%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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 08:46:46 EDT 2022

% Result   : Theorem 6.14s 2.06s
% Output   : Proof 7.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SEU126+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n017.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Mon Jun 20 09:52:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.47/0.58          ____       _                          
% 0.47/0.58    ___  / __ \_____(_)___  ________  __________
% 0.47/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.47/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.47/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.47/0.58  
% 0.47/0.58  A Theorem Prover for First-Order Logic
% 0.47/0.58  (ePrincess v.1.0)
% 0.47/0.58  
% 0.47/0.58  (c) Philipp Rümmer, 2009-2015
% 0.47/0.58  (c) Peter Backeman, 2014-2015
% 0.47/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.47/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.47/0.58  Bug reports to peter@backeman.se
% 0.47/0.58  
% 0.47/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.47/0.58  
% 0.47/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.92  Prover 0: Preprocessing ...
% 2.17/1.14  Prover 0: Warning: ignoring some quantifiers
% 2.25/1.16  Prover 0: Constructing countermodel ...
% 3.95/1.61  Prover 0: gave up
% 3.95/1.61  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.95/1.64  Prover 1: Preprocessing ...
% 4.71/1.74  Prover 1: Warning: ignoring some quantifiers
% 4.71/1.74  Prover 1: Constructing countermodel ...
% 5.26/1.87  Prover 1: gave up
% 5.26/1.87  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 5.26/1.90  Prover 2: Preprocessing ...
% 5.86/1.99  Prover 2: Warning: ignoring some quantifiers
% 5.86/2.00  Prover 2: Constructing countermodel ...
% 6.14/2.06  Prover 2: proved (182ms)
% 6.14/2.06  
% 6.14/2.06  No countermodel exists, formula is valid
% 6.14/2.06  % SZS status Theorem for theBenchmark
% 6.14/2.06  
% 6.14/2.06  Generating proof ... Warning: ignoring some quantifiers
% 7.41/2.34  found it (size 32)
% 7.41/2.34  
% 7.41/2.34  % SZS output start Proof for theBenchmark
% 7.41/2.34  Assumed formulas after preprocessing and simplification: 
% 7.41/2.34  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v4 = 0) &  ~ (v2 = v1) & empty(v5) = 0 & empty(v3) = v4 & empty(empty_set) = 0 & subset(v0, v1) = 0 & set_union2(v0, v1) = v2 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v9, v7) = v10) |  ~ (set_union2(v6, v8) = v9) |  ? [v11] : (( ~ (v11 = 0) & subset(v8, v7) = v11) | ( ~ (v11 = 0) & subset(v6, v7) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v8) = v10) |  ? [v11] : (( ~ (v11 = 0) & in(v9, v7) = v11) | ( ~ (v11 = 0) & in(v9, v6) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (set_union2(v6, v7) = v8) |  ~ (in(v9, v8) = v10) |  ? [v11] :  ? [v12] : ( ~ (v12 = 0) &  ~ (v11 = 0) & in(v9, v7) = v12 & in(v9, v6) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (set_union2(v6, v7) = v8) |  ~ (in(v9, v7) = v10) |  ? [v11] : ((v11 = 0 & in(v9, v6) = 0) | ( ~ (v11 = 0) & in(v9, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (set_union2(v6, v7) = v8) |  ~ (in(v9, v6) = v10) |  ? [v11] : ((v11 = 0 & in(v9, v7) = 0) | ( ~ (v11 = 0) & in(v9, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v7) = v10) |  ? [v11] : ((v11 = 0 & v10 = 0 & in(v9, v6) = 0) | ( ~ (v11 = 0) & in(v9, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v6) = v10) |  ? [v11] : ((v11 = 0 & v10 = 0 & in(v9, v7) = 0) | ( ~ (v11 = 0) & in(v9, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v6, v7) = v8) |  ~ (in(v9, v7) = v10) |  ? [v11] : ((v11 = 0 & in(v9, v8) = 0) | ( ~ (v11 = 0) &  ~ (v10 = 0) & in(v9, v6) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_union2(v6, v7) = v8) |  ~ (in(v9, v6) = v10) |  ? [v11] : ((v11 = 0 & in(v9, v8) = 0) | ( ~ (v11 = 0) &  ~ (v10 = 0) & in(v9, v7) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v7, v8) = 0) |  ~ (subset(v6, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v6, v7) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v6, v8) = v9) |  ~ (subset(v6, v7) = 0) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v6, v7) = 0) |  ~ (in(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & in(v8, v6) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (disjoint(v9, v8) = v7) |  ~ (disjoint(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (subset(v9, v8) = v7) |  ~ (subset(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (set_intersection2(v9, v8) = v7) |  ~ (set_intersection2(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (set_union2(v9, v8) = v7) |  ~ (set_union2(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (in(v9, v8) = v7) |  ~ (in(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v8) = 0) |  ? [v10] : ( ~ (v10 = 0) & disjoint(v6, v7) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v8) = 0) | (in(v9, v7) = 0 & in(v9, v6) = 0)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v7) = 0) |  ? [v10] : ((v10 = 0 & in(v9, v8) = 0) | ( ~ (v10 = 0) & in(v9, v6) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v6, v7) = v8) |  ~ (in(v9, v6) = 0) |  ? [v10] : ((v10 = 0 & in(v9, v8) = 0) | ( ~ (v10 = 0) & in(v9, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v6, v7) = v8) |  ~ (in(v9, v8) = 0) |  ? [v10] : ((v10 = 0 & in(v9, v7) = 0) | (v10 = 0 & in(v9, v6) = 0))) &  ? [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v6 |  ~ (set_intersection2(v7, v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (((v13 = 0 & v12 = 0 & in(v10, v8) = 0 & in(v10, v7) = 0) | (v11 = 0 & in(v10, v6) = 0)) & (( ~ (v13 = 0) & in(v10, v8) = v13) | ( ~ (v12 = 0) & in(v10, v7) = v12) | ( ~ (v11 = 0) & in(v10, v6) = v11)))) &  ? [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v6 |  ~ (set_union2(v7, v8) = v9) |  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (((v13 = 0 & in(v10, v8) = 0) | (v12 = 0 & in(v10, v7) = 0) | (v11 = 0 & in(v10, v6) = 0)) & (( ~ (v13 = 0) &  ~ (v12 = 0) & in(v10, v8) = v13 & in(v10, v7) = v12) | ( ~ (v11 = 0) & in(v10, v6) = v11)))) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = empty_set |  ~ (set_intersection2(v6, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & disjoint(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (disjoint(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = 0) & disjoint(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (disjoint(v6, v7) = v8) |  ? [v9] :  ? [v10] : (set_intersection2(v6, v7) = v9 & in(v10, v9) = 0)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (disjoint(v6, v7) = v8) |  ? [v9] : ( ~ (v9 = empty_set) & set_intersection2(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (disjoint(v6, v7) = v8) |  ? [v9] : (in(v9, v7) = 0 & in(v9, v6) = 0)) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (subset(v6, v7) = v8) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & in(v9, v7) = v10 & in(v9, v6) = 0)) &  ! [v6] :  ! [v7] :  ! [v8] : (v7 = v6 |  ~ (empty(v8) = v7) |  ~ (empty(v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (disjoint(v6, v7) = 0) |  ~ (in(v8, v7) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v6) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (disjoint(v6, v7) = 0) |  ~ (in(v8, v6) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (subset(v7, v8) = 0) |  ~ (subset(v6, v7) = 0) | subset(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (subset(v6, v7) = 0) |  ~ (in(v8, v6) = 0) | in(v8, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_intersection2(v7, v6) = v8) | set_intersection2(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_intersection2(v6, v7) = v8) | set_intersection2(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_intersection2(v6, v7) = v8) |  ? [v9] :  ? [v10] : ((v10 = 0 & in(v9, v8) = 0) | (v9 = 0 & disjoint(v6, v7) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_union2(v7, v6) = v8) | set_union2(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_union2(v7, v6) = v8) |  ? [v9] : ((v9 = 0 & empty(v6) = 0) | ( ~ (v9 = 0) & empty(v8) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_union2(v6, v7) = v8) | subset(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_union2(v6, v7) = v8) | set_union2(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (set_union2(v6, v7) = v8) |  ? [v9] : ((v9 = 0 & empty(v6) = 0) | ( ~ (v9 = 0) & empty(v8) = v9))) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (empty(v7) = 0) |  ~ (empty(v6) = 0)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (subset(v7, v6) = 0) |  ? [v8] : ( ~ (v8 = 0) & subset(v6, v7) = v8)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (subset(v6, v7) = 0) |  ? [v8] : ( ~ (v8 = 0) & subset(v7, v6) = v8)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (set_intersection2(v6, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (set_union2(v6, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ (set_union2(v6, empty_set) = v7)) &  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (subset(v6, v6) = v7)) &  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (subset(empty_set, v6) = v7)) &  ! [v6] :  ! [v7] : ( ~ (disjoint(v6, v7) = 0) | disjoint(v7, v6) = 0) &  ! [v6] :  ! [v7] : ( ~ (disjoint(v6, v7) = 