TSTP Solution File: SET592+3 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n012.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 00:20:32 EDT 2022

% Result   : Theorem 2.06s 1.19s
% Output   : Proof 2.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n012.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 09:49:58 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.58          ____       _                          
% 0.19/0.58    ___  / __ \_____(_)___  ________  __________
% 0.19/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.58  
% 0.19/0.58  A Theorem Prover for First-Order Logic
% 0.19/0.59  (ePrincess v.1.0)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2015
% 0.19/0.59  (c) Peter Backeman, 2014-2015
% 0.19/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59  Bug reports to peter@backeman.se
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.45/0.92  Prover 0: Preprocessing ...
% 1.85/1.09  Prover 0: Warning: ignoring some quantifiers
% 1.96/1.11  Prover 0: Constructing countermodel ...
% 2.06/1.19  Prover 0: proved (557ms)
% 2.06/1.19  
% 2.06/1.19  No countermodel exists, formula is valid
% 2.06/1.19  % SZS status Theorem for theBenchmark
% 2.06/1.19  
% 2.06/1.19  Generating proof ... Warning: ignoring some quantifiers
% 2.82/1.36  found it (size 6)
% 2.82/1.36  
% 2.82/1.36  % SZS output start Proof for theBenchmark
% 2.82/1.36  Assumed formulas after preprocessing and simplification: 
% 2.82/1.36  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v0 = empty_set) & intersection(v1, v2) = empty_set & subset(v0, v2) & subset(v0, v1) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v4 = v3 |  ~ (intersection(v6, v5) = v4) |  ~ (intersection(v6, v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (intersection(v4, v5) = v6) |  ~ subset(v3, v5) |  ~ subset(v3, v4) | subset(v3, v6)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (intersection(v3, v4) = v6) |  ~ member(v5, v6) | member(v5, v4)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (intersection(v3, v4) = v6) |  ~ member(v5, v6) | member(v5, v3)) &  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (intersection(v3, v4) = v6) |  ~ member(v5, v4) |  ~ member(v5, v3) | member(v5, v6)) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v4, v3) = v5) | intersection(v3, v4) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v3, v4) = v5) | intersection(v4, v3) = v5) &  ! [v3] :  ! [v4] :  ! [v5] : ( ~ member(v5, v3) |  ~ subset(v3, v4) | member(v5, v4)) &  ! [v3] :  ! [v4] : (v4 = v3 |  ~ subset(v4, v3) |  ~ subset(v3, v4)) &  ! [v3] :  ! [v4] : ( ~ empty(v3) |  ~ member(v4, v3)) &  ! [v3] : (v3 = empty_set |  ~ subset(v3, empty_set)) &  ! [v3] :  ~ member(v3, empty_set) &  ? [v3] :  ? [v4] : (v4 = v3 |  ? [v5] : (( ~ member(v5, v4) |  ~ member(v5, v3)) & (member(v5, v4) | member(v5, v3)))) &  ? [v3] :  ? [v4] : (subset(v3, v4) |  ? [v5] : (member(v5, v3) &  ~ member(v5, v4))) &  ? [v3] : (empty(v3) |  ? [v4] : member(v4, v3)) &  ? [v3] : subset(v3, v3))
% 2.82/1.40  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.82/1.40  | (1)  ~ (all_0_2_2 = empty_set) & intersection(all_0_1_1, all_0_0_0) = empty_set & subset(all_0_2_2, all_0_0_0) & subset(all_0_2_2, all_0_1_1) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ subset(v0, v2) |  ~ subset(v0, v1) | subset(v0, v3)) &  ! [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] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1)) &  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0)) &  ! [v0] : (v0 = empty_set |  ~ subset(v0, empty_set)) &  ! [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)
% 2.82/1.41  |
% 2.82/1.41  | Applying alpha-rule on (1) yields:
% 2.82/1.41  | (2)  ! [v0] :  ~ member(v0, empty_set)
% 2.82/1.41  | (3)  ? [v0] : (empty(v0) |  ? [v1] : member(v1, v0))
% 2.82/1.41  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3))
% 2.82/1.41  | (5)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.82/1.41  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 2.82/1.41  | (7)  ! [v0] : (v0 = empty_set |  ~ subset(v0, empty_set))
% 2.82/1.41  | (8)  ~ (all_0_2_2 = empty_set)
% 2.82/1.41  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v1, v2) = v3) |  ~ subset(v0, v2) |  ~ subset(v0, v1) | subset(v0, v3))
% 2.82/1.41  | (10) subset(all_0_2_2, all_0_0_0)
% 2.82/1.41  | (11)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 2.82/1.42  | (12) subset(all_0_2_2, all_0_1_1)
% 2.82/1.42  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 2.82/1.42  | (14)  ? [v0] : subset(v0, v0)
% 2.82/1.42  | (15) intersection(all_0_1_1, all_0_0_0) = empty_set
% 2.82/1.42  | (16)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 2.82/1.42  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1))
% 2.82/1.42  | (18)  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0))
% 2.82/1.42  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1))
% 2.82/1.42  | (20)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 2.82/1.42  | (21)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 2.82/1.42  |
% 2.82/1.42  | Instantiating formula (9) with empty_set, all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms intersection(all_0_1_1, all_0_0_0) = empty_set, subset(all_0_2_2, all_0_0_0), subset(all_0_2_2, all_0_1_1), yields:
% 2.82/1.42  | (22) subset(all_0_2_2, empty_set)
% 2.82/1.42  |
% 2.82/1.42  | Instantiating formula (7) with all_0_2_2 and discharging atoms subset(all_0_2_2, empty_set), yields:
% 2.82/1.42  | (23) all_0_2_2 = empty_set
% 2.82/1.42  |
% 2.82/1.42  | Equations (23) can reduce 8 to:
% 2.82/1.42  | (24) $false
% 2.82/1.42  |
% 2.82/1.42  |-The branch is then unsatisfiable
% 2.82/1.42  % SZS output end Proof for theBenchmark
% 2.82/1.42  
% 2.82/1.42  825ms
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