%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Tue Jul 19 00:21:05 EDT 2022

% Result   : Theorem 4.84s 1.88s
% Output   : Proof 6.59s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.08/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.16/0.37  % Computer : n016.cluster.edu
% 0.16/0.37  % Model    : x86_64 x86_64
% 0.16/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37  % Memory   : 8042.1875MB
% 0.16/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit : 300
% 0.16/0.37  % WCLimit  : 600
% 0.16/0.37  % DateTime : Mon Jul 11 00:10:57 EDT 2022
% 0.16/0.37  % CPUTime  : 
% 0.60/0.61          ____       _                          
% 0.60/0.61    ___  / __ \_____(_)___  ________  __________
% 0.60/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.60/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.60/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.60/0.61  
% 0.60/0.61  A Theorem Prover for First-Order Logic
% 0.60/0.62  (ePrincess v.1.0)
% 0.60/0.62  
% 0.60/0.62  (c) Philipp Rümmer, 2009-2015
% 0.60/0.62  (c) Peter Backeman, 2014-2015
% 0.60/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.60/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.60/0.62  Bug reports to peter@backeman.se
% 0.60/0.62  
% 0.60/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.60/0.62  
% 0.60/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.48/0.97  Prover 0: Preprocessing ...
% 2.06/1.19  Prover 0: Warning: ignoring some quantifiers
% 2.08/1.21  Prover 0: Constructing countermodel ...
% 2.79/1.44  Prover 0: gave up
% 2.79/1.44  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.12/1.46  Prover 1: Preprocessing ...
% 3.48/1.54  Prover 1: Warning: ignoring some quantifiers
% 3.48/1.55  Prover 1: Constructing countermodel ...
% 4.18/1.72  Prover 1: gave up
% 4.18/1.72  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.18/1.74  Prover 2: Preprocessing ...
% 4.74/1.81  Prover 2: Warning: ignoring some quantifiers
% 4.74/1.81  Prover 2: Constructing countermodel ...
% 4.84/1.88  Prover 2: proved (162ms)
% 4.84/1.88  
% 4.84/1.88  No countermodel exists, formula is valid
% 4.84/1.88  % SZS status Theorem for theBenchmark
% 4.84/1.88  
% 4.84/1.88  Generating proof ... Warning: ignoring some quantifiers
% 6.17/2.18  found it (size 29)
% 6.17/2.18  
% 6.17/2.18  % SZS output start Proof for theBenchmark
% 6.17/2.18  Assumed formulas after preprocessing and simplification: 
% 6.17/2.18  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & union(v1, v2) = v3 & intersection(v0, v2) = empty_set & subset(v0, v3) = 0 & subset(v0, v1) = v4 &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v8, v9) = v10) |  ~ (intersection(v5, v7) = v9) |  ~ (intersection(v5, v6) = v8) |  ? [v11] : (union(v6, v7) = v11 & intersection(v5, v11) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (member(v7, v8) = v9) |  ~ (union(v5, v6) = v8) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) &  ~ (v10 = 0) & member(v7, v6) = v11 & member(v7, v5) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (member(v7, v8) = v9) |  ~ (intersection(v5, v6) = v8) |  ? [v10] : (( ~ (v10 = 0) & member(v7, v6) = v10) | ( ~ (v10 = 0) & member(v7, v5) = v10))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (union(v6, v7) = v8) |  ~ (intersection(v5, v8) = v9) |  ? [v10] :  ? [v11] : (union(v10, v11) = v9 & intersection(v5, v7) = v11 & intersection(v5, v6) = v10)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (member(v7, v6) = v8) |  ~ (subset(v5, v6) = 0) |  ? [v9] : ( ~ (v9 = 0) & member(v7, v5) = v9)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (member(v8, v7) = v6) |  ~ (member(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (union(v8, v7) = v6) |  ~ (union(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection(v8, v7) = v6) |  ~ (intersection(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (subset(v8, v7) = v6) |  ~ (subset(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (member(v7, v8) = 0) |  ~ (union(v5, v6) = v8) |  ? [v9] : ((v9 = 0 & member(v7, v6) = 0) | (v9 = 0 & member(v7, v5) = 0))) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (member(v7, v8) = 0) |  ~ (intersection(v5, v6) = v8) | (member(v7, v6) = 0 & member(v7, v5) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v5 |  ~ (intersection(v5, v6) = v7) |  ? [v8] : ( ~ (v8 = 0) & subset(v5, v6) = v8)) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (subset(v5, v6) = v7) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & member(v8, v6) = v9 & member(v8, v5) = 0)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (empty(v7) = v6) |  ~ (empty(v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (member(v7, v5) = 0) |  ~ (subset(v5, v6) = 0) | member(v7, v6) = 0) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (union(v6, v5) = v7) | union(v5, v6) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (union(v5, v6) = v7) | union(v6, v5) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection(v6, v5) = v7) | intersection(v5, v6) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection(v5, v6) = v7) | intersection(v6, v5) = v7) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (intersection(v5, v6) = v7) | subset(v7, v5) = 0) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (union(v5, empty_set) = v6)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (subset(v6, v5) = 0) |  ? [v7] : ( ~ (v7 = 0) & subset(v5, v6) = v7)) &  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (subset(v5, v6) = 0) |  ? [v7] : ( ~ (v7 = 0) & subset(v6, v5) = v7)) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (empty(v5) = v6) |  ? [v7] : member(v7, v5) = 0) &  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (subset(v5, v5) = v6)) &  ! [v5] :  ! [v6] : ( ~ (empty(v5) = 0) |  ~ (member(v6, v5) = 0)) &  ! [v5] :  ! [v6] : ( ~ (subset(v5, v6) = 0) | intersection(v5, v6) = v5) &  ! [v5] :  ~ (member(v5, empty_set) = 0) &  ? [v5] :  ? [v6] :  ? [v7] : member(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : union(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : intersection(v6, v5) = v7 &  ? [v5] :  ? [v6] :  ? [v7] : subset(v6, v5) = v7 &  ? [v5] :  ? [v6] : (v6 = v5 |  ? [v7] :  ? [v8] :  ? [v9] : (((v9 = 0 & member(v7, v6) = 0) | (v8 = 0 & member(v7, v5) = 0)) & (( ~ (v9 = 0) & member(v7, v6) = v9) | ( ~ (v8 = 0) & member(v7, v5) = v8)))) &  ? [v5] :  ? [v6] : empty(v5) = v6)
% 6.17/2.21  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 6.17/2.21  | (1)  ~ (all_0_0_0 = 0) & union(all_0_3_3, all_0_2_2) = all_0_1_1 & intersection(all_0_4_4, all_0_2_2) = empty_set & subset(all_0_4_4, all_0_1_1) = 0 & subset(all_0_4_4, all_0_3_3) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ (intersection(v0, v2) = v4) |  ~ (intersection(v0, v1) = v3) |  ? [v6] : (union(v1, v2) = v6 & intersection(v0, v6) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (member(v2, v3) = v4) |  ~ (union(v0, v1) = v3) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (member(v2, v3) = v4) |  ~ (intersection(v0, v1) = v3) |  ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (union(v1, v2) = v3) |  ~ (intersection(v0, v3) = v4) |  ? [v5] :  ? [v6] : (union(v5, v6) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (member(v2, v1) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (member(v2, v3) = 0) |  ~ (union(v0, v1) = v3) |  ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (member(v2, v3) = 0) |  ~ (intersection(v0, v1) = v3) | (member(v2, v1) = 0 & member(v2, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (intersection(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member(v2, v0) = 0) |  ~ (subset(v0, v1) = 0) | member(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0) = 0) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (union(v0, empty_set) = v1)) &  ! [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 = 0 |  ~ (empty(v0) = v1) |  ? [v2] : member(v2, v0) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (empty(v0) = 0) |  ~ (member(v1, v0) = 0)) &  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) | intersection(v0, v1) = v0) &  ! [v0] :  ~ (member(v0, empty_set) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : member(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : union(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2 &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3)))) &  ? [v0] :  ? [v1] : empty(v0) = v1
% 6.59/2.22  |
% 6.59/2.22  | Applying alpha-rule on (1) yields:
% 6.59/2.22  | (2) union(all_0_3_3, all_0_2_2) = all_0_1_1
% 6.59/2.22  | (3)  ? [v0] :  ? [v1] :  ? [v2] : subset(v1, v0) = v2
% 6.59/2.22  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (member(v3, v2) = v1) |  ~ (member(v3, v2) = v0))
% 6.59/2.22  | (5)  ! [v0] :  ! [v1] : ( ~ (subset(v0, v1) = 0) | intersection(v0, v1) = v0)
% 6.59/2.22  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 6.59/2.22  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 6.59/2.23  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0) = 0)
% 6.59/2.23  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 6.59/2.23  | (10)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v1, v0) = v2))
% 6.59/2.23  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 6.59/2.23  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 6.59/2.23  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (member(v2, v3) = 0) |  ~ (union(v0, v1) = v3) |  ? [v4] : ((v4 = 0 & member(v2, v1) = 0) | (v4 = 0 & member(v2, v0) = 0)))
% 6.59/2.23  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (member(v2, v3) = v4) |  ~ (union(v0, v1) = v3) |  ? [v5] :  ? [v6] : ( ~ (v6 = 0) &  ~ (v5 = 0) & member(v2, v1) = v6 & member(v2, v0) = v5))
% 6.59/2.23  | (15)  ! [v0] :  ~ (member(v0, empty_set) = 0)
% 6.59/2.23  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (union(v1, v2) = v3) |  ~ (intersection(v0, v3) = v4) |  ? [v5] :  ? [v6] : (union(v5, v6) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5))
% 6.59/2.23  | (17)  ~ (all_0_0_0 = 0)
% 6.59/2.23  | (18)  ? [v0] :  ? [v1] :  ? [v2] : intersection(v1, v0) = v2
% 6.59/2.23  | (19)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] :  ? [v3] :  ? [v4] : (((v4 = 0 & member(v2, v1) = 0) | (v3 = 0 & member(v2, v0) = 0)) & (( ~ (v4 = 0) & member(v2, v1) = v4) | ( ~ (v3 = 0) & member(v2, v0) = v3))))
% 6.59/2.23  | (20)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (union(v0, empty_set) = v1))
% 6.59/2.23  | (21) subset(all_0_4_4, all_0_1_1) = 0
% 6.59/2.23  | (22)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (member(v2, v0) = 0) |  ~ (subset(v0, v1) = 0) | member(v2, v1) = 0)
% 6.59/2.23  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 6.59/2.23  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (member(v2, v1) = v3) |  ~ (subset(v0, v1) = 0) |  ? [v4] : ( ~ (v4 = 0) & member(v2, v0) = v4))
% 6.59/2.23  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (member(v2, v3) = v4) |  ~ (intersection(v0, v1) = v3) |  ? [v5] : (( ~ (v5 = 0) & member(v2, v1) = v5) | ( ~ (v5 = 0) & member(v2, v0) = v5)))
% 6.59/2.23  | (26)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (subset(v0, v0) = v1))
% 6.59/2.23  | (27)  ? [v0] :  ? [v1] : empty(v0) = v1