0) | set_intersection2(v6, v7) = empty_set) &  ! [v6] :  ! [v7] : ( ~ (disjoint(v6, v7) = 0) |  ? [v8] : (set_intersection2(v6, v7) = v8 &  ! [v9] :  ~ (in(v9, v8) = 0))) &  ! [v6] :  ! [v7] : ( ~ (set_intersection2(v6, v7) = empty_set) | disjoint(v6, v7) = 0) &  ! [v6] :  ! [v7] : ( ~ (in(v7, v6) = 0) |  ? [v8] : ( ~ (v8 = 0) & in(v6, v7) = v8)) &  ! [v6] :  ! [v7] : ( ~ (in(v6, v7) = 0) |  ? [v8] : ( ~ (v8 = 0) & empty(v7) = v8)) &  ! [v6] :  ! [v7] : ( ~ (in(v6, v7) = 0) |  ? [v8] : ( ~ (v8 = 0) & in(v7, v6) = v8)) &  ! [v6] : (v6 = empty_set |  ~ (empty(v6) = 0)) &  ! [v6] : (v6 = empty_set |  ~ (subset(v6, empty_set) = 0)) &  ! [v6] :  ~ (in(v6, empty_set) = 0) &  ? [v6] :  ? [v7] :  ? [v8] : disjoint(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : subset(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : set_intersection2(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : set_union2(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : in(v7, v6) = v8 &  ? [v6] :  ? [v7] : empty(v6) = v7 &  ? [v6] : (v6 = empty_set |  ? [v7] : in(v7, v6) = 0))
% 7.41/2.39  | 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 yields:
% 7.41/2.39  | (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_3_3 = all_0_4_4) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & subset(all_0_5_5, all_0_4_4) = 0 & set_union2(all_0_5_5, all_0_4_4) = all_0_3_3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v1) = v4) |  ~ (set_union2(v0, v2) = v3) |  ? [v5] : (( ~ (v5 = 0) & subset(v2, v1) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) &  ~ (v4 = 0) & in(v3, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) &  ~ (v4 = 0) & in(v3, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v1, v2) = 0) |  ~ (subset(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) &  ! [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, v1) = 0) |  ~ (in(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0)) &  ! [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 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0)) &  ! [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, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = 0) |  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) &  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) &  ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5)))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] :  ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(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 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v1, v2) = 0) |  ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0) &  ! [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) |  ? [v3] :  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2)) &  ! [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 = 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_intersection2(v0, v1) = empty_set) &  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) |  ? [v2] : (set_intersection2(v0, v1) = v2 &  ! [v3] :  ~ (in(v3, v2) = 0))) &  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (in(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = 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] :  ~ (in(v0, empty_set) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : disjoint(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : set_intersection2(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : set_union2(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2 &  ? [v0] :  ? [v1] : empty(v0) = v1 &  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 7.41/2.41  |
% 7.41/2.41  | Applying alpha-rule on (1) yields:
% 7.41/2.41  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = 0) |  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v0) = v4)))
% 7.41/2.41  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] :  ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 7.41/2.41  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ? [v5] : (( ~ (v5 = 0) & in(v3, v1) = v5) | ( ~ (v5 = 0) & in(v3, v0) = v5)))
% 7.41/2.41  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 7.41/2.41  | (6)  ? [v0] :  ? [v1] :  ? [v2] : set_intersection2(v1, v0) = v2
% 7.41/2.41  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v2) = v4) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5))
% 7.41/2.41  | (8)  ! [v0] :  ! [v1] : ( ~ (set_intersection2(v0, v1) = empty_set) | disjoint(v0, v1) = 0)
