TSTP Solution File: SEU171+2 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU171+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n026.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 08:47:17 EDT 2022

% Result   : Theorem 23.74s 6.40s
% Output   : Proof 28.02s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU171+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sun Jun 19 02:12:55 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.47/0.59          ____       _                          
% 0.47/0.59    ___  / __ \_____(_)___  ________  __________
% 0.47/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.47/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.47/0.59  
% 0.47/0.59  A Theorem Prover for First-Order Logic
% 0.47/0.59  (ePrincess v.1.0)
% 0.47/0.59  
% 0.47/0.59  (c) Philipp Rümmer, 2009-2015
% 0.47/0.59  (c) Peter Backeman, 2014-2015
% 0.47/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.59  Bug reports to peter@backeman.se
% 0.47/0.59  
% 0.47/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.59  
% 0.47/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.08/1.03  Prover 0: Preprocessing ...
% 4.05/1.56  Prover 0: Warning: ignoring some quantifiers
% 4.21/1.60  Prover 0: Constructing countermodel ...
% 21.86/5.93  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 22.26/6.03  Prover 1: Preprocessing ...
% 23.20/6.25  Prover 1: Warning: ignoring some quantifiers
% 23.20/6.26  Prover 1: Constructing countermodel ...
% 23.74/6.39  Prover 1: proved (461ms)
% 23.74/6.40  Prover 0: stopped
% 23.74/6.40  
% 23.74/6.40  No countermodel exists, formula is valid
% 23.74/6.40  % SZS status Theorem for theBenchmark
% 23.74/6.40  
% 23.74/6.40  Generating proof ... Warning: ignoring some quantifiers
% 27.16/7.18  found it (size 43)
% 27.16/7.18  
% 27.16/7.18  % SZS output start Proof for theBenchmark
% 27.16/7.18  Assumed formulas after preprocessing and simplification: 
% 27.16/7.18  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] :  ? [v10] : ( ~ (v9 = 0) &  ~ (v7 = 0) &  ~ (v6 = 0) &  ~ (v1 = empty_set) & subset_complement(v1, v3) = v4 & element(v5, v1) = 0 & element(v3, v2) = 0 & empty(v10) = 0 & empty(v8) = v9 & empty(empty_set) = 0 & powerset(v1) = v2 & powerset(empty_set) = v0 & singleton(empty_set) = v0 & in(v5, v4) = v7 & in(v5, v3) = v6 &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v17 = 0 |  ~ (cartesian_product2(v13, v14) = v16) |  ~ (ordered_pair(v11, v12) = v15) |  ~ (in(v15, v16) = v17) |  ? [v18] :  ? [v19] : (in(v12, v14) = v19 & in(v11, v13) = v18 & ( ~ (v19 = 0) |  ~ (v18 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v17 = 0 |  ~ (cartesian_product2(v12, v14) = v16) |  ~ (cartesian_product2(v11, v13) = v15) |  ~ (subset(v15, v16) = v17) |  ? [v18] :  ? [v19] : (subset(v13, v14) = v19 & subset(v11, v12) = v18 & ( ~ (v19 = 0) |  ~ (v18 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] :  ! [v17] : (v15 = 0 |  ~ (cartesian_product2(v11, v12) = v13) |  ~ (ordered_pair(v16, v17) = v14) |  ~ (in(v14, v13) = v15) |  ? [v18] :  ? [v19] : (in(v17, v12) = v19 & in(v16, v11) = v18 & ( ~ (v19 = 0) |  ~ (v18 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (set_difference(v12, v14) = v15) |  ~ (singleton(v13) = v14) |  ~ (subset(v11, v15) = v16) |  ? [v17] :  ? [v18] : (subset(v11, v12) = v17 & in(v13, v11) = v18 & ( ~ (v17 = 0) | v18 = 0))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (set_difference(v12, v13) = v15) |  ~ (set_difference(v11, v13) = v14) |  ~ (subset(v14, v15) = v16) |  ? [v17] : ( ~ (v17 = 0) & subset(v11, v12) = v17)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : (v16 = 0 |  ~ (subset(v14, v15) = v16) |  ~ (set_intersection2(v12, v13) = v15) |  ~ (set_intersection2(v11, v13) = v14) |  ? [v17] : ( ~ (v17 = 0) & subset(v11, v12) = v17)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (cartesian_product2(v13, v14) = v16) |  ~ (ordered_pair(v11, v12) = v15) |  ~ (in(v15, v16) = 0) | (in(v12, v14) = 0 & in(v11, v13) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] :  ! [v16] : ( ~ (cartesian_product2(v12, v13) = v15) |  ~ (cartesian_product2(v11, v13) = v14) |  ~ (subset(v14, v15) = v16) |  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] : (cartesian_product2(v13, v12) = v19 & cartesian_product2(v13, v11) = v18 & subset(v18, v19) = v20 & subset(v11, v12) = v17 & ( ~ (v17 = 0) | (v20 = 0 & v16 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (subset_complement(v11, v12) = v14) |  ~ (element(v14, v13) = v15) |  ~ (powerset(v11) = v13) |  ? [v16] : ( ~ (v16 = 0) & element(v12, v13) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (element(v12, v13) = 0) |  ~ (powerset(v11) = v13) |  ~ (in(v14, v11) = v15) |  ? [v16] : ( ~ (v16 = 0) & in(v14, v12) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (subset(v14, v13) = v15) |  ~ (unordered_pair(v11, v12) = v14) |  ? [v16] :  ? [v17] : (in(v12, v13) = v17 & in(v11, v13) = v16 & ( ~ (v17 = 0) |  ~ (v16 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (subset(v14, v12) = v15) |  ~ (set_union2(v11, v13) = v14) |  ? [v16] :  ? [v17] : (subset(v13, v12) = v17 & subset(v11, v12) = v16 & ( ~ (v17 = 0) |  ~ (v16 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (subset(v11, v14) = v15) |  ~ (set_intersection2(v12, v13) = v14) |  ? [v16] :  ? [v17] : (subset(v11, v13) = v17 & subset(v11, v12) = v16 & ( ~ (v17 = 0) |  ~ (v16 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (set_union2(v11, v12) = v13) |  ~ (in(v14, v11) = v15) |  ? [v16] :  ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | v17 = 0))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v14 = v12 |  ~ (ordered_pair(v13, v14) = v15) |  ~ (ordered_pair(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v14 = v11 | v13 = v11 |  ~ (unordered_pair(v13, v14) = v15) |  ~ (unordered_pair(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v14 = 0 |  ~ (union(v11) = v12) |  ~ (in(v13, v15) = 0) |  ~ (in(v13, v12) = v14) |  ? [v16] : ( ~ (v16 = 0) & in(v15, v11) = v16)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v13 = v11 |  ~ (ordered_pair(v13, v14) = v15) |  ~ (ordered_pair(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (set_difference(v11, v12) = v13) |  ~ (in(v14, v11) = v15) |  ? [v16] :  ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | (v15 = 0 &  ~ (v17 = 0))))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (singleton(v11) = v14) |  ~ (unordered_pair(v13, v14) = v15) |  ~ (unordered_pair(v11, v12) = v13) | ordered_pair(v11, v12) = v15) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (set_intersection2(v11, v12) = v13) |  ~ (in(v14, v11) = v15) |  ? [v16] :  ? [v17] : (in(v14, v13) = v16 & in(v14, v12) = v17 & ( ~ (v16 = 0) | (v17 = 0 & v15 = 0)))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : ( ~ (set_union2(v11, v12) = v13) |  ~ (in(v14, v11) = v15) |  ? [v16] :  ? [v17] : (in(v14, v13) = v17 & in(v14, v12) = v16 & (v17 = 0 | ( ~ (v16 = 0) &  ~ (v15 = 0))))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v12 | v14 = v11 |  ~ (unordered_pair(v11, v12) = v13) |  ~ (in(v14, v13) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v12 |  ~ (subset_complement(v11, v13) = v14) |  ~ (subset_complement(v11, v12) = v13) |  ? [v15] :  ? [v16] : ( ~ (v16 = 0) & element(v12, v15) = v16 & powerset(v11) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v12 |  ~ (set_difference(v12, v11) = v13) |  ~ (set_union2(v11, v13) = v14) |  ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v12 |  ~ (singleton(v11) = v13) |  ~ (set_union2(v13, v12) = v14) |  ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (set_difference(v11, v13) = v14) |  ~ (singleton(v12) = v13) | in(v12, v11) = 0) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (disjoint(v13, v12) = v14) |  ~ (singleton(v11) = v13) | in(v11, v12) = 0) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (disjoint(v12, v13) = 0) |  ~ (disjoint(v11, v13) = v14) |  ? [v15] : ( ~ (v15 = 0) & subset(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (set_difference(v11, v12) = v13) |  ~ (subset(v13, v11) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (union(v12) = v13) |  ~ (subset(v11, v13) = v14) |  ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (powerset(v11) = v12) |  ~ (subset(v13, v11) = v14) |  ? [v15] : ( ~ (v15 = 0) & in(v13, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (singleton(v11) = v13) |  ~ (subset(v13, v12) = v14) |  ? [v15] : ( ~ (v15 = 0) & in(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (subset(v13, v11) = v14) |  ~ (set_intersection2(v11, v12) = v13)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (subset(v11, v13) = v14) |  ~ (subset(v11, v12) = 0) |  ? [v15] : ( ~ (v15 = 0) & subset(v12, v13) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (subset(v11, v13) = v14) |  ~ (set_union2(v11, v12) = v13)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (unordered_pair(v11, v12) = v13) |  ~ (in(v12, v13) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (unordered_pair(v11, v12) = v13) |  ~ (in(v11, v13) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v13 = v12 |  ~ (singleton(v11) = v14) |  ~ (unordered_pair(v12, v13) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (are_equipotent(v14, v13) = v12) |  ~ (are_equipotent(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (disjoint(v14, v13) = v12) |  ~ (disjoint(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (subset_complement(v14, v13) = v12) |  ~ (subset_complement(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (set_difference(v14, v13) = v12) |  ~ (set_difference(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (cartesian_product2(v14, v13) = v12) |  ~ (cartesian_product2(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (ordered_pair(v14, v13) = v12) |  ~ (ordered_pair(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (element(v14, v13) = v12) |  ~ (element(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (singleton(v12) = v14) |  ~ (singleton(v11) = v13) |  ~ (subset(v13, v14) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (singleton(v11) = v14) |  ~ (unordered_pair(v12, v13) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (subset(v14, v13) = v12) |  ~ (subset(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (set_intersection2(v14, v13) = v12) |  ~ (set_intersection2(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (set_union2(v14, v13) = v12) |  ~ (set_union2(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (unordered_pair(v14, v13) = v12) |  ~ (unordered_pair(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (proper_subset(v14, v13) = v12) |  ~ (proper_subset(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v12 = v11 |  ~ (in(v14, v13) = v12) |  ~ (in(v14, v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_difference(v13, v12) = v14) |  ~ (set_union2(v11, v12) = v13) | set_difference(v11, v12) = v14) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_difference(v12, v11) = v13) |  ~ (set_union2(v11, v13) = v14) | set_union2(v11, v12) = v14) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_difference(v11, v13) = v14) |  ~ (set_difference(v11, v12) = v13) | set_intersection2(v11, v12) = v14) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_difference(v11, v12) = v13) |  ~ (in(v14, v11) = 0) |  ? [v15] :  ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & (v16 = 0 | v15 = 0))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (cartesian_product2(v11, v12) = v13) |  ~ (in(v14, v13) = 0) |  ? [v15] :  ? [v16] : (ordered_pair(v15, v16) = v14 & in(v16, v12) = 0 & in(v15, v11) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (element(v14, v13) = 0) |  ~ (element(v12, v13) = 0) |  ~ (powerset(v11) = v13) |  ? [v15] :  ? [v16] :  ? [v17] : (disjoint(v12, v14) = v15 & subset_complement(v11, v14) = v16 & subset(v12, v16) = v17 & ( ~ (v17 = 0) | v15 = 0) & ( ~ (v15 = 0) | v17 = 0))) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (subset(v14, v13) = 0) |  ~ (unordered_pair(v11, v12) = v14) | (in(v12, v13) = 0 & in(v11, v13) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) |  ~ (in(v14, v13) = 0) |  ? [v15] : ( ~ (v15 = 0) & disjoint(v11, v12) = v15)) &  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : ( ~ (set_intersection2(v11, v12) = v13) |  ~ (in(v14, v11) = 