.25  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0))
% 31.54/8.25  | (81)  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 31.54/8.25  | (82)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (set_difference(v0, v1) = v2) |  ~ (subset(v2, v0) = v3))
% 31.54/8.25  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (subset(v3, v4) = v5) |  ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ? [v6] : ( ~ (v6 = 0) & subset(v0, v1) = v6))
% 31.54/8.25  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = 0 |  ~ (union(v0) = v1) |  ~ (in(v2, v4) = 0) |  ~ (in(v2, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & in(v4, v0) = v5))
% 31.54/8.25  | (85)  ! [v0] :  ~ (proper_subset(v0, v0) = 0)
% 31.54/8.25  | (86)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1))
% 31.54/8.25  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v3, v1) = v5))
% 31.54/8.25  | (88) empty(all_0_0_0) = 0
% 31.54/8.25  | (89)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] :  ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 31.54/8.25  | (90)  ~ (all_0_5_5 = empty_set)
% 31.54/8.25  | (91)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 31.54/8.25  | (92)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ (subset(v2, v3) = 0))
% 31.54/8.25  | (93)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v2, v3) = v5) |  ~ (ordered_pair(v0, v1) = v4) |  ~ (in(v4, v5) = 0) | (in(v1, v3) = 0 & in(v0, v2) = 0))
% 31.54/8.25  | (94)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 31.54/8.25  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 31.54/8.25  | (96)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 31.54/8.25  | (97)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset_complement(v0, v1) = v3) |  ~ (element(v3, v2) = v4) |  ~ (powerset(v0) = v2) |  ? [v5] : ( ~ (v5 = 0) & element(v1, v2) = v5))
% 31.54/8.25  | (98)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v3 = v0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v3, v2) = 0))
% 31.54/8.25  | (99)  ~ (all_0_1_1 = 0)
% 31.54/8.25  | (100)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 31.54/8.25  | (101)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 31.54/8.25  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3))
% 31.54/8.25  | (103)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 31.54/8.25  | (104)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 31.54/8.25  | (105)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1))
% 31.54/8.25  | (106)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 31.54/8.25  | (107)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 31.54/8.26  | (108)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (element(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 31.54/8.26  | (109)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (cartesian_product2(v1, v2) = v4) |  ~ (cartesian_product2(v0, v2) = v3) |  ~ (subset(v3, v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (cartesian_product2(v2, v1) = v8 & cartesian_product2(v2, v0) = v7 & subset(v7, v8) = v9 & subset(v0, v1) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v5 = 0))))
% 31.54/8.26  | (110)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (subset_complement(v0, v2) = v3) |  ~ (subset_complement(v0, v1) = v2) |  ? [v4] :  ? [v5] : ( ~ (v5 = 0) & element(v1, v4) = v5 & powerset(v0) = v4))
% 31.54/8.26  | (111)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v0 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4))
% 31.54/8.26  | (112)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 31.54/8.26  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v1, v2) = v3))
% 31.54/8.26  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 31.54/8.26  | (115)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (complements_of_subsets(v0, v1) = v4) |  ~ (element(v4, v3) = v5) |  ~ (powerset(v2) = v3) |  ~ (powerset(v0) = v2) |  ? [v6] : ( ~ (v6 = 0) & element(v1, v3) = v6))
% 31.54/8.26  | (116)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (set_union2(v0, v1) = v2))
% 31.54/8.26  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = 0)))
% 31.54/8.26  | (118) complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set
% 31.54/8.26  | (119)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 31.54/8.26  | (120)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 31.54/8.26  | (121)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 31.54/8.26  | (122)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.54/8.26  | (123)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 31.54/8.26  | (124)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] :  ? [v6] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0))))
% 31.54/8.26  | (125)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v1) = v4) |  ~ (set_union2(v0, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v2, v1) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
