%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n026.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 00:20:53 EDT 2022

% Result   : Theorem 2.74s 1.44s
% Output   : Proof 4.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SET620+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.08  % Command  : ePrincess-casc -timeout=%d %s
% 0.07/0.28  % Computer : n026.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit : 300
% 0.07/0.28  % WCLimit  : 600
% 0.07/0.28  % DateTime : Mon Jul 11 06:03:42 EDT 2022
% 0.07/0.28  % CPUTime  : 
% 0.48/0.53          ____       _                          
% 0.48/0.53    ___  / __ \_____(_)___  ________  __________
% 0.48/0.53   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.48/0.53  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.48/0.53  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.48/0.53  
% 0.48/0.53  A Theorem Prover for First-Order Logic
% 0.48/0.53  (ePrincess v.1.0)
% 0.48/0.53  
% 0.48/0.53  (c) Philipp Rümmer, 2009-2015
% 0.48/0.53  (c) Peter Backeman, 2014-2015
% 0.48/0.53  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.48/0.53  Free software under GNU Lesser General Public License (LGPL).
% 0.48/0.53  Bug reports to peter@backeman.se
% 0.48/0.53  
% 0.48/0.53  For more information, visit http://user.uu.se/~petba168/breu/
% 0.48/0.53  
% 0.48/0.53  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.50/0.59  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.21/0.90  Prover 0: Preprocessing ...
% 1.89/1.18  Prover 0: Warning: ignoring some quantifiers
% 1.89/1.21  Prover 0: Constructing countermodel ...
% 2.74/1.44  Prover 0: proved (846ms)
% 2.74/1.44  
% 2.74/1.44  No countermodel exists, formula is valid
% 2.74/1.44  % SZS status Theorem for theBenchmark
% 2.74/1.44  
% 2.74/1.44  Generating proof ... Warning: ignoring some quantifiers
% 4.18/1.78  found it (size 27)
% 4.18/1.78  
% 4.18/1.78  % SZS output start Proof for theBenchmark
% 4.18/1.78  Assumed formulas after preprocessing and simplification: 
% 4.18/1.78  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v5 = v2) & intersection(v0, v1) = v4 & difference(v3, v4) = v5 & union(v0, v1) = v3 & symmetric_difference(v0, v1) = v2 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (difference(v7, v8) = v10) |  ~ (difference(v6, v8) = v9) |  ~ (union(v9, v10) = v11) |  ? [v12] : (difference(v12, v8) = v11 & union(v6, v7) = v12)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (difference(v9, v8) = v10) |  ~ (union(v6, v7) = v9) |  ? [v11] :  ? [v12] : (difference(v7, v8) = v12 & difference(v6, v8) = v11 & union(v11, v12) = 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] : (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] : ( ~ (intersection(v6, v7) = v8) |  ~ (difference(v6, v8) = v9) | difference(v6, v7) = v9) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (difference(v6, v7) = v9) |  ~ member(v8, v9) |  ~ member(v8, v7)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (difference(v6, v7) = v9) |  ~ member(v8, v9) | member(v8, v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (difference(v6, v7) = v9) |  ~ member(v8, v6) | member(v8, v9) | member(v8, v7)) &  ! [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] : ( ~ (difference(v6, v7) = v8) |  ? [v9] : (intersection(v6, v7) = v9 & difference(v6, v9) = 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))
% 4.40/1.85  | 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:
% 4.40/1.85  | (1)  ~ (all_0_0_0 = all_0_3_3) & intersection(all_0_5_5, all_0_4_4) = all_0_1_1 & difference(all_0_2_2, all_0_1_1) = all_0_0_0 & union(all_0_5_5, all_0_4_4) = all_0_2_2 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (difference(v1, v2) = v4) |  ~ (difference(v0, v2) = v3) |  ~ (union(v3, v4) = v5) |  ? [v6] : (difference(v6, v2) = v5 & union(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v3, v2) = v4) |  ~ (union(v0, v1) = v3) |  ? [v5] :  ? [v6] : (difference(v1, v2) = v6 & difference(v0, v2) = v5 & union(v5, v6) = 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] : (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] : ( ~ (intersection(v0, v1) = v2) |  ~ (difference(v0, v2) = v3) | difference(v0, v1) = v3) &  ! [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] : ( ~ (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] : ( ~ (difference(v0, v1) = v2) |  ? [v3] : (intersection(v0, v1) = v3 & difference(v0, v3) = 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)
