%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU133+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n029.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 08:46:50 EDT 2022

% Result   : Theorem 4.79s 1.75s
% Output   : Proof 6.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : SEU133+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.33  % Computer : n029.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sun Jun 19 22:40:15 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.17/0.57          ____       _                          
% 0.17/0.57    ___  / __ \_____(_)___  ________  __________
% 0.17/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.17/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.17/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.17/0.57  
% 0.17/0.57  A Theorem Prover for First-Order Logic
% 0.17/0.57  (ePrincess v.1.0)
% 0.17/0.57  
% 0.17/0.57  (c) Philipp Rümmer, 2009-2015
% 0.17/0.57  (c) Peter Backeman, 2014-2015
% 0.17/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.17/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.17/0.57  Bug reports to peter@backeman.se
% 0.17/0.57  
% 0.17/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.17/0.57  
% 0.17/0.57  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/0.92  Prover 0: Preprocessing ...
% 2.56/1.19  Prover 0: Warning: ignoring some quantifiers
% 2.61/1.21  Prover 0: Constructing countermodel ...
% 3.94/1.52  Prover 0: gave up
% 3.94/1.52  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.04/1.56  Prover 1: Preprocessing ...
% 4.79/1.70  Prover 1: Warning: ignoring some quantifiers
% 4.79/1.70  Prover 1: Constructing countermodel ...
% 4.79/1.75  Prover 1: proved (224ms)
% 4.79/1.75  
% 4.79/1.75  No countermodel exists, formula is valid
% 4.79/1.75  % SZS status Theorem for theBenchmark
% 4.79/1.75  
% 4.79/1.75  Generating proof ... Warning: ignoring some quantifiers
% 5.88/1.97  found it (size 18)
% 5.88/1.97  
% 5.88/1.97  % SZS output start Proof for theBenchmark
% 5.88/1.97  Assumed formulas after preprocessing and simplification: 
% 5.88/1.97  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : ( ~ (v5 = 0) &  ~ (v3 = 0) & empty(v6) = 0 & empty(v4) = v5 & empty(empty_set) = 0 & set_difference(v0, v1) = v2 & subset(v2, v0) = v3 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (set_difference(v8, v9) = v11) |  ~ (set_difference(v7, v9) = v10) |  ~ (subset(v10, v11) = v12) |  ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 |  ~ (subset(v10, v11) = v12) |  ~ (set_intersection2(v8, v9) = v11) |  ~ (set_intersection2(v7, v9) = v10) |  ? [v13] : ( ~ (v13 = 0) & subset(v7, v8) = v13)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v10, v8) = v11) |  ~ (set_union2(v7, v9) = v10) |  ? [v12] :  ? [v13] : (subset(v9, v8) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (subset(v7, v10) = v11) |  ~ (set_intersection2(v8, v9) = v10) |  ? [v12] :  ? [v13] : (subset(v7, v9) = v13 & subset(v7, v8) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (set_union2(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | v13 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_difference(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v11 = 0 &  ~ (v13 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v12 & in(v10, v8) = v13 & ( ~ (v12 = 0) | (v13 = 0 & v11 = 0)))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (set_union2(v7, v8) = v9) |  ~ (in(v10, v7) = v11) |  ? [v12] :  ? [v13] : (in(v10, v9) = v13 & in(v10, v8) = v12 & (v13 = 0 | ( ~ (v12 = 0) &  ~ (v11 = 0))))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v9, v7) = v10) |  ~ (set_intersection2(v7, v8) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v7, v9) = v10) |  ~ (subset(v7, v8) = 0) |  ? [v11] : ( ~ (v11 = 0) & subset(v8, v9) = v11)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (subset(v7, v9) = v10) |  ~ (set_union2(v7, v8) = v9)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (disjoint(v10, v9) = v8) |  ~ (disjoint(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (set_difference(v10, v9) = v8) |  ~ (set_difference(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (subset(v10, v9) = v8) |  ~ (subset(v10, v9) = v7)) &  ! [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 |  ~ (in(v10, v9) = v8) |  ~ (in(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_difference(v7, v8) = v9) |  ~ (in(v10, v7) = 0) |  ? [v11] :  ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & (v12 = 0 | v11 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (set_intersection2(v7, v8) = v9) |  ~ (in(v10, v7) = 0) |  ? [v11] :  ? [v12] : (in(v10, v9) = v12 & in(v10, v8) = v11 & ( ~ (v11 = 0) | v12 = 0))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_difference(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v13 = 0) |  ~ (v12 = 0) | v14 = 0) & (v12 = 0 | (v13 = 0 &  ~ (v14 = 0))))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_intersection2(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v14 = 0) |  ~ (v13 = 0) |  ~ (v12 = 0)) & (v12 = 0 | (v14 = 0 & v13 = 0)))) &  ? [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v7 |  ~ (set_union2(v8, v9) = v10) |  ? [v11] :  ? [v12] :  ? [v13] :  ? [v14] : (in(v11, v9) = v14 & in(v11, v8) = v13 & in(v11, v7) = v12 & ( ~ (v12 = 0) | ( ~ (v14 = 0) &  ~ (v13 = 0))) & (v14 = 0 | v13 = 0 | v12 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (set_union2(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v7 |  ~ (set_intersection2(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = empty_set |  ~ (set_difference(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & subset(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (disjoint(v7, v8) = v9) |  ? [v10] :  ? [v11] : (set_intersection2(v7, v8) = v10 & in(v11, v10) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (disjoint(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = empty_set) & set_intersection2(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (disjoint(v7, v8) = v9) |  ? [v10] : (in(v10, v8) = 0 & in(v10, v7) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (subset(v7, v8) = v9) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & in(v10, v8) = v11 & in(v10, v7) = 0)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (empty(v9) = v8) |  ~ (empty(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (disjoint(v7, v8) = 0) |  ~ (in(v9, v7) = 0) |  ? [v10] : ( ~ (v10 = 0) & in(v9, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (subset(v7, v8) = 0) |  ~ (in(v9, v7) = 0) | in(v9, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_intersection2(v7, v8) = v9) | set_intersection2(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v8, v7) = v9) |  ? [v10] :  ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) | set_union2(v8, v7) = v9) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (set_union2(v7, v8) = v9) |  ? [v10] :  ? [v11] : (empty(v9) = v11 & empty(v7) = v10 & ( ~ (v11 = 0) | v10 = 0))) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (empty(v8) = 0) |  ~ (empty(v7) = 0)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (set_difference(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = v7 |  ~ (subset(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & subset(v8, v7) = v9)) &  ! [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 = empty_set |  ~ (set_difference(empty_set, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = empty_set |  ~ (set_intersection2(v7, empty_set) = v8)) &  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (subset(v7, v7) = v8)) &  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (subset(empty_set, v7) = v8)) &  ! [v7] :  ! [v8] : ( ~ (disjoint(v7, v8) = 0) | disjoint(v8, v7) = 0) &  ! [v7] :  ! [v8] : ( ~ (disjoint(v7, v8) = 0) | set_intersection2(v7, v8) = empty_set) &  ! [v7] :  ! [v8] : ( ~ (disjoint(v7, v8) = 0) |  ? [v9] : (set_intersection2(v7, v8) = v9 &  ! [v10] :  ~ (in(v10, v9) = 0))) &  ! [v7] :  ! [v8] : ( ~ (set_difference(v7, v8) = empty_set) | subset(v7, v8) = 0) &  ! [v7] :  ! [v8] : ( ~ (in(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & empty(v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (in(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & in(v8, v7) = v9)) &  ! [v7] : (v7 = empty_set |  ~ (empty(v7) = 0)) &  ! [v7] : (v7 = empty_set |  ~ (subset(v7, empty_set) = 0)) &  ! [v7] :  ~ (in(v7, empty_set) = 0) &  ? [v7] :  ? [v8] : (v8 = v7 |  ? [v9] :  ? [v10] :  ? [v11] : (in(v9, v8) = v11 & in(v9, v7) = v10 & ( ~ (v11 = 0) |  ~ (v10 = 0)) & (v11 = 0 | v10 = 0))) &  ? [v7] : (v7 = empty_set |  ? [v8] : in(v8, v7) = 0))
