TSTP Solution File: SYN413+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN413+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n024.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 : Thu Jul 21 05:02:13 EDT 2022

% Result   : Theorem 5.34s 2.22s
% Output   : Proof 6.67s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SYN413+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n024.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jul 12 00:07:13 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.56/0.56          ____       _                          
% 0.56/0.56    ___  / __ \_____(_)___  ________  __________
% 0.56/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.56  
% 0.56/0.56  A Theorem Prover for First-Order Logic
% 0.56/0.57  (ePrincess v.1.0)
% 0.56/0.57  
% 0.56/0.57  (c) Philipp Rümmer, 2009-2015
% 0.56/0.57  (c) Peter Backeman, 2014-2015
% 0.56/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.57  Bug reports to peter@backeman.se
% 0.56/0.57  
% 0.56/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.57  
% 0.56/0.57  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.62/0.61  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.10/0.82  Prover 0: Preprocessing ...
% 1.25/0.87  Prover 0: Warning: ignoring some quantifiers
% 1.34/0.89  Prover 0: Constructing countermodel ...
% 1.51/1.01  Prover 0: gave up
% 1.51/1.01  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.74/1.03  Prover 1: Preprocessing ...
% 1.74/1.07  Prover 1: Warning: ignoring some quantifiers
% 1.74/1.07  Prover 1: Constructing countermodel ...
% 1.98/1.08  Prover 1: gave up
% 1.98/1.08  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.98/1.09  Prover 2: Preprocessing ...
% 1.98/1.14  Prover 2: Warning: ignoring some quantifiers
% 1.98/1.14  Prover 2: Constructing countermodel ...
% 1.98/1.16  Prover 2: gave up
% 2.27/1.16  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.27/1.17  Prover 3: Preprocessing ...
% 2.27/1.17  Prover 3: Warning: ignoring some quantifiers
% 2.27/1.17  Prover 3: Constructing countermodel ...
% 2.44/1.21  Prover 3: gave up
% 2.44/1.21  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.44/1.21  Prover 4: Preprocessing ...
% 2.55/1.25  Prover 4: Warning: ignoring some quantifiers
% 2.55/1.25  Prover 4: Constructing countermodel ...
% 3.65/1.54  Prover 4: gave up
% 3.65/1.54  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.65/1.55  Prover 5: Preprocessing ...
% 3.65/1.56  Prover 5: Warning: ignoring some quantifiers
% 3.65/1.56  Prover 5: Constructing countermodel ...
% 3.65/1.57  Prover 5: gave up
% 3.65/1.57  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.65/1.57  Prover 6: Preprocessing ...
% 3.65/1.59  Prover 6: Warning: ignoring some quantifiers
% 3.65/1.59  Prover 6: Constructing countermodel ...
% 3.65/1.60  Prover 6: gave up
% 3.65/1.60  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.65/1.61  Prover 7: Preprocessing ...
% 3.65/1.61  Prover 7: Proving ...
% 5.34/2.22  Prover 7: proved (623ms)
% 5.34/2.22  
% 5.34/2.22  % SZS status Theorem for theBenchmark
% 5.34/2.22  
% 5.34/2.22  Generating proof ... found it (size 28)
% 6.67/2.61  
% 6.67/2.61  % SZS output start Proof for theBenchmark
% 6.67/2.62  Assumed formulas after preprocessing and simplification: 
% 6.67/2.62  | (0)  ? [v0] :  ! [v1] : f(v1, v0) &  ! [v0] :  ? [v1] : ( ! [v2] : ( ~ f(v2, v1) | (f(v2, v0) &  ~ f(v2, v2))) &  ! [v2] : ( ~ f(v2, v0) | f(v2, v2) | f(v2, v1)))
% 6.67/2.62  | Applying alpha-rule on (0) yields:
% 6.67/2.62  | (1)  ? [v0] :  ! [v1] : f(v1, v0)
% 6.67/2.62  | (2)  ! [v0] :  ? [v1] : ( ! [v2] : ( ~ f(v2, v1) | (f(v2, v0) &  ~ f(v2, v2))) &  ! [v2] : ( ~ f(v2, v0) | f(v2, v2) | f(v2, v1)))
% 6.67/2.62  |
% 6.67/2.62  | Instantiating (1) with all_0_0_0 yields:
% 6.67/2.62  | (3)  ! [v0] : f(v0, all_0_0_0)
% 6.67/2.62  |
% 6.67/2.62  | Introducing new symbol ex_10_0_2 defined by:
% 6.67/2.62  | (4) ex_10_0_2 = all_0_0_0
% 6.67/2.62  |
% 6.67/2.62  | Instantiating formula (2) with ex_10_0_2 yields:
% 6.67/2.62  | (5)  ? [v0] : ( ! [v1] : ( ~ f(v1, v0) | (f(v1, ex_10_0_2) &  ~ f(v1, v1))) &  ! [v1] : ( ~ f(v1, ex_10_0_2) | f(v1, v1) | f(v1, v0)))
% 6.67/2.62  |
% 6.67/2.62  | Instantiating (5) with all_11_0_3 yields:
% 6.67/2.62  | (6)  ! [v0] : ( ~ f(v0, all_11_0_3) | (f(v0, ex_10_0_2) &  ~ f(v0, v0))) &  ! [v0] : ( ~ f(v0, ex_10_0_2) | f(v0, v0) | f(v0, all_11_0_3))
% 6.67/2.62  |
% 6.67/2.62  | Applying alpha-rule on (6) yields:
% 6.67/2.62  | (7)  ! [v0] : ( ~ f(v0, all_11_0_3) | (f(v0, ex_10_0_2) &  ~ f(v0, v0)))
% 6.67/2.62  | (8)  ! [v0] : ( ~ f(v0, ex_10_0_2) | f(v0, v0) | f(v0, all_11_0_3))
% 6.67/2.62  |
% 6.67/2.62  | Introducing new symbol ex_28_0_4 defined by:
% 6.67/2.62  | (9) ex_28_0_4 = all_11_0_3
% 6.67/2.62  |
% 6.67/2.62  | Instantiating formula (3) with ex_28_0_4 yields:
% 6.67/2.62  | (10) f(ex_28_0_4, all_0_0_0)
% 6.67/2.62  |
% 6.67/2.62  | Instantiating formula (7) with ex_28_0_4 yields:
% 6.67/2.62  | (11)  ~ f(ex_28_0_4, all_11_0_3) | (f(ex_28_0_4, ex_10_0_2) &  ~ f(ex_28_0_4, ex_28_0_4))
% 6.67/2.62  |
% 6.67/2.62  | Instantiating formula (8) with ex_28_0_4 yields:
% 6.67/2.62  | (12)  ~ f(ex_28_0_4, ex_10_0_2) | f(ex_28_0_4, ex_28_0_4) | f(ex_28_0_4, all_11_0_3)
% 6.67/2.62  |
% 6.67/2.62  +-Applying beta-rule and splitting (12), into two cases.