% 31.54/8.26  | (126)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 31.54/8.26  | (127)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 31.54/8.26  | (128)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v2) = v0) |  ~ (singleton(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 31.54/8.26  | (129)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 31.54/8.26  | (130)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 31.54/8.26  | (131)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v0, v3) = v4) |  ~ (set_intersection2(v1, v2) = v3) |  ? [v5] :  ? [v6] : (subset(v0, v2) = v6 & subset(v0, v1) = v5 & ( ~ (v6 = 0) |  ~ (v5 = 0))))
% 31.54/8.26  | (132)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3))
% 31.54/8.26  | (133)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (in(v0, v1) = v2))
% 31.54/8.26  | (134)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 31.54/8.26  | (135)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1))
% 31.54/8.26  | (136)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 31.54/8.26  | (137) empty(all_0_2_2) = all_0_1_1
% 31.54/8.26  | (138)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (empty(v1) = v2) |  ~ (empty(v0) = 0) |  ? [v3] : (element(v1, v0) = v3 & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0)))
% 31.97/8.27  | (139)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v0 | v2 = v0 |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v4))
% 31.97/8.27  | (140)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (element(v0, v2) = v3) |  ~ (powerset(v1) = v2) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 31.97/8.27  | (141)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v1, v3) = 0) |  ~ (powerset(v2) = v3) |  ~ (powerset(v0) = v2) |  ? [v4] : (complements_of_subsets(v0, v1) = v4 &  ! [v5] : (v5 = v4 |  ~ (element(v5, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (subset_complement(v0, v6) = v8 & element(v6, v2) = 0 & in(v8, v1) = v9 & in(v6, v5) = v7 & ( ~ (v9 = 0) |  ~ (v7 = 0)) & (v9 = 0 | v7 = 0))) &  ! [v5] : ( ~ (element(v5, v2) = 0) |  ~ (element(v4, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (subset_complement(v0, v5) = v7 & in(v7, v1) = v8 & in(v5, v4) = v6 & ( ~ (v8 = 0) | v6 = 0) & ( ~ (v6 = 0) | v8 = 0)))))
% 31.97/8.27  | (142)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 31.97/8.27  | (143)  ? [v0] :  ? [v1] : (in(v0, v1) = 0 &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (are_equipotent(v2, v1) = v3) |  ? [v4] :  ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ? [v4] :  ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v2] : ( ~ (in(v2, v1) = 0) |  ? [v3] : (in(v3, v1) = 0 &  ! [v4] : ( ~ (subset(v4, v2) = 0) | in(v4, v3) = 0))))
% 31.97/8.27  | (144)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 31.97/8.27  | (145)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (proper_subset(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 31.97/8.27  | (146)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (union(v1) = v2) |  ~ (subset(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 31.97/8.27  | (147)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 31.97/8.27  | (148)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ (in(v2, v1) = 0))
% 31.97/8.27  | (149)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (union(v1) = v2) |  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ! [v8] : ( ~ (in(v3, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v1) = v9))) & (v4 = 0 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0))))
% 31.97/8.27  | (150)  ! [v0] :  ! [v1] :  ! [v2] : (v0 = empty_set |  ~ (element(v2, v1) = 0) |  ~ (powerset(v0) = v1) |  ? [v3] : (subset_complement(v0, v2) = v3 &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (in(v4, v3) = v5) |  ? [v6] :  ? [v7] : (element(v4, v0) = v6 & in(v4, v2) = v7 & ( ~ (v6 = 0) | v7 = 0)))))
% 31.97/8.27  | (151)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 31.97/8.27  | (152)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset_complement(v3, v2) = v1) |  ~ (subset_complement(v3, v2) = v0))
% 31.97/8.27  | (153)  ? [v0] :  ? [v1] : (in(v0, v1) = 0 &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (powerset(v2) = v3) |  ~ (in(v3, v1) = v4) |  ? [v5] : ( ~ (v5 = 0) & in(v2, v1) = v5)) &  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (are_equipotent(v2, v1) = v3) |  ? [v4] :  ? [v5] : (subset(v2, v1) = v4 & in(v2, v1) = v5 & ( ~ (v4 = 0) | v5 = 0))) &  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ? [v4] :  ? [v5] : (in(v3, v1) = v5 & in(v2, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))))
% 31.97/8.27  | (154)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (element(v1, v3) = 0) |  ~ (powerset(v2) = v3) |  ~ (in(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & empty(v2) = v4))
% 31.97/8.27  | (155)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ? [v4] :  ? [v5] : (in(v4, v0) = v5 & ( ~ (v5 = 0) | ( ~ (v4 = v2) &  ~ (v4 = v1))) & (v5 = 0 | v4 = v2 | v4 = v1)))
% 31.97/8.27  | (156)  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 31.97/8.27  | (157) powerset(empty_set) = all_0_7_7
% 31.97/8.27  | (158)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 31.97/8.27  | (159)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 31.97/8.27  | (160)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 31.97/8.27  | (161)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = 0 |  ~ (cartesian_product2(v0, v1) = v2) |  ~ (ordered_pair(v5, v6) = v3) |  ~ (in(v3, v2) = v4) |  ? [v7] :  ? [v8] : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) |  ~ (v7 = 0))))