0) |  ? [v15] :  ? [v16] : (in(v14, v13) = v16 & in(v14, v12) = v15 & ( ~ (v15 = 0) | v16 = 0))) &  ? [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (set_difference(v12, v13) = v14) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v17 = 0) |  ~ (v16 = 0) | v18 = 0) & (v16 = 0 | (v17 = 0 &  ~ (v18 = 0))))) &  ? [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (cartesian_product2(v12, v13) = v14) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] :  ? [v19] :  ? [v20] :  ? [v21] : (in(v15, v11) = v16 & ( ~ (v16 = 0) |  ! [v22] :  ! [v23] : ( ~ (ordered_pair(v22, v23) = v15) |  ? [v24] :  ? [v25] : (in(v23, v13) = v25 & in(v22, v12) = v24 & ( ~ (v25 = 0) |  ~ (v24 = 0))))) & (v16 = 0 | (v21 = v15 & v20 = 0 & v19 = 0 & ordered_pair(v17, v18) = v15 & in(v18, v13) = 0 & in(v17, v12) = 0)))) &  ? [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (set_intersection2(v12, v13) = v14) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v18 = 0) |  ~ (v17 = 0) |  ~ (v16 = 0)) & (v16 = 0 | (v18 = 0 & v17 = 0)))) &  ? [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (set_union2(v12, v13) = v14) |  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (in(v15, v13) = v18 & in(v15, v12) = v17 & in(v15, v11) = v16 & ( ~ (v16 = 0) | ( ~ (v18 = 0) &  ~ (v17 = 0))) & (v18 = 0 | v17 = 0 | v16 = 0))) &  ? [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = v11 |  ~ (unordered_pair(v12, v13) = v14) |  ? [v15] :  ? [v16] : (in(v15, v11) = v16 & ( ~ (v16 = 0) | ( ~ (v15 = v13) &  ~ (v15 = v12))) & (v16 = 0 | v15 = v13 | v15 = v12))) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v12 |  ~ (set_union2(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 | v11 = empty_set |  ~ (singleton(v12) = v13) |  ~ (subset(v11, v13) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (singleton(v11) = v12) |  ~ (in(v13, v12) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (set_intersection2(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = empty_set |  ~ (set_difference(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = empty_set |  ~ (set_intersection2(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & disjoint(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = v11 |  ~ (proper_subset(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & subset(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (disjoint(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = v11) & set_difference(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (disjoint(v11, v12) = v13) |  ? [v14] : (in(v14, v12) = 0 & in(v14, v11) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (singleton(v12) = v11) |  ~ (subset(v11, v11) = v13)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (singleton(v11) = v12) |  ~ (subset(empty_set, v12) = v13)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (singleton(v11) = v12) |  ~ (in(v11, v12) = v13)) &  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (subset(v11, v12) = v13) |  ? [v14] :  ? [v15] : ( ~ (v15 = 0) & in(v14, v12) = v15 & in(v14, v11) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (union(v13) = v12) |  ~ (union(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (empty(v13) = v12) |  ~ (empty(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (powerset(v13) = v12) |  ~ (powerset(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : (v12 = v11 |  ~ (singleton(v13) = v12) |  ~ (singleton(v13) = v11)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (disjoint(v13, v12) = 0) |  ~ (singleton(v11) = v13) |  ? [v14] : ( ~ (v14 = 0) & in(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (disjoint(v11, v12) = 0) |  ~ (in(v13, v11) = 0) |  ? [v14] : ( ~ (v14 = 0) & in(v13, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (set_difference(v11, v13) = v11) |  ~ (singleton(v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & in(v12, v11) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (union(v11) = v12) |  ~ (in(v13, v12) = 0) |  ? [v14] : (in(v14, v11) = 0 & in(v13, v14) = 0)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (ordered_pair(v11, v12) = v13) |  ? [v14] : ( ~ (v14 = 0) & empty(v13) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (element(v12, v13) = 0) |  ~ (powerset(v11) = v13) |  ? [v14] : (subset_complement(v11, v12) = v14 & set_difference(v11, v12) = v14)) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (element(v12, v11) = v13) |  ? [v14] :  ? [v15] : (empty(v12) = v15 & empty(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = 0) | v13 = 0) & ( ~ (v13 = 0) | v15 = 0))))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (element(v12, v11) = v13) |  ? [v14] :  ? [v15] : (empty(v11) = v14 & in(v12, v11) = v15 & (v14 = 0 | (( ~ (v15 = 0) | v13 = 0) & ( ~ (v13 = 0) | v15 = 0))))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (powerset(v11) = v12) |  ~ (subset(v13, v11) = 0) | in(v13, v12) = 0) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (singleton(v11) = v13) |  ~ (subset(v13, v12) = 0) | in(v11, v12) = 0) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (subset(v11, v12) = 0) |  ~ (in(v13, v11) = 0) | in(v13, v12) = 0) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) | set_intersection2(v12, v11) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (set_intersection2(v11, v12) = v13) |  ? [v14] :  ? [v15] : ((v15 = 0 & in(v14, v13) = 0) | (v14 = 0 & disjoint(v11, v12) = 0))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (set_union2(v12, v11) = v13) |  ? [v14] :  ? [v15] : (empty(v13) = v15 & empty(v11) = v14 & ( ~ (v15 = 0) | v14 = 0))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (set_union2(v11, v12) = v13) | set_union2(v12, v11) = v13) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (set_union2(v11, v12) = v13) |  ? [v14] :  ? [v15] : (empty(v13) = v15 & empty(v11) = v14 & ( ~ (v15 = 0) | v14 = 0))) &  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (unordered_pair(v11, v12) = v13) | unordered_pair(v12, v11) = v13) &  ? [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (union(v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] :  ? [v17] :  ? [v18] : (in(v14, v11) = v15 & ( ~ (v15 = 0) |  ! [v19] : ( ~ (in(v14, v19) = 0) |  ? [v20] : ( ~ (v20 = 0) & in(v19, v12) = v20))) & (v15 = 0 | (v18 = 0 & v17 = 0 & in(v16, v12) = 0 & in(v14, v16) = 0)))) &  ? [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (powerset(v12) = v13) |  ? [v14] :  ? [v15] :  ? [v16] : (subset(v14, v12) = v16 & in(v14, v11) = v15 & ( ~ (v16 = 0) |  ~ (v15 = 0)) & (v16 = 0 | v15 = 0))) &  ? [v11] :  ! [v12] :  ! [v13] : (v13 = v11 |  ~ (singleton(v12) = v13) |  ? [v14] :  ? [v15] : (in(v14, v11) = v15 & ( ~ (v15 = 0) |  ~ (v14 = v12)) & (v15 = 0 | v14 = v12))) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (set_difference(v11, empty_set) = v12)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (empty(v12) = 0) |  ~ (empty(v11) = 0)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (subset(v11, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & subset(v12, v11) = v13)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (set_intersection2(v11, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (set_union2(v11, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = v11 |  ~ (set_union2(v11, empty_set) = v12)) &  ! [v11] :  ! [v12] : (v12 = empty_set |  ~ (set_difference(empty_set, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = empty_set |  ~ (set_intersection2(v11, empty_set) = v12)) &  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v11, v11) = v12)) &  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(empty_set, v11) = v12)) &  ! [v11] :  ! [v12] : ( ~ (disjoint(v11, v12) = 0) | disjoint(v12, v11) = 0) &  ! [v11] :  ! [v12] : ( ~ (disjoint(v11, v12) = 0) | set_difference(v11, v12) = v11) &  ! [v11] :  ! [v12] : ( ~ (set_difference(v11, v12) = empty_set) | subset(v11, v12) = 0) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) | union(v12) = v11) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] :  ? [v14] :  ? [v15] : ((v14 = 0 &  ~ (v15 = 0) & element(v13, v12) = 0 & empty(v13) = v15) | (v13 = 0 & empty(v11) = 0))) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) &  ! [v11] :  ! [v12] : ( ~ (powerset(v11) = v12) |  ? [v13] : (element(v13, v12) = 0 & empty(v13) = 0)) &  ! [v11] :  ! [v12] : ( ~ (set_intersection2(v11, v12) = empty_set) | disjoint(v11, v12) = 0) &  ! [v11] :  ! [v12] : ( ~ (unordered_pair(v11, v11) = v12) | singleton(v11) = v12) &  ! [v11] :  ! [v12] : ( ~ (proper_subset(v12, v11) = 0) |  ? [v13] : ( ~ (v13 = 0) & subset(v11, v12) = v13)) &  ! [v11] :  ! [v12] : ( ~ (proper_subset(v11, v12) = 0) | subset(v11, v12) = 0) &  ! [v11] :  ! [v12] : ( ~ (proper_subset(v11, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & proper_subset(v12, v11) = v13)) &  ! [v11] :  ! [v12] : ( ~ (in(v11, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & empty(v12) = v13)) &  ! [v11] :  ! [v12] : ( ~ (in(v11, v12) = 0) |  ? [v13] : ( ~ (v13 = 0) & in(v12, v11) = v13)) &  ! [v11] : (v11 = empty_set |  ~ (empty(v11) = 0)) &  ! [v11] : (v11 = empty_set |  ~ (subset(v11, empty_set) = 0)) &  ! [v11] :  ~ (singleton(v11) = empty_set) &  ! [v11] :  ~ (proper_subset(v11, v11) = 0) &  ! [v11] :  ~ (in(v11, empty_set) = 0) &  ? [v11] :  ? [v12] : (v12 = v11 |  ? [v13] :  ? [v14] :  ? [v15] : (in(v13, v12) = v15 & in(v13, v11) = v14 & ( ~ (v15 = 0) |  ~ (v14 = 0)) & (v15 = 0 | v14 = 0))) &  ? [v11] :  ? [v12] : element(v12, v11) = 0 &  ? [v11] :  ? [v12] : (in(v11, v12) = 0 &  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 |  ~ (powerset(v13) = v14) |  ~ (in(v14, v12) = v15) |  ? [v16] : ( ~ (v16 = 0) & in(v13, v12) = v16)) &  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (are_equipotent(v13, v12) = v14) |  ? [v15] :  ? [v16] : (subset(v13, v12) = v15 & in(v13, v12) = v16 & ( ~ (v15 = 0) | v16 = 0))) &  ! [v13] :  ! [v14] : ( ~ (subset(v14, v13) = 0) |  ? [v15] :  ? [v16] : (in(v14, v12) = v16 & in(v13, v12) = v15 & ( ~ (v15 = 0) | v16 = 0)))) &  ? [v11] :  ? [v12] : (in(v11, v12) = 0 &  ! [v13] :  ! [v14] : (v14 = 0 |  ~ (are_equipotent(v13, v12) = v14) |  ? [v15] :  ? [v16] : (subset(v13, v12) = v15 & in(v13, v12) = v16 & ( ~ (v15 = 0) | v16 = 0))) &  ! [v13] :  ! [v14] : ( ~ (subset(v14, v13) = 0) |  ? [v15] :  ? [v16] : (in(v14, v12) = v16 & in(v13, v12) = v15 & ( ~ (v15 = 0) | v16 = 0))) &  ! [v13] : ( ~ (in(v13, v12) = 0) |  ? [v14] : (in(v14, v12) = 0 &  ! [v15] : ( ~ (subset(v15, v13) = 0) | in(v15, v14) = 0)))) &  ? [v11] : (v11 = empty_set |  ? [v12] : in(v12, v11) = 0))
% 27.54/7.25  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9, all_0_10_10 yields:
% 27.54/7.25  | (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_3_3 = 0) &  ~ (all_0_4_4 = 0) &  ~ (all_0_9_9 = empty_set) & subset_complement(all_0_9_9, all_0_7_7) = all_0_6_6 & element(all_0_5_5, all_0_9_9) = 0 & element(all_0_7_7, all_0_8_8) = 0 & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & powerset(all_0_9_9) = all_0_8_8 & powerset(empty_set) = all_0_10_10 & singleton(empty_set) = all_0_10_10 & in(all_0_5_5, all_0_6_6) = all_0_3_3 & in(all_0_5_5, all_0_7_7) = all_0_4_4 &  ! [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 |  ~ (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, 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 |  ~ (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 |  ~ (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] : ( ~ (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 |  ~ (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] : ( ~ (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(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) &  ! [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] : ( ~ (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 |  ~ (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] : ( ~ (powerset(v0) = v1) | union(v1) = v0) &  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0))) &  ! [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)
% 27.54/7.28  |
% 27.54/7.28  | Applying alpha-rule on (1) yields:
% 27.54/7.28  | (2)  ! [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))))
% 27.54/7.28  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v0 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4))