% 4.62/1.86  |
% 4.62/1.86  | Applying alpha-rule on (1) yields:
% 4.62/1.86  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 4.62/1.86  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 4.62/1.87  | (4)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 4.62/1.87  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 4.62/1.87  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2))
% 4.62/1.87  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1))
% 4.62/1.87  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v1) | member(v2, v3))
% 4.62/1.87  | (9)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 4.62/1.87  | (10) difference(all_0_2_2, all_0_1_1) = all_0_0_0
% 4.62/1.87  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) |  ~ member(v2, v1))
% 4.62/1.87  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v0, v1) |  ~ member(v2, v0) | member(v2, v1))
% 4.62/1.87  | (13) intersection(all_0_5_5, all_0_4_4) = all_0_1_1
% 4.62/1.87  | (14)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 4.62/1.87  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 4.62/1.87  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (symmetric_difference(v3, v2) = v1) |  ~ (symmetric_difference(v3, v2) = v0))
% 4.62/1.87  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v2) |  ~ (difference(v0, v2) = v3) | difference(v0, v1) = v3)
% 4.62/1.87  | (18) union(all_0_5_5, all_0_4_4) = all_0_2_2
% 4.62/1.87  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 4.62/1.87  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 4.62/1.88  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 4.62/1.88  | (22)  ? [v0] : subset(v0, v0)
% 4.62/1.88  | (23)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 4.62/1.88  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 4.62/1.88  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v0) = v3) |  ~ (difference(v0, v1) = v2) |  ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 4.62/1.88  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3))
% 4.62/1.88  | (27)  ~ (all_0_0_0 = all_0_3_3)
% 4.62/1.88  | (28)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 4.62/1.88  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 4.62/1.88  | (30) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3
% 4.62/1.88  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v3, v2) = v4) |  ~ (union(v0, v1) = v3) |  ? [v5] :  ? [v6] : (difference(v1, v2) = v6 & difference(v0, v2) = v5 & union(v5, v6) = v4))
% 4.62/1.88  | (32)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (difference(v0, v1) = v2) |  ? [v3] : (intersection(v0, v1) = v3 & difference(v0, v3) = v2))
% 4.62/1.88  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3))
% 4.62/1.88  | (34)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 4.62/1.88  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 4.62/1.89  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (difference(v1, v2) = v4) |  ~ (difference(v0, v2) = v3) |  ~ (union(v3, v4) = v5) |  ? [v6] : (difference(v6, v2) = v5 & union(v0, v1) = v6))
% 4.62/1.89  |
% 4.62/1.89  | Instantiating formula (35) 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:
% 4.62/1.89  | (37) intersection(all_0_4_4, all_0_5_5) = all_0_1_1
% 4.62/1.89  |
% 4.62/1.89  | Instantiating formula (31) with all_0_0_0, all_0_2_2, all_0_1_1, all_0_4_4, all_0_5_5 and discharging atoms difference(all_0_2_2, all_0_1_1) = all_0_0_0, union(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 4.62/1.89  | (38)  ? [v0] :  ? [v1] : (difference(all_0_4_4, all_0_1_1) = v1 & difference(all_0_5_5, all_0_1_1) = v0 & union(v0, v1) = all_0_0_0)
% 4.62/1.89  |
% 4.62/1.89  | Instantiating formula (24) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.62/1.89  | (39) symmetric_difference(all_0_4_4, all_0_5_5) = all_0_3_3
% 4.62/1.89  |
% 4.62/1.89  | Instantiating formula (6) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 4.62/1.89  | (40)  ? [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_3_3)
% 4.62/1.89  |
% 4.62/1.89  | Instantiating (38) with all_13_0_11, all_13_1_12 yields:
% 4.62/1.89  | (41) difference(all_0_4_4, all_0_1_1) = all_13_0_11 & difference(all_0_5_5, all_0_1_1) = all_13_1_12 & union(all_13_1_12, all_13_0_11) = all_0_0_0
% 4.62/1.89  |
% 4.62/1.89  | Applying alpha-rule on (41) yields:
% 4.62/1.89  | (42) difference(all_0_4_4, all_0_1_1) = all_13_0_11
% 4.62/1.89  | (43) difference(all_0_5_5, all_0_1_1) = all_13_1_12
% 4.62/1.89  | (44) union(all_13_1_12, all_13_0_11) = all_0_0_0
% 4.62/1.89  |
% 4.62/1.89  | Instantiating (40) with all_15_0_13, all_15_1_14 yields:
% 4.62/1.89  | (45) difference(all_0_4_4, all_0_5_5) = all_15_0_13 & difference(all_0_5_5, all_0_4_4) = all_15_1_14 & union(all_15_1_14, all_15_0_13) = all_0_3_3
% 4.62/1.89  |
% 4.62/1.89  | Applying alpha-rule on (45) yields:
% 4.62/1.89  | (46) difference(all_0_4_4, all_0_5_5) = all_15_0_13
% 4.62/1.89  | (47) difference(all_0_5_5, all_0_4_4) = all_15_1_14
% 4.62/1.89  | (48) union(all_15_1_14, all_15_0_13) = all_0_3_3
% 4.62/1.89  |
% 4.62/1.89  | Instantiating formula (17) with 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_1_1) = all_13_0_11, yields:
% 4.62/1.90  | (49) difference(all_0_4_4, all_0_5_5) = all_13_0_11
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (17) with 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_1_1) = all_13_1_12, yields:
% 4.62/1.90  | (50) difference(all_0_5_5, all_0_4_4) = all_13_1_12
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (6) with all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms symmetric_difference(all_0_4_4, all_0_5_5) = all_0_3_3, yields:
% 4.62/1.90  | (51)  ? [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_3_3)
% 4.62/1.90  |
% 4.62/1.90  | Instantiating (51) with all_35_0_23, all_35_1_24 yields:
% 4.62/1.90  | (52) difference(all_0_4_4, all_0_5_5) = all_35_1_24 & difference(all_0_5_5, all_0_4_4) = all_35_0_23 & union(all_35_1_24, all_35_0_23) = all_0_3_3
% 4.62/1.90  |
% 4.62/1.90  | Applying alpha-rule on (52) yields:
% 4.62/1.90  | (53) difference(all_0_4_4, all_0_5_5) = all_35_1_24
% 4.62/1.90  | (54) difference(all_0_5_5, all_0_4_4) = all_35_0_23
% 4.62/1.90  | (55) union(all_35_1_24, all_35_0_23) = all_0_3_3
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (15) with all_0_4_4, all_0_5_5, all_35_1_24, all_15_0_13 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_35_1_24, difference(all_0_4_4, all_0_5_5) = all_15_0_13, yields:
% 4.62/1.90  | (56) all_35_1_24 = all_15_0_13
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (15) with all_0_4_4, all_0_5_5, all_13_0_11, all_35_1_24 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_35_1_24, difference(all_0_4_4, all_0_5_5) = all_13_0_11, yields:
% 4.62/1.90  | (57) all_35_1_24 = all_13_0_11
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (15) with all_0_5_5, all_0_4_4, all_35_0_23, all_15_1_14 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_35_0_23, difference(all_0_5_5, all_0_4_4) = all_15_1_14, yields:
% 4.62/1.90  | (58) all_35_0_23 = all_15_1_14
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (15) with all_0_5_5, all_0_4_4, all_13_1_12, all_35_0_23 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_35_0_23, difference(all_0_5_5, all_0_4_4) = all_13_1_12, yields:
% 4.62/1.90  | (59) all_35_0_23 = all_13_1_12
% 4.62/1.90  |
% 4.62/1.90  | Combining equations (58,59) yields a new equation:
% 4.62/1.90  | (60) all_15_1_14 = all_13_1_12
% 4.62/1.90  |
% 4.62/1.90  | Simplifying 60 yields:
% 4.62/1.90  | (61) all_15_1_14 = all_13_1_12
% 4.62/1.90  |
% 4.62/1.90  | Combining equations (56,57) yields a new equation:
% 4.62/1.90  | (62) all_15_0_13 = all_13_0_11
% 4.62/1.90  |
% 4.62/1.90  | Simplifying 62 yields:
% 4.62/1.90  | (63) all_15_0_13 = all_13_0_11
% 4.62/1.90  |
% 4.62/1.90  | From (61)(63) and (48) follows:
% 4.62/1.90  | (64) union(all_13_1_12, all_13_0_11) = all_0_3_3
% 4.62/1.90  |
% 4.62/1.90  | Instantiating formula (21) with all_13_1_12, all_13_0_11, all_0_3_3, all_0_0_0 and discharging atoms union(all_13_1_12, all_13_0_11) = all_0_0_0, union(all_13_1_12, all_13_0_11) = all_0_3_3, yields:
% 4.62/1.91  | (65) all_0_0_0 = all_0_3_3
% 4.62/1.91  |
% 4.62/1.91  | Equations (65) can reduce 27 to:
% 4.62/1.91  | (66) $false
% 4.62/1.91  |
% 4.62/1.91  |-The branch is then unsatisfiable
% 4.62/1.91  % SZS output end Proof for theBenchmark
% 4.62/1.91  
% 4.62/1.91  1364ms
%------------------------------------------------------------------------------