TSTP Solution File: SYN965+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN965+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.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 05:06:08 EDT 2022

% Result   : Theorem 4.51s 1.93s
% Output   : Proof 5.56s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SYN965+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.33  % Computer : n023.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Mon Jul 11 18:42:54 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.18/0.57          ____       _                          
% 0.18/0.57    ___  / __ \_____(_)___  ________  __________
% 0.18/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.18/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.18/0.57  
% 0.18/0.57  A Theorem Prover for First-Order Logic
% 0.18/0.58  (ePrincess v.1.0)
% 0.18/0.58  
% 0.18/0.58  (c) Philipp Rümmer, 2009-2015
% 0.18/0.58  (c) Peter Backeman, 2014-2015
% 0.18/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58  Bug reports to peter@backeman.se
% 0.18/0.58  
% 0.18/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58  
% 0.18/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.72/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.29/0.88  Prover 0: Preprocessing ...
% 1.39/0.93  Prover 0: Warning: ignoring some quantifiers
% 1.39/0.95  Prover 0: Constructing countermodel ...
% 1.89/1.11  Prover 0: gave up
% 1.89/1.11  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.89/1.12  Prover 1: Preprocessing ...
% 1.89/1.16  Prover 1: Warning: ignoring some quantifiers
% 1.89/1.16  Prover 1: Constructing countermodel ...
% 1.89/1.17  Prover 1: gave up
% 1.89/1.17  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.89/1.18  Prover 2: Preprocessing ...
% 2.28/1.22  Prover 2: Warning: ignoring some quantifiers
% 2.34/1.22  Prover 2: Constructing countermodel ...
% 2.36/1.24  Prover 2: gave up
% 2.36/1.24  Prover 3: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.36/1.24  Prover 3: Preprocessing ...
% 2.36/1.25  Prover 3: Warning: ignoring some quantifiers
% 2.36/1.25  Prover 3: Constructing countermodel ...
% 2.36/1.30  Prover 3: gave up
% 2.36/1.30  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=complete
% 2.67/1.31  Prover 4: Preprocessing ...
% 2.67/1.34  Prover 4: Warning: ignoring some quantifiers
% 2.67/1.34  Prover 4: Constructing countermodel ...
% 2.96/1.42  Prover 4: gave up
% 2.96/1.42  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.96/1.42  Prover 5: Preprocessing ...
% 2.96/1.44  Prover 5: Warning: ignoring some quantifiers
% 2.96/1.44  Prover 5: Constructing countermodel ...
% 2.96/1.44  Prover 5: gave up
% 2.96/1.44  Prover 6: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.96/1.45  Prover 6: Preprocessing ...
% 2.96/1.47  Prover 6: Warning: ignoring some quantifiers
% 2.96/1.47  Prover 6: Constructing countermodel ...
% 3.28/1.48  Prover 6: gave up
% 3.28/1.48  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximalOutermost -resolutionMethod=normal -ignoreQuantifiers -generateTriggers=all
% 3.28/1.48  Prover 7: Preprocessing ...
% 3.28/1.49  Prover 7: Proving ...