% 27.54/7.28  | (4)  ? [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)))
% 27.54/7.28  | (5)  ! [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))))
% 27.54/7.28  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 27.54/7.28  | (7)  ! [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))
% 27.54/7.28  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 27.54/7.28  | (9)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & proper_subset(v1, v0) = v2))
% 27.54/7.28  | (10)  ! [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))
% 27.54/7.28  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 27.54/7.28  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (subset(empty_set, v1) = v2))
% 27.54/7.28  | (13)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 27.54/7.28  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 27.54/7.28  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (are_equipotent(v3, v2) = v1) |  ~ (are_equipotent(v3, v2) = v0))
% 27.54/7.28  | (16)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 27.54/7.28  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 27.54/7.28  | (18) powerset(all_0_9_9) = all_0_8_8
% 27.54/7.28  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v0 | v2 = v0 |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v4))
% 27.54/7.28  | (20)  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 27.54/7.28  | (21)  ? [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))))
% 27.54/7.28  | (22)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (union(v2) = v1) |  ~ (union(v2) = v0))
% 27.54/7.28  | (23)  ? [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)))))
% 27.54/7.28  | (24)  ! [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)))
% 27.54/7.28  | (25)  ! [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))))
% 27.54/7.28  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v2 = v1 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3))
% 27.99/7.28  | (27)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 27.99/7.28  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ (set_intersection2(v0, v1) = v2))
% 27.99/7.28  | (29)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 27.99/7.28  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 27.99/7.28  | (31)  ! [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))
% 27.99/7.28  | (32)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1))
% 27.99/7.28  | (33) subset_complement(all_0_9_9, all_0_7_7) = all_0_6_6
% 27.99/7.28  | (34)  ? [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)))
% 27.99/7.28  | (35)  ? [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))))
% 27.99/7.28  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v0, v2) = v3))
% 27.99/7.28  | (37)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v0) = v1) |  ~ (in(v0, v1) = v2))
% 27.99/7.29  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 27.99/7.29  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ (in(v2, v1) = 0))
% 27.99/7.29  | (40)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1))
% 27.99/7.29  | (41)  ! [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))
% 27.99/7.29  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (singleton(v0) = v2) |  ~ (set_union2(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 27.99/7.29  | (43)  ? [v0] :  ? [v1] : element(v1, v0) = 0
% 27.99/7.29  | (44) empty(empty_set) = 0
% 27.99/7.29  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (disjoint(v1, v2) = 0) |  ~ (disjoint(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 27.99/7.29  | (46)  ! [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)))))
% 27.99/7.29  | (47) powerset(empty_set) = all_0_10_10
% 27.99/7.29  | (48)  ! [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))))
% 27.99/7.29  | (49)  ~ (all_0_3_3 = 0)
% 27.99/7.29  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (ordered_pair(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & empty(v2) = v3))
% 27.99/7.29  | (51)  ~ (all_0_4_4 = 0)
% 27.99/7.29  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v3 = v0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v3, v2) = 0))
% 27.99/7.29  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 27.99/7.29  | (54)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0) = v1) |  ~ (in(v2, v1) = 0) |  ? [v3] : (in(v3, v0) = 0 & in(v2, v3) = 0))
% 27.99/7.29  | (55)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v1) = v4 & empty(v0) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 27.99/7.29  | (56)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 27.99/7.29  | (57)  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0))
% 27.99/7.29  | (58) empty(all_0_0_0) = 0
% 27.99/7.29  | (59)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 27.99/7.29  | (60)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 | v1 = v0 |  ~ (proper_subset(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 28.02/7.29  | (61)  ! [v0] :  ~ (singleton(v0) = empty_set)
% 28.02/7.29  | (62)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 28.02/7.29  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 28.02/7.29  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (disjoint(v2, v1) = v3) |  ~ (singleton(v0) = v2) | in(v0, v1) = 0)
% 28.02/7.29  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v2, v1) = v4))
% 28.02/7.29  | (66)  ~ (all_0_9_9 = empty_set)
% 28.02/7.29  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 28.02/7.29  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 28.02/7.29  | (69)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 28.02/7.29  | (70)  ~ (all_0_1_1 = 0)
% 28.02/7.29  | (71)  ! [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))))
% 28.02/7.29  | (72)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 28.02/7.29  | (73)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 28.02/7.29  | (74)  ! [v0] :  ~ (in(v0, empty_set) = 0)
% 28.02/7.29  | (75) element(all_0_7_7, all_0_8_8) = 0
% 28.02/7.29  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3))
% 28.02/7.29  | (77)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 28.02/7.29  | (78)  ! [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)))))