% 31.97/8.27  | (162)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v1) = v0) |  ~ (subset(v0, v0) = v2))
% 31.97/8.27  | (163)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 31.97/8.27  | (164)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (complements_of_subsets(v3, v2) = v1) |  ~ (complements_of_subsets(v3, v2) = v0))
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (136) with all_0_3_3, all_0_4_4 and discharging atoms powerset(all_0_4_4) = all_0_3_3, yields:
% 31.97/8.28  | (165)  ? [v0] : (element(v0, all_0_3_3) = 0 & empty(v0) = 0)
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (23) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms element(all_0_5_5, all_0_3_3) = 0, powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, yields:
% 31.97/8.28  | (166)  ? [v0] : (complements_of_subsets(all_0_6_6, v0) = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_5_5) = v0)
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (141) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms element(all_0_5_5, all_0_3_3) = 0, powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, yields:
% 31.97/8.28  | (167)  ? [v0] : (complements_of_subsets(all_0_6_6, all_0_5_5) = v0 &  ! [v1] : (v1 = v0 |  ~ (element(v1, all_0_3_3) = 0) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (subset_complement(all_0_6_6, v2) = v4 & element(v2, all_0_4_4) = 0 & in(v4, all_0_5_5) = v5 & in(v2, v1) = v3 & ( ~ (v5 = 0) |  ~ (v3 = 0)) & (v5 = 0 | v3 = 0))) &  ! [v1] : ( ~ (element(v1, all_0_4_4) = 0) |  ~ (element(v0, all_0_3_3) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & in(v3, all_0_5_5) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (136) with all_0_4_4, all_0_6_6 and discharging atoms powerset(all_0_6_6) = all_0_4_4, yields:
% 31.97/8.28  | (168)  ? [v0] : (element(v0, all_0_4_4) = 0 & empty(v0) = 0)
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (136) with all_0_7_7, empty_set and discharging atoms powerset(empty_set) = all_0_7_7, yields:
% 31.97/8.28  | (169)  ? [v0] : (element(v0, all_0_7_7) = 0 & empty(v0) = 0)
% 31.97/8.28  |
% 31.97/8.28  | Instantiating (167) with all_45_0_26 yields:
% 31.97/8.28  | (170) complements_of_subsets(all_0_6_6, all_0_5_5) = all_45_0_26 &  ! [v0] : (v0 = all_45_0_26 |  ~ (element(v0, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, all_0_5_5) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) |  ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) &  ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) |  ~ (element(all_45_0_26, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, all_0_5_5) = v3 & in(v0, all_45_0_26) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 31.97/8.28  |
% 31.97/8.28  | Applying alpha-rule on (170) yields:
% 31.97/8.28  | (171) complements_of_subsets(all_0_6_6, all_0_5_5) = all_45_0_26
% 31.97/8.28  | (172)  ! [v0] : (v0 = all_45_0_26 |  ~ (element(v0, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, all_0_5_5) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) |  ~ (v2 = 0)) & (v4 = 0 | v2 = 0)))
% 31.97/8.28  | (173)  ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) |  ~ (element(all_45_0_26, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, all_0_5_5) = v3 & in(v0, all_45_0_26) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (172) with all_0_5_5 and discharging atoms element(all_0_5_5, all_0_3_3) = 0, yields:
% 31.97/8.28  | (174) all_45_0_26 = all_0_5_5 |  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & element(v0, all_0_4_4) = 0 & in(v2, all_0_5_5) = v3 & in(v0, all_0_5_5) = v1 & ( ~ (v3 = 0) |  ~ (v1 = 0)) & (v3 = 0 | v1 = 0))
% 31.97/8.28  |
% 31.97/8.28  | Instantiating (166) with all_48_0_27 yields:
% 31.97/8.28  | (175) complements_of_subsets(all_0_6_6, all_48_0_27) = all_0_5_5 & complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27
% 31.97/8.28  |
% 31.97/8.28  | Applying alpha-rule on (175) yields:
% 31.97/8.28  | (176) complements_of_subsets(all_0_6_6, all_48_0_27) = all_0_5_5
% 31.97/8.28  | (177) complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27
% 31.97/8.28  |
% 31.97/8.28  | Instantiating (169) with all_54_0_32 yields:
% 31.97/8.28  | (178) element(all_54_0_32, all_0_7_7) = 0 & empty(all_54_0_32) = 0
% 31.97/8.28  |
% 31.97/8.28  | Applying alpha-rule on (178) yields:
% 31.97/8.28  | (179) element(all_54_0_32, all_0_7_7) = 0
% 31.97/8.28  | (180) empty(all_54_0_32) = 0
% 31.97/8.28  |
% 31.97/8.28  | Instantiating (168) with all_71_0_41 yields:
% 31.97/8.28  | (181) element(all_71_0_41, all_0_4_4) = 0 & empty(all_71_0_41) = 0
% 31.97/8.28  |
% 31.97/8.28  | Applying alpha-rule on (181) yields:
% 31.97/8.28  | (182) element(all_71_0_41, all_0_4_4) = 0
% 31.97/8.28  | (183) empty(all_71_0_41) = 0
% 31.97/8.28  |
% 31.97/8.28  | Instantiating (165) with all_77_0_45 yields:
% 31.97/8.28  | (184) element(all_77_0_45, all_0_3_3) = 0 & empty(all_77_0_45) = 0
% 31.97/8.28  |
% 31.97/8.28  | Applying alpha-rule on (184) yields:
% 31.97/8.28  | (185) element(all_77_0_45, all_0_3_3) = 0
% 31.97/8.28  | (186) empty(all_77_0_45) = 0
