%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n018.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 00:20:52 EDT 2022

% Result   : Theorem 2.51s 1.32s
% Output   : Proof 4.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 20:55:28 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.58          ____       _                          
% 0.18/0.58    ___  / __ \_____(_)___  ________  __________
% 0.18/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.58  
% 0.18/0.58  A Theorem Prover for First-Order Logic
% 0.18/0.58  (ePrincess v.1.0)
% 0.18/0.58  
% 0.18/0.58  (c) Philipp Rümmer, 2009-2015
% 0.18/0.58  (c) Peter Backeman, 2014-2015
% 0.18/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58  Bug reports to peter@backeman.se
% 0.18/0.58  
% 0.18/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58  
% 0.18/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.66/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.91  Prover 0: Preprocessing ...
% 1.87/1.12  Prover 0: Warning: ignoring some quantifiers
% 1.87/1.14  Prover 0: Constructing countermodel ...
% 2.51/1.32  Prover 0: proved (685ms)
% 2.51/1.32  
% 2.51/1.32  No countermodel exists, formula is valid
% 2.51/1.32  % SZS status Theorem for theBenchmark
% 2.51/1.32  
% 2.51/1.32  Generating proof ... Warning: ignoring some quantifiers
% 3.72/1.60  found it (size 41)
% 3.72/1.60  
% 3.72/1.60  % SZS output start Proof for theBenchmark
% 3.72/1.60  Assumed formulas after preprocessing and simplification: 
% 3.72/1.60  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v2) & intersection(v0, v1) = v4 & union(v3, v4) = v5 & union(v0, v1) = v2 & symmetric_difference(v0, v1) = v3 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = v6 |  ~ (intersection(v6, v7) = v8) |  ~ (difference(v6, v7) = v9) |  ~ (union(v8, v9) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (difference(v7, v6) = v9) |  ~ (difference(v6, v7) = v8) |  ~ (union(v8, v9) = v10) | symmetric_difference(v6, v7) = v10) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v9, v8) = v10) |  ~ (union(v6, v7) = v9) |  ? [v11] : (union(v7, v8) = v11 & union(v6, v11) = v10)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (union(v7, v8) = v9) |  ~ (union(v6, v9) = v10) |  ? [v11] : (union(v11, v8) = v10 & union(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = v6 |  ~ (intersection(v6, v7) = v8) |  ~ (union(v6, v8) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (intersection(v9, v8) = v7) |  ~ (intersection(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (difference(v9, v8) = v7) |  ~ (difference(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (union(v9, v8) = v7) |  ~ (union(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (symmetric_difference(v9, v8) = v7) |  ~ (symmetric_difference(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection(v6, v7) = v9) |  ~ member(v8, v9) | member(v8, v7)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection(v6, v7) = v9) |  ~ member(v8, v9) | member(v8, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection(v6, v7) = v9) |  ~ member(v8, v7) |  ~ member(v8, v6) | member(v8, v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (union(v6, v7) = v9) |  ~ member(v8, v9) | member(v8, v7) | member(v8, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (union(v6, v7) = v9) |  ~ member(v8, v7) | member(v8, v9)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (union(v6, v7) = v9) |  ~ member(v8, v6) | member(v8, v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v7, v6) = v8) | intersection(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v6, v7) = v8) | intersection(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v7, v6) = v8) | union(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v6, v7) = v8) | union(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (symmetric_difference(v7, v6) = v8) | symmetric_difference(v6, v7) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) | symmetric_difference(v7, v6) = v8) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (symmetric_difference(v6, v7) = v8) |  ? [v9] :  ? [v10] : (difference(v7, v6) = v10 & difference(v6, v7) = v9 & union(v9, v10) = v8)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ subset(v6, v7) |  ~ member(v8, v6) | member(v8, v7)) &  ! [v6] :  ! [v7] : (v7 = v6 |  ~ subset(v7, v6) |  ~ subset(v6, v7)) &  ? [v6] :  ? [v7] : (v7 = v6 |  ? [v8] : (( ~ member(v8, v7) |  ~ member(v8, v6)) & (member(v8, v7) | member(v8, v6)))) &  ? [v6] :  ? [v7] : (subset(v6, v7) |  ? [v8] : (member(v8, v6) &  ~ member(v8, v7))) &  ? [v6] : subset(v6, v6))
% 4.07/1.65  | 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:
% 4.07/1.65  | (1)  ~ (all_0_0_0 = all_0_3_3) & intersection(all_0_5_5, all_0_4_4) = all_0_1_1 & union(all_0_2_2, all_0_1_1) = all_0_0_0 & union(all_0_5_5, all_0_4_4) = all_0_3_3 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v0 |  ~ (intersection(v0, v1) = v2) |  ~ (difference(v0, v1) = v3) |  ~ (union(v2, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v0) = v3) |  ~ (difference(v0, v1) = v2) |  ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (union(v3, v2) = v4) |  ~ (union(v0, v1) = v3) |  ? [v5] : (union(v1, v2) = v5 & union(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (union(v1, v2) = v3) |  ~ (union(v0, v3) = v4) |  ? [v5] : (union(v5, v2) = v4 & union(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (intersection(v0, v1) = v2) |  ~ (union(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (symmetric_difference(v3, v2) = v1) |  ~ (symmetric_difference(v3, v2) = v0)) &  ! [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] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1) | member(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v1) | member(v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3)) &  ! [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] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ member(v2, v0) | member(v2, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1)) &  ? [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] : subset(v0, v0)
% 4.07/1.66  |
% 4.07/1.66  | Applying alpha-rule on (1) yields:
% 4.07/1.66  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3))
% 4.07/1.66  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2))
% 4.07/1.66  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 4.07/1.66  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (union(v1, v2) = v3) |  ~ (union(v0, v3) = v4) |  ? [v5] : (union(v5, v2) = v4 & union(v0, v1) = v5))
% 4.07/1.66  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = v0 |  ~ (intersection(v0, v1) = v2) |  ~ (union(v0, v2) = v3))
% 4.07/1.66  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 4.07/1.66  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ member(v2, v0) | member(v2, v1))
% 4.07/1.66  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (union(v3, v2) = v4) |  ~ (union(v0, v1) = v3) |  ? [v5] : (union(v1, v2) = v5 & union(v0, v5) = v4))