% 28.02/7.29  | (79)  ! [v0] :  ~ (proper_subset(v0, v0) = 0)
% 28.02/7.29  | (80)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ (in(v1, v2) = v3))
% 28.02/7.29  | (81)  ! [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))
% 28.02/7.29  | (82)  ! [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))
% 28.02/7.29  | (83)  ? [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))))
% 28.02/7.29  | (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))
% 28.02/7.29  | (85)  ! [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))))
% 28.02/7.29  | (86)  ! [v0] :  ! [v1] : ( ~ (proper_subset(v0, v1) = 0) | subset(v0, v1) = 0)
% 28.02/7.29  | (87) element(all_0_5_5, all_0_9_9) = 0
% 28.02/7.29  | (88)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 28.02/7.29  | (89)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 28.02/7.29  | (90)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : ((v3 = 0 &  ~ (v4 = 0) & element(v2, v1) = 0 & empty(v2) = v4) | (v2 = 0 & empty(v0) = 0)))
% 28.02/7.29  | (91)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (set_union2(v0, v1) = v2))
% 28.02/7.29  | (92)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 28.02/7.29  | (93)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (element(v1, v2) = 0) |  ~ (powerset(v0) = v2) |  ? [v3] : (subset_complement(v0, v1) = v3 & set_difference(v0, v1) = v3))
% 28.02/7.29  | (94)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 28.02/7.29  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset_complement(v3, v2) = v1) |  ~ (subset_complement(v3, v2) = v0))
% 28.02/7.29  | (96)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (proper_subset(v3, v2) = v1) |  ~ (proper_subset(v3, v2) = v0))
% 28.02/7.29  | (97)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (union(v1) = v2) |  ~ (subset(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 28.02/7.29  | (98)  ! [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)))))
% 28.02/7.29  | (99)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 28.02/7.29  | (100)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 28.02/7.29  | (101)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_difference(v0, v1) = v0)
% 28.02/7.29  | (102)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 28.02/7.29  | (103)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ (subset(v0, v2) = 0))
% 28.02/7.30  | (104)  ! [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)))
% 28.02/7.30  | (105)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v2, v1) = 0) |  ~ (singleton(v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v0, v1) = v3))
% 28.02/7.30  | (106)  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 28.02/7.30  | (107)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v2) = v0) |  ~ (singleton(v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & in(v1, v0) = v3))
% 28.02/7.30  | (108)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 28.02/7.30  | (109)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 28.02/7.30  | (110)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (ordered_pair(v3, v2) = v1) |  ~ (ordered_pair(v3, v2) = v0))
% 28.02/7.30  | (111) in(all_0_5_5, all_0_6_6) = all_0_3_3
% 28.02/7.30  | (112)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 28.02/7.30  | (113)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (set_difference(v0, v1) = v2) |  ~ (subset(v2, v0) = v3))
% 28.02/7.30  | (114)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 28.02/7.30  | (115)  ! [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)))
% 28.02/7.30  | (116)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) | union(v1) = v0)
% 28.02/7.30  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (subset(v3, v2) = 0) |  ~ (unordered_pair(v0, v1) = v3) | (in(v1, v2) = 0 & in(v0, v2) = 0))
% 28.02/7.30  | (118)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (element(v3, v2) = v1) |  ~ (element(v3, v2) = v0))
% 28.02/7.30  | (119)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 28.02/7.30  | (120)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v0, v1) = v4))
% 28.02/7.30  | (121)  ! [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))
% 28.02/7.30  | (122)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] :  ? [v4] : (in(v3, v0) = v4 & ( ~ (v4 = 0) |  ~ (v3 = v1)) & (v4 = 0 | v3 = v1)))
% 28.02/7.30  | (123)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ (subset(v2, v1) = 0) | in(v0, v1) = 0)
% 28.02/7.30  | (124)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 28.02/7.30  | (125)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 28.02/7.30  | (126)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 28.02/7.30  | (127)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 28.02/7.30  | (128) in(all_0_5_5, all_0_7_7) = all_0_4_4
% 28.02/7.30  | (129)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = v0) & set_difference(v0, v1) = v3))
% 28.02/7.30  | (130)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 28.02/7.30  | (131)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (singleton(v0) = v3) |  ~ (unordered_pair(v2, v3) = v4) |  ~ (unordered_pair(v0, v1) = v2) | ordered_pair(v0, v1) = v4)
% 28.02/7.30  | (132)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1))
% 28.02/7.30  | (133)  ! [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))))
% 28.02/7.30  | (134)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v0, v2) = v3) |  ~ (singleton(v1) = v2) | in(v1, v0) = 0)
% 28.02/7.30  | (135)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 28.02/7.30  | (136)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
% 28.02/7.30  | (137)  ! [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)))
% 28.02/7.30  | (138)  ? [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))))
% 28.02/7.30  | (139)  ! [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)))
% 28.02/7.30  | (140)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 28.02/7.30  | (141)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (singleton(v1) = v0) |  ~ (subset(v0, v0) = v2))