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (164) with all_0_6_6, all_0_5_5, all_48_0_27, empty_set and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27, complements_of_subsets(all_0_6_6, all_0_5_5) = empty_set, yields:
% 31.97/8.28  | (187) all_48_0_27 = empty_set
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (164) with all_0_6_6, all_0_5_5, all_45_0_26, all_48_0_27 and discharging atoms complements_of_subsets(all_0_6_6, all_0_5_5) = all_48_0_27, complements_of_subsets(all_0_6_6, all_0_5_5) = all_45_0_26, yields:
% 31.97/8.28  | (188) all_48_0_27 = all_45_0_26
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (4) with all_77_0_45 and discharging atoms empty(all_77_0_45) = 0, yields:
% 31.97/8.28  | (189) all_77_0_45 = empty_set
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (19) with all_71_0_41, all_77_0_45 and discharging atoms empty(all_77_0_45) = 0, empty(all_71_0_41) = 0, yields:
% 31.97/8.28  | (190) all_77_0_45 = all_71_0_41
% 31.97/8.28  |
% 31.97/8.28  | Instantiating formula (19) with all_54_0_32, all_77_0_45 and discharging atoms empty(all_77_0_45) = 0, empty(all_54_0_32) = 0, yields:
% 31.97/8.28  | (191) all_77_0_45 = all_54_0_32
% 31.97/8.28  |
% 31.97/8.28  | Combining equations (191,190) yields a new equation:
% 31.97/8.28  | (192) all_71_0_41 = all_54_0_32
% 31.97/8.28  |
% 31.97/8.28  | Combining equations (189,190) yields a new equation:
% 31.97/8.28  | (193) all_71_0_41 = empty_set
% 31.97/8.28  |
% 32.07/8.28  | Combining equations (193,192) yields a new equation:
% 32.07/8.28  | (194) all_54_0_32 = empty_set
% 32.07/8.28  |
% 32.07/8.28  | Combining equations (187,188) yields a new equation:
% 32.07/8.28  | (195) all_45_0_26 = empty_set
% 32.07/8.28  |
% 32.07/8.28  | Combining equations (195,188) yields a new equation:
% 32.07/8.28  | (187) all_48_0_27 = empty_set
% 32.07/8.28  |
% 32.07/8.28  | Combining equations (194,192) yields a new equation:
% 32.07/8.28  | (193) all_71_0_41 = empty_set
% 32.07/8.28  |
% 32.07/8.28  | Combining equations (193,190) yields a new equation:
% 32.07/8.28  | (189) all_77_0_45 = empty_set
% 32.07/8.28  |
% 32.07/8.28  | From (187) and (176) follows:
% 32.07/8.28  | (199) complements_of_subsets(all_0_6_6, empty_set) = all_0_5_5
% 32.07/8.28  |
% 32.07/8.28  | From (189) and (185) follows:
% 32.07/8.29  | (200) element(empty_set, all_0_3_3) = 0
% 32.07/8.29  |
% 32.07/8.29  | From (193) and (182) follows:
% 32.07/8.29  | (201) element(empty_set, all_0_4_4) = 0
% 32.07/8.29  |
% 32.07/8.29  +-Applying beta-rule and splitting (174), into two cases.
% 32.07/8.29  |-Branch one:
% 32.07/8.29  | (202) all_45_0_26 = all_0_5_5
% 32.07/8.29  |
% 32.07/8.29  	| Combining equations (202,195) yields a new equation:
% 32.07/8.29  	| (203) all_0_5_5 = empty_set
% 32.07/8.29  	|
% 32.07/8.29  	| Simplifying 203 yields:
% 32.07/8.29  	| (204) all_0_5_5 = empty_set
% 32.07/8.29  	|
% 32.07/8.29  	| Equations (204) can reduce 90 to:
% 32.07/8.29  	| (205) $false
% 32.07/8.29  	|
% 32.07/8.29  	|-The branch is then unsatisfiable
% 32.07/8.29  |-Branch two:
% 32.07/8.29  | (206)  ~ (all_45_0_26 = all_0_5_5)
% 32.07/8.29  | (207)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & element(v0, all_0_4_4) = 0 & in(v2, all_0_5_5) = v3 & in(v0, all_0_5_5) = v1 & ( ~ (v3 = 0) |  ~ (v1 = 0)) & (v3 = 0 | v1 = 0))
% 32.07/8.29  |
% 32.07/8.29  	| Instantiating (207) with all_102_0_50, all_102_1_51, all_102_2_52, all_102_3_53 yields:
% 32.07/8.29  	| (208) subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51 & element(all_102_3_53, all_0_4_4) = 0 & in(all_102_1_51, all_0_5_5) = all_102_0_50 & in(all_102_3_53, all_0_5_5) = all_102_2_52 & ( ~ (all_102_0_50 = 0) |  ~ (all_102_2_52 = 0)) & (all_102_0_50 = 0 | all_102_2_52 = 0)
% 32.07/8.29  	|
% 32.07/8.29  	| Applying alpha-rule on (208) yields:
% 32.07/8.29  	| (209) in(all_102_3_53, all_0_5_5) = all_102_2_52
% 32.07/8.29  	| (210) subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51
% 32.07/8.29  	| (211) in(all_102_1_51, all_0_5_5) = all_102_0_50
% 32.07/8.29  	| (212) element(all_102_3_53, all_0_4_4) = 0
% 32.07/8.29  	| (213)  ~ (all_102_0_50 = 0) |  ~ (all_102_2_52 = 0)
% 32.07/8.29  	| (214) all_102_0_50 = 0 | all_102_2_52 = 0
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (2) with all_102_3_53, all_0_4_4, all_102_3_53, all_0_6_6 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29  	| (215)  ? [v0] :  ? [v1] :  ? [v2] : (disjoint(all_102_3_53, all_102_3_53) = v0 & subset_complement(all_0_6_6, all_102_3_53) = v1 & subset(all_102_3_53, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (127) with all_0_4_4, all_102_3_53, all_0_6_6 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29  	| (216)  ? [v0] : (subset_complement(all_0_6_6, all_102_3_53) = v0 & set_difference(all_0_6_6, all_102_3_53) = v0)
