TSTP Solution File: SEU142+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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 08:46:55 EDT 2022

% Result   : Theorem 9.40s 3.15s
% Output   : Proof 12.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU142+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n017.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 : Mon Jun 20 09:03:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.20/0.60          ____       _                          
% 0.20/0.60    ___  / __ \_____(_)___  ________  __________
% 0.20/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.20/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.20/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.20/0.60  
% 0.20/0.60  A Theorem Prover for First-Order Logic
% 0.20/0.60  (ePrincess v.1.0)
% 0.20/0.60  
% 0.20/0.60  (c) Philipp Rümmer, 2009-2015
% 0.20/0.60  (c) Peter Backeman, 2014-2015
% 0.20/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.20/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.20/0.60  Bug reports to peter@backeman.se
% 0.20/0.60  
% 0.20/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.20/0.60  
% 0.20/0.60  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.31/0.92  Prover 0: Preprocessing ...
% 1.69/1.08  Prover 0: Warning: ignoring some quantifiers
% 1.84/1.10  Prover 0: Constructing countermodel ...
% 2.08/1.26  Prover 0: gave up
% 2.08/1.26  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.08/1.28  Prover 1: Preprocessing ...
% 2.63/1.33  Prover 1: Warning: ignoring some quantifiers
% 2.63/1.34  Prover 1: Constructing countermodel ...
% 2.75/1.39  Prover 1: gave up
% 2.75/1.39  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.75/1.40  Prover 2: Preprocessing ...
% 3.09/1.44  Prover 2: Warning: ignoring some quantifiers
% 3.09/1.45  Prover 2: Constructing countermodel ...
% 3.27/1.50  Prover 2: gave up
% 3.27/1.50  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.27/1.51  Prover 3: Preprocessing ...
% 3.27/1.53  Prover 3: Warning: ignoring some quantifiers
% 3.27/1.54  Prover 3: Constructing countermodel ...
% 3.63/1.58  Prover 3: gave up
% 3.63/1.58  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 3.63/1.59  Prover 4: Preprocessing ...
% 3.84/1.63  Prover 4: Warning: ignoring some quantifiers
% 3.84/1.64  Prover 4: Constructing countermodel ...
% 4.42/1.77  Prover 4: gave up
% 4.42/1.77  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.42/1.78  Prover 5: Preprocessing ...
% 4.65/1.80  Prover 5: Warning: ignoring some quantifiers
% 4.65/1.80  Prover 5: Constructing countermodel ...
% 4.65/1.84  Prover 5: gave up
% 4.65/1.84  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 4.65/1.85  Prover 6: Preprocessing ...
% 5.05/1.87  Prover 6: Warning: ignoring some quantifiers
% 5.05/1.87  Prover 6: Constructing countermodel ...
% 5.12/1.90  Prover 6: gave up
% 5.12/1.90  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 5.12/1.91  Prover 7: Preprocessing ...
% 5.34/1.93  Prover 7: Proving ...