% 4.07/1.66  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 4.07/1.66  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 4.07/1.66  | (12) union(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.07/1.66  | (13) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2
% 4.07/1.66  | (14)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 4.07/1.66  | (15)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 4.07/1.66  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v1) | member(v2, v3))
% 4.07/1.66  | (17)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 4.07/1.66  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 4.07/1.66  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 4.07/1.66  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 4.07/1.67  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 4.07/1.67  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 4.07/1.67  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1))
% 4.07/1.67  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3))
% 4.07/1.67  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 4.07/1.67  | (26)  ? [v0] : subset(v0, v0)
% 4.07/1.67  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v0) = v3) |  ~ (difference(v0, v1) = v2) |  ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 4.07/1.67  | (28)  ~ (all_0_0_0 = all_0_3_3)
% 4.07/1.67  | (29) union(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.07/1.67  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v0 |  ~ (intersection(v0, v1) = v2) |  ~ (difference(v0, v1) = v3) |  ~ (union(v2, v3) = v4))
% 4.07/1.67  | (31) intersection(all_0_5_5, all_0_4_4) = all_0_1_1
% 4.07/1.67  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 4.07/1.67  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (symmetric_difference(v3, v2) = v1) |  ~ (symmetric_difference(v3, v2) = v0))
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (19) with all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, yields:
% 4.07/1.67  | (34) intersection(all_0_4_4, all_0_5_5) = all_0_1_1
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (11) with all_0_0_0, all_0_2_2, all_0_1_1 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.07/1.67  | (35) union(all_0_1_1, all_0_2_2) = all_0_0_0
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (11) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms union(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.07/1.67  | (36) union(all_0_4_4, all_0_5_5) = all_0_3_3
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (21) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 4.07/1.67  | (37) symmetric_difference(all_0_4_4, all_0_5_5) = all_0_2_2
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (3) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 4.07/1.67  | (38)  ? [v0] :  ? [v1] : (difference(all_0_4_4, all_0_5_5) = v1 & difference(all_0_5_5, all_0_4_4) = v0 & union(v0, v1) = all_0_2_2)
% 4.07/1.67  |
% 4.07/1.67  | Instantiating (38) with all_13_0_11, all_13_1_12 yields:
% 4.07/1.67  | (39) difference(all_0_4_4, all_0_5_5) = all_13_0_11 & difference(all_0_5_5, all_0_4_4) = all_13_1_12 & union(all_13_1_12, all_13_0_11) = all_0_2_2
% 4.07/1.67  |
% 4.07/1.67  | Applying alpha-rule on (39) yields:
% 4.07/1.67  | (40) difference(all_0_4_4, all_0_5_5) = all_13_0_11
% 4.07/1.67  | (41) difference(all_0_5_5, all_0_4_4) = all_13_1_12
% 4.07/1.67  | (42) union(all_13_1_12, all_13_0_11) = all_0_2_2
