%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n021.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 08:47:01 EDT 2022

% Result   : Theorem 4.08s 1.58s
% Output   : Proof 6.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU150+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n021.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Mon Jun 20 00:04:03 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.50/0.58          ____       _                          
% 0.50/0.58    ___  / __ \_____(_)___  ________  __________
% 0.50/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.50/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.50/0.58  
% 0.50/0.58  A Theorem Prover for First-Order Logic
% 0.50/0.58  (ePrincess v.1.0)
% 0.50/0.58  
% 0.50/0.58  (c) Philipp Rümmer, 2009-2015
% 0.50/0.58  (c) Peter Backeman, 2014-2015
% 0.50/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.58  Bug reports to peter@backeman.se
% 0.50/0.58  
% 0.50/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.58  
% 0.50/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.50/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.69/0.98  Prover 0: Preprocessing ...
% 3.17/1.40  Prover 0: Warning: ignoring some quantifiers
% 3.42/1.43  Prover 0: Constructing countermodel ...
% 4.08/1.58  Prover 0: proved (947ms)
% 4.08/1.58  
% 4.08/1.58  No countermodel exists, formula is valid
% 4.08/1.58  % SZS status Theorem for theBenchmark
% 4.08/1.58  
% 4.08/1.58  Generating proof ... Warning: ignoring some quantifiers
% 5.74/1.94  found it (size 9)
% 5.74/1.94  
% 5.74/1.94  % SZS output start Proof for theBenchmark
% 5.74/1.94  Assumed formulas after preprocessing and simplification: 
% 5.74/1.94  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v3 = v2) & powerset(empty_set) = v0 & singleton(v1) = v4 & singleton(empty_set) = v0 & unordered_pair(v2, v3) = v4 & empty(v6) & empty(empty_set) &  ~ empty(v5) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v8, v10) = v11) |  ~ (singleton(v9) = v10) |  ~ subset(v7, v8) | subset(v7, v11) | in(v9, v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v8, v9) = v11) |  ~ (set_difference(v7, v9) = v10) |  ~ subset(v7, v8) | subset(v10, v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_intersection2(v8, v9) = v11) |  ~ (set_intersection2(v7, v9) = v10) |  ~ subset(v7, v8) | subset(v10, v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v8 | v10 = v7 |  ~ (unordered_pair(v7, v8) = v9) |  ~ in(v10, v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v8 |  ~ (set_difference(v8, v7) = v9) |  ~ (set_union2(v7, v9) = v10) |  ~ subset(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_difference(v10, v9) = v8) |  ~ (set_difference(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (singleton(v8) = v10) |  ~ (singleton(v7) = v9) |  ~ subset(v9, v10)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (singleton(v7) = v10) |  ~ (unordered_pair(v8, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_intersection2(v10, v9) = v8) |  ~ (set_intersection2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_union2(v10, v9) = v8) |  ~ (set_union2(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unordered_pair(v10, v9) = v8) |  ~ (unordered_pair(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v9, v8) = v10) |  ~ (set_union2(v7, v8) = v9) | set_difference(v7, v8) = v10) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v8, v7) = v9) |  ~ (set_union2(v7, v9) = v10) | set_union2(v7, v8) = v10) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v9) = v10) |  ~ (set_difference(v7, v8) = v9) | set_intersection2(v7, v8) = v10) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v8) = v9) |  ~ in(v10, v9) |  ~ in(v10, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v8) = v9) |  ~ in(v10, v9) | in(v10, v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v8) = v9) |  ~ in(v10, v7) | in(v10, v9) | in(v10, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v8, v9) = v10) |  ~ subset(v7, v9) |  ~ subset(v7, v8) | subset(v7, v10)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ disjoint(v7, v8) |  ~ in(v10, v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ in(v10, v9) | in(v10, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ in(v10, v9) | in(v10, v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ in(v10, v8) |  ~ in(v10, v7) | in(v10, v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v7, v9) = v10) |  ~ subset(v9, v8) |  ~ subset(v7, v8) | subset(v10, v8)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v7, v8) = v9) |  ~ in(v10, v9) | in(v10, v8) | in(v10, v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v7, v8) = v9) |  ~ in(v10, v8) | in(v10, v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v7, v8) = v9) |  ~ in(v10, v7) | in(v10, v9)) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_difference(v8, v9) = v10) |  ? [v11] : (( ~ in(v11, v8) |  ~ in(v11, v7) | in(v11, v9)) & (in(v11, v7) | (in(v11, v8) &  ~ in(v11, v9))))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_intersection2(v8, v9) = v10) |  ? [v11] : (( ~ in(v11, v9) |  ~ in(v11, v8) |  ~ in(v11, v7)) & (in(v11, v7) | (in(v11, v9) & in(v11, v8))))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_union2(v8, v9) = v10) |  ? [v11] : (( ~ in(v11, v7) | ( ~ in(v11, v9) &  ~ in(v11, v8))) & (in(v11, v9) | in(v11, v8) | in(v11, v7)))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (unordered_pair(v8, v9) = v10) |  ? [v11] : ((v11 = v9 | v11 = v8 | in(v11, v7)) & ( ~ in(v11, v7) | ( ~ (v11 = v9) &  ~ (v11 = v8))))) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v7, v8) = v9) |  ~ subset(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 | v7 = empty_set |  ~ (singleton(v8) = v9) |  ~ subset(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (set_difference(v7, v8) = v9) |  ~ disjoint(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (singleton(v7) = v8) |  ~ in(v9, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (set_intersection2(v7, v8) = v9) |  ~ subset(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_difference(v7, v8) = v9) |  ~ subset(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_intersection2(v7, v8) = v9) |  ~ disjoint(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (powerset(v9) = v8) |  ~ (powerset(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (singleton(v9) = v8) |  ~ (singleton(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_difference(v7, v8) = v9) | subset(v9, v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_difference(v7, v8) = v9) |  ? [v10] : (set_difference(v10, v8) = v9 & set_union2(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (powerset(v7) = v8) |  ~ subset(v9, v7) | in(v9, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (powerset(v7) = v8) |  ~ in(v9, v8) | subset(v9, v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (singleton(v7) = v9) |  ~ subset(v9, v8) | in(v7, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (singleton(v7) = v9) |  ~ in(v7, v8) | subset(v9, v8)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v8, v7) = v9) | set_intersection2(v7, v8) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | disjoint(v7, v8) |  ? [v10] : in(v10, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | subset(v9, v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) |  ? [v10] : (set_difference(v7, v10) = v9 & set_difference(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v8, v7) = v9) |  ~ empty(v9) | empty(v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v8, v7) = v9) | set_union2(v7, v8) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) |  ~ empty(v9) | empty(v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) | subset(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) |  ? [v10] : (set_difference(v8, v7) = v10 & set_union2(v7, v10) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v8, v7) = v9) | unordered_pair(v7, v8) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | unordered_pair(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v8, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unordered_pair(v7, v8) = v9) | in(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ disjoint(v8, v9) |  ~ subset(v7, v8) | disjoint(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ disjoint(v7, v8) |  ~ in(v9, v8) |  ~ in(v9, v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ subset(v8, v9) |  ~ subset(v7, v8) | subset(v7, v9)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ subset(v7, v8) |  ~ in(v9, v7) | in(v9, v8)) &  ? [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (powerset(v8) = v9) |  ? [v10] : (( ~ subset(v10, v8) |  ~ in(v10, v7)) & (subset(v10, v8) | in(v10, v7)))) &  ? [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (singleton(v8) = v9) |  ? [v10] : (( ~ (v10 = v8) |  ~ in(v8, v7)) & (v10 = v8 | in(v10, v7)))) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_difference(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_intersection2(v7, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_union2(v7, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_union2(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ empty(v8) |  ~ empty(v7)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ subset(v8, v7) |  ~ subset(v7, v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ subset(v7, v8) | proper_subset(v7, v8)) &  ! [v7] :  ! [v8] : (v8 = empty_set |  ~ (set_difference(empty_set, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = empty_set |  ~ (set_intersection2(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : ( ~ (set_difference(v7, v8) = v7) | disjoint(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ (singleton(v8) = v7) | subset(v7, v7)) &  ! [v7] :  ! [v8] : ( ~ (singleton(v7) = v8) | unordered_pair(v7, v7) = v8) &  ! [v7] :  ! [v8] : ( ~ (singleton(v7) = v8) | subset(empty_set, v8)) &  ! [v7] :  ! [v8] : ( ~ (singleton(v7) = v8) | in(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ (set_intersection2(v7, v8) = empty_set) | disjoint(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ (unordered_pair(v7, v7) = v8) | singleton(v7) = v8) &  ! [v7] :  ! [v8] : ( ~ empty(v8) |  ~ in(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ disjoint(v7, v8) | disjoint(v8, v7)) &  ! [v7] :  ! [v8] : ( ~ subset(v7, v8) |  ~ proper_subset(v8, v7)) &  ! [v7] :  ! [v8] : ( ~ proper_subset(v8, v7) |  ~ proper_subset(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ proper_subset(v7, v8) | subset(v7, v8)) &  ! [v7] :  ! [v8] : ( ~ in(v8, v7) |  ~ in(v7, v8)) &  ! [v7] : (v7 = empty_set |  ~ empty(v7)) &  ! [v7] : (v7 = empty_set |  ~ subset(v7, empty_set)) &  ! [v7] :  ~ (singleton(v7) = empty_set) &  ! [v7] :  ~ proper_subset(v7, v7) &  ! [v7] :  ~ in(v7, empty_set) &  ? [v7] :  ? [v8] : (v8 = v7 |  ? [v9] : (( ~ in(v9, v8) |  ~ in(v9, v7)) & (in(v9, v8) | in(v9, v7)))) &  ? [v7] :  ? [v8] : (disjoint(v7, v8) |  ? [v9] : (in(v9, v8) & in(v9, v7))) &  ? [v7] :  ? [v8] : (subset(v7, v8) |  ? [v9] : (in(v9, v7) &  ~ in(v9, v8))) &  ? [v7] : (v7 = empty_set |  ? [v8] : in(v8, v7)) &  ? [v7] : subset(v7, v7) &  ? [v7] : subset(empty_set, v7))
% 5.94/2.00  | 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 yields:
% 5.94/2.00  | (1)  ~ (all_0_3_3 = all_0_4_4) & powerset(empty_set) = all_0_6_6 & singleton(all_0_5_5) = all_0_2_2 & singleton(empty_set) = all_0_6_6 & unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) &  ~ empty(all_0_1_1) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v3) = v4) |  ~ (singleton(v2) = v3) |  ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v3 = v0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ subset(v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3)) &  ! [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] : ( ~ (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, v2) |  ~ in(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ in(v3, v0) | in(v3, v2) | in(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) |  ~ subset(v0, v2) |  ~ subset(v0, v1) | subset(v0, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1) |  ~ in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v2) = v3) |  ~ subset(v2, v1) |  ~ subset(v0, v1) | subset(v3, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1) | in(v3, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v1) | in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v0) | in(v3, v2)) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v1) |  ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) &  ~ in(v4, v2))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v2) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1))))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) &  ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0)))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) &  ~ (v4 = v1))))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_difference(v0, v1) = v2) |  ~ disjoint(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ in(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1)) &  ! [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] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) |  ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ subset(v2, v0) | in(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ in(v2, v1) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ subset(v2, v1) | in(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ in(v0, v1) | subset(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) |  ? [v3] : in(v3, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ disjoint(v1, v2) |  ~ subset(v0, v1) | disjoint(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ disjoint(v0, v1) |  ~ in(v2, v1) |  ~ in(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ in(v2, v0) | in(v2, v1)) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (powerset(v1) = v2) |  ? [v3] : (( ~ subset(v3, v1) |  ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0)))) &  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] : (( ~ (v3 = v1) |  ~ in(v1, v0)) & (v3 = v1 | in(v3, v0)))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1)) &  ! [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 = v0 |  ~ empty(v1) |  ~ empty(v0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v0, v1) | proper_subset(v0, 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] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1) &  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ~ proper_subset(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ proper_subset(v1, v0) |  ~ proper_subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ! [v0] : (v0 = empty_set |  ~ empty(v0)) &  ! [v0] : (v0 = empty_set |  ~ subset(v0, empty_set)) &  ! [v0] :  ~ (singleton(v0) = empty_set) &  ! [v0] :  ~ proper_subset(v0, v0) &  ! [v0] :  ~ in(v0, empty_set) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) &  ? [v0] :  ? [v1] : (disjoint(v0, v1) |  ? [v2] : (in(v2, v1) & in(v2, v0))) &  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (in(v2, v0) &  ~ in(v2, v1))) &  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0)) &  ? [v0] : subset(v0, v0) &  ? [v0] : subset(empty_set, v0)
% 5.94/2.02  |
% 5.94/2.02  | Applying alpha-rule on (1) yields:
% 5.94/2.02  | (2)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v0, v1) | proper_subset(v0, v1))
% 5.94/2.02  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : (set_difference(v1, v0) = v3 & set_union2(v0, v3) = v2))
% 5.94/2.02  | (4)  ! [v0] :  ! [v1] : ( ~ (unordered_pair(v0, v0) = v1) | singleton(v0) = v1)
% 5.94/2.02  | (5)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | unordered_pair(v0, v0) = v1)
% 5.94/2.02  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v1) |  ~ in(v3, v0) | in(v3, v2))
% 5.94/2.02  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 5.94/2.02  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ~ subset(v0, v1))
% 5.94/2.02  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ in(v0, v1) | subset(v2, v1))
% 5.94/2.02  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (singleton(v0) = v2) |  ~ subset(v2, v1) | in(v0, v1))
% 5.94/2.02  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v3) = v4) |  ~ (singleton(v2) = v3) |  ~ subset(v0, v1) | subset(v0, v4) | in(v2, v0))
% 5.94/2.02  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1))
% 5.94/2.02  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 5.94/2.02  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v0, v2))
% 5.94/2.02  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v2) = v3) |  ~ subset(v2, v1) |  ~ subset(v0, v1) | subset(v3, v1))
% 5.94/2.02  | (16)  ! [v0] :  ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 5.94/2.02  | (17)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (in(v2, v0) &  ~ in(v2, v1)))
% 5.94/2.02  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v0) | in(v3, v2))
% 5.94/2.02  | (19)  ! [v0] : (v0 = empty_set |  ~ empty(v0))
% 5.94/2.02  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 5.94/2.03  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0))
% 5.94/2.03  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 5.94/2.03  | (23)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 5.94/2.03  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ subset(v0, v1))
% 5.94/2.03  | (25)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1))
% 5.94/2.03  | (26)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) | subset(v2, v0))
% 5.94/2.03  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v1, v2) = v3) |  ~ subset(v0, v2) |  ~ subset(v0, v1) | subset(v0, v3))
% 5.94/2.03  | (28)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v1) = v2) |  ? [v3] : (( ~ (v3 = v1) |  ~ in(v1, v0)) & (v3 = v1 | in(v3, v0))))