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (141) with all_0_3_3, all_0_4_4, empty_set, all_0_6_6 and discharging atoms element(empty_set, all_0_3_3) = 0, powerset(all_0_4_4) = all_0_3_3, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29  	| (217)  ? [v0] : (complements_of_subsets(all_0_6_6, empty_set) = v0 &  ! [v1] : (v1 = v0 |  ~ (element(v1, all_0_3_3) = 0) |  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (subset_complement(all_0_6_6, v2) = v4 & element(v2, all_0_4_4) = 0 & in(v4, empty_set) = v5 & in(v2, v1) = v3 & ( ~ (v5 = 0) |  ~ (v3 = 0)) & (v5 = 0 | v3 = 0))) &  ! [v1] : ( ~ (element(v1, all_0_4_4) = 0) |  ~ (element(v0, all_0_3_3) = 0) |  ? [v2] :  ? [v3] :  ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & in(v3, empty_set) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (173) with all_102_3_53 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, yields:
% 32.07/8.29  	| (218)  ~ (element(all_45_0_26, all_0_3_3) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, all_0_5_5) = v2 & in(all_102_3_53, all_45_0_26) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (2) with all_102_3_53, all_0_4_4, empty_set, all_0_6_6 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, element(empty_set, all_0_4_4) = 0, powerset(all_0_6_6) = all_0_4_4, yields:
% 32.07/8.29  	| (219)  ? [v0] :  ? [v1] :  ? [v2] : (disjoint(empty_set, all_102_3_53) = v0 & subset_complement(all_0_6_6, all_102_3_53) = v1 & subset(empty_set, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating (217) with all_138_0_56 yields:
% 32.07/8.29  	| (220) complements_of_subsets(all_0_6_6, empty_set) = all_138_0_56 &  ! [v0] : (v0 = all_138_0_56 |  ~ (element(v0, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, empty_set) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) |  ~ (v2 = 0)) & (v4 = 0 | v2 = 0))) &  ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) |  ~ (element(all_138_0_56, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, empty_set) = v3 & in(v0, all_138_0_56) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 32.07/8.29  	|
% 32.07/8.29  	| Applying alpha-rule on (220) yields:
% 32.07/8.29  	| (221) complements_of_subsets(all_0_6_6, empty_set) = all_138_0_56
% 32.07/8.29  	| (222)  ! [v0] : (v0 = all_138_0_56 |  ~ (element(v0, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (subset_complement(all_0_6_6, v1) = v3 & element(v1, all_0_4_4) = 0 & in(v3, empty_set) = v4 & in(v1, v0) = v2 & ( ~ (v4 = 0) |  ~ (v2 = 0)) & (v4 = 0 | v2 = 0)))
% 32.07/8.29  	| (223)  ! [v0] : ( ~ (element(v0, all_0_4_4) = 0) |  ~ (element(all_138_0_56, all_0_3_3) = 0) |  ? [v1] :  ? [v2] :  ? [v3] : (subset_complement(all_0_6_6, v0) = v2 & in(v2, empty_set) = v3 & in(v0, all_138_0_56) = v1 & ( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0)))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (223) with all_102_3_53 and discharging atoms element(all_102_3_53, all_0_4_4) = 0, yields:
% 32.07/8.29  	| (224)  ~ (element(all_138_0_56, all_0_3_3) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, empty_set) = v2 & in(all_102_3_53, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating formula (223) with empty_set and discharging atoms element(empty_set, all_0_4_4) = 0, yields:
% 32.07/8.29  	| (225)  ~ (element(all_138_0_56, all_0_3_3) = 0) |  ? [v0] :  ? [v1] :  ? [v2] : (subset_complement(all_0_6_6, empty_set) = v1 & in(v1, empty_set) = v2 & in(empty_set, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating (215) with all_152_0_64, all_152_1_65, all_152_2_66 yields:
% 32.07/8.29  	| (226) disjoint(all_102_3_53, all_102_3_53) = all_152_2_66 & subset_complement(all_0_6_6, all_102_3_53) = all_152_1_65 & subset(all_102_3_53, all_152_1_65) = all_152_0_64 & ( ~ (all_152_0_64 = 0) | all_152_2_66 = 0) & ( ~ (all_152_2_66 = 0) | all_152_0_64 = 0)
% 32.07/8.29  	|
% 32.07/8.29  	| Applying alpha-rule on (226) yields:
% 32.07/8.29  	| (227) disjoint(all_102_3_53, all_102_3_53) = all_152_2_66
% 32.07/8.29  	| (228) subset_complement(all_0_6_6, all_102_3_53) = all_152_1_65
% 32.07/8.29  	| (229) subset(all_102_3_53, all_152_1_65) = all_152_0_64
% 32.07/8.29  	| (230)  ~ (all_152_0_64 = 0) | all_152_2_66 = 0
% 32.07/8.29  	| (231)  ~ (all_152_2_66 = 0) | all_152_0_64 = 0
% 32.07/8.29  	|
% 32.07/8.29  	| Instantiating (219) with all_162_0_73, all_162_1_74, all_162_2_75 yields:
% 32.07/8.29  	| (232) disjoint(empty_set, all_102_3_53) = all_162_2_75 & subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74 & subset(empty_set, all_162_1_74) = all_162_0_73 & ( ~ (all_162_0_73 = 0) | all_162_2_75 = 0) & ( ~ (all_162_2_75 = 0) | all_162_0_73 = 0)
% 32.07/8.29  	|
% 32.07/8.29  	| Applying alpha-rule on (232) yields:
% 32.07/8.29  	| (233)  ~ (all_162_0_73 = 0) | all_162_2_75 = 0
% 32.07/8.29  	| (234) subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74
% 32.07/8.29  	| (235) disjoint(empty_set, all_102_3_53) = all_162_2_75
% 32.07/8.29  	| (236)  ~ (all_162_2_75 = 0) | all_162_0_73 = 0
% 32.07/8.29  	| (237) subset(empty_set, all_162_1_74) = all_162_0_73
% 32.07/8.30  	|
% 32.07/8.30  	| Instantiating (216) with all_176_0_85 yields:
% 32.07/8.30  	| (238) subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85 & set_difference(all_0_6_6, all_102_3_53) = all_176_0_85
% 32.07/8.30  	|
% 32.07/8.30  	| Applying alpha-rule on (238) yields:
% 32.07/8.30  	| (239) subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85
% 32.07/8.30  	| (240) set_difference(all_0_6_6, all_102_3_53) = all_176_0_85
% 32.07/8.30  	|
% 32.07/8.30  	+-Applying beta-rule and splitting (218), into two cases.