% 6.20/2.02  | 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:
% 6.20/2.02  | (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_3_3 = 0) & empty(all_0_0_0) = 0 & empty(all_0_2_2) = all_0_1_1 & empty(empty_set) = 0 & set_difference(all_0_6_6, all_0_5_5) = all_0_4_4 & subset(all_0_4_4, all_0_6_6) = all_0_3_3 &  ! [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] : (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] : ( ~ (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] : ( ~ (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 = 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] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(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 |  ~ (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_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] : ( ~ (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 |  ~ (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] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [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 = 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, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3)) &  ! [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_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] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1)) &  ! [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_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_difference(v0, v1) = empty_set) | subset(v0, v1) = 0) &  ! [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] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0))) &  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 6.20/2.03  |
% 6.20/2.03  | Applying alpha-rule on (1) yields:
% 6.20/2.03  | (2) empty(all_0_2_2) = all_0_1_1
% 6.20/2.03  | (3)  ! [v0] :  ! [v1] : ( ~ (set_difference(v0, v1) = empty_set) | subset(v0, v1) = 0)
% 6.20/2.03  | (4)  ! [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)))
% 6.20/2.04  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (set_intersection2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 6.20/2.04  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) | set_union2(v1, v0) = v2)
% 6.20/2.04  | (7) set_difference(all_0_6_6, all_0_5_5) = all_0_4_4
% 6.20/2.04  | (8)  ! [v0] : (v0 = empty_set |  ~ (empty(v0) = 0))
% 6.20/2.04  | (9)  ? [v0] : (v0 = empty_set |  ? [v1] : in(v1, v0) = 0)
% 6.20/2.04  | (10)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : (in(v3, v1) = 0 & in(v3, v0) = 0))
% 6.20/2.04  | (11)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | disjoint(v1, v0) = 0)
% 6.20/2.04  | (12)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) |  ? [v2] : (set_intersection2(v0, v1) = v2 &  ! [v3] :  ~ (in(v3, v2) = 0)))
% 6.20/2.04  | (13)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_difference(empty_set, v0) = v1))
% 6.20/2.04  | (14)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (set_union2(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 6.20/2.04  | (15)  ! [v0] : (v0 = empty_set |  ~ (subset(v0, empty_set) = 0))
% 6.20/2.04  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v2, v0) = v3) |  ~ (set_intersection2(v0, v1) = v2))
% 6.20/2.04  | (17)  ! [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))
% 6.20/2.04  | (18)  ! [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))
% 6.20/2.04  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (disjoint(v0, v1) = 0) |  ~ (in(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & in(v2, v1) = v3))
% 6.20/2.04  | (20)  ~ (all_0_1_1 = 0)
% 6.20/2.04  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (subset(v0, v1) = 0) |  ~ (in(v2, v0) = 0) | in(v2, v1) = 0)
% 6.20/2.04  | (22)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, v0) = v1))
% 6.20/2.04  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_intersection2(v0, v1) = v2) | set_intersection2(v1, v0) = v2)
% 6.20/2.04  | (24)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 6.20/2.04  | (25)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (in(v2, v1) = v4 & in(v2, v0) = v3 & ( ~ (v4 = 0) |  ~ (v3 = 0)) & (v4 = 0 | v3 = 0)))
