TSTP Solution File: SYN954+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN954+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n021.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 05:06:04 EDT 2022

% Result   : Theorem 2.53s 1.35s
% Output   : Proof 3.43s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SYN954+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 17:13:08 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.56/0.60          ____       _                          
% 0.56/0.60    ___  / __ \_____(_)___  ________  __________
% 0.56/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.60  
% 0.56/0.60  A Theorem Prover for First-Order Logic
% 0.56/0.61  (ePrincess v.1.0)
% 0.56/0.61  
% 0.56/0.61  (c) Philipp Rümmer, 2009-2015
% 0.56/0.61  (c) Peter Backeman, 2014-2015
% 0.56/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.61  Bug reports to peter@backeman.se
% 0.56/0.61  
% 0.56/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.61  
% 0.56/0.61  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.25/0.91  Prover 0: Preprocessing ...
% 1.39/0.96  Prover 0: Warning: ignoring some quantifiers
% 1.39/0.97  Prover 0: Constructing countermodel ...
% 1.51/1.07  Prover 0: gave up
% 1.51/1.07  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.72/1.09  Prover 1: Preprocessing ...
% 2.04/1.17  Prover 1: Constructing countermodel ...
% 2.11/1.21  Prover 1: gave up
% 2.11/1.21  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.11/1.22  Prover 2: Preprocessing ...
% 2.23/1.27  Prover 2: Warning: ignoring some quantifiers
% 2.23/1.27  Prover 2: Constructing countermodel ...
% 2.53/1.34  Prover 2: proved (130ms)
% 2.53/1.35  
% 2.53/1.35  No countermodel exists, formula is valid
% 2.53/1.35  % SZS status Theorem for theBenchmark
% 2.53/1.35  
% 2.53/1.35  Generating proof ... Warning: ignoring some quantifiers
% 3.08/1.59  found it (size 50)
% 3.08/1.59  
% 3.08/1.59  % SZS output start Proof for theBenchmark
% 3.08/1.59  Assumed formulas after preprocessing and simplification: 
% 3.08/1.59  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (p(v1) = v3 & p(v0) = v2 &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (p(v6) = v5) |  ~ (p(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (q(v6) = v5) |  ~ (q(v6) = v4)) &  ! [v4] :  ! [v5] : ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (p(v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (v3 = 0) |  ~ (v2 = 0) |  ~ (q(v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (v3 = 0) | v5 = 0 |  ~ (p(v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (v3 = 0) |  ~ (q(v4) = v5) | p(v4) = 0) &  ! [v4] :  ! [v5] : ( ~ (v2 = 0) | v5 = 0 |  ~ (q(v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (v2 = 0) |  ~ (p(v4) = v5) | q(v4) = 0) &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (p(v4) = v5) | q(v4) = 0) &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (p(v4) = v5) |  ? [v6] : ( ~ (v6 = 0) & q(v4) = v6)) &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (q(v4) = v5) | p(v4) = 0) &  ! [v4] : ( ~ (q(v4) = 0) | p(v4) = 0) &  ? [v4] :  ? [v5] : p(v4) = v5 &  ? [v4] :  ? [v5] : q(v4) = v5)
% 3.08/1.62  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 3.08/1.62  | (1) p(all_0_2_2) = all_0_0_0 & p(all_0_3_3) = all_0_1_1 &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2) = v0)) &  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0) |  ~ (p(v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0) |  ~ (q(v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 |  ~ (p(v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) |  ~ (q(v0) = v1) | p(v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (all_0_1_1 = 0) | v1 = 0 |  ~ (q(v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (all_0_1_1 = 0) |  ~ (p(v0) = v1) | q(v0) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (p(v0) = v1) | q(v0) = 0) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (p(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & q(v0) = v2)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (q(v0) = v1) | p(v0) = 0) &  ! [v0] : ( ~ (q(v0) = 0) | p(v0) = 0) &  ? [v0] :  ? [v1] : p(v0) = v1 &  ? [v0] :  ? [v1] : q(v0) = v1