% 32.07/8.30  	|-Branch one:
% 32.07/8.30  	| (241)  ~ (element(all_45_0_26, all_0_3_3) = 0)
% 32.07/8.30  	|
% 32.07/8.30  		| From (195) and (241) follows:
% 32.07/8.30  		| (242)  ~ (element(empty_set, all_0_3_3) = 0)
% 32.07/8.30  		|
% 32.07/8.30  		| Using (200) and (242) yields:
% 32.07/8.30  		| (243) $false
% 32.07/8.30  		|
% 32.07/8.30  		|-The branch is then unsatisfiable
% 32.07/8.30  	|-Branch two:
% 32.07/8.30  	| (244) element(all_45_0_26, all_0_3_3) = 0
% 32.07/8.30  	| (245)  ? [v0] :  ? [v1] :  ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, all_0_5_5) = v2 & in(all_102_3_53, all_45_0_26) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.30  	|
% 32.07/8.30  		| Instantiating (245) with all_276_0_126, all_276_1_127, all_276_2_128 yields:
% 32.07/8.30  		| (246) subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127 & in(all_276_1_127, all_0_5_5) = all_276_0_126 & in(all_102_3_53, all_45_0_26) = all_276_2_128 & ( ~ (all_276_0_126 = 0) | all_276_2_128 = 0) & ( ~ (all_276_2_128 = 0) | all_276_0_126 = 0)
% 32.07/8.30  		|
% 32.07/8.30  		| Applying alpha-rule on (246) yields:
% 32.07/8.30  		| (247) in(all_102_3_53, all_45_0_26) = all_276_2_128
% 32.07/8.30  		| (248) subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127
% 32.07/8.30  		| (249) in(all_276_1_127, all_0_5_5) = all_276_0_126
% 32.07/8.30  		| (250)  ~ (all_276_2_128 = 0) | all_276_0_126 = 0
% 32.07/8.30  		| (251)  ~ (all_276_0_126 = 0) | all_276_2_128 = 0
% 32.07/8.30  		|
% 32.07/8.30  		| From (195) and (247) follows:
% 32.07/8.30  		| (252) in(all_102_3_53, empty_set) = all_276_2_128
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (164) with all_0_6_6, empty_set, all_138_0_56, all_0_5_5 and discharging atoms complements_of_subsets(all_0_6_6, empty_set) = all_138_0_56, complements_of_subsets(all_0_6_6, empty_set) = all_0_5_5, yields:
% 32.07/8.30  		| (253) all_138_0_56 = all_0_5_5
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (152) with all_0_6_6, all_102_3_53, all_176_0_85, all_276_1_127 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127, subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85, yields:
% 32.07/8.30  		| (254) all_276_1_127 = all_176_0_85
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (152) with all_0_6_6, all_102_3_53, all_162_1_74, all_102_1_51 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74, subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51, yields:
% 32.07/8.30  		| (255) all_162_1_74 = all_102_1_51
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (152) with all_0_6_6, all_102_3_53, all_162_1_74, all_176_0_85 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_176_0_85, subset_complement(all_0_6_6, all_102_3_53) = all_162_1_74, yields:
% 32.07/8.30  		| (256) all_176_0_85 = all_162_1_74
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (152) with all_0_6_6, all_102_3_53, all_152_1_65, all_276_1_127 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_276_1_127, subset_complement(all_0_6_6, all_102_3_53) = all_152_1_65, yields:
% 32.07/8.30  		| (257) all_276_1_127 = all_152_1_65
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (134) with all_102_1_51, all_0_5_5, all_276_0_126, all_102_0_50 and discharging atoms in(all_102_1_51, all_0_5_5) = all_102_0_50, yields:
% 32.07/8.30  		| (258) all_276_0_126 = all_102_0_50 |  ~ (in(all_102_1_51, all_0_5_5) = all_276_0_126)
% 32.07/8.30  		|
% 32.07/8.30  		| Instantiating formula (30) with all_102_3_53 yields:
% 32.07/8.30  		| (259)  ~ (in(all_102_3_53, empty_set) = 0)
% 32.07/8.30  		|
% 32.07/8.30  		| Combining equations (254,257) yields a new equation:
% 32.07/8.30  		| (260) all_176_0_85 = all_152_1_65
% 32.07/8.30  		|
% 32.07/8.30  		| Simplifying 260 yields:
% 32.07/8.30  		| (261) all_176_0_85 = all_152_1_65
% 32.07/8.30  		|
% 32.07/8.30  		| Combining equations (256,261) yields a new equation:
% 32.07/8.30  		| (262) all_162_1_74 = all_152_1_65
% 32.07/8.30  		|
% 32.07/8.30  		| Simplifying 262 yields:
% 32.07/8.30  		| (263) all_162_1_74 = all_152_1_65
% 32.07/8.30  		|
% 32.07/8.30  		| Combining equations (255,263) yields a new equation:
% 32.07/8.30  		| (264) all_152_1_65 = all_102_1_51
% 32.07/8.30  		|
% 32.07/8.30  		| Combining equations (264,257) yields a new equation:
% 32.07/8.30  		| (265) all_276_1_127 = all_102_1_51
% 32.07/8.30  		|
% 32.07/8.30  		| From (264) and (228) follows:
% 32.07/8.30  		| (210) subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51
% 32.07/8.30  		|
% 32.07/8.30  		| From (265) and (249) follows:
% 32.07/8.30  		| (267) in(all_102_1_51, all_0_5_5) = all_276_0_126
% 32.07/8.30  		|
% 32.07/8.30  		+-Applying beta-rule and splitting (225), into two cases.