% 9.40/3.15  Prover 7: proved (1250ms)
% 9.40/3.15  
% 9.40/3.15  % SZS status Theorem for theBenchmark
% 9.40/3.15  
% 9.40/3.15  Generating proof ... found it (size 45)
% 12.53/3.94  
% 12.53/3.94  % SZS output start Proof for theBenchmark
% 12.53/3.94  Assumed formulas after preprocessing and simplification: 
% 12.53/3.94  | (0)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) &  ~ (v4 = v0)))))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 |  ~ in(v3, v2)) &  ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) &  ~ (v3 = v0))))) &  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0)))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ (v3 = v0) |  ~ in(v0, v2)) & (v3 = v0 | in(v3, v2))))) &  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) &  ! [v2] : (v2 = v0 |  ~ in(v2, v1)))) &  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1)) &  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) & singleton(v0) = v2 & unordered_pair(v0, v0) = v1)
% 12.53/3.97  | Applying alpha-rule on (0) yields:
% 12.53/3.97  | (1)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (singleton(v2) = v1) |  ~ (singleton(v2) = v0))
% 12.53/3.97  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | ( ! [v3] : (v3 = v1 | v3 = v0 |  ~ in(v3, v2)) &  ! [v3] : (in(v3, v2) | ( ~ (v3 = v1) &  ~ (v3 = v0)))))
% 12.53/3.97  | (3)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) |  ! [v3] : (v3 = v2 |  ? [v4] : ((v4 = v1 | v4 = v0 | in(v4, v3)) & ( ~ in(v4, v3) | ( ~ (v4 = v1) &  ~ (v4 = v0))))))
% 12.53/3.97  | (4)  ! [v0] :  ! [v1] : (v1 = v0 |  ? [v2] : (( ~ in(v2, v1) |  ~ in(v2, v0)) & (in(v2, v1) | in(v2, v0))))
% 12.53/3.97  | (5)  ! [v0] :  ! [v1] : ( ~ in(v1, v0) |  ~ in(v0, v1))
% 12.53/3.97  | (6)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) | (in(v0, v1) &  ! [v2] : (v2 = v0 |  ~ in(v2, v1))))
% 12.53/3.97  | (7)  ! [v0] :  ! [v1] : ( ~ (singleton(v0) = v1) |  ! [v2] : (v2 = v1 |  ? [v3] : (( ~ (v3 = v0) |  ~ in(v0, v2)) & (v3 = v0 | in(v3, v2)))))
% 12.53/3.97  | (8)  ? [v0] :  ? [v1] :  ? [v2] : ( ~ (v2 = v1) & singleton(v0) = v2 & unordered_pair(v0, v0) = v1)
% 12.53/3.97  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unordered_pair(v3, v2) = v1) |  ~ (unordered_pair(v3, v2) = v0))
% 12.53/3.97  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (unordered_pair(v0, v1) = v2) | unordered_pair(v1, v0) = v2)
% 12.88/3.97  |
% 12.88/3.97  | Instantiating (8) with all_1_0_0, all_1_1_1, all_1_2_2 yields:
% 12.88/3.97  | (11)  ~ (all_1_0_0 = all_1_1_1) & singleton(all_1_2_2) = all_1_0_0 & unordered_pair(all_1_2_2, all_1_2_2) = all_1_1_1
% 12.88/3.97  |
% 12.88/3.97  | Applying alpha-rule on (11) yields:
% 12.88/3.97  | (12)  ~ (all_1_0_0 = all_1_1_1)
% 12.88/3.97  | (13) singleton(all_1_2_2) = all_1_0_0
% 12.88/3.97  | (14) unordered_pair(all_1_2_2, all_1_2_2) = all_1_1_1
% 12.88/3.97  |
% 12.88/3.97  | Instantiating formula (6) with all_1_0_0, all_1_2_2 and discharging atoms singleton(all_1_2_2) = all_1_0_0, yields:
% 12.88/3.97  | (15) in(all_1_2_2, all_1_0_0) &  ! [v0] : (v0 = all_1_2_2 |  ~ in(v0, all_1_0_0))
% 12.88/3.97  |
% 12.88/3.98  | Applying alpha-rule on (15) yields:
% 12.88/3.98  | (16) in(all_1_2_2, all_1_0_0)
% 12.88/3.98  | (17)  ! [v0] : (v0 = all_1_2_2 |  ~ in(v0, all_1_0_0))
% 12.88/3.98  |
% 12.88/3.98  | Instantiating formula (2) with all_1_1_1, all_1_2_2, all_1_2_2 and discharging atoms unordered_pair(all_1_2_2, all_1_2_2) = all_1_1_1, yields:
% 12.88/3.98  | (18) in(all_1_2_2, all_1_1_1) &  ! [v0] : (v0 = all_1_2_2 |  ~ in(v0, all_1_1_1))
% 12.88/3.98  |
% 12.88/3.98  | Applying alpha-rule on (18) yields:
% 12.88/3.98  | (19) in(all_1_2_2, all_1_1_1)
% 12.88/3.98  | (20)  ! [v0] : (v0 = all_1_2_2 |  ~ in(v0, all_1_1_1))
% 12.88/3.98  |
% 12.88/3.98  | Introducing new symbol ex_17_1_4 defined by:
% 12.88/3.98  | (21) ex_17_1_4 = all_1_0_0
% 12.88/3.98  |
% 12.88/3.98  | Introducing new symbol ex_17_0_3 defined by:
% 12.88/3.98  | (22) ex_17_0_3 = all_1_1_1
% 12.88/3.98  |
% 12.88/3.98  | Instantiating formula (4) with ex_17_0_3, ex_17_1_4 yields:
% 12.88/3.98  | (23) ex_17_0_3 = ex_17_1_4 |  ? [v0] : (( ~ in(v0, ex_17_0_3) |  ~ in(v0, ex_17_1_4)) & (in(v0, ex_17_0_3) | in(v0, ex_17_1_4)))
% 12.90/3.98  |
% 12.90/3.98  +-Applying beta-rule and splitting (23), into two cases.
