TSTP Solution File: SET603+3 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.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 00:20:40 EDT 2022

% Result   : Theorem 11.04s 3.26s
% Output   : Proof 13.47s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET603+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Sun Jul 10 14:59:41 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.51/0.60          ____       _                          
% 0.51/0.60    ___  / __ \_____(_)___  ________  __________
% 0.51/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.51/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.51/0.60  
% 0.51/0.60  A Theorem Prover for First-Order Logic
% 0.51/0.60  (ePrincess v.1.0)
% 0.51/0.60  
% 0.51/0.60  (c) Philipp Rümmer, 2009-2015
% 0.51/0.60  (c) Peter Backeman, 2014-2015
% 0.51/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60  Bug reports to peter@backeman.se
% 0.51/0.60  
% 0.51/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60  
% 0.51/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.69/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.91  Prover 0: Preprocessing ...
% 1.69/1.05  Prover 0: Warning: ignoring some quantifiers
% 1.69/1.07  Prover 0: Constructing countermodel ...
% 2.12/1.19  Prover 0: gave up
% 2.12/1.19  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.12/1.21  Prover 1: Preprocessing ...
% 2.40/1.28  Prover 1: Warning: ignoring some quantifiers
% 2.40/1.29  Prover 1: Constructing countermodel ...
% 2.40/1.31  Prover 1: gave up
% 2.40/1.31  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.58/1.33  Prover 2: Preprocessing ...
% 2.79/1.39  Prover 2: Warning: ignoring some quantifiers
% 2.79/1.40  Prover 2: Constructing countermodel ...
% 2.79/1.43  Prover 2: gave up
% 2.79/1.43  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.79/1.44  Prover 3: Preprocessing ...
% 3.18/1.46  Prover 3: Warning: ignoring some quantifiers
% 3.18/1.46  Prover 3: Constructing countermodel ...
% 3.34/1.49  Prover 3: gave up
% 3.34/1.49  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.34/1.50  Prover 4: Preprocessing ...
% 3.69/1.57  Prover 4: Warning: ignoring some quantifiers
% 3.69/1.57  Prover 4: Constructing countermodel ...
% 4.90/1.89  Prover 4: gave up
% 4.90/1.89  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.90/1.90  Prover 5: Preprocessing ...
% 5.27/1.94  Prover 5: Warning: ignoring some quantifiers
% 5.27/1.94  Prover 5: Constructing countermodel ...
% 5.27/1.95  Prover 5: gave up
% 5.27/1.95  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 5.27/1.96  Prover 6: Preprocessing ...
% 5.56/1.99  Prover 6: Warning: ignoring some quantifiers
% 5.56/1.99  Prover 6: Constructing countermodel ...
% 5.56/2.01  Prover 6: gave up
% 5.56/2.01  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.56/2.02  Prover 7: Preprocessing ...
% 5.56/2.03  Prover 7: Proving ...
% 11.04/3.26  Prover 7: proved (1252ms)
% 11.04/3.26  
% 11.04/3.26  % SZS status Theorem for theBenchmark
% 11.04/3.26  
% 11.04/3.26  Generating proof ... found it (size 43)
% 13.12/3.79  
% 13.12/3.79  % SZS output start Proof for theBenchmark
% 13.12/3.79  Assumed formulas after preprocessing and simplification: 
