TSTP Solution File: SEU160+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU160+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n020.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 08:47:07 EDT 2022

% Result   : Theorem 1.69s 1.06s
% Output   : Proof 2.30s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SEU160+1 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.32  % Computer : n020.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit : 300
% 0.13/0.32  % WCLimit  : 600
% 0.13/0.32  % DateTime : Mon Jun 20 03:29:48 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.19/0.56          ____       _                          
% 0.19/0.56    ___  / __ \_____(_)___  ________  __________
% 0.19/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.56  
% 0.19/0.56  A Theorem Prover for First-Order Logic
% 0.19/0.57  (ePrincess v.1.0)
% 0.19/0.57  
% 0.19/0.57  (c) Philipp Rümmer, 2009-2015
% 0.19/0.57  (c) Peter Backeman, 2014-2015
% 0.19/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.57  Bug reports to peter@backeman.se
% 0.19/0.57  
% 0.19/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.57  
% 0.19/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.73/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.86  Prover 0: Preprocessing ...
% 1.50/0.95  Prover 0: Warning: ignoring some quantifiers
% 1.50/0.97  Prover 0: Constructing countermodel ...
% 1.69/1.06  Prover 0: proved (445ms)
% 1.69/1.06  
% 1.69/1.06  No countermodel exists, formula is valid
% 1.69/1.06  % SZS status Theorem for theBenchmark
% 1.69/1.06  
% 1.69/1.06  Generating proof ... Warning: ignoring some quantifiers
% 2.24/1.21  found it (size 21)
% 2.24/1.21  
% 2.24/1.21  % SZS output start Proof for theBenchmark
% 2.24/1.21  Assumed formulas after preprocessing and simplification: 
% 2.24/1.21  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (singleton(v1) = v2 & empty(v4) & empty(empty_set) &  ~ empty(v3) &  ! [v5] :  ! [v6] :  ! [v7] : (v7 = v5 | v5 = empty_set |  ~ (singleton(v6) = v7) |  ~ subset(v5, v7)) &  ! [v5] :  ! [v6] :  ! [v7] : (v6 = v5 |  ~ (singleton(v7) = v6) |  ~ (singleton(v7) = v5)) &  ! [v5] :  ! [v6] : ( ~ (singleton(v6) = v5) | subset(v5, v5)) &  ! [v5] :  ! [v6] : ( ~ (singleton(v5) = v6) | subset(empty_set, v6)) &  ? [v5] : subset(v5, v5) & (( ~ (v2 = v0) &  ~ (v0 = empty_set) & subset(v0, v2)) | ( ~ subset(v0, v2) & (v2 = v0 | v0 = empty_set))))
% 2.30/1.25  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 2.30/1.25  | (1) singleton(all_0_3_3) = all_0_2_2 & empty(all_0_0_0) & empty(empty_set) &  ~ empty(all_0_1_1) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ subset(v0, v2)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0)) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1)) &  ? [v0] : subset(v0, v0) & (( ~ (all_0_2_2 = all_0_4_4) &  ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)) | ( ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set)))
% 2.30/1.25  |
% 2.30/1.25  | Applying alpha-rule on (1) yields:
% 2.30/1.25  | (2)  ! [v0] :  ! [v1] : ( ~ (singleton(v1) = v0) | subset(v0, v0))
% 2.30/1.25  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v0 | v0 = empty_set |  ~ (singleton(v1) = v2) |  ~ subset(v0, v2))
% 2.30/1.25  | (4) empty(empty_set)
% 2.30/1.25  | (5)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | subset(empty_set, v1))
% 2.30/1.25  | (6) ( ~ (all_0_2_2 = all_0_4_4) &  ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)) | ( ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set))
% 2.30/1.25  | (7)  ? [v0] : subset(v0, v0)
% 2.30/1.26  | (8)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 2.30/1.26  | (9) empty(all_0_0_0)
% 2.30/1.26  | (10) singleton(all_0_3_3) = all_0_2_2
% 2.30/1.26  | (11)  ~ empty(all_0_1_1)
% 2.30/1.26  |
% 2.30/1.26  | Instantiating formula (2) with all_0_3_3, all_0_2_2 and discharging atoms singleton(all_0_3_3) = all_0_2_2, yields:
% 2.30/1.26  | (12) subset(all_0_2_2, all_0_2_2)
% 2.30/1.26  |
% 2.30/1.26  | Instantiating formula (5) with all_0_2_2, all_0_3_3 and discharging atoms singleton(all_0_3_3) = all_0_2_2, yields:
% 2.30/1.26  | (13) subset(empty_set, all_0_2_2)
% 2.30/1.26  |
% 2.30/1.26  +-Applying beta-rule and splitting (6), into two cases.