% 6.67/2.62  |-Branch one:
% 6.67/2.62  | (13)  ~ f(ex_28_0_4, ex_10_0_2)
% 6.67/2.62  |
% 6.67/2.62  	| From (9) and (10) follows:
% 6.67/2.62  	| (14) f(all_11_0_3, all_0_0_0)
% 6.67/2.62  	|
% 6.67/2.62  	| From (9)(4) and (13) follows:
% 6.67/2.62  	| (15)  ~ f(all_11_0_3, all_0_0_0)
% 6.67/2.62  	|
% 6.67/2.62  	| Using (14) and (15) yields:
% 6.67/2.62  	| (16) $false
% 6.67/2.62  	|
% 6.67/2.62  	|-The branch is then unsatisfiable
% 6.67/2.62  |-Branch two:
% 6.67/2.62  | (17) f(ex_28_0_4, ex_28_0_4) | f(ex_28_0_4, all_11_0_3)
% 6.67/2.62  |
% 6.67/2.62  	+-Applying beta-rule and splitting (17), into two cases.
% 6.67/2.62  	|-Branch one:
% 6.67/2.62  	| (18) f(ex_28_0_4, ex_28_0_4)
% 6.67/2.62  	|
% 6.67/2.62  		+-Applying beta-rule and splitting (11), into two cases.
% 6.67/2.62  		|-Branch one:
% 6.67/2.62  		| (19)  ~ f(ex_28_0_4, all_11_0_3)
% 6.67/2.62  		|
% 6.67/2.62  			| From (9)(9) and (18) follows:
% 6.67/2.62  			| (20) f(all_11_0_3, all_11_0_3)
% 6.67/2.62  			|
% 6.67/2.62  			| From (9) and (19) follows:
% 6.67/2.62  			| (21)  ~ f(all_11_0_3, all_11_0_3)
% 6.67/2.62  			|
% 6.67/2.62  			| Using (20) and (21) yields:
% 6.67/2.62  			| (16) $false
% 6.67/2.62  			|
% 6.67/2.62  			|-The branch is then unsatisfiable
% 6.67/2.62  		|-Branch two:
% 6.67/2.62  		| (23) f(ex_28_0_4, ex_10_0_2) &  ~ f(ex_28_0_4, ex_28_0_4)
% 6.67/2.63  		|
% 6.67/2.63  			| Applying alpha-rule on (23) yields:
% 6.67/2.63  			| (24) f(ex_28_0_4, ex_10_0_2)
% 6.67/2.63  			| (25)  ~ f(ex_28_0_4, ex_28_0_4)
% 6.67/2.63  			|
% 6.67/2.63  			| Using (18) and (25) yields:
% 6.67/2.63  			| (16) $false
% 6.67/2.63  			|
% 6.67/2.63  			|-The branch is then unsatisfiable
% 6.67/2.63  	|-Branch two:
% 6.67/2.63  	| (25)  ~ f(ex_28_0_4, ex_28_0_4)
% 6.67/2.63  	| (28) f(ex_28_0_4, all_11_0_3)
% 6.67/2.63  	|
% 6.67/2.63  		| From (9) and (28) follows:
% 6.67/2.63  		| (20) f(all_11_0_3, all_11_0_3)
% 6.67/2.63  		|
% 6.67/2.63  		| From (9)(9) and (25) follows:
% 6.67/2.63  		| (21)  ~ f(all_11_0_3, all_11_0_3)
% 6.67/2.63  		|
% 6.67/2.63  		| Using (20) and (21) yields:
% 6.67/2.63  		| (16) $false
% 6.67/2.63  		|
% 6.67/2.63  		|-The branch is then unsatisfiable
% 6.67/2.63  % SZS output end Proof for theBenchmark
% 6.67/2.63  
% 6.67/2.63  2051ms
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