% 13.12/3.79  | (0)  ? [v0] : ( ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v2 = v1 |  ~ (difference(v4, v3) = v2) |  ~ (difference(v4, v3) = v1)) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v2) = v4) |  ~ member(v3, v4) | (member(v3, v1) &  ~ member(v3, v2))) &  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (difference(v1, v2) = v4) |  ~ member(v3, v1) | member(v3, v4) | member(v3, v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ~ subset(v2, v1) |  ~ subset(v1, v2)) &  ! [v1] :  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ member(v3, v2) |  ~ member(v3, v1)) & (member(v3, v2) | member(v3, v1)))) &  ! [v1] :  ! [v2] : ( ~ subset(v1, v2) |  ! [v3] : ( ~ member(v3, v1) | member(v3, v2))) &  ! [v1] :  ! [v2] : (subset(v1, v2) |  ? [v3] : (member(v3, v1) &  ~ member(v3, v2))) &  ! [v1] : ( ~ empty(v1) |  ! [v2] :  ~ member(v2, v1)) &  ! [v1] :  ~ member(v1, v0) &  ! [v1] : (empty(v1) |  ? [v2] : member(v2, v1)) &  ! [v1] : subset(v1, v1) &  ? [v1] :  ? [v2] : ( ~ (v2 = v1) & difference(v1, v0) = v2))
% 13.12/3.81  | Instantiating (0) with all_0_0_0 yields:
% 13.12/3.81  | (1)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) | (member(v2, v0) &  ~ member(v2, v1))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3) | member(v2, v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, 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] :  ! [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1))) &  ! [v0] : ( ~ empty(v0) |  ! [v1] :  ~ member(v1, v0)) &  ! [v0] :  ~ member(v0, all_0_0_0) &  ! [v0] : (empty(v0) |  ? [v1] : member(v1, v0)) &  ! [v0] : subset(v0, v0) &  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & difference(v0, all_0_0_0) = v1)
% 13.47/3.82  |
% 13.47/3.82  | Applying alpha-rule on (1) yields:
% 13.47/3.82  | (2)  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ member(v2, v1) |  ~ member(v2, v0)) & (member(v2, v1) | member(v2, v0))))
% 13.47/3.82  | (3)  ! [v0] : (empty(v0) |  ? [v1] : member(v1, v0))
% 13.47/3.82  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v0) | member(v2, v3) | member(v2, v1))
% 13.47/3.82  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (difference(v3, v2) = v1) |  ~ (difference(v3, v2) = v0))
% 13.47/3.82  | (6)  ! [v0] : subset(v0, v0)
% 13.47/3.82  | (7)  ? [v0] :  ? [v1] : ( ~ (v1 = v0) & difference(v0, all_0_0_0) = v1)
% 13.47/3.82  | (8)  ! [v0] :  ! [v1] : ( ~ subset(v0, v1) |  ! [v2] : ( ~ member(v2, v0) | member(v2, v1)))
% 13.47/3.82  | (9)  ! [v0] : ( ~ empty(v0) |  ! [v1] :  ~ member(v1, v0))
% 13.47/3.82  | (10)  ! [v0] :  ! [v1] : (subset(v0, v1) |  ? [v2] : (member(v2, v0) &  ~ member(v2, v1)))
% 13.47/3.82  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (difference(v0, v1) = v3) |  ~ member(v2, v3) | (member(v2, v0) &  ~ member(v2, v1)))
% 13.47/3.82  | (12)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ subset(v1, v0) |  ~ subset(v0, v1))
% 13.47/3.82  | (13)  ! [v0] :  ~ member(v0, all_0_0_0)
% 13.47/3.82  |
% 13.47/3.82  | Instantiating (7) with all_2_0_1, all_2_1_2 yields:
% 13.47/3.82  | (14)  ~ (all_2_0_1 = all_2_1_2) & difference(all_2_1_2, all_0_0_0) = all_2_0_1
% 13.47/3.82  |
% 13.47/3.82  | Applying alpha-rule on (14) yields:
% 13.47/3.82  | (15)  ~ (all_2_0_1 = all_2_1_2)
% 13.47/3.82  | (16) difference(all_2_1_2, all_0_0_0) = all_2_0_1
% 13.47/3.82  |
% 13.47/3.82  | Introducing new symbol ex_10_1_4 defined by:
% 13.47/3.82  | (17) ex_10_1_4 = all_2_1_2
% 13.47/3.82  |
% 13.47/3.82  | Introducing new symbol ex_10_0_3 defined by:
% 13.47/3.82  | (18) ex_10_0_3 = all_2_0_1
% 13.47/3.82  |
% 13.47/3.83  | Instantiating formula (2) with ex_10_0_3, ex_10_1_4 yields:
% 13.47/3.83  | (19) ex_10_0_3 = ex_10_1_4 |  ? [v0] : (( ~ member(v0, ex_10_0_3) |  ~ member(v0, ex_10_1_4)) & (member(v0, ex_10_0_3) | member(v0, ex_10_1_4)))
% 13.47/3.83  |
% 13.47/3.83  +-Applying beta-rule and splitting (19), into two cases.