% 2.30/1.26  |-Branch one:
% 2.30/1.26  | (14)  ~ (all_0_2_2 = all_0_4_4) &  ~ (all_0_4_4 = empty_set) & subset(all_0_4_4, all_0_2_2)
% 2.30/1.26  |
% 2.30/1.26  	| Applying alpha-rule on (14) yields:
% 2.30/1.26  	| (15)  ~ (all_0_2_2 = all_0_4_4)
% 2.30/1.26  	| (16)  ~ (all_0_4_4 = empty_set)
% 2.30/1.26  	| (17) subset(all_0_4_4, all_0_2_2)
% 2.30/1.26  	|
% 2.30/1.26  	| Instantiating formula (3) with all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms singleton(all_0_3_3) = all_0_2_2, subset(all_0_4_4, all_0_2_2), yields:
% 2.30/1.26  	| (18) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set
% 2.30/1.26  	|
% 2.30/1.26  	+-Applying beta-rule and splitting (18), into two cases.
% 2.30/1.26  	|-Branch one:
% 2.30/1.26  	| (19) all_0_4_4 = empty_set
% 2.30/1.26  	|
% 2.30/1.26  		| Equations (19) can reduce 16 to:
% 2.30/1.26  		| (20) $false
% 2.30/1.26  		|
% 2.30/1.26  		|-The branch is then unsatisfiable
% 2.30/1.26  	|-Branch two:
% 2.30/1.26  	| (16)  ~ (all_0_4_4 = empty_set)
% 2.30/1.26  	| (22) all_0_2_2 = all_0_4_4
% 2.30/1.26  	|
% 2.30/1.26  		| Equations (22) can reduce 15 to:
% 2.30/1.26  		| (20) $false
% 2.30/1.26  		|
% 2.30/1.26  		|-The branch is then unsatisfiable
% 2.30/1.26  |-Branch two:
% 2.30/1.26  | (24)  ~ subset(all_0_4_4, all_0_2_2) & (all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set)
% 2.30/1.26  |
% 2.30/1.26  	| Applying alpha-rule on (24) yields:
% 2.30/1.26  	| (25)  ~ subset(all_0_4_4, all_0_2_2)
% 2.30/1.26  	| (18) all_0_2_2 = all_0_4_4 | all_0_4_4 = empty_set
% 2.30/1.26  	|
% 2.30/1.26  	+-Applying beta-rule and splitting (18), into two cases.
% 2.30/1.26  	|-Branch one:
% 2.30/1.26  	| (19) all_0_4_4 = empty_set
% 2.30/1.26  	|
% 2.30/1.26  		| From (19) and (25) follows:
% 2.30/1.26  		| (28)  ~ subset(empty_set, all_0_2_2)
% 2.30/1.26  		|
% 2.30/1.26  		| Using (13) and (28) yields:
% 2.30/1.26  		| (29) $false
% 2.30/1.26  		|
% 2.30/1.26  		|-The branch is then unsatisfiable
% 2.30/1.26  	|-Branch two:
% 2.30/1.26  	| (16)  ~ (all_0_4_4 = empty_set)
% 2.30/1.27  	| (22) all_0_2_2 = all_0_4_4
% 2.30/1.27  	|
% 2.30/1.27  		| From (22)(22) and (12) follows:
% 2.30/1.27  		| (32) subset(all_0_4_4, all_0_4_4)
% 2.30/1.27  		|
% 2.30/1.27  		| From (22) and (25) follows:
% 2.30/1.27  		| (33)  ~ subset(all_0_4_4, all_0_4_4)
% 2.30/1.27  		|
% 2.30/1.27  		| Using (32) and (33) yields:
% 2.30/1.27  		| (29) $false
% 2.30/1.27  		|
% 2.30/1.27  		|-The branch is then unsatisfiable
% 2.30/1.27  % SZS output end Proof for theBenchmark
% 2.30/1.27  
% 2.30/1.27  690ms
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