% 6.59/2.23  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (member(v2, v3) = 0) |  ~ (intersection(v0, v1) = v3) | (member(v2, v1) = 0 & member(v2, v0) = 0))
% 6.59/2.23  | (29)  ? [v0] :  ? [v1] :  ? [v2] : union(v1, v0) = v2
% 6.59/2.23  | (30)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (empty(v0) = v1) |  ? [v2] : member(v2, v0) = 0)
% 6.59/2.23  | (31) intersection(all_0_4_4, all_0_2_2) = empty_set
% 6.59/2.23  | (32)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (empty(v2) = v1) |  ~ (empty(v2) = v0))
% 6.59/2.23  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (subset(v3, v2) = v1) |  ~ (subset(v3, v2) = v0))
% 6.59/2.24  | (34)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (subset(v0, v1) = v2) |  ? [v3] :  ? [v4] : ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0))
% 6.59/2.24  | (35)  ? [v0] :  ? [v1] :  ? [v2] : member(v1, v0) = v2
% 6.59/2.24  | (36) subset(all_0_4_4, all_0_3_3) = all_0_0_0
% 6.59/2.24  | (37)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (subset(v1, v0) = 0) |  ? [v2] : ( ~ (v2 = 0) & subset(v0, v1) = v2))
% 6.59/2.24  | (38)  ! [v0] :  ! [v1] : ( ~ (empty(v0) = 0) |  ~ (member(v1, v0) = 0))
% 6.59/2.24  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ (intersection(v0, v2) = v4) |  ~ (intersection(v0, v1) = v3) |  ? [v6] : (union(v1, v2) = v6 & intersection(v0, v6) = v5))
% 6.59/2.24  | (40)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (intersection(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & subset(v0, v1) = v3))
% 6.59/2.24  |
% 6.59/2.24  | Instantiating formula (7) with all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 6.59/2.24  | (41) union(all_0_2_2, all_0_3_3) = all_0_1_1
% 6.59/2.24  |
% 6.59/2.24  | Instantiating formula (5) with all_0_1_1, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_1_1) = 0, yields:
% 6.59/2.24  | (42) intersection(all_0_4_4, all_0_1_1) = all_0_4_4
% 6.59/2.24  |
% 6.59/2.24  | Instantiating formula (34) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms subset(all_0_4_4, all_0_3_3) = all_0_0_0, yields:
% 6.59/2.24  | (43) all_0_0_0 = 0 |  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0)
% 6.59/2.24  |
% 6.59/2.24  +-Applying beta-rule and splitting (43), into two cases.
% 6.59/2.24  |-Branch one:
% 6.59/2.24  | (44) all_0_0_0 = 0
% 6.59/2.24  |
% 6.59/2.24  	| Equations (44) can reduce 17 to:
% 6.59/2.24  	| (45) $false
% 6.59/2.24  	|
% 6.59/2.24  	|-The branch is then unsatisfiable
% 6.59/2.24  |-Branch two:
% 6.59/2.24  | (17)  ~ (all_0_0_0 = 0)
% 6.59/2.24  | (47)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & member(v0, all_0_3_3) = v1 & member(v0, all_0_4_4) = 0)
% 6.59/2.24  |
% 6.59/2.24  	| Instantiating (47) with all_24_0_21, all_24_1_22 yields:
% 6.59/2.24  	| (48)  ~ (all_24_0_21 = 0) & member(all_24_1_22, all_0_3_3) = all_24_0_21 & member(all_24_1_22, all_0_4_4) = 0
% 6.59/2.24  	|
% 6.59/2.24  	| Applying alpha-rule on (48) yields:
% 6.59/2.24  	| (49)  ~ (all_24_0_21 = 0)
% 6.59/2.24  	| (50) member(all_24_1_22, all_0_3_3) = all_24_0_21
% 6.59/2.24  	| (51) member(all_24_1_22, all_0_4_4) = 0
% 6.59/2.24  	|
% 6.59/2.24  	| Instantiating formula (16) with all_0_4_4, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms union(all_0_3_3, all_0_2_2) = all_0_1_1, intersection(all_0_4_4, all_0_1_1) = all_0_4_4, yields:
% 6.59/2.24  	| (52)  ? [v0] :  ? [v1] : (union(v0, v1) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = v1 & intersection(all_0_4_4, all_0_3_3) = v0)
% 6.59/2.24  	|
% 6.59/2.24  	| Instantiating formula (16) with all_0_4_4, all_0_1_1, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms union(all_0_2_2, all_0_3_3) = all_0_1_1, intersection(all_0_4_4, all_0_1_1) = all_0_4_4, yields:
% 6.59/2.24  	| (53)  ? [v0] :  ? [v1] : (union(v0, v1) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = v0 & intersection(all_0_4_4, all_0_3_3) = v1)
% 6.59/2.24  	|
% 6.59/2.24  	| Instantiating (52) with all_32_0_23, all_32_1_24 yields:
% 6.59/2.24  	| (54) union(all_32_1_24, all_32_0_23) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = all_32_0_23 & intersection(all_0_4_4, all_0_3_3) = all_32_1_24
% 6.59/2.24  	|
% 6.59/2.24  	| Applying alpha-rule on (54) yields:
% 6.59/2.24  	| (55) union(all_32_1_24, all_32_0_23) = all_0_4_4
% 6.59/2.25  	| (56) intersection(all_0_4_4, all_0_2_2) = all_32_0_23
% 6.59/2.25  	| (57) intersection(all_0_4_4, all_0_3_3) = all_32_1_24
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating (53) with all_34_0_25, all_34_1_26 yields:
% 6.59/2.25  	| (58) union(all_34_1_26, all_34_0_25) = all_0_4_4 & intersection(all_0_4_4, all_0_2_2) = all_34_1_26 & intersection(all_0_4_4, all_0_3_3) = all_34_0_25
% 6.59/2.25  	|
% 6.59/2.25  	| Applying alpha-rule on (58) yields:
% 6.59/2.25  	| (59) union(all_34_1_26, all_34_0_25) = all_0_4_4
% 6.59/2.25  	| (60) intersection(all_0_4_4, all_0_2_2) = all_34_1_26
% 6.59/2.25  	| (61) intersection(all_0_4_4, all_0_3_3) = all_34_0_25
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating formula (23) with all_0_4_4, all_0_2_2, all_34_1_26, empty_set and discharging atoms intersection(all_0_4_4, all_0_2_2) = all_34_1_26, intersection(all_0_4_4, all_0_2_2) = empty_set, yields:
% 6.59/2.25  	| (62) all_34_1_26 = empty_set
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating formula (23) with all_0_4_4, all_0_2_2, all_32_0_23, all_34_1_26 and discharging atoms intersection(all_0_4_4, all_0_2_2) = all_34_1_26, intersection(all_0_4_4, all_0_2_2) = all_32_0_23, yields:
% 6.59/2.25  	| (63) all_34_1_26 = all_32_0_23
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating formula (23) with all_0_4_4, all_0_3_3, all_32_1_24, all_34_0_25 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_34_0_25, intersection(all_0_4_4, all_0_3_3) = all_32_1_24, yields:
% 6.59/2.25  	| (64) all_34_0_25 = all_32_1_24
% 6.59/2.25  	|
% 6.59/2.25  	| Combining equations (63,62) yields a new equation:
% 6.59/2.25  	| (65) all_32_0_23 = empty_set
% 6.59/2.25  	|
% 6.59/2.25  	| Simplifying 65 yields:
% 6.59/2.25  	| (66) all_32_0_23 = empty_set
% 6.59/2.25  	|
% 6.59/2.25  	| From (66) and (55) follows:
% 6.59/2.25  	| (67) union(all_32_1_24, empty_set) = all_0_4_4
% 6.59/2.25  	|
% 6.59/2.25  	| From (64) and (61) follows:
% 6.59/2.25  	| (57) intersection(all_0_4_4, all_0_3_3) = all_32_1_24
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating formula (20) with all_0_4_4, all_32_1_24 and discharging atoms union(all_32_1_24, empty_set) = all_0_4_4, yields:
% 6.59/2.25  	| (69) all_32_1_24 = all_0_4_4
% 6.59/2.25  	|
% 6.59/2.25  	| From (69) and (57) follows:
% 6.59/2.25  	| (70) intersection(all_0_4_4, all_0_3_3) = all_0_4_4
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating formula (28) with all_0_4_4, all_24_1_22, all_0_3_3, all_0_4_4 and discharging atoms member(all_24_1_22, all_0_4_4) = 0, intersection(all_0_4_4, all_0_3_3) = all_0_4_4, yields:
% 6.59/2.25  	| (71) member(all_24_1_22, all_0_3_3) = 0
% 6.59/2.25  	|
% 6.59/2.25  	| Instantiating formula (4) with all_24_1_22, all_0_3_3, 0, all_24_0_21 and discharging atoms member(all_24_1_22, all_0_3_3) = all_24_0_21, member(all_24_1_22, all_0_3_3) = 0, yields:
% 6.59/2.25  	| (72) all_24_0_21 = 0
% 6.59/2.25  	|
% 6.59/2.25  	| Equations (72) can reduce 49 to:
% 6.59/2.25  	| (45) $false
% 6.59/2.25  	|
% 6.59/2.25  	|-The branch is then unsatisfiable
% 6.59/2.25  % SZS output end Proof for theBenchmark
% 6.59/2.25  
% 6.59/2.25  1625ms
%------------------------------------------------------------------------------