% 28.02/7.30  | (142) singleton(empty_set) = all_0_10_10
% 28.02/7.30  | (143)  ! [v0] :  ! [v1] : ( ~ (powerset(v0) = v1) |  ? [v2] : (element(v2, v1) = 0 & empty(v2) = 0))
% 28.02/7.30  | (144)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 28.02/7.30  | (145)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 28.02/7.30  | (146) empty(all_0_2_2) = all_0_1_1
% 28.02/7.30  | (147)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 28.02/7.30  | (148)  ? [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))))
% 28.02/7.30  | (149)  ? [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)))
% 28.02/7.30  | (150)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ (subset(v2, v3) = 0))
% 28.02/7.30  | (151)  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 28.02/7.30  | (152)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v3 = v1 |  ~ (ordered_pair(v2, v3) = v4) |  ~ (ordered_pair(v0, v1) = v4))
% 28.02/7.30  | (153)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (cartesian_product2(v3, v2) = v1) |  ~ (cartesian_product2(v3, v2) = v0))
% 28.02/7.30  | (154)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ (subset(v2, v0) = 0) | in(v2, v1) = 0)
% 28.02/7.30  | (155)  ! [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))))
% 28.02/7.30  |
% 28.02/7.30  | Instantiating formula (55) with 0, all_0_5_5, all_0_9_9 and discharging atoms element(all_0_5_5, all_0_9_9) = 0, yields:
% 28.02/7.30  | (156)  ? [v0] :  ? [v1] : (empty(all_0_5_5) = v1 & empty(all_0_9_9) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 28.02/7.30  |
% 28.02/7.30  | Instantiating formula (78) with 0, all_0_5_5, all_0_9_9 and discharging atoms element(all_0_5_5, all_0_9_9) = 0, yields:
% 28.02/7.30  | (157)  ? [v0] :  ? [v1] : (empty(all_0_9_9) = v0 & in(all_0_5_5, all_0_9_9) = v1 & (v1 = 0 | v0 = 0))
% 28.02/7.30  |
% 28.02/7.30  | Instantiating formula (104) with all_0_7_7, all_0_8_8, all_0_7_7, all_0_9_9 and discharging atoms element(all_0_7_7, all_0_8_8) = 0, powerset(all_0_9_9) = all_0_8_8, yields:
% 28.02/7.30  | (158)  ? [v0] :  ? [v1] :  ? [v2] : (disjoint(all_0_7_7, all_0_7_7) = v0 & subset_complement(all_0_9_9, all_0_7_7) = v1 & subset(all_0_7_7, v1) = v2 & ( ~ (v2 = 0) | v0 = 0) & ( ~ (v0 = 0) | v2 = 0))
% 28.02/7.30  |
% 28.02/7.30  | Instantiating formula (93) with all_0_8_8, all_0_7_7, all_0_9_9 and discharging atoms element(all_0_7_7, all_0_8_8) = 0, powerset(all_0_9_9) = all_0_8_8, yields:
% 28.02/7.30  | (159)  ? [v0] : (subset_complement(all_0_9_9, all_0_7_7) = v0 & set_difference(all_0_9_9, all_0_7_7) = v0)
% 28.02/7.30  |
% 28.02/7.30  | Instantiating (159) with all_54_0_36 yields:
% 28.02/7.30  | (160) subset_complement(all_0_9_9, all_0_7_7) = all_54_0_36 & set_difference(all_0_9_9, all_0_7_7) = all_54_0_36
% 28.02/7.30  |
% 28.02/7.30  | Applying alpha-rule on (160) yields:
% 28.02/7.30  | (161) subset_complement(all_0_9_9, all_0_7_7) = all_54_0_36
% 28.02/7.30  | (162) set_difference(all_0_9_9, all_0_7_7) = all_54_0_36
% 28.02/7.30  |
% 28.02/7.30  | Instantiating (158) with all_63_0_40, all_63_1_41, all_63_2_42 yields:
% 28.02/7.30  | (163) disjoint(all_0_7_7, all_0_7_7) = all_63_2_42 & subset_complement(all_0_9_9, all_0_7_7) = all_63_1_41 & subset(all_0_7_7, all_63_1_41) = all_63_0_40 & ( ~ (all_63_0_40 = 0) | all_63_2_42 = 0) & ( ~ (all_63_2_42 = 0) | all_63_0_40 = 0)
% 28.02/7.30  |
% 28.02/7.30  | Applying alpha-rule on (163) yields:
% 28.02/7.30  | (164)  ~ (all_63_0_40 = 0) | all_63_2_42 = 0
% 28.02/7.30  | (165) disjoint(all_0_7_7, all_0_7_7) = all_63_2_42
% 28.02/7.30  | (166) subset_complement(all_0_9_9, all_0_7_7) = all_63_1_41
% 28.02/7.30  | (167)  ~ (all_63_2_42 = 0) | all_63_0_40 = 0
% 28.02/7.31  | (168) subset(all_0_7_7, all_63_1_41) = all_63_0_40
% 28.02/7.31  |
% 28.02/7.31  | Instantiating (157) with all_71_0_48, all_71_1_49 yields:
% 28.02/7.31  | (169) empty(all_0_9_9) = all_71_1_49 & in(all_0_5_5, all_0_9_9) = all_71_0_48 & (all_71_0_48 = 0 | all_71_1_49 = 0)
% 28.02/7.31  |
% 28.02/7.31  | Applying alpha-rule on (169) yields:
% 28.02/7.31  | (170) empty(all_0_9_9) = all_71_1_49
% 28.02/7.31  | (171) in(all_0_5_5, all_0_9_9) = all_71_0_48
% 28.02/7.31  | (172) all_71_0_48 = 0 | all_71_1_49 = 0
% 28.02/7.31  |
% 28.02/7.31  | Instantiating (156) with all_73_0_50, all_73_1_51 yields:
% 28.02/7.31  | (173) empty(all_0_5_5) = all_73_0_50 & empty(all_0_9_9) = all_73_1_51 & ( ~ (all_73_1_51 = 0) | all_73_0_50 = 0)
% 28.02/7.31  |
% 28.02/7.31  | Applying alpha-rule on (173) yields:
% 28.02/7.31  | (174) empty(all_0_5_5) = all_73_0_50
% 28.02/7.31  | (175) empty(all_0_9_9) = all_73_1_51
% 28.02/7.31  | (176)  ~ (all_73_1_51 = 0) | all_73_0_50 = 0
% 28.02/7.31  |
% 28.02/7.31  | Instantiating formula (95) with all_0_9_9, all_0_7_7, all_63_1_41, all_0_6_6 and discharging atoms subset_complement(all_0_9_9, all_0_7_7) = all_63_1_41, subset_complement(all_0_9_9, all_0_7_7) = all_0_6_6, yields:
% 28.02/7.31  | (177) all_63_1_41 = all_0_6_6
% 28.02/7.31  |
% 28.02/7.31  | Instantiating formula (95) with all_0_9_9, all_0_7_7, all_54_0_36, all_63_1_41 and discharging atoms subset_complement(all_0_9_9, all_0_7_7) = all_63_1_41, subset_complement(all_0_9_9, all_0_7_7) = all_54_0_36, yields:
% 28.02/7.31  | (178) all_63_1_41 = all_54_0_36
% 28.02/7.31  |
% 28.02/7.31  | Instantiating formula (77) with all_0_9_9 yields:
% 28.02/7.31  | (179) all_0_9_9 = empty_set |  ~ (empty(all_0_9_9) = 0)
% 28.02/7.31  |
% 28.02/7.31  | Instantiating formula (68) with all_0_9_9, all_71_1_49, all_73_1_51 and discharging atoms empty(all_0_9_9) = all_73_1_51, empty(all_0_9_9) = all_71_1_49, yields:
% 28.02/7.31  | (180) all_73_1_51 = all_71_1_49
% 28.02/7.31  |
% 28.02/7.31  | Combining equations (177,178) yields a new equation:
% 28.02/7.31  | (181) all_54_0_36 = all_0_6_6
% 28.02/7.31  |
% 28.02/7.31  | From (181) and (162) follows:
% 28.02/7.31  | (182) set_difference(all_0_9_9, all_0_7_7) = all_0_6_6
% 28.02/7.31  |
% 28.02/7.31  | From (180) and (175) follows:
% 28.02/7.31  | (170) empty(all_0_9_9) = all_71_1_49
% 28.02/7.31  |
% 28.02/7.31  +-Applying beta-rule and splitting (179), into two cases.