% 7.41/2.41  | (9)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 7.41/2.41  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 7.41/2.41  | (11)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_union2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (((v7 = 0 & in(v4, v2) = 0) | (v6 = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) &  ~ (v6 = 0) & in(v4, v2) = v7 & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 7.41/2.41  | (12)  ? [v0] :  ? [v1] : empty(v0) = v1
% 7.41/2.41  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4))
% 7.41/2.41  | (14)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 7.41/2.42  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 7.41/2.42  | (16)  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0))
% 7.41/2.42  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) &  ~ (v4 = 0) & in(v3, v1) = v5)))
% 7.41/2.42  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) |  ? [v4] : ((v4 = 0 & in(v3, v1) = 0) | (v4 = 0 & in(v3, v0) = 0)))
% 7.41/2.42  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 7.41/2.42  | (20)  ! [v0] :  ! [v1] : ( ~ (in(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v0, v1) = v2))
% 7.41/2.42  | (21) subset(all_0_5_5, all_0_4_4) = 0
% 7.41/2.42  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 7.41/2.42  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v1, v0) = v2) | set_intersection2(v0, v1) = v2)
% 7.41/2.42  | (24)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 7.41/2.42  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) |  ? [v3] :  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))
% 7.41/2.42  | (26)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 7.41/2.42  | (27)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 7.41/2.42  | (28)  ! [v0] :  ~ (in(v0, empty_set) = 0)
% 7.41/2.42  | (29)  ~ (all_0_1_1 = 0)
% 7.41/2.42  | (30)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v0) = v3))
% 7.41/2.42  | (31)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 7.41/2.42  | (32) set_union2(all_0_5_5, all_0_4_4) = all_0_3_3
% 7.41/2.42  | (33)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) |  ? [v2] : (set_intersection2(v0, v1) = v2 &  ! [v3] :  ~ (in(v3, v2) = 0)))
% 7.41/2.42  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 7.41/2.42  | (35)  ? [v0] :  ? [v1] :  ? [v2] : disjoint(v1, v0) = v2
% 7.41/2.42  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (subset(v3, v1) = v4) |  ~ (set_union2(v0, v2) = v3) |  ? [v5] : (( ~ (v5 = 0) & subset(v2, v1) = v5) | ( ~ (v5 = 0) & subset(v0, v1) = v5)))
% 7.41/2.42  | (37)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 7.41/2.42  | (38)  ? [v0] :  ? [v1] :  ? [v2] : set_union2(v1, v0) = v2
% 7.41/2.42  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 7.41/2.42  | (40)  ? [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (set_intersection2(v1, v2) = v3) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (((v7 = 0 & v6 = 0 & in(v4, v2) = 0 & in(v4, v1) = 0) | (v5 = 0 & in(v4, v0) = 0)) & (( ~ (v7 = 0) & in(v4, v2) = v7) | ( ~ (v6 = 0) & in(v4, v1) = v6) | ( ~ (v5 = 0) & in(v4, v0) = v5))))
% 7.41/2.43  | (41)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 7.41/2.43  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 7.41/2.43  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v2) = 0) | (in(v3, v1) = 0 & in(v3, v0) = 0))
% 7.41/2.43  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v1) = 0) |  ~ (in(v2, v1) = v3) |  ? [v4] : ( ~ (v4 = 0) & in(v2, v0) = v4))
% 7.41/2.43  | (45)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 7.41/2.43  | (46)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 7.41/2.43  | (47)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) | set_union2(v0, v1) = v2)
% 7.41/2.43  | (48)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 7.41/2.43  | (49)  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 7.41/2.43  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 7.41/2.43  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v0) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 7.41/2.43  | (52)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 7.41/2.43  | (53)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & disjoint(v0, v1) = v3))
% 7.41/2.43  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = 0) |  ? [v4] : ((v4 = 0 & in(v3, v2) = 0) | ( ~ (v4 = 0) & in(v3, v1) = v4)))
% 7.41/2.43  | (55) empty(all_0_0_0) = 0
% 7.41/2.43  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_union2(v0, v1) = v2) |  ~ (in(v3, v1) = v4) |  ? [v5] : ((v5 = 0 & in(v3, v2) = 0) | ( ~ (v5 = 0) &  ~ (v4 = 0) & in(v3, v0) = v5)))
% 7.41/2.43  | (57)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 7.87/2.43  | (58)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 7.87/2.43  | (59)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1))