% 6.20/2.04  | (26)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & in(v1, v0) = v2))
% 6.20/2.04  | (27)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_intersection2(v0, v0) = v1))
% 6.20/2.04  | (28)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_union2(v0, empty_set) = v1))
% 6.20/2.04  | (29)  ! [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))))
% 6.20/2.04  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 6.20/2.04  | (31)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0))
% 6.20/2.04  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (disjoint(v3, v2) = v1) |  ~ (disjoint(v3, v2) = v0))
% 6.20/2.04  | (33)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(empty_set, v0) = v1))
% 6.20/2.04  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_difference(v3, v2) = v1) |  ~ (set_difference(v3, v2) = v0))
% 6.20/2.04  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_intersection2(v3, v2) = v1) |  ~ (set_intersection2(v3, v2) = v0))
% 6.20/2.05  | (36)  ! [v0] :  ! [v1] : ( ~ (in(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & empty(v1) = v2))
% 6.20/2.05  | (37)  ? [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)))))
% 6.20/2.05  | (38)  ! [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))))
% 6.20/2.05  | (39)  ? [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))))
% 6.20/2.05  | (40)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (empty(v1) = 0) |  ~ (empty(v0) = 0))
% 6.20/2.05  | (41)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (set_difference(v0, empty_set) = v1))
% 6.20/2.05  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (in(v3, v2) = v1) |  ~ (in(v3, v2) = v0))
% 6.20/2.05  | (43)  ! [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)))
% 6.20/2.05  | (44)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = empty_set) & set_intersection2(v0, v1) = v3))
% 6.20/2.05  | (45) empty(empty_set) = 0
% 6.20/2.05  | (46)  ! [v0] :  ! [v1] : ( ~ (disjoint(v0, v1) = 0) | set_intersection2(v0, v1) = empty_set)
% 6.20/2.05  | (47)  ! [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))))
% 6.20/2.05  | (48)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v0, v1) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 6.20/2.05  | (49)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (set_difference(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 6.20/2.05  | (50)  ! [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)))))
% 6.20/2.05  | (51) subset(all_0_4_4, all_0_6_6) = all_0_3_3
% 6.20/2.05  | (52)  ! [v0] :  ! [v1] : (v1 = empty_set |  ~ (set_intersection2(v0, empty_set) = v1))
% 6.20/2.05  | (53)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (set_union2(v1, v0) = v2) |  ? [v3] :  ? [v4] : (empty(v2) = v4 & empty(v0) = v3 & ( ~ (v4 = 0) | v3 = 0)))
% 6.20/2.05  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (set_union2(v0, v1) = v2))
% 6.20/2.05  | (55)  ? [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)))
% 6.20/2.05  | (56)  ! [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)))))
% 6.20/2.05  | (57) empty(all_0_0_0) = 0
% 6.20/2.05  | (58)  ~ (all_0_3_3 = 0)
% 6.20/2.05  | (59)  ! [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)))
% 6.20/2.05  | (60)  ! [v0] :  ~ (in(v0, empty_set) = 0)
% 6.20/2.06  | (61)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 6.20/2.06  | (62)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 6.20/2.06  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (subset(v0, v2) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & subset(v1, v2) = v4))
% 6.20/2.06  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (set_union2(v3, v2) = v1) |  ~ (set_union2(v3, v2) = v0))
% 6.20/2.06  | (65)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (disjoint(v0, v1) = v2) |  ? [v3] :  ? [v4] : (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0))
% 6.20/2.06  |
% 6.20/2.06  | Instantiating formula (31) with all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_6_6) = all_0_3_3, yields:
% 6.20/2.06  | (66) all_0_3_3 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 6.20/2.06  |
% 6.20/2.06  +-Applying beta-rule and splitting (66), into two cases.
