TSTP Solution File: SET633+3 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.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 00:21:02 EDT 2022

% Result   : Theorem 2.24s 1.20s
% Output   : Proof 3.11s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SET633+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.33  % Computer : n023.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Sat Jul  9 22:22:10 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.59          ____       _                          
% 0.20/0.59    ___  / __ \_____(_)___  ________  __________
% 0.20/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.20/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.20/0.59  
% 0.20/0.59  A Theorem Prover for First-Order Logic
% 0.20/0.59  (ePrincess v.1.0)
% 0.20/0.59  
% 0.20/0.59  (c) Philipp Rümmer, 2009-2015
% 0.20/0.59  (c) Peter Backeman, 2014-2015
% 0.20/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.59  Bug reports to peter@backeman.se
% 0.20/0.59  
% 0.20/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.59  
% 0.20/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.41/0.91  Prover 0: Preprocessing ...
% 1.87/1.08  Prover 0: Warning: ignoring some quantifiers
% 1.87/1.10  Prover 0: Constructing countermodel ...
% 2.24/1.20  Prover 0: proved (556ms)
% 2.24/1.20  
% 2.24/1.20  No countermodel exists, formula is valid
% 2.24/1.20  % SZS status Theorem for theBenchmark
% 2.24/1.20  
% 2.24/1.20  Generating proof ... Warning: ignoring some quantifiers
% 2.90/1.39  found it (size 10)
% 2.90/1.39  
% 2.90/1.39  % SZS output start Proof for theBenchmark
% 2.90/1.40  Assumed formulas after preprocessing and simplification: 
% 2.90/1.40  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & symmetric_difference(v0, v1) = v5 & subset(v4, v2) & subset(v3, v2) &  ~ subset(v5, v2) &  ! [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 |  ~ (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] : ( ~ (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, v8) = v9) |  ~ subset(v8, v7) |  ~ subset(v6, v7) | subset(v9, v7)) &  ! [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] : ( ~ member(v8, v6) |  ~ subset(v6, v7) | member(v8, 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))
% 2.90/1.43  | 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:
% 2.90/1.43  | (1) difference(all_0_4_4, all_0_5_5) = all_0_1_1 & difference(all_0_5_5, all_0_4_4) = all_0_2_2 & symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0 & subset(all_0_1_1, all_0_3_3) & subset(all_0_2_2, all_0_3_3) &  ~ subset(all_0_0_0, all_0_3_3) &  ! [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 |  ~ (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] : ( ~ (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, v2) = v3) |  ~ subset(v2, v1) |  ~ subset(v0, v1) | subset(v3, 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] : ( ~ (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] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, 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)
% 2.90/1.44  |
% 2.90/1.44  | Applying alpha-rule on (1) yields:
% 2.90/1.44  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) | symmetric_difference(v1, v0) = v2)
% 2.90/1.44  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v1, v0) = v2) | symmetric_difference(v0, v1) = v2)
% 2.90/1.44  | (4)  ~ subset(all_0_0_0, all_0_3_3)
% 2.90/1.44  | (5)  ? [v0] : subset(v0, v0)
% 2.90/1.44  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1))
% 2.90/1.44  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 2.90/1.44  | (8)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.90/1.44  | (9) subset(all_0_1_1, all_0_3_3)
% 2.90/1.44  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v2) = v3) |  ~ subset(v2, v1) |  ~ subset(v0, v1) | subset(v3, v1))
% 2.90/1.45  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 2.90/1.45  | (12) symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0
% 2.90/1.45  | (13)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 2.90/1.45  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 2.90/1.45  | (15)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 2.90/1.45  | (16)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 2.90/1.45  | (17) subset(all_0_2_2, all_0_3_3)
% 2.90/1.45  | (18) difference(all_0_5_5, all_0_4_4) = all_0_2_2
% 2.90/1.45  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) |  ~ member(v2, v1))
% 2.90/1.45  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (symmetric_difference(v0, v1) = v2) |  ? [v3] :  ? [v4] : (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2))
% 2.90/1.45  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (symmetric_difference(v3, v2) = v1) |  ~ (symmetric_difference(v3, v2) = v0))
% 2.90/1.45  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 2.90/1.45  | (23) difference(all_0_4_4, all_0_5_5) = all_0_1_1
% 2.90/1.45  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v0) = v3) |  ~ (difference(v0, v1) = v2) |  ~ (union(v2, v3) = v4) | symmetric_difference(v0, v1) = v4)
% 2.90/1.45  |
% 2.90/1.45  | Instantiating formula (20) with all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms symmetric_difference(all_0_5_5, all_0_4_4) = all_0_0_0, yields:
% 2.90/1.45  | (25)  ? [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_0_0)
% 2.90/1.45  |
% 2.90/1.45  | Instantiating (25) with all_13_0_11, all_13_1_12 yields:
% 2.90/1.45  | (26) 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_0_0
% 2.90/1.45  |
% 2.90/1.45  | Applying alpha-rule on (26) yields:
% 2.90/1.45  | (27) difference(all_0_4_4, all_0_5_5) = all_13_0_11
% 2.90/1.45  | (28) difference(all_0_5_5, all_0_4_4) = all_13_1_12
% 2.90/1.45  | (29) union(all_13_1_12, all_13_0_11) = all_0_0_0
% 2.90/1.45  |
% 2.90/1.45  | Instantiating formula (14) with all_0_4_4, all_0_5_5, all_13_0_11, all_0_1_1 and discharging atoms difference(all_0_4_4, all_0_5_5) = all_13_0_11, difference(all_0_4_4, all_0_5_5) = all_0_1_1, yields:
% 2.90/1.45  | (30) all_13_0_11 = all_0_1_1
% 2.90/1.45  |
% 2.90/1.45  | Instantiating formula (14) with all_0_5_5, all_0_4_4, all_13_1_12, all_0_2_2 and discharging atoms difference(all_0_5_5, all_0_4_4) = all_13_1_12, difference(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 2.90/1.45  | (31) all_13_1_12 = all_0_2_2
% 2.90/1.45  |
% 3.11/1.45  | From (31)(30) and (29) follows:
% 3.11/1.46  | (32) union(all_0_2_2, all_0_1_1) = all_0_0_0
% 3.11/1.46  |
% 3.11/1.46  | Instantiating formula (10) with all_0_0_0, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms union(all_0_2_2, all_0_1_1) = all_0_0_0, subset(all_0_1_1, all_0_3_3), subset(all_0_2_2, all_0_3_3),  ~ subset(all_0_0_0, all_0_3_3), yields:
% 3.11/1.46  | (33) $false
% 3.11/1.46  |
% 3.11/1.46  |-The branch is then unsatisfiable
% 3.11/1.46  % SZS output end Proof for theBenchmark
% 3.11/1.46  
% 3.11/1.46  854ms
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