%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n019.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 00:21:03 EDT 2022

% Result   : Theorem 2.72s 1.35s
% Output   : Proof 4.28s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET635+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % 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 : Sun Jul 10 13:36:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.48/0.59          ____       _                          
% 0.48/0.59    ___  / __ \_____(_)___  ________  __________
% 0.48/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.48/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.48/0.59  
% 0.48/0.59  A Theorem Prover for First-Order Logic
% 0.48/0.60  (ePrincess v.1.0)
% 0.48/0.60  
% 0.48/0.60  (c) Philipp Rümmer, 2009-2015
% 0.48/0.60  (c) Peter Backeman, 2014-2015
% 0.48/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.60  Bug reports to peter@backeman.se
% 0.48/0.60  
% 0.48/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.60  
% 0.48/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.93  Prover 0: Preprocessing ...
% 1.97/1.14  Prover 0: Warning: ignoring some quantifiers
% 2.03/1.16  Prover 0: Constructing countermodel ...
% 2.72/1.34  Prover 0: proved (695ms)
% 2.72/1.35  
% 2.72/1.35  No countermodel exists, formula is valid
% 2.72/1.35  % SZS status Theorem for theBenchmark
% 2.72/1.35  
% 2.72/1.35  Generating proof ... Warning: ignoring some quantifiers
% 3.99/1.67  found it (size 19)
% 3.99/1.67  
% 3.99/1.67  % SZS output start Proof for theBenchmark
% 3.99/1.67  Assumed formulas after preprocessing and simplification: 
% 3.99/1.67  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v7 = v4) & difference(v5, v6) = v7 & difference(v1, v2) = v3 & intersection(v0, v3) = v4 & intersection(v0, v2) = v6 & intersection(v0, v1) = v5 &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (union(v11, v12) = v13) |  ~ (difference(v8, v10) = v12) |  ~ (difference(v8, v9) = v11) |  ? [v14] : (difference(v8, v14) = v13 & intersection(v9, v10) = v14)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (difference(v11, v10) = v12) |  ~ (intersection(v8, v9) = v11) |  ? [v13] : (difference(v9, v10) = v13 & intersection(v8, v13) = v12)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (difference(v9, v10) = v11) |  ~ (intersection(v8, v11) = v12) |  ? [v13] : (difference(v13, v10) = v12 & intersection(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (difference(v8, v11) = v12) |  ~ (intersection(v9, v10) = v11) |  ? [v13] :  ? [v14] : (union(v13, v14) = v12 & difference(v8, v10) = v14 & difference(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (union(v11, v10) = v9) |  ~ (union(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (difference(v11, v10) = v9) |  ~ (difference(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (intersection(v11, v10) = v9) |  ~ (intersection(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (difference(v8, v9) = v11) |  ~ member(v10, v11) |  ~ member(v10, v9)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (difference(v8, v9) = v11) |  ~ member(v10, v11) | member(v10, v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (difference(v8, v9) = v11) |  ~ member(v10, v8) | member(v10, v11) | member(v10, v9)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (intersection(v8, v9) = v11) |  ~ member(v10, v11) | member(v10, v9)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (intersection(v8, v9) = v11) |  ~ member(v10, v11) | member(v10, v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (intersection(v8, v9) = v11) |  ~ member(v10, v9) |  ~ member(v10, v8) | member(v10, v11)) &  ! [v8] :  ! [v9] :  ! [v10] : (v10 = empty_set |  ~ (difference(v8, v9) = v10) |  ~ subset(v8, v9)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v9, v8) = v10) | union(v8, v9) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v8, v9) = v10) | union(v9, v8) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (intersection(v9, v8) = v10) | intersection(v8, v9) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (intersection(v8, v9) = v10) | intersection(v9, v8) = v10) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (intersection(v8, v9) = v10) | subset(v10, v8)) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ member(v10, v8) |  ~ subset(v8, v9) | member(v10, v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ (union(v8, empty_set) = v9)) &  ! [v8] :  ! [v9] : (v9 = v8 |  ~ subset(v9, v8) |  ~ subset(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ (difference(v8, v9) = empty_set) | subset(v8, v9)) &  ! [v8] :  ! [v9] : ( ~ empty(v8) |  ~ member(v9, v8)) &  ! [v8] :  ~ member(v8, empty_set) &  ? [v8] :  ? [v9] : (v9 = v8 |  ? [v10] : (( ~ member(v10, v9) |  ~ member(v10, v8)) & (member(v10, v9) | member(v10, v8)))) &  ? [v8] :  ? [v9] : (subset(v8, v9) |  ? [v10] : (member(v10, v8) &  ~ member(v10, v9))) &  ? [v8] : (empty(v8) |  ? [v9] : member(v9, v8)) &  ? [v8] : subset(v8, v8))