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (9) with all_0_0_0, all_0_2_2, all_0_1_1, all_13_0_11, all_13_1_12 and discharging atoms union(all_13_1_12, all_13_0_11) = all_0_2_2, union(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 4.07/1.67  | (43)  ? [v0] : (union(all_13_0_11, all_0_1_1) = v0 & union(all_13_1_12, v0) = all_0_0_0)
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_13_0_11, all_13_1_12, all_0_1_1 and discharging atoms union(all_13_1_12, all_13_0_11) = all_0_2_2, union(all_0_1_1, all_0_2_2) = all_0_0_0, yields:
% 4.07/1.67  | (44)  ? [v0] : (union(v0, all_13_0_11) = all_0_0_0 & union(all_0_1_1, all_13_1_12) = v0)
% 4.07/1.67  |
% 4.07/1.67  | Instantiating formula (3) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_4_4, all_0_5_5) = all_0_2_2, yields:
% 4.07/1.67  | (45)  ? [v0] :  ? [v1] : (difference(all_0_4_4, all_0_5_5) = v0 & difference(all_0_5_5, all_0_4_4) = v1 & union(v0, v1) = all_0_2_2)
% 4.07/1.67  |
% 4.07/1.67  | Instantiating (45) with all_21_0_13, all_21_1_14 yields:
% 4.07/1.67  | (46) difference(all_0_4_4, all_0_5_5) = all_21_1_14 & difference(all_0_5_5, all_0_4_4) = all_21_0_13 & union(all_21_1_14, all_21_0_13) = all_0_2_2
% 4.07/1.67  |
% 4.07/1.67  | Applying alpha-rule on (46) yields:
% 4.07/1.68  | (47) difference(all_0_4_4, all_0_5_5) = all_21_1_14
% 4.07/1.68  | (48) difference(all_0_5_5, all_0_4_4) = all_21_0_13
% 4.07/1.68  | (49) union(all_21_1_14, all_21_0_13) = all_0_2_2
% 4.07/1.68  |
% 4.07/1.68  | Instantiating (43) with all_23_0_15 yields:
% 4.07/1.68  | (50) union(all_13_0_11, all_0_1_1) = all_23_0_15 & union(all_13_1_12, all_23_0_15) = all_0_0_0
% 4.07/1.68  |
% 4.07/1.68  | Applying alpha-rule on (50) yields:
% 4.07/1.68  | (51) union(all_13_0_11, all_0_1_1) = all_23_0_15
% 4.07/1.68  | (52) union(all_13_1_12, all_23_0_15) = all_0_0_0
% 4.07/1.68  |
% 4.07/1.68  | Instantiating (44) with all_25_0_16 yields:
% 4.07/1.68  | (53) union(all_25_0_16, all_13_0_11) = all_0_0_0 & union(all_0_1_1, all_13_1_12) = all_25_0_16
% 4.07/1.68  |
% 4.07/1.68  | Applying alpha-rule on (53) yields:
% 4.07/1.68  | (54) union(all_25_0_16, all_13_0_11) = all_0_0_0
% 4.07/1.68  | (55) union(all_0_1_1, all_13_1_12) = all_25_0_16
% 4.07/1.68  |
% 4.07/1.68  | Instantiating formula (7) with all_0_4_4, all_0_5_5, all_21_1_14, all_13_0_11 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_21_1_14, difference(all_0_4_4, all_0_5_5) = all_13_0_11, yields:
% 4.07/1.68  | (56) all_21_1_14 = all_13_0_11
% 4.07/1.68  |
% 4.07/1.68  | Instantiating formula (7) with all_0_5_5, all_0_4_4, all_21_0_13, all_13_1_12 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_21_0_13, difference(all_0_5_5, all_0_4_4) = all_13_1_12, yields:
% 4.07/1.68  | (57) all_21_0_13 = all_13_1_12
% 4.07/1.68  |
% 4.07/1.68  | Instantiating formula (30) with all_25_0_16, all_13_1_12, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms intersection(all_0_5_5, all_0_4_4) = all_0_1_1, difference(all_0_5_5, all_0_4_4) = all_13_1_12, union(all_0_1_1, all_13_1_12) = all_25_0_16, yields:
% 4.07/1.68  | (58) all_25_0_16 = all_0_5_5
% 4.07/1.68  |
% 4.07/1.68  | From (56) and (47) follows:
% 4.07/1.68  | (40) difference(all_0_4_4, all_0_5_5) = all_13_0_11
% 4.07/1.68  |
% 4.07/1.68  | From (56)(57) and (49) follows:
% 4.07/1.68  | (60) union(all_13_0_11, all_13_1_12) = all_0_2_2
% 4.07/1.68  |
% 4.07/1.68  | From (58) and (55) follows:
% 4.07/1.68  | (61) union(all_0_1_1, all_13_1_12) = all_0_5_5
% 4.07/1.68  |
% 4.07/1.68  | Instantiating formula (5) with all_0_0_0, all_0_2_2, all_13_1_12, all_13_0_11, all_0_1_1 and discharging atoms union(all_13_0_11, all_13_1_12) = all_0_2_2, union(all_0_1_1, all_0_2_2) = all_0_0_0, yields:
% 4.07/1.68  | (62)  ? [v0] : (union(v0, all_13_1_12) = all_0_0_0 & union(all_0_1_1, all_13_0_11) = v0)
% 4.07/1.68  |
% 4.07/1.68  | Instantiating formula (11) with all_23_0_15, all_13_0_11, all_0_1_1 and discharging atoms union(all_13_0_11, all_0_1_1) = all_23_0_15, yields:
% 4.07/1.68  | (63) union(all_0_1_1, all_13_0_11) = all_23_0_15
% 4.07/1.68  |
% 4.07/1.68  | Instantiating formula (11) with all_0_0_0, all_13_1_12, all_23_0_15 and discharging atoms union(all_13_1_12, all_23_0_15) = all_0_0_0, yields:
% 4.07/1.68  | (64) union(all_23_0_15, all_13_1_12) = all_0_0_0
% 4.29/1.68  |
% 4.29/1.68  | Instantiating formula (5) with all_0_3_3, all_0_5_5, all_13_1_12, all_0_1_1, all_0_4_4 and discharging atoms union(all_0_1_1, all_13_1_12) = all_0_5_5, union(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 4.29/1.68  | (65)  ? [v0] : (union(v0, all_13_1_12) = all_0_3_3 & union(all_0_4_4, all_0_1_1) = v0)
% 4.29/1.68  |
% 4.29/1.68  | Instantiating (62) with all_39_0_18 yields:
% 4.29/1.68  | (66) union(all_39_0_18, all_13_1_12) = all_0_0_0 & union(all_0_1_1, all_13_0_11) = all_39_0_18
% 4.29/1.68  |
% 4.29/1.68  | Applying alpha-rule on (66) yields:
% 4.29/1.68  | (67) union(all_39_0_18, all_13_1_12) = all_0_0_0
% 4.29/1.68  | (68) union(all_0_1_1, all_13_0_11) = all_39_0_18
% 4.29/1.68  |
% 4.29/1.68  | Instantiating (65) with all_43_0_20 yields:
% 4.29/1.68  | (69) union(all_43_0_20, all_13_1_12) = all_0_3_3 & union(all_0_4_4, all_0_1_1) = all_43_0_20
% 4.29/1.68  |
% 4.29/1.68  | Applying alpha-rule on (69) yields:
% 4.29/1.68  | (70) union(all_43_0_20, all_13_1_12) = all_0_3_3
% 4.29/1.68  | (71) union(all_0_4_4, all_0_1_1) = all_43_0_20
% 4.29/1.68  |
% 4.29/1.68  | Instantiating formula (30) with all_39_0_18, all_13_0_11, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_1_1, difference(all_0_4_4, all_0_5_5) = all_13_0_11, union(all_0_1_1, all_13_0_11) = all_39_0_18, yields:
% 4.29/1.68  | (72) all_39_0_18 = all_0_4_4
% 4.29/1.68  |
% 4.29/1.68  | Instantiating formula (22) with all_0_1_1, all_13_0_11, all_23_0_15, all_39_0_18 and discharging atoms union(all_0_1_1, all_13_0_11) = all_39_0_18, union(all_0_1_1, all_13_0_11) = all_23_0_15, yields:
% 4.29/1.69  | (73) all_39_0_18 = all_23_0_15
% 4.29/1.69  |
% 4.29/1.69  | Instantiating formula (6) with all_43_0_20, all_0_1_1, all_0_5_5, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_5_5) = all_0_1_1, union(all_0_4_4, all_0_1_1) = all_43_0_20, yields:
% 4.29/1.69  | (74) all_43_0_20 = all_0_4_4
% 4.29/1.69  |
% 4.29/1.69  | Combining equations (72,73) yields a new equation:
% 4.29/1.69  | (75) all_23_0_15 = all_0_4_4
% 4.29/1.69  |
% 4.29/1.69  | From (74) and (70) follows:
% 4.29/1.69  | (76) union(all_0_4_4, all_13_1_12) = all_0_3_3
% 4.29/1.69  |
% 4.29/1.69  | From (75) and (64) follows:
% 4.29/1.69  | (77) union(all_0_4_4, all_13_1_12) = all_0_0_0
% 4.29/1.69  |
% 4.29/1.69  | Instantiating formula (22) with all_0_4_4, all_13_1_12, all_0_3_3, all_0_0_0 and discharging atoms union(all_0_4_4, all_13_1_12) = all_0_0_0, union(all_0_4_4, all_13_1_12) = all_0_3_3, yields:
% 4.29/1.69  | (78) all_0_0_0 = all_0_3_3
% 4.29/1.69  |
% 4.29/1.69  | Equations (78) can reduce 28 to:
% 4.29/1.69  | (79) $false
% 4.29/1.69  |
% 4.29/1.69  |-The branch is then unsatisfiable
% 4.29/1.69  % SZS output end Proof for theBenchmark
% 4.29/1.69  
% 4.29/1.69  1097ms
%------------------------------------------------------------------------------