% 13.47/3.83  |-Branch one:
% 13.47/3.83  | (20) ex_10_0_3 = ex_10_1_4
% 13.47/3.83  |
% 13.47/3.83  	| Combining equations (20,18) yields a new equation:
% 13.47/3.83  	| (21) ex_10_1_4 = all_2_0_1
% 13.47/3.83  	|
% 13.47/3.83  	| Simplifying 21 yields:
% 13.47/3.83  	| (22) ex_10_1_4 = all_2_0_1
% 13.47/3.83  	|
% 13.47/3.83  	| Combining equations (22,17) yields a new equation:
% 13.47/3.83  	| (23) all_2_0_1 = all_2_1_2
% 13.47/3.83  	|
% 13.47/3.83  	| Simplifying 23 yields:
% 13.47/3.83  	| (24) all_2_0_1 = all_2_1_2
% 13.47/3.83  	|
% 13.47/3.83  	| Equations (24) can reduce 15 to:
% 13.47/3.83  	| (25) $false
% 13.47/3.83  	|
% 13.47/3.83  	|-The branch is then unsatisfiable
% 13.47/3.83  |-Branch two:
% 13.47/3.83  | (26)  ? [v0] : (( ~ member(v0, ex_10_0_3) |  ~ member(v0, ex_10_1_4)) & (member(v0, ex_10_0_3) | member(v0, ex_10_1_4)))
% 13.47/3.83  |
% 13.47/3.83  	| Instantiating (26) with all_13_0_5 yields:
% 13.47/3.83  	| (27) ( ~ member(all_13_0_5, ex_10_0_3) |  ~ member(all_13_0_5, ex_10_1_4)) & (member(all_13_0_5, ex_10_0_3) | member(all_13_0_5, ex_10_1_4))
% 13.47/3.83  	|
% 13.47/3.83  	| Applying alpha-rule on (27) yields:
% 13.47/3.83  	| (28)  ~ member(all_13_0_5, ex_10_0_3) |  ~ member(all_13_0_5, ex_10_1_4)
% 13.47/3.83  	| (29) member(all_13_0_5, ex_10_0_3) | member(all_13_0_5, ex_10_1_4)
% 13.47/3.83  	|
% 13.47/3.83  	+-Applying beta-rule and splitting (28), into two cases.
% 13.47/3.83  	|-Branch one:
% 13.47/3.83  	| (30)  ~ member(all_13_0_5, ex_10_0_3)
% 13.47/3.83  	|
% 13.47/3.83  		+-Applying beta-rule and splitting (29), into two cases.
% 13.47/3.83  		|-Branch one:
% 13.47/3.83  		| (31) member(all_13_0_5, ex_10_0_3)
% 13.47/3.83  		|
% 13.47/3.83  			| Using (31) and (30) yields:
% 13.47/3.83  			| (32) $false
% 13.47/3.83  			|
% 13.47/3.83  			|-The branch is then unsatisfiable
% 13.47/3.83  		|-Branch two:
% 13.47/3.83  		| (33) member(all_13_0_5, ex_10_1_4)
% 13.47/3.83  		|
% 13.47/3.83  			| Instantiating formula (13) with all_13_0_5 yields:
% 13.47/3.83  			| (34)  ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83  			|
% 13.47/3.83  			| Instantiating formula (4) with all_2_0_1, all_13_0_5, all_0_0_0, all_2_1_2 and discharging atoms difference(all_2_1_2, all_0_0_0) = all_2_0_1,  ~ member(all_13_0_5, all_0_0_0), yields:
% 13.47/3.83  			| (35)  ~ member(all_13_0_5, all_2_1_2) | member(all_13_0_5, all_2_0_1)
% 13.47/3.83  			|
% 13.47/3.83  			+-Applying beta-rule and splitting (35), into two cases.