% 4.08/1.74  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 4.08/1.74  | (1)  ~ (all_0_0_0 = all_0_3_3) & difference(all_0_2_2, all_0_1_1) = all_0_0_0 & difference(all_0_6_6, all_0_5_5) = all_0_4_4 & intersection(all_0_7_7, all_0_4_4) = all_0_3_3 & intersection(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection(all_0_7_7, all_0_6_6) = all_0_2_2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ (difference(v0, v2) = v4) |  ~ (difference(v0, v1) = v3) |  ? [v6] : (difference(v0, v6) = v5 & intersection(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v3, v2) = v4) |  ~ (intersection(v0, v1) = v3) |  ? [v5] : (difference(v1, v2) = v5 & intersection(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v2) = v3) |  ~ (intersection(v0, v3) = v4) |  ? [v5] : (difference(v5, v2) = v4 & intersection(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v0, v3) = v4) |  ~ (intersection(v1, v2) = v3) |  ? [v5] :  ? [v6] : (union(v5, v6) = v4 & difference(v0, v2) = v6 & difference(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) |  ~ member(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (difference(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [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)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (union(v0, empty_set) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0)) &  ! [v0] :  ~ member(v0, empty_set) &  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0)))) &  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1))) &  ? [v0] : (empty(v0) |  ? [v1] : member(v1, v0)) &  ? [v0] : subset(v0, v0)
% 4.22/1.76  |
% 4.22/1.76  | Applying alpha-rule on (1) yields:
% 4.22/1.76  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = empty_set |  ~ (difference(v0, v1) = v2) |  ~ subset(v0, v1))
% 4.22/1.76  | (3) difference(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.22/1.76  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 4.22/1.76  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 4.22/1.76  | (6)  ~ (all_0_0_0 = all_0_3_3)
% 4.22/1.76  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1))
% 4.22/1.76  | (8) difference(all_0_6_6, all_0_5_5) = all_0_4_4
% 4.28/1.76  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 4.28/1.76  | (10)  ? [v0] : subset(v0, v0)
% 4.28/1.76  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v2) = v3) |  ~ (intersection(v0, v3) = v4) |  ? [v5] : (difference(v5, v2) = v4 & intersection(v0, v1) = v5))
% 4.28/1.76  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 4.28/1.76  | (13)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 4.28/1.76  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 4.28/1.76  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 4.28/1.76  | (16)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 4.28/1.77  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3))
% 4.28/1.77  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 4.28/1.77  | (19)  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0))
% 4.28/1.77  | (20)  ! [v0] :  ~ member(v0, empty_set)
% 4.28/1.77  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1))
% 4.28/1.77  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (union(v3, v4) = v5) |  ~ (difference(v0, v2) = v4) |  ~ (difference(v0, v1) = v3) |  ? [v6] : (difference(v0, v6) = v5 & intersection(v1, v2) = v6))
% 4.28/1.77  | (23)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 4.28/1.77  | (24) intersection(all_0_7_7, all_0_4_4) = all_0_3_3
% 4.28/1.77  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v3, v2) = v4) |  ~ (intersection(v0, v1) = v3) |  ? [v5] : (difference(v1, v2) = v5 & intersection(v0, v5) = v4))
% 4.28/1.77  | (26) intersection(all_0_7_7, all_0_6_6) = all_0_2_2
% 4.28/1.77  | (27)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 4.28/1.77  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0))