% 6.20/2.06  |-Branch one:
% 6.20/2.06  | (67) all_0_3_3 = 0
% 6.20/2.06  |
% 6.20/2.06  	| Equations (67) can reduce 58 to:
% 6.20/2.06  	| (68) $false
% 6.20/2.06  	|
% 6.20/2.06  	|-The branch is then unsatisfiable
% 6.20/2.06  |-Branch two:
% 6.20/2.06  | (58)  ~ (all_0_3_3 = 0)
% 6.20/2.06  | (70)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & in(v0, all_0_4_4) = 0 & in(v0, all_0_6_6) = v1)
% 6.20/2.06  |
% 6.20/2.06  	| Instantiating (70) with all_55_0_14, all_55_1_15 yields:
% 6.20/2.06  	| (71)  ~ (all_55_0_14 = 0) & in(all_55_1_15, all_0_4_4) = 0 & in(all_55_1_15, all_0_6_6) = all_55_0_14
% 6.20/2.06  	|
% 6.20/2.06  	| Applying alpha-rule on (71) yields:
% 6.20/2.06  	| (72)  ~ (all_55_0_14 = 0)
% 6.20/2.06  	| (73) in(all_55_1_15, all_0_4_4) = 0
% 6.20/2.06  	| (74) in(all_55_1_15, all_0_6_6) = all_55_0_14
% 6.20/2.06  	|
% 6.20/2.06  	| Instantiating formula (56) with all_55_0_14, all_55_1_15, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms set_difference(all_0_6_6, all_0_5_5) = all_0_4_4, in(all_55_1_15, all_0_6_6) = all_55_0_14, yields:
% 6.20/2.06  	| (75)  ? [v0] :  ? [v1] : (in(all_55_1_15, all_0_4_4) = v0 & in(all_55_1_15, all_0_5_5) = v1 & ( ~ (v0 = 0) | (all_55_0_14 = 0 &  ~ (v1 = 0))))
% 6.20/2.06  	|
% 6.20/2.06  	| Instantiating (75) with all_62_0_16, all_62_1_17 yields:
% 6.20/2.06  	| (76) in(all_55_1_15, all_0_4_4) = all_62_1_17 & in(all_55_1_15, all_0_5_5) = all_62_0_16 & ( ~ (all_62_1_17 = 0) | (all_55_0_14 = 0 &  ~ (all_62_0_16 = 0)))
% 6.20/2.06  	|
% 6.20/2.06  	| Applying alpha-rule on (76) yields:
% 6.20/2.06  	| (77) in(all_55_1_15, all_0_4_4) = all_62_1_17
% 6.20/2.06  	| (78) in(all_55_1_15, all_0_5_5) = all_62_0_16
% 6.20/2.06  	| (79)  ~ (all_62_1_17 = 0) | (all_55_0_14 = 0 &  ~ (all_62_0_16 = 0))
% 6.20/2.06  	|
% 6.20/2.06  	+-Applying beta-rule and splitting (79), into two cases.
% 6.20/2.06  	|-Branch one:
% 6.20/2.06  	| (80)  ~ (all_62_1_17 = 0)
% 6.20/2.06  	|
% 6.20/2.06  		| Instantiating formula (42) with all_55_1_15, all_0_4_4, all_62_1_17, 0 and discharging atoms in(all_55_1_15, all_0_4_4) = all_62_1_17, in(all_55_1_15, all_0_4_4) = 0, yields:
% 6.20/2.06  		| (81) all_62_1_17 = 0
% 6.20/2.06  		|
% 6.20/2.06  		| Equations (81) can reduce 80 to:
% 6.20/2.06  		| (68) $false
% 6.20/2.06  		|
% 6.20/2.06  		|-The branch is then unsatisfiable
% 6.20/2.06  	|-Branch two:
% 6.20/2.06  	| (81) all_62_1_17 = 0
% 6.20/2.06  	| (84) all_55_0_14 = 0 &  ~ (all_62_0_16 = 0)
% 6.20/2.06  	|
% 6.20/2.06  		| Applying alpha-rule on (84) yields:
% 6.20/2.06  		| (85) all_55_0_14 = 0
% 6.20/2.06  		| (86)  ~ (all_62_0_16 = 0)
% 6.20/2.06  		|
% 6.20/2.06  		| Equations (85) can reduce 72 to:
% 6.20/2.06  		| (68) $false
% 6.20/2.06  		|
% 6.20/2.06  		|-The branch is then unsatisfiable
% 6.20/2.06  % SZS output end Proof for theBenchmark
% 6.20/2.06  
% 6.20/2.06  1480ms
%------------------------------------------------------------------------------