% 32.07/8.30  		|-Branch one:
% 32.07/8.30  		| (268)  ~ (element(all_138_0_56, all_0_3_3) = 0)
% 32.07/8.30  		|
% 32.07/8.30  			| From (253) and (268) follows:
% 32.07/8.30  			| (269)  ~ (element(all_0_5_5, all_0_3_3) = 0)
% 32.07/8.30  			|
% 32.07/8.30  			| Using (53) and (269) yields:
% 32.07/8.30  			| (243) $false
% 32.07/8.30  			|
% 32.07/8.30  			|-The branch is then unsatisfiable
% 32.07/8.30  		|-Branch two:
% 32.07/8.30  		| (271) element(all_138_0_56, all_0_3_3) = 0
% 32.07/8.30  		| (272)  ? [v0] :  ? [v1] :  ? [v2] : (subset_complement(all_0_6_6, empty_set) = v1 & in(v1, empty_set) = v2 & in(empty_set, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.30  		|
% 32.07/8.30  			| From (253) and (271) follows:
% 32.07/8.30  			| (53) element(all_0_5_5, all_0_3_3) = 0
% 32.07/8.30  			|
% 32.07/8.30  			+-Applying beta-rule and splitting (258), into two cases.
% 32.07/8.30  			|-Branch one:
% 32.07/8.30  			| (274)  ~ (in(all_102_1_51, all_0_5_5) = all_276_0_126)
% 32.07/8.30  			|
% 32.07/8.30  				| Using (267) and (274) yields:
% 32.07/8.30  				| (243) $false
% 32.07/8.30  				|
% 32.07/8.30  				|-The branch is then unsatisfiable
% 32.07/8.30  			|-Branch two:
% 32.07/8.30  			| (267) in(all_102_1_51, all_0_5_5) = all_276_0_126
% 32.07/8.30  			| (277) all_276_0_126 = all_102_0_50
% 32.07/8.30  			|
% 32.07/8.30  				+-Applying beta-rule and splitting (224), into two cases.
% 32.07/8.30  				|-Branch one:
% 32.07/8.30  				| (268)  ~ (element(all_138_0_56, all_0_3_3) = 0)
% 32.07/8.30  				|
% 32.07/8.30  					| From (253) and (268) follows:
% 32.07/8.30  					| (269)  ~ (element(all_0_5_5, all_0_3_3) = 0)
% 32.07/8.30  					|
% 32.07/8.30  					| Using (53) and (269) yields:
% 32.07/8.30  					| (243) $false
% 32.07/8.30  					|
% 32.07/8.30  					|-The branch is then unsatisfiable
% 32.07/8.30  				|-Branch two:
% 32.07/8.30  				| (271) element(all_138_0_56, all_0_3_3) = 0
% 32.07/8.30  				| (282)  ? [v0] :  ? [v1] :  ? [v2] : (subset_complement(all_0_6_6, all_102_3_53) = v1 & in(v1, empty_set) = v2 & in(all_102_3_53, all_138_0_56) = v0 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 32.07/8.30  				|
% 32.07/8.30  					| Instantiating (282) with all_359_0_147, all_359_1_148, all_359_2_149 yields:
% 32.07/8.30  					| (283) subset_complement(all_0_6_6, all_102_3_53) = all_359_1_148 & in(all_359_1_148, empty_set) = all_359_0_147 & in(all_102_3_53, all_138_0_56) = all_359_2_149 & ( ~ (all_359_0_147 = 0) | all_359_2_149 = 0) & ( ~ (all_359_2_149 = 0) | all_359_0_147 = 0)
% 32.07/8.30  					|
% 32.07/8.30  					| Applying alpha-rule on (283) yields:
% 32.07/8.30  					| (284) in(all_102_3_53, all_138_0_56) = all_359_2_149
% 32.07/8.30  					| (285) in(all_359_1_148, empty_set) = all_359_0_147
% 32.07/8.30  					| (286)  ~ (all_359_0_147 = 0) | all_359_2_149 = 0
% 32.07/8.30  					| (287)  ~ (all_359_2_149 = 0) | all_359_0_147 = 0
% 32.07/8.30  					| (288) subset_complement(all_0_6_6, all_102_3_53) = all_359_1_148
% 32.07/8.30  					|
% 32.07/8.30  					| From (253) and (284) follows:
% 32.07/8.30  					| (289) in(all_102_3_53, all_0_5_5) = all_359_2_149
% 32.07/8.30  					|
% 32.07/8.30  					| Instantiating formula (152) with all_0_6_6, all_102_3_53, all_359_1_148, all_102_1_51 and discharging atoms subset_complement(all_0_6_6, all_102_3_53) = all_359_1_148, subset_complement(all_0_6_6, all_102_3_53) = all_102_1_51, yields:
% 32.07/8.30  					| (290) all_359_1_148 = all_102_1_51
% 32.07/8.30  					|
% 32.07/8.30  					| Instantiating formula (30) with all_359_1_148 yields:
% 32.07/8.30  					| (291)  ~ (in(all_359_1_148, empty_set) = 0)
% 32.07/8.30  					|
% 32.07/8.30  					| Instantiating formula (134) with all_102_3_53, all_0_5_5, all_359_2_149, all_102_2_52 and discharging atoms in(all_102_3_53, all_0_5_5) = all_359_2_149, in(all_102_3_53, all_0_5_5) = all_102_2_52, yields:
% 32.07/8.30  					| (292) all_359_2_149 = all_102_2_52
% 32.07/8.30  					|
% 32.07/8.30  					| Using (252) and (259) yields:
% 32.07/8.30  					| (293)  ~ (all_276_2_128 = 0)
% 32.07/8.30  					|
% 32.07/8.30  					| From (290) and (285) follows:
% 32.07/8.30  					| (294) in(all_102_1_51, empty_set) = all_359_0_147
% 32.07/8.30  					|
% 32.07/8.30  					| From (290) and (291) follows:
% 32.07/8.30  					| (295)  ~ (in(all_102_1_51, empty_set) = 0)
% 32.07/8.30  					|
% 32.07/8.30  					+-Applying beta-rule and splitting (251), into two cases.
% 32.07/8.30  					|-Branch one:
% 32.07/8.30  					| (296)  ~ (all_276_0_126 = 0)
% 32.07/8.30  					|
% 32.07/8.30  						| Equations (277) can reduce 296 to:
% 32.07/8.30  						| (297)  ~ (all_102_0_50 = 0)
% 32.07/8.30  						|
% 32.07/8.30  						+-Applying beta-rule and splitting (214), into two cases.
% 32.07/8.30  						|-Branch one:
% 32.07/8.30  						| (298) all_102_0_50 = 0
% 32.07/8.30  						|
% 32.07/8.30  							| Equations (298) can reduce 297 to:
% 32.07/8.30  							| (205) $false
% 32.07/8.30  							|
% 32.07/8.30  							|-The branch is then unsatisfiable
% 32.07/8.30  						|-Branch two:
% 32.07/8.30  						| (297)  ~ (all_102_0_50 = 0)
% 32.07/8.30  						| (301) all_102_2_52 = 0
% 32.07/8.30  						|
% 32.07/8.30  							| Combining equations (301,292) yields a new equation:
% 32.07/8.30  							| (302) all_359_2_149 = 0
% 32.07/8.30  							|
% 32.07/8.31  							+-Applying beta-rule and splitting (287), into two cases.
% 32.07/8.31  							|-Branch one:
% 32.07/8.31  							| (303)  ~ (all_359_2_149 = 0)
% 32.07/8.31  							|
% 32.07/8.31  								| Equations (302) can reduce 303 to:
% 32.07/8.31  								| (205) $false
% 32.07/8.31  								|
% 32.07/8.31  								|-The branch is then unsatisfiable
% 32.07/8.31  							|-Branch two:
% 32.07/8.31  							| (302) all_359_2_149 = 0
% 32.07/8.31  							| (306) all_359_0_147 = 0
% 32.07/8.31  							|
% 32.07/8.31  								| From (306) and (294) follows:
% 32.07/8.31  								| (307) in(all_102_1_51, empty_set) = 0
% 32.07/8.31  								|
% 32.07/8.31  								| Using (307) and (295) yields:
% 32.07/8.31  								| (243) $false
% 32.07/8.31  								|
% 32.07/8.31  								|-The branch is then unsatisfiable
% 32.07/8.31  					|-Branch two:
% 32.07/8.31  					| (309) all_276_0_126 = 0
% 32.07/8.31  					| (310) all_276_2_128 = 0
% 32.07/8.31  					|
% 32.07/8.31  						| Equations (310) can reduce 293 to:
% 32.07/8.31  						| (205) $false
% 32.07/8.31  						|
% 32.07/8.31  						|-The branch is then unsatisfiable
% 32.07/8.31  % SZS output end Proof for theBenchmark
% 32.07/8.31  
% 32.07/8.31  7664ms
%------------------------------------------------------------------------------