% 12.90/3.98  |-Branch one:
% 12.90/3.98  | (24) ex_17_0_3 = ex_17_1_4
% 12.90/3.98  |
% 12.90/3.98  	| Combining equations (24,22) yields a new equation:
% 12.90/3.98  	| (25) ex_17_1_4 = all_1_1_1
% 12.90/3.98  	|
% 12.90/3.98  	| Simplifying 25 yields:
% 12.90/3.98  	| (26) ex_17_1_4 = all_1_1_1
% 12.90/3.98  	|
% 12.90/3.98  	| Combining equations (26,21) yields a new equation:
% 12.90/3.98  	| (27) all_1_0_0 = all_1_1_1
% 12.90/3.98  	|
% 12.90/3.98  	| Equations (27) can reduce 12 to:
% 12.90/3.98  	| (28) $false
% 12.90/3.98  	|
% 12.90/3.98  	|-The branch is then unsatisfiable
% 12.90/3.98  |-Branch two:
% 12.90/3.98  | (29)  ? [v0] : (( ~ in(v0, ex_17_0_3) |  ~ in(v0, ex_17_1_4)) & (in(v0, ex_17_0_3) | in(v0, ex_17_1_4)))
% 12.90/3.98  |
% 12.90/3.98  	| Instantiating (29) with all_20_0_5 yields:
% 12.90/3.98  	| (30) ( ~ in(all_20_0_5, ex_17_0_3) |  ~ in(all_20_0_5, ex_17_1_4)) & (in(all_20_0_5, ex_17_0_3) | in(all_20_0_5, ex_17_1_4))
% 12.90/3.98  	|
% 12.90/3.98  	| Applying alpha-rule on (30) yields:
% 12.90/3.98  	| (31)  ~ in(all_20_0_5, ex_17_0_3) |  ~ in(all_20_0_5, ex_17_1_4)
% 12.90/3.98  	| (32) in(all_20_0_5, ex_17_0_3) | in(all_20_0_5, ex_17_1_4)
% 12.90/3.98  	|
% 12.90/3.98  	+-Applying beta-rule and splitting (32), into two cases.
% 12.90/3.98  	|-Branch one:
% 12.90/3.98  	| (33) in(all_20_0_5, ex_17_0_3)
% 12.90/3.98  	|
% 12.90/3.98  		+-Applying beta-rule and splitting (31), into two cases.
% 12.90/3.98  		|-Branch one:
% 12.90/3.98  		| (34)  ~ in(all_20_0_5, ex_17_0_3)
% 12.90/3.98  		|
% 12.90/3.98  			| Using (33) and (34) yields:
% 12.90/3.98  			| (35) $false
% 12.90/3.98  			|
% 12.90/3.98  			|-The branch is then unsatisfiable
% 12.90/3.98  		|-Branch two:
% 12.90/3.98  		| (36)  ~ in(all_20_0_5, ex_17_1_4)
% 12.90/3.98  		|
% 12.90/3.98  			| Instantiating formula (20) with all_20_0_5 yields:
% 12.90/3.98  			| (37) all_20_0_5 = all_1_2_2 |  ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98  			|
% 12.90/3.98  			+-Applying beta-rule and splitting (37), into two cases.