% 5.94/2.03  | (29)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 5.94/2.03  | (30)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (singleton(v0) = v1) |  ~ in(v2, v1))
% 5.94/2.03  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v2) = v3) |  ~ (set_difference(v0, v1) = v2) | set_intersection2(v0, v1) = v3)
% 5.94/2.03  | (32)  ? [v0] :  ? [v1] : (disjoint(v0, v1) |  ? [v2] : (in(v2, v1) & in(v2, v0)))
% 5.94/2.03  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v1) | in(v3, v0))
% 5.94/2.03  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 5.94/2.03  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 5.94/2.03  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) | set_union2(v0, v1) = v3)
% 5.94/2.03  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 5.94/2.03  | (38)  ? [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (powerset(v1) = v2) |  ? [v3] : (( ~ subset(v3, v1) |  ~ in(v3, v0)) & (subset(v3, v1) | in(v3, v0))))
% 5.94/2.03  | (39)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ in(v2, v0) | in(v2, v1))
% 5.94/2.03  | (40)  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0))
% 5.94/2.03  | (41)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 5.94/2.03  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v1, v0) = v2) | unordered_pair(v0, v1) = v2)
% 5.94/2.03  | (43)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 5.94/2.03  | (44)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : (set_difference(v0, v3) = v2 & set_difference(v0, v1) = v3))
% 5.94/2.03  | (45)  ? [v0] : subset(empty_set, v0)
% 5.94/2.03  | (46)  ! [v0] :  ~ proper_subset(v0, v0)
% 5.94/2.03  | (47) empty(empty_set)
% 5.94/2.03  | (48)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (powerset(v2) = v1) |  ~ (powerset(v2) = v0))
% 5.94/2.03  | (49) powerset(empty_set) = all_0_6_6
% 5.94/2.03  | (50)  ! [v0] :  ! [v1] : ( ~ proper_subset(v0, v1) | subset(v0, v1))
% 5.94/2.03  | (51)  ! [v0] :  ~ in(v0, empty_set)
% 5.94/2.03  | (52)  ! [v0] :  ~ (singleton(v0) = empty_set)
% 5.94/2.03  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1) |  ~ in(v3, v2))
% 5.94/2.03  | (54)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v0) | ( ~ in(v4, v2) &  ~ in(v4, v1))) & (in(v4, v2) | in(v4, v1) | in(v4, v0))))
% 5.94/2.03  | (55)  ! [v0] :  ! [v1] : ( ~ disjoint(v0, v1) | disjoint(v1, v0))
% 5.94/2.03  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
% 5.94/2.03  | (57)  ~ (all_0_3_3 = all_0_4_4)
% 5.94/2.03  | (58)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_difference(v0, v1) = v2) |  ~ disjoint(v0, v1))
% 5.94/2.03  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v1) = v3) |  ~ (singleton(v0) = v2) |  ~ subset(v2, v3))
% 5.94/2.04  | (60) unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2
% 5.94/2.04  | (61)  ! [v0] :  ! [v1] : ( ~ empty(v1) |  ~ in(v0, v1))
% 5.94/2.04  | (62)  ! [v0] : (v0 = empty_set |  ~ subset(v0, empty_set))
% 5.94/2.04  | (63)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 6.20/2.04  | (64) singleton(all_0_5_5) = all_0_2_2
% 6.20/2.04  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | disjoint(v0, v1) |  ? [v3] : in(v3, v2))
% 6.20/2.04  | (66)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ subset(v0, v2))
% 6.20/2.04  | (67)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (singleton(v0) = v3) |  ~ (unordered_pair(v1, v2) = v3))
% 6.20/2.04  | (68)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ~ disjoint(v0, v1))
% 6.20/2.04  | (69)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ disjoint(v1, v2) |  ~ subset(v0, v1) | disjoint(v0, v2))
% 6.20/2.04  | (70)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | in(v0, v1))
% 6.20/2.04  | (71) empty(all_0_0_0)
% 6.20/2.04  | (72)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v1, v2) = v4) |  ~ (set_intersection2(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4))
% 6.20/2.04  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 |  ~ (set_difference(v1, v0) = v2) |  ~ (set_union2(v0, v2) = v3) |  ~ subset(v0, v1))
% 6.20/2.04  | (74)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ empty(v1) |  ~ empty(v0))
% 6.20/2.04  | (75)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1))
% 6.20/2.04  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ in(v3, v0) | in(v3, v2) | in(v3, v1))
% 6.20/2.04  | (77)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 6.20/2.04  | (78)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ~ subset(v0, v1))