% 13.47/3.83  			|-Branch one:
% 13.47/3.83  			| (36)  ~ member(all_13_0_5, all_2_1_2)
% 13.47/3.83  			|
% 13.47/3.83  				| From (17) and (33) follows:
% 13.47/3.83  				| (37) member(all_13_0_5, all_2_1_2)
% 13.47/3.83  				|
% 13.47/3.83  				| Using (37) and (36) yields:
% 13.47/3.83  				| (32) $false
% 13.47/3.83  				|
% 13.47/3.83  				|-The branch is then unsatisfiable
% 13.47/3.83  			|-Branch two:
% 13.47/3.83  			| (39) member(all_13_0_5, all_2_0_1)
% 13.47/3.83  			|
% 13.47/3.83  				| From (18) and (30) follows:
% 13.47/3.83  				| (40)  ~ member(all_13_0_5, all_2_0_1)
% 13.47/3.83  				|
% 13.47/3.83  				| Using (39) and (40) yields:
% 13.47/3.83  				| (32) $false
% 13.47/3.83  				|
% 13.47/3.83  				|-The branch is then unsatisfiable
% 13.47/3.83  	|-Branch two:
% 13.47/3.83  	| (31) member(all_13_0_5, ex_10_0_3)
% 13.47/3.83  	| (43)  ~ member(all_13_0_5, ex_10_1_4)
% 13.47/3.83  	|
% 13.47/3.83  		| Instantiating formula (13) with all_13_0_5 yields:
% 13.47/3.83  		| (34)  ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83  		|
% 13.47/3.83  		| Instantiating formula (11) with all_2_0_1, all_13_0_5, all_0_0_0, all_2_1_2 and discharging atoms difference(all_2_1_2, all_0_0_0) = all_2_0_1, yields:
% 13.47/3.83  		| (45)  ~ member(all_13_0_5, all_2_0_1) | (member(all_13_0_5, all_2_1_2) &  ~ member(all_13_0_5, all_0_0_0))
% 13.47/3.83  		|
% 13.47/3.83  		| Instantiating formula (4) with all_2_0_1, all_13_0_5, all_0_0_0, all_2_1_2 and discharging atoms difference(all_2_1_2, all_0_0_0) = all_2_0_1,  ~ member(all_13_0_5, all_0_0_0), yields:
% 13.47/3.83  		| (35)  ~ member(all_13_0_5, all_2_1_2) | member(all_13_0_5, all_2_0_1)
% 13.47/3.83  		|
% 13.47/3.83  		+-Applying beta-rule and splitting (35), into two cases.
% 13.47/3.83  		|-Branch one:
% 13.47/3.83  		| (36)  ~ member(all_13_0_5, all_2_1_2)
% 13.47/3.83  		|
% 13.47/3.83  			+-Applying beta-rule and splitting (45), into two cases.
% 13.47/3.83  			|-Branch one:
% 13.47/3.83  			| (40)  ~ member(all_13_0_5, all_2_0_1)
% 13.47/3.83  			|
% 13.47/3.83  				| From (18) and (31) follows:
% 13.47/3.83  				| (39) member(all_13_0_5, all_2_0_1)
% 13.47/3.83  				|
% 13.47/3.83  				| Using (39) and (40) yields:
% 13.47/3.83  				| (32) $false
% 13.47/3.83  				|
% 13.47/3.83  				|-The branch is then unsatisfiable
% 13.47/3.83  			|-Branch two:
% 13.47/3.83  			| (51) member(all_13_0_5, all_2_1_2) &  ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83  			|
% 13.47/3.83  				| Applying alpha-rule on (51) yields:
% 13.47/3.83  				| (37) member(all_13_0_5, all_2_1_2)
% 13.47/3.83  				| (34)  ~ member(all_13_0_5, all_0_0_0)
% 13.47/3.83  				|
% 13.47/3.83  				| Using (37) and (36) yields:
% 13.47/3.83  				| (32) $false
% 13.47/3.83  				|
% 13.47/3.83  				|-The branch is then unsatisfiable
% 13.47/3.83  		|-Branch two:
% 13.47/3.83  		| (37) member(all_13_0_5, all_2_1_2)
% 13.47/3.83  		| (39) member(all_13_0_5, all_2_0_1)
% 13.47/3.83  		|
% 13.47/3.83  			| From (17) and (43) follows:
% 13.47/3.83  			| (36)  ~ member(all_13_0_5, all_2_1_2)
% 13.47/3.83  			|
% 13.47/3.83  			| Using (37) and (36) yields:
% 13.47/3.83  			| (32) $false
% 13.47/3.83  			|
% 13.47/3.83  			|-The branch is then unsatisfiable
% 13.47/3.83  % SZS output end Proof for theBenchmark
% 13.47/3.84  
% 13.47/3.84  3226ms
%------------------------------------------------------------------------------