% 4.51/1.93  Prover 7: proved (449ms)
% 4.51/1.93  
% 4.51/1.93  % SZS status Theorem for theBenchmark
% 4.51/1.93  
% 4.51/1.93  Generating proof ... found it (size 30)
% 5.34/2.29  
% 5.34/2.29  % SZS output start Proof for theBenchmark
% 5.34/2.29  Assumed formulas after preprocessing and simplification: 
% 5.34/2.29  | (0)  ! [v0] :  ? [v1] :  ! [v2] : ((p(v2, v1) &  ! [v3] :  ~ p(v3, v2)) | (p(v2, v0) & p(v0, v2) &  ~ p(v2, v1)))
% 5.34/2.29  | Introducing new symbol ex_0_0_0 defined by:
% 5.34/2.29  | (1) ex_0_0_0 = arbitrary_constant
% 5.34/2.29  |
% 5.34/2.29  | Instantiating formula (0) with ex_0_0_0 yields:
% 5.34/2.29  | (2)  ? [v0] :  ! [v1] : ((p(v1, v0) &  ! [v2] :  ~ p(v2, v1)) | (p(v1, ex_0_0_0) & p(ex_0_0_0, v1) &  ~ p(v1, v0)))
% 5.34/2.29  |
% 5.34/2.29  | Instantiating (2) with all_1_0_1 yields:
% 5.34/2.29  | (3)  ! [v0] : ((p(v0, all_1_0_1) &  ! [v1] :  ~ p(v1, v0)) | (p(v0, ex_0_0_0) & p(ex_0_0_0, v0) &  ~ p(v0, all_1_0_1)))
% 5.56/2.29  |
% 5.56/2.29  | Introducing new symbol ex_3_0_2 defined by:
% 5.56/2.29  | (4) ex_3_0_2 = all_1_0_1
% 5.56/2.29  |
% 5.56/2.29  | Instantiating formula (0) with ex_3_0_2 yields:
% 5.56/2.29  | (5)  ? [v0] :  ! [v1] : ((p(v1, v0) &  ! [v2] :  ~ p(v2, v1)) | (p(v1, ex_3_0_2) & p(ex_3_0_2, v1) &  ~ p(v1, v0)))
% 5.56/2.29  |
% 5.56/2.29  | Instantiating (5) with all_4_0_3 yields:
% 5.56/2.29  | (6)  ! [v0] : ((p(v0, all_4_0_3) &  ! [v1] :  ~ p(v1, v0)) | (p(v0, ex_3_0_2) & p(ex_3_0_2, v0) &  ~ p(v0, all_4_0_3)))
% 5.56/2.30  |
% 5.56/2.30  | Introducing new symbol ex_6_0_4 defined by:
% 5.56/2.30  | (7) ex_6_0_4 = all_1_0_1
% 5.56/2.30  |
% 5.56/2.30  | Instantiating formula (3) with ex_6_0_4 yields:
% 5.56/2.30  | (8) (p(ex_6_0_4, all_1_0_1) &  ! [v0] :  ~ p(v0, ex_6_0_4)) | (p(ex_6_0_4, ex_0_0_0) & p(ex_0_0_0, ex_6_0_4) &  ~ p(ex_6_0_4, all_1_0_1))
% 5.56/2.30  |
% 5.56/2.30  +-Applying beta-rule and splitting (8), into two cases.
% 5.56/2.30  |-Branch one:
% 5.56/2.30  | (9) p(ex_6_0_4, all_1_0_1) &  ! [v0] :  ~ p(v0, ex_6_0_4)
% 5.56/2.30  |
% 5.56/2.30  	| Applying alpha-rule on (9) yields:
% 5.56/2.30  	| (10) p(ex_6_0_4, all_1_0_1)
% 5.56/2.30  	| (11)  ! [v0] :  ~ p(v0, ex_6_0_4)
% 5.56/2.30  	|
% 5.56/2.30  	| Instantiating formula (11) with all_1_0_1 yields:
% 5.56/2.30  	| (12)  ~ p(all_1_0_1, ex_6_0_4)
% 5.56/2.30  	|
% 5.56/2.30  	| From (7) and (10) follows:
% 5.56/2.30  	| (13) p(all_1_0_1, all_1_0_1)
% 5.56/2.30  	|
% 5.56/2.30  	| From (7) and (12) follows:
% 5.56/2.30  	| (14)  ~ p(all_1_0_1, all_1_0_1)
% 5.56/2.30  	|