% 6.20/2.04  | (79)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ~ empty(v2) | empty(v0))
% 6.20/2.04  | (80)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1))
% 6.20/2.04  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v1 | v3 = v0 |  ~ (unordered_pair(v0, v1) = v2) |  ~ in(v3, v2))
% 6.20/2.04  | (82)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 6.20/2.04  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 6.20/2.04  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_difference(v1, v2) = v4) |  ~ (set_difference(v0, v2) = v3) |  ~ subset(v0, v1) | subset(v3, v4))
% 6.20/2.04  | (85)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | in(v1, v2))
% 6.20/2.04  | (86)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ~ empty(v2) | empty(v0))
% 6.20/2.04  | (87)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | subset(v2, v0))
% 6.20/2.04  | (88)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = v0) | disjoint(v0, v1))
% 6.20/2.04  | (89)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 6.20/2.04  | (90) singleton(empty_set) = all_0_6_6
% 6.20/2.04  | (91)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ disjoint(v0, v1) |  ~ in(v2, v1) |  ~ in(v2, v0))
% 6.20/2.05  | (92)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2))
% 6.20/2.05  | (93)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_difference(v0, v1) = v2) |  ? [v3] : (set_difference(v3, v1) = v2 & set_union2(v0, v1) = v3))
% 6.20/2.05  | (94)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2))
% 6.20/2.05  | (95)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ in(v3, v1) | in(v3, v2))
% 6.20/2.05  | (96)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v2, v1) = v3) |  ~ (set_union2(v0, v1) = v2) | set_difference(v0, v1) = v3)
% 6.20/2.05  | (97)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v2) |  ~ in(v4, v1) |  ~ in(v4, v0)) & (in(v4, v0) | (in(v4, v2) & in(v4, v1)))))
% 6.20/2.05  | (98)  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ~ proper_subset(v1, v0))
% 6.20/2.05  | (99)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 6.20/2.05  | (100)  ! [v0] :  ! [v1] : ( ~ proper_subset(v1, v0) |  ~ proper_subset(v0, v1))
% 6.20/2.05  | (101)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ in(v3, v2) | in(v3, v0))
% 6.20/2.05  | (102)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_difference(v1, v2) = v3) |  ? [v4] : (( ~ in(v4, v1) |  ~ in(v4, v0) | in(v4, v2)) & (in(v4, v0) | (in(v4, v1) &  ~ in(v4, v2)))))
% 6.20/2.05  | (103)  ? [v0] : subset(v0, v0)
% 6.20/2.05  | (104)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ in(v2, v1) | subset(v2, v0))
% 6.20/2.05  | (105)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (powerset(v0) = v1) |  ~ subset(v2, v0) | in(v2, v1))
% 6.20/2.05  | (106)  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1))
% 6.20/2.05  | (107)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (unordered_pair(v1, v2) = v3) |  ? [v4] : ((v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ in(v4, v0) | ( ~ (v4 = v2) &  ~ (v4 = v1)))))
% 6.20/2.05  | (108)  ~ empty(all_0_1_1)
% 6.20/2.05  | (109)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_difference(v0, v1) = v2) |  ~ in(v3, v2) |  ~ in(v3, v1))
% 6.20/2.05  |
% 6.20/2.05  | Instantiating formula (67) with all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, unordered_pair(all_0_4_4, all_0_3_3) = all_0_2_2, yields:
% 6.20/2.05  | (110) all_0_4_4 = all_0_5_5
% 6.20/2.05  |
% 6.20/2.05  | Equations (110) can reduce 57 to:
% 6.20/2.05  | (111)  ~ (all_0_3_3 = all_0_5_5)
% 6.20/2.05  |
% 6.20/2.05  | From (110) and (60) follows:
% 6.20/2.05  | (112) unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2
% 6.20/2.05  |
% 6.20/2.05  | Instantiating formula (85) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms unordered_pair(all_0_5_5, all_0_3_3) = all_0_2_2, yields:
% 6.20/2.05  | (113) in(all_0_3_3, all_0_2_2)
% 6.20/2.05  |
% 6.20/2.05  | Instantiating formula (30) with all_0_3_3, all_0_2_2, all_0_5_5 and discharging atoms singleton(all_0_5_5) = all_0_2_2, in(all_0_3_3, all_0_2_2), yields:
% 6.20/2.05  | (114) all_0_3_3 = all_0_5_5
% 6.20/2.05  |
% 6.20/2.05  | Equations (114) can reduce 111 to:
% 6.20/2.05  | (115) $false
% 6.20/2.05  |
% 6.20/2.05  |-The branch is then unsatisfiable
% 6.20/2.05  % SZS output end Proof for theBenchmark
% 6.20/2.05  
% 6.20/2.05  1465ms
%------------------------------------------------------------------------------