% 3.08/1.63  |
% 3.08/1.63  | Applying alpha-rule on (1) yields:
% 3.08/1.63  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0))
% 3.08/1.63  | (3)  ? [v0] :  ? [v1] : q(v0) = v1
% 3.08/1.63  | (4)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (q(v0) = v1) | p(v0) = 0)
% 3.08/1.63  | (5)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (p(v0) = v1) | q(v0) = 0)
% 3.08/1.63  | (6)  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0) |  ~ (q(v0) = v1))
% 3.08/1.63  | (7) p(all_0_2_2) = all_0_0_0
% 3.43/1.63  | (8)  ! [v0] :  ! [v1] : ( ~ (all_0_1_1 = 0) |  ~ (p(v0) = v1) | q(v0) = 0)
% 3.43/1.63  | (9)  ! [v0] :  ! [v1] : ( ~ (all_0_1_1 = 0) | v1 = 0 |  ~ (q(v0) = v1))
% 3.43/1.63  | (10)  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0) |  ~ (p(v0) = v1))
% 3.43/1.63  | (11) p(all_0_3_3) = all_0_1_1
% 3.43/1.63  | (12)  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) |  ~ (q(v0) = v1) | p(v0) = 0)
% 3.43/1.63  | (13)  ? [v0] :  ? [v1] : p(v0) = v1
% 3.43/1.63  | (14)  ! [v0] :  ! [v1] : ( ~ (all_0_0_0 = 0) | v1 = 0 |  ~ (p(v0) = v1))
% 3.43/1.63  | (15)  ! [v0] : ( ~ (q(v0) = 0) | p(v0) = 0)
% 3.43/1.63  | (16)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (p(v0) = v1) |  ? [v2] : ( ~ (v2 = 0) & q(v0) = v2))
% 3.43/1.63  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2) = v0))
% 3.43/1.63  |
% 3.43/1.63  | Instantiating (3) with all_3_0_4, all_3_1_5 yields:
% 3.43/1.63  | (18) q(all_3_1_5) = all_3_0_4
% 3.43/1.63  |
% 3.43/1.63  | Instantiating formula (10) with 0, all_0_3_3 yields:
% 3.43/1.63  | (19)  ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0) |  ~ (p(all_0_3_3) = 0)
% 3.43/1.63  |
% 3.43/1.63  | Instantiating formula (9) with all_3_0_4, all_3_1_5 and discharging atoms q(all_3_1_5) = all_3_0_4, yields:
% 3.43/1.63  | (20)  ~ (all_0_1_1 = 0) | all_3_0_4 = 0
% 3.43/1.64  |
% 3.43/1.64  | Instantiating formula (8) with all_0_0_0, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_0_0, yields:
% 3.43/1.64  | (21)  ~ (all_0_1_1 = 0) | q(all_0_2_2) = 0
% 3.43/1.64  |
% 3.43/1.64  | Instantiating formula (16) with all_0_0_0, all_0_2_2 and discharging atoms p(all_0_2_2) = all_0_0_0, yields:
% 3.43/1.64  | (22) all_0_0_0 = 0 |  ? [v0] : ( ~ (v0 = 0) & q(all_0_2_2) = v0)
% 3.43/1.64  |
% 3.43/1.64  | Instantiating formula (8) with 0, all_0_3_3 yields:
% 3.43/1.64  | (23)  ~ (all_0_1_1 = 0) |  ~ (p(all_0_3_3) = 0) | q(all_0_3_3) = 0
% 3.43/1.64  |
% 3.43/1.64  | Instantiating formula (5) with all_0_1_1, all_0_3_3 and discharging atoms p(all_0_3_3) = all_0_1_1, yields:
% 3.43/1.64  | (24) all_0_1_1 = 0 | q(all_0_3_3) = 0
% 3.43/1.64  |
% 3.43/1.64  | Instantiating formula (16) with all_0_1_1, all_0_3_3 and discharging atoms p(all_0_3_3) = all_0_1_1, yields:
% 3.43/1.64  | (25) all_0_1_1 = 0 |  ? [v0] : ( ~ (v0 = 0) & q(all_0_3_3) = v0)
% 3.43/1.64  |
% 3.43/1.64  +-Applying beta-rule and splitting (24), into two cases.
% 3.43/1.64  |-Branch one:
% 3.43/1.64  | (26) q(all_0_3_3) = 0
% 3.43/1.64  |
% 3.43/1.64  	+-Applying beta-rule and splitting (25), into two cases.
% 3.43/1.64  	|-Branch one:
% 3.43/1.64  	| (27) all_0_1_1 = 0
% 3.43/1.64  	|
% 3.43/1.64  		| From (27) and (11) follows:
% 3.43/1.64  		| (28) p(all_0_3_3) = 0
% 3.43/1.64  		|
% 3.43/1.64  		+-