% 4.28/1.77  | (29)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (union(v0, empty_set) = v1))
% 4.28/1.77  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) |  ~ member(v2, v1))
% 4.28/1.77  | (31)  ? [v0] : (empty(v0) |  ? [v1] : member(v1, v0))
% 4.28/1.77  | (32)  ! [v0] :  ! [v1] : ( ~ (difference(v0, v1) = empty_set) | subset(v0, v1))
% 4.28/1.77  | (33) intersection(all_0_7_7, all_0_5_5) = all_0_1_1
% 4.28/1.77  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 4.28/1.77  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 4.28/1.77  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v0, v3) = v4) |  ~ (intersection(v1, v2) = v3) |  ? [v5] :  ? [v6] : (union(v5, v6) = v4 & difference(v0, v2) = v6 & difference(v0, v1) = v5))
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (11) with all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 and discharging atoms difference(all_0_6_6, all_0_5_5) = all_0_4_4, intersection(all_0_7_7, all_0_4_4) = all_0_3_3, yields:
% 4.28/1.78  | (37)  ? [v0] : (difference(v0, all_0_5_5) = all_0_3_3 & intersection(all_0_7_7, all_0_6_6) = v0)
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (36) with all_0_0_0, all_0_1_1, all_0_5_5, all_0_7_7, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_0_0_0, intersection(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 4.28/1.78  | (38)  ? [v0] :  ? [v1] : (union(v0, v1) = all_0_0_0 & difference(all_0_2_2, all_0_5_5) = v1 & difference(all_0_2_2, all_0_7_7) = v0)
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (28) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 4.28/1.78  | (39) subset(all_0_2_2, all_0_7_7)
% 4.28/1.78  |
% 4.28/1.78  | Instantiating (37) with all_16_0_15 yields:
% 4.28/1.78  | (40) difference(all_16_0_15, all_0_5_5) = all_0_3_3 & intersection(all_0_7_7, all_0_6_6) = all_16_0_15
% 4.28/1.78  |
% 4.28/1.78  | Applying alpha-rule on (40) yields:
% 4.28/1.78  | (41) difference(all_16_0_15, all_0_5_5) = all_0_3_3
% 4.28/1.78  | (42) intersection(all_0_7_7, all_0_6_6) = all_16_0_15
% 4.28/1.78  |
% 4.28/1.78  | Instantiating (38) with all_18_0_16, all_18_1_17 yields:
% 4.28/1.78  | (43) union(all_18_1_17, all_18_0_16) = all_0_0_0 & difference(all_0_2_2, all_0_5_5) = all_18_0_16 & difference(all_0_2_2, all_0_7_7) = all_18_1_17
% 4.28/1.78  |
% 4.28/1.78  | Applying alpha-rule on (43) yields:
% 4.28/1.78  | (44) union(all_18_1_17, all_18_0_16) = all_0_0_0
% 4.28/1.78  | (45) difference(all_0_2_2, all_0_5_5) = all_18_0_16
% 4.28/1.78  | (46) difference(all_0_2_2, all_0_7_7) = all_18_1_17
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (9) with all_0_7_7, all_0_6_6, all_16_0_15, all_0_2_2 and discharging atoms intersection(all_0_7_7, all_0_6_6) = all_16_0_15, intersection(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 4.28/1.78  | (47) all_16_0_15 = all_0_2_2
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (2) with all_18_1_17, all_0_7_7, all_0_2_2 and discharging atoms difference(all_0_2_2, all_0_7_7) = all_18_1_17, subset(all_0_2_2, all_0_7_7), yields:
% 4.28/1.78  | (48) all_18_1_17 = empty_set
% 4.28/1.78  |
% 4.28/1.78  | From (48) and (44) follows:
% 4.28/1.78  | (49) union(empty_set, all_18_0_16) = all_0_0_0
% 4.28/1.78  |
% 4.28/1.78  | From (47) and (41) follows:
% 4.28/1.78  | (50) difference(all_0_2_2, all_0_5_5) = all_0_3_3
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (5) with all_0_2_2, all_0_5_5, all_0_3_3, all_18_0_16 and discharging atoms difference(all_0_2_2, all_0_5_5) = all_18_0_16, difference(all_0_2_2, all_0_5_5) = all_0_3_3, yields:
% 4.28/1.78  | (51) all_18_0_16 = all_0_3_3
% 4.28/1.78  |
% 4.28/1.78  | From (51) and (49) follows:
% 4.28/1.78  | (52) union(empty_set, all_0_3_3) = all_0_0_0
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (14) with all_0_0_0, empty_set, all_0_3_3 and discharging atoms union(empty_set, all_0_3_3) = all_0_0_0, yields:
% 4.28/1.78  | (53) union(all_0_3_3, empty_set) = all_0_0_0
% 4.28/1.78  |
% 4.28/1.78  | Instantiating formula (29) with all_0_0_0, all_0_3_3 and discharging atoms union(all_0_3_3, empty_set) = all_0_0_0, yields:
% 4.28/1.78  | (54) all_0_0_0 = all_0_3_3
% 4.28/1.78  |
% 4.28/1.78  | Equations (54) can reduce 6 to:
% 4.28/1.78  | (55) $false
% 4.28/1.78  |
% 4.28/1.78  |-The branch is then unsatisfiable
% 4.28/1.79  % SZS output end Proof for theBenchmark
% 4.28/1.79  
% 4.28/1.79  1180ms
%------------------------------------------------------------------------------