% 12.90/3.98  			|-Branch one:
% 12.90/3.98  			| (38)  ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98  			|
% 12.90/3.98  				| From (22) and (33) follows:
% 12.90/3.98  				| (39) in(all_20_0_5, all_1_1_1)
% 12.90/3.98  				|
% 12.90/3.98  				| Using (39) and (38) yields:
% 12.90/3.98  				| (35) $false
% 12.90/3.98  				|
% 12.90/3.98  				|-The branch is then unsatisfiable
% 12.90/3.98  			|-Branch two:
% 12.90/3.98  			| (41) all_20_0_5 = all_1_2_2
% 12.90/3.98  			|
% 12.90/3.98  				| From (41) and (36) follows:
% 12.90/3.98  				| (42)  ~ in(all_1_2_2, ex_17_1_4)
% 12.90/3.98  				|
% 12.90/3.98  				| From (21) and (42) follows:
% 12.90/3.98  				| (43)  ~ in(all_1_2_2, all_1_0_0)
% 12.90/3.98  				|
% 12.90/3.98  				| Using (16) and (43) yields:
% 12.90/3.98  				| (35) $false
% 12.90/3.98  				|
% 12.90/3.98  				|-The branch is then unsatisfiable
% 12.90/3.98  	|-Branch two:
% 12.90/3.98  	| (34)  ~ in(all_20_0_5, ex_17_0_3)
% 12.90/3.98  	| (46) in(all_20_0_5, ex_17_1_4)
% 12.90/3.98  	|
% 12.90/3.98  		| Instantiating formula (17) with all_20_0_5 yields:
% 12.90/3.98  		| (47) all_20_0_5 = all_1_2_2 |  ~ in(all_20_0_5, all_1_0_0)
% 12.90/3.98  		|
% 12.90/3.98  		| Instantiating formula (20) with all_20_0_5 yields:
% 12.90/3.98  		| (37) all_20_0_5 = all_1_2_2 |  ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98  		|
% 12.90/3.98  		+-Applying beta-rule and splitting (37), into two cases.
% 12.90/3.98  		|-Branch one:
% 12.90/3.98  		| (38)  ~ in(all_20_0_5, all_1_1_1)
% 12.90/3.98  		|
% 12.90/3.98  			+-Applying beta-rule and splitting (47), into two cases.
% 12.90/3.98  			|-Branch one:
% 12.90/3.98  			| (50)  ~ in(all_20_0_5, all_1_0_0)
% 12.90/3.98  			|
% 12.90/3.98  				| From (21) and (46) follows:
% 12.90/3.98  				| (51) in(all_20_0_5, all_1_0_0)
% 12.90/3.98  				|
% 12.90/3.98  				| Using (51) and (50) yields:
% 12.90/3.98  				| (35) $false
% 12.90/3.98  				|
% 12.90/3.98  				|-The branch is then unsatisfiable
% 12.90/3.98  			|-Branch two:
% 12.90/3.98  			| (41) all_20_0_5 = all_1_2_2
% 12.90/3.98  			|
% 12.90/3.98  				| From (41) and (38) follows:
% 12.90/3.98  				| (54)  ~ in(all_1_2_2, all_1_1_1)
% 12.90/3.98  				|
% 12.90/3.98  				| Using (19) and (54) yields:
% 12.90/3.98  				| (35) $false
% 12.90/3.98  				|
% 12.90/3.98  				|-The branch is then unsatisfiable
% 12.90/3.98  		|-Branch two:
% 12.90/3.98  		| (41) all_20_0_5 = all_1_2_2
% 12.90/3.98  		|
% 12.90/3.98  			| From (41) and (34) follows:
% 12.90/3.98  			| (57)  ~ in(all_1_2_2, ex_17_0_3)
% 12.90/3.98  			|
% 12.90/3.98  			| From (22) and (57) follows:
% 12.90/3.98  			| (54)  ~ in(all_1_2_2, all_1_1_1)
% 12.90/3.98  			|
% 12.90/3.98  			| Using (19) and (54) yields:
% 12.90/3.98  			| (35) $false
% 12.90/3.98  			|
% 12.90/3.98  			|-The branch is then unsatisfiable
% 12.90/3.98  % SZS output end Proof for theBenchmark
% 12.90/3.99  
% 12.90/3.99  3376ms
%------------------------------------------------------------------------------