% 28.02/7.31  |-Branch one:
% 28.02/7.31  | (184)  ~ (empty(all_0_9_9) = 0)
% 28.02/7.31  |
% 28.02/7.31  	| Using (170) and (184) yields:
% 28.02/7.31  	| (185)  ~ (all_71_1_49 = 0)
% 28.02/7.31  	|
% 28.02/7.31  	+-Applying beta-rule and splitting (172), into two cases.
% 28.02/7.31  	|-Branch one:
% 28.02/7.31  	| (186) all_71_0_48 = 0
% 28.02/7.31  	|
% 28.02/7.31  		| From (186) and (171) follows:
% 28.02/7.31  		| (187) in(all_0_5_5, all_0_9_9) = 0
% 28.02/7.31  		|
% 28.02/7.31  		| Instantiating formula (115) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_9_9 and discharging atoms set_difference(all_0_9_9, all_0_7_7) = all_0_6_6, in(all_0_5_5, all_0_9_9) = 0, yields:
% 28.02/7.31  		| (188)  ? [v0] :  ? [v1] : (in(all_0_5_5, all_0_6_6) = v1 & in(all_0_5_5, all_0_7_7) = v0 & (v1 = 0 | v0 = 0))
% 28.02/7.31  		|
% 28.02/7.31  		| Instantiating (188) with all_130_0_74, all_130_1_75 yields:
% 28.02/7.31  		| (189) in(all_0_5_5, all_0_6_6) = all_130_0_74 & in(all_0_5_5, all_0_7_7) = all_130_1_75 & (all_130_0_74 = 0 | all_130_1_75 = 0)
% 28.02/7.31  		|
% 28.02/7.31  		| Applying alpha-rule on (189) yields:
% 28.02/7.31  		| (190) in(all_0_5_5, all_0_6_6) = all_130_0_74
% 28.02/7.31  		| (191) in(all_0_5_5, all_0_7_7) = all_130_1_75
% 28.02/7.31  		| (192) all_130_0_74 = 0 | all_130_1_75 = 0
% 28.02/7.31  		|
% 28.02/7.31  		| Instantiating formula (6) with all_0_5_5, all_0_6_6, all_130_0_74, all_0_3_3 and discharging atoms in(all_0_5_5, all_0_6_6) = all_130_0_74, in(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 28.02/7.31  		| (193) all_130_0_74 = all_0_3_3
% 28.02/7.31  		|
% 28.02/7.31  		| Instantiating formula (6) with all_0_5_5, all_0_7_7, all_130_1_75, all_0_4_4 and discharging atoms in(all_0_5_5, all_0_7_7) = all_130_1_75, in(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 28.02/7.31  		| (194) all_130_1_75 = all_0_4_4
% 28.02/7.31  		|
% 28.02/7.31  		+-Applying beta-rule and splitting (192), into two cases.
% 28.02/7.31  		|-Branch one:
% 28.02/7.31  		| (195) all_130_0_74 = 0
% 28.02/7.31  		|
% 28.02/7.31  			| Combining equations (193,195) yields a new equation:
% 28.02/7.31  			| (196) all_0_3_3 = 0
% 28.02/7.31  			|
% 28.02/7.31  			| Simplifying 196 yields:
% 28.02/7.31  			| (197) all_0_3_3 = 0
% 28.02/7.31  			|
% 28.02/7.31  			| Equations (197) can reduce 49 to:
% 28.02/7.31  			| (198) $false
% 28.02/7.31  			|
% 28.02/7.31  			|-The branch is then unsatisfiable
% 28.02/7.31  		|-Branch two:
% 28.02/7.31  		| (199)  ~ (all_130_0_74 = 0)
% 28.02/7.31  		| (200) all_130_1_75 = 0
% 28.02/7.31  		|
% 28.02/7.31  			| Combining equations (194,200) yields a new equation:
% 28.02/7.31  			| (201) all_0_4_4 = 0
% 28.02/7.31  			|
% 28.02/7.31  			| Simplifying 201 yields:
% 28.02/7.31  			| (202) all_0_4_4 = 0
% 28.02/7.31  			|
% 28.02/7.31  			| Equations (202) can reduce 51 to:
% 28.02/7.31  			| (198) $false
% 28.02/7.31  			|
% 28.02/7.31  			|-The branch is then unsatisfiable
% 28.02/7.31  	|-Branch two:
% 28.02/7.31  	| (204)  ~ (all_71_0_48 = 0)
% 28.02/7.31  	| (205) all_71_1_49 = 0
% 28.02/7.31  	|
% 28.02/7.31  		| Equations (205) can reduce 185 to:
% 28.02/7.31  		| (198) $false
% 28.02/7.31  		|
% 28.02/7.31  		|-The branch is then unsatisfiable
% 28.02/7.31  |-Branch two:
% 28.02/7.31  | (207) empty(all_0_9_9) = 0
% 28.02/7.31  | (208) all_0_9_9 = empty_set
% 28.02/7.31  |
% 28.02/7.31  	| Equations (208) can reduce 66 to:
% 28.02/7.31  	| (198) $false
% 28.02/7.31  	|
% 28.02/7.31  	|-The branch is then unsatisfiable
% 28.02/7.31  % SZS output end Proof for theBenchmark
% 28.02/7.31  
% 28.02/7.31  6709ms
%------------------------------------------------------------------------------