% 7.87/2.43  | (60)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 7.87/2.43  | (61)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 7.87/2.43  | (62) empty(empty_set) = 0
% 7.87/2.44  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (set_intersection2(v0, v1) = v2) |  ~ (in(v3, v0) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & in(v3, v1) = 0) | ( ~ (v5 = 0) & in(v3, v2) = v5)))
% 7.87/2.44  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 7.87/2.44  | (65)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 7.87/2.44  | (66)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | subset(v0, v2) = 0)
% 7.87/2.44  | (67)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 7.87/2.44  | (68)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 7.87/2.44  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v1, v2) = 0) |  ~ (subset(v0, v2) = v3) |  ? [v4] : ( ~ (v4 = 0) & subset(v0, v1) = v4))
% 7.87/2.44  | (70)  ? [v0] :  ? [v1] :  ? [v2] : in(v1, v0) = v2
% 7.87/2.44  | (71)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 7.87/2.44  | (72)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & empty(v0) = 0) | ( ~ (v3 = 0) & empty(v2) = v3)))
% 7.87/2.44  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 7.87/2.44  | (74) empty(all_0_2_2) = all_0_1_1
% 7.87/2.44  | (75)  ~ (all_0_3_3 = all_0_4_4)
% 7.87/2.44  | (76)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v1, v2) = 0) |  ~ (subset(v0, v1) = 0) | subset(v0, v2) = 0)
% 7.87/2.44  |
% 7.87/2.44  | Instantiating formula (47) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms set_union2(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 7.87/2.44  | (77) set_union2(all_0_4_4, all_0_5_5) = all_0_3_3
% 7.87/2.44  |
% 7.87/2.44  | Instantiating formula (66) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms set_union2(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 7.87/2.44  | (78) subset(all_0_4_4, all_0_3_3) = 0
% 7.87/2.44  |
% 7.87/2.44  | Instantiating formula (67) with all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_4_4, all_0_3_3) = 0, yields:
% 7.87/2.44  | (79) all_0_3_3 = all_0_4_4 |  ? [v0] : ( ~ (v0 = 0) & subset(all_0_3_3, all_0_4_4) = v0)
% 7.87/2.44  |
% 7.87/2.44  +-Applying beta-rule and splitting (79), into two cases.
% 7.87/2.44  |-Branch one:
% 7.87/2.44  | (80) all_0_3_3 = all_0_4_4
% 7.87/2.44  |
% 7.87/2.44  	| Equations (80) can reduce 75 to:
% 7.87/2.44  	| (81) $false
% 7.87/2.44  	|
% 7.87/2.44  	|-The branch is then unsatisfiable
% 7.87/2.44  |-Branch two:
% 7.87/2.44  | (75)  ~ (all_0_3_3 = all_0_4_4)
% 7.87/2.44  | (83)  ? [v0] : ( ~ (v0 = 0) & subset(all_0_3_3, all_0_4_4) = v0)
% 7.87/2.44  |
% 7.87/2.44  	| Instantiating (83) with all_51_0_30 yields:
% 7.87/2.44  	| (84)  ~ (all_51_0_30 = 0) & subset(all_0_3_3, all_0_4_4) = all_51_0_30
% 7.87/2.44  	|
% 7.87/2.44  	| Applying alpha-rule on (84) yields:
% 7.87/2.44  	| (85)  ~ (all_51_0_30 = 0)
% 7.87/2.44  	| (86) subset(all_0_3_3, all_0_4_4) = all_51_0_30
% 7.87/2.44  	|
% 7.87/2.44  	| Instantiating formula (36) with all_51_0_30, all_0_3_3, all_0_4_4, all_0_4_4, all_0_5_5 and discharging atoms subset(all_0_3_3, all_0_4_4) = all_51_0_30, set_union2(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 7.87/2.44  	| (87) all_51_0_30 = 0 |  ? [v0] : (( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_5_5, all_0_4_4) = v0))
% 7.87/2.44  	|
% 7.87/2.44  	| Instantiating formula (69) with all_51_0_30, all_0_4_4, all_0_5_5, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = all_51_0_30, subset(all_0_5_5, all_0_4_4) = 0, yields:
% 7.87/2.44  	| (88) all_51_0_30 = 0 |  ? [v0] : ( ~ (v0 = 0) & subset(all_0_3_3, all_0_5_5) = v0)
% 7.87/2.44  	|
% 7.87/2.44  	| Instantiating formula (71) with all_51_0_30, all_0_4_4, all_0_3_3 and discharging atoms subset(all_0_3_3, all_0_4_4) = all_51_0_30, yields:
% 7.87/2.44  	| (89) all_51_0_30 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_3_3) = 0 & in(v0, all_0_4_4) = v1)
% 7.87/2.44  	|
% 7.87/2.44  	+-Applying beta-rule and splitting (89), into two cases.
% 7.87/2.44  	|-Branch one:
% 7.87/2.44  	| (90) all_51_0_30 = 0
% 7.87/2.45  	|
% 7.87/2.45  		| Equations (90) can reduce 85 to:
% 7.87/2.45  		| (81) $false
% 7.87/2.45  		|
% 7.87/2.45  		|-The branch is then unsatisfiable
% 7.87/2.45  	|-Branch two:
% 7.87/2.45  	| (85)  ~ (all_51_0_30 = 0)
% 7.87/2.45  	| (93)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_3_3) = 0 & in(v0, all_0_4_4) = v1)
% 7.87/2.45  	|
% 7.87/2.45  		+-Applying beta-rule and splitting (88), into two cases.