% 5.56/2.30  	| Using (13) and (14) yields:
% 5.56/2.30  	| (15) $false
% 5.56/2.30  	|
% 5.56/2.30  	|-The branch is then unsatisfiable
% 5.56/2.30  |-Branch two:
% 5.56/2.30  | (16) p(ex_6_0_4, ex_0_0_0) & p(ex_0_0_0, ex_6_0_4) &  ~ p(ex_6_0_4, all_1_0_1)
% 5.56/2.30  |
% 5.56/2.30  	| Applying alpha-rule on (16) yields:
% 5.56/2.30  	| (17) p(ex_6_0_4, ex_0_0_0)
% 5.56/2.30  	| (18) p(ex_0_0_0, ex_6_0_4)
% 5.56/2.30  	| (19)  ~ p(ex_6_0_4, all_1_0_1)
% 5.56/2.30  	|
% 5.56/2.30  	| Introducing new symbol ex_18_0_7 defined by:
% 5.56/2.30  	| (20) ex_18_0_7 = all_1_0_1
% 5.56/2.30  	|
% 5.56/2.30  	| Instantiating formula (6) with ex_18_0_7 yields:
% 5.56/2.30  	| (21) (p(ex_18_0_7, all_4_0_3) &  ! [v0] :  ~ p(v0, ex_18_0_7)) | (p(ex_18_0_7, ex_3_0_2) & p(ex_3_0_2, ex_18_0_7) &  ~ p(ex_18_0_7, all_4_0_3))
% 5.56/2.30  	|
% 5.56/2.30  	+-Applying beta-rule and splitting (21), into two cases.
% 5.56/2.30  	|-Branch one:
% 5.56/2.30  	| (22) p(ex_18_0_7, all_4_0_3) &  ! [v0] :  ~ p(v0, ex_18_0_7)
% 5.56/2.30  	|
% 5.56/2.30  		| Applying alpha-rule on (22) yields:
% 5.56/2.30  		| (23) p(ex_18_0_7, all_4_0_3)
% 5.56/2.30  		| (24)  ! [v0] :  ~ p(v0, ex_18_0_7)
% 5.56/2.30  		|
% 5.56/2.30  		| Instantiating formula (24) with ex_0_0_0 yields:
% 5.56/2.30  		| (25)  ~ p(ex_0_0_0, ex_18_0_7)
% 5.56/2.30  		|
% 5.56/2.30  		| From (1)(7) and (18) follows:
% 5.56/2.30  		| (26) p(arbitrary_constant, all_1_0_1)
% 5.56/2.30  		|
% 5.56/2.30  		| From (1)(20) and (25) follows:
% 5.56/2.30  		| (27)  ~ p(arbitrary_constant, all_1_0_1)
% 5.56/2.30  		|
% 5.56/2.30  		| Using (26) and (27) yields:
% 5.56/2.30  		| (15) $false
% 5.56/2.30  		|
% 5.56/2.30  		|-The branch is then unsatisfiable
% 5.56/2.30  	|-Branch two:
% 5.56/2.30  	| (29) p(ex_18_0_7, ex_3_0_2) & p(ex_3_0_2, ex_18_0_7) &  ~ p(ex_18_0_7, all_4_0_3)
% 5.56/2.30  	|
% 5.56/2.30  		| Applying alpha-rule on (29) yields:
% 5.56/2.30  		| (30) p(ex_18_0_7, ex_3_0_2)
% 5.56/2.30  		| (31) p(ex_3_0_2, ex_18_0_7)
% 5.56/2.30  		| (32)  ~ p(ex_18_0_7, all_4_0_3)
% 5.56/2.30  		|
% 5.56/2.30  		| From (4)(20) and (31) follows:
% 5.56/2.30  		| (13) p(all_1_0_1, all_1_0_1)
% 5.56/2.30  		|
% 5.56/2.30  		| From (7) and (19) follows:
% 5.56/2.30  		| (14)  ~ p(all_1_0_1, all_1_0_1)
% 5.56/2.31  		|
% 5.56/2.31  		| Using (13) and (14) yields:
% 5.56/2.31  		| (15) $false
% 5.56/2.31  		|
% 5.56/2.31  		|-The branch is then unsatisfiable
% 5.56/2.31  % SZS output end Proof for theBenchmark
% 5.56/2.31  
% 5.56/2.31  1712ms
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