TSTP Solution File: SET585+3 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n009.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 00:20:28 EDT 2022

% Result   : Theorem 2.11s 1.21s
% Output   : Proof 3.01s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET585+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n009.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 13:52:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.49/0.58          ____       _                          
% 0.49/0.58    ___  / __ \_____(_)___  ________  __________
% 0.49/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.49/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.49/0.58  
% 0.49/0.58  A Theorem Prover for First-Order Logic
% 0.49/0.58  (ePrincess v.1.0)
% 0.49/0.58  
% 0.49/0.58  (c) Philipp Rümmer, 2009-2015
% 0.49/0.58  (c) Peter Backeman, 2014-2015
% 0.49/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.58  Bug reports to peter@backeman.se
% 0.49/0.58  
% 0.49/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.58  
% 0.49/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.92  Prover 0: Preprocessing ...
% 1.88/1.09  Prover 0: Warning: ignoring some quantifiers
% 1.88/1.11  Prover 0: Constructing countermodel ...
% 2.11/1.20  Prover 0: proved (571ms)
% 2.11/1.21  
% 2.11/1.21  No countermodel exists, formula is valid
% 2.11/1.21  % SZS status Theorem for theBenchmark
% 2.11/1.21  
% 2.11/1.21  Generating proof ... Warning: ignoring some quantifiers
% 2.84/1.38  found it (size 6)
% 2.84/1.38  
% 2.84/1.38  % SZS output start Proof for theBenchmark
% 2.84/1.38  Assumed formulas after preprocessing and simplification: 
% 2.84/1.38  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (intersection(v0, v1) = v3 & union(v0, v2) = v4 &  ~ subset(v3, v4) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection(v8, v7) = v6) |  ~ (intersection(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (union(v8, v7) = v6) |  ~ (union(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v5, v6) = v8) |  ~ member(v7, v8) | member(v7, v6)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v5, v6) = v8) |  ~ member(v7, v8) | member(v7, v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection(v5, v6) = v8) |  ~ member(v7, v6) |  ~ member(v7, v5) | member(v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v5, v6) = v8) |  ~ member(v7, v8) | member(v7, v6) | member(v7, v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v5, v6) = v8) |  ~ member(v7, v6) | member(v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (union(v5, v6) = v8) |  ~ member(v7, v5) | member(v7, v8)) &  ! [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)) &  ! [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] : ( ~ (union(v5, v6) = v7) | subset(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ member(v7, v5) |  ~ subset(v5, v6) | member(v7, v6)) &  ! [v5] :  ! [v6] :  ! [v7] : ( ~ subset(v6, v7) |  ~ subset(v5, v6) | subset(v5, v7)) &  ? [v5] :  ? [v6] : (v6 = v5 |  ? [v7] : (( ~ member(v7, v6) |  ~ member(v7, v5)) & (member(v7, v6) | member(v7, v5)))) &  ? [v5] :  ? [v6] : (subset(v5, v6) |  ? [v7] : (member(v7, v5) &  ~ member(v7, v6))) &  ? [v5] : subset(v5, v5))
% 3.01/1.42  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 3.01/1.42  | (1) intersection(all_0_4_4, all_0_3_3) = all_0_1_1 & union(all_0_4_4, all_0_2_2) = all_0_0_0 &  ~ subset(all_0_1_1, all_0_0_0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(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] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0)) &  ! [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] : ( ~ (union(v0, v1) = v2) | subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2)) &  ? [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)
% 3.01/1.43  |
% 3.01/1.43  | Applying alpha-rule on (1) yields:
% 3.01/1.43  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (union(v3, v2) = v1) |  ~ (union(v3, v2) = v0))
% 3.01/1.43  | (3) union(all_0_4_4, all_0_2_2) = all_0_0_0
% 3.01/1.43  | (4)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 3.01/1.44  | (5)  ? [v0] : subset(v0, v0)
% 3.01/1.44  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | subset(v0, v2))
% 3.01/1.44  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1))
% 3.01/1.44  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | subset(v2, v0))
% 3.01/1.44  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ~ subset(v0, v1) | subset(v0, v2))
% 3.01/1.44  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1))
% 3.01/1.44  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 3.01/1.44  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 3.01/1.44  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3))
% 3.01/1.44  | (14) intersection(all_0_4_4, all_0_3_3) = all_0_1_1
% 3.01/1.44  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 3.01/1.44  | (16)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 3.01/1.44  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v1) | member(v2, v3))
% 3.01/1.44  | (18)  ~ subset(all_0_1_1, all_0_0_0)
% 3.01/1.44  | (19)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v0, v1) = v2) | union(v1, v0) = v2)
% 3.01/1.44  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (union(v1, v0) = v2) | union(v0, v1) = v2)
% 3.01/1.44  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3))
% 3.01/1.44  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (union(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1) | member(v2, v0))
% 3.01/1.44  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 3.01/1.44  |
% 3.01/1.44  | Instantiating formula (8) with all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 3.01/1.44  | (24) subset(all_0_1_1, all_0_4_4)
% 3.01/1.44  |
% 3.01/1.44  | Instantiating formula (6) with all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms union(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 3.01/1.44  | (25) subset(all_0_4_4, all_0_0_0)
% 3.01/1.44  |
% 3.01/1.44  | Instantiating formula (9) with all_0_0_0, all_0_4_4, all_0_1_1 and discharging atoms subset(all_0_1_1, all_0_4_4), subset(all_0_4_4, all_0_0_0),  ~ subset(all_0_1_1, all_0_0_0), yields:
% 3.01/1.44  | (26) $false
% 3.01/1.44  |
% 3.01/1.44  |-The branch is then unsatisfiable
% 3.01/1.44  % SZS output end Proof for theBenchmark
% 3.01/1.44  
% 3.01/1.44  849ms
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