% 7.87/2.45  		|-Branch one:
% 7.87/2.45  		| (90) all_51_0_30 = 0
% 7.87/2.45  		|
% 7.87/2.45  			| Equations (90) can reduce 85 to:
% 7.87/2.45  			| (81) $false
% 7.87/2.45  			|
% 7.87/2.45  			|-The branch is then unsatisfiable
% 7.87/2.45  		|-Branch two:
% 7.87/2.45  		| (85)  ~ (all_51_0_30 = 0)
% 7.87/2.45  		| (97)  ? [v0] : ( ~ (v0 = 0) & subset(all_0_3_3, all_0_5_5) = v0)
% 7.87/2.45  		|
% 7.87/2.45  			+-Applying beta-rule and splitting (87), into two cases.
% 7.87/2.45  			|-Branch one:
% 7.87/2.45  			| (90) all_51_0_30 = 0
% 7.87/2.45  			|
% 7.87/2.45  				| Equations (90) can reduce 85 to:
% 7.87/2.45  				| (81) $false
% 7.87/2.45  				|
% 7.87/2.45  				|-The branch is then unsatisfiable
% 7.87/2.45  			|-Branch two:
% 7.87/2.45  			| (85)  ~ (all_51_0_30 = 0)
% 7.87/2.45  			| (101)  ? [v0] : (( ~ (v0 = 0) & subset(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & subset(all_0_5_5, all_0_4_4) = v0))
% 7.87/2.45  			|
% 7.87/2.45  				| Instantiating (101) with all_74_0_34 yields:
% 7.87/2.45  				| (102) ( ~ (all_74_0_34 = 0) & subset(all_0_4_4, all_0_4_4) = all_74_0_34) | ( ~ (all_74_0_34 = 0) & subset(all_0_5_5, all_0_4_4) = all_74_0_34)
% 7.87/2.45  				|
% 7.87/2.45  				+-Applying beta-rule and splitting (102), into two cases.
% 7.87/2.45  				|-Branch one:
% 7.87/2.45  				| (103)  ~ (all_74_0_34 = 0) & subset(all_0_4_4, all_0_4_4) = all_74_0_34
% 7.87/2.45  				|
% 7.87/2.45  					| Applying alpha-rule on (103) yields:
% 7.87/2.45  					| (104)  ~ (all_74_0_34 = 0)
% 7.87/2.45  					| (105) subset(all_0_4_4, all_0_4_4) = all_74_0_34
% 7.87/2.45  					|
% 7.87/2.45  					| Instantiating formula (14) with all_74_0_34, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_4_4) = all_74_0_34, yields:
% 7.87/2.45  					| (106) all_74_0_34 = 0
% 7.87/2.45  					|
% 7.87/2.45  					| Equations (106) can reduce 104 to:
% 7.87/2.45  					| (81) $false
% 7.87/2.45  					|
% 7.87/2.45  					|-The branch is then unsatisfiable
% 7.87/2.45  				|-Branch two:
% 7.87/2.45  				| (108)  ~ (all_74_0_34 = 0) & subset(all_0_5_5, all_0_4_4) = all_74_0_34
% 7.87/2.45  				|
% 7.87/2.45  					| Applying alpha-rule on (108) yields:
% 7.87/2.45  					| (104)  ~ (all_74_0_34 = 0)
% 7.87/2.45  					| (110) subset(all_0_5_5, all_0_4_4) = all_74_0_34
% 7.87/2.45  					|
% 7.87/2.45  					| Instantiating formula (64) with all_0_5_5, all_0_4_4, all_74_0_34, 0 and discharging atoms subset(all_0_5_5, all_0_4_4) = all_74_0_34, subset(all_0_5_5, all_0_4_4) = 0, yields:
% 7.87/2.45  					| (106) all_74_0_34 = 0
% 7.87/2.45  					|
% 7.87/2.45  					| Equations (106) can reduce 104 to:
% 7.87/2.45  					| (81) $false
% 7.87/2.45  					|
% 7.87/2.45  					|-The branch is then unsatisfiable
% 7.87/2.45  % SZS output end Proof for theBenchmark
% 7.87/2.45  
% 7.87/2.45  1856ms
%------------------------------------------------------------------------------