TSTP Solution File: SET639+3 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n019.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 00:21:06 EDT 2022

% Result   : Theorem 2.19s 1.14s
% Output   : Proof 2.82s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.33  % Computer : n019.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sat Jul  9 21:09:38 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.55/0.58          ____       _                          
% 0.55/0.58    ___  / __ \_____(_)___  ________  __________
% 0.55/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.55/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.55/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.55/0.58  
% 0.55/0.58  A Theorem Prover for First-Order Logic
% 0.55/0.58  (ePrincess v.1.0)
% 0.55/0.58  
% 0.55/0.58  (c) Philipp Rümmer, 2009-2015
% 0.55/0.58  (c) Peter Backeman, 2014-2015
% 0.55/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.55/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.55/0.58  Bug reports to peter@backeman.se
% 0.55/0.58  
% 0.55/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.55/0.58  
% 0.55/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.55/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.43/0.89  Prover 0: Preprocessing ...
% 1.84/1.05  Prover 0: Warning: ignoring some quantifiers
% 1.84/1.06  Prover 0: Constructing countermodel ...
% 2.19/1.14  Prover 0: proved (515ms)
% 2.19/1.14  
% 2.19/1.14  No countermodel exists, formula is valid
% 2.19/1.14  % SZS status Theorem for theBenchmark
% 2.19/1.15  
% 2.19/1.15  Generating proof ... Warning: ignoring some quantifiers
% 2.49/1.32  found it (size 6)
% 2.49/1.32  
% 2.49/1.32  % SZS output start Proof for theBenchmark
% 2.49/1.32  Assumed formulas after preprocessing and simplification: 
% 2.49/1.32  | (0)  ? [v0] :  ? [v1] : ( ~ (v0 = empty_set) & intersection(v1, v0) = empty_set & subset(v0, v1) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (intersection(v5, v4) = v3) |  ~ (intersection(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v2, v3) = v5) |  ~ member(v4, v5) | member(v4, v3)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v2, v3) = v5) |  ~ member(v4, v5) | member(v4, v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (intersection(v2, v3) = v5) |  ~ member(v4, v3) |  ~ member(v4, v2) | member(v4, v5)) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v2 |  ~ (intersection(v2, v3) = v4) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection(v3, v2) = v4) | intersection(v2, v3) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (intersection(v2, v3) = v4) | intersection(v3, v2) = v4) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ member(v4, v2) |  ~ subset(v2, v3) | member(v4, v3)) &  ! [v2] :  ! [v3] : (v3 = v2 |  ~ subset(v3, v2) |  ~ subset(v2, v3)) &  ! [v2] :  ! [v3] : ( ~ empty(v2) |  ~ member(v3, v2)) &  ! [v2] :  ~ member(v2, empty_set) &  ? [v2] :  ? [v3] : (v3 = v2 |  ? [v4] : (( ~ member(v4, v3) |  ~ member(v4, v2)) & (member(v4, v3) | member(v4, v2)))) &  ? [v2] :  ? [v3] : (subset(v2, v3) |  ? [v4] : (member(v4, v2) &  ~ member(v4, v3))) &  ? [v2] : (empty(v2) |  ? [v3] : member(v3, v2)) &  ? [v2] : subset(v2, v2))
% 2.67/1.36  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 2.67/1.36  | (1)  ~ (all_0_1_1 = empty_set) & intersection(all_0_0_0, all_0_1_1) = empty_set & 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] : ( ~ (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] : (v2 = v0 |  ~ (intersection(v0, v1) = v2) |  ~ subset(v0, v1)) &  ! [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] :  ~ 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)
% 2.67/1.36  |
% 2.67/1.36  | Applying alpha-rule on (1) yields:
% 2.67/1.36  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v1) |  ~ member(v2, v0) | member(v2, v3))
% 2.67/1.36  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v1))
% 2.67/1.36  | (4)  ? [v0] :  ? [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 2.67/1.36  | (5)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 2.82/1.36  | (6)  ! [v0] :  ! [v1] : ( ~ empty(v0) |  ~ member(v1, v0))
% 2.82/1.36  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v0, v1) = v2) | intersection(v1, v0) = v2)
% 2.82/1.37  | (8)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection(v1, v0) = v2) | intersection(v0, v1) = v2)
% 2.82/1.37  | (9)  ? [v0] : subset(v0, v0)
% 2.82/1.37  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection(v0, v1) = v3) |  ~ member(v2, v3) | member(v2, v0))
% 2.82/1.37  | (11) subset(all_0_1_1, all_0_0_0)
% 2.82/1.37  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection(v3, v2) = v1) |  ~ (intersection(v3, v2) = v0))
% 2.82/1.37  | (13) intersection(all_0_0_0, all_0_1_1) = empty_set
% 2.82/1.37  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ member(v2, v0) |  ~ subset(v0, v1) | member(v2, v1))
% 2.82/1.37  | (15)  ? [v0] : (empty(v0) |  ? [v1] : member(v1, v0))
% 2.82/1.37  | (16)  ? [v0] :  ? [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 2.82/1.37  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 |  ~ (intersection(v0, v1) = v2) |  ~ subset(v0, v1))
% 2.82/1.37  | (18)  ! [v0] :  ~ member(v0, empty_set)
% 2.82/1.37  | (19)  ~ (all_0_1_1 = empty_set)
% 2.82/1.37  |
% 2.82/1.37  | Instantiating formula (8) with empty_set, all_0_0_0, all_0_1_1 and discharging atoms intersection(all_0_0_0, all_0_1_1) = empty_set, yields:
% 2.82/1.37  | (20) intersection(all_0_1_1, all_0_0_0) = empty_set
% 2.82/1.37  |
% 2.82/1.37  | Instantiating formula (17) with empty_set, all_0_0_0, all_0_1_1 and discharging atoms intersection(all_0_1_1, all_0_0_0) = empty_set, subset(all_0_1_1, all_0_0_0), yields:
% 2.82/1.37  | (21) all_0_1_1 = empty_set
% 2.82/1.37  |
% 2.82/1.37  | Equations (21) can reduce 19 to:
% 2.82/1.37  | (22) $false
% 2.82/1.37  |
% 2.82/1.37  |-The branch is then unsatisfiable
% 2.82/1.37  % SZS output end Proof for theBenchmark
% 2.82/1.37  
% 2.82/1.37  785ms
%------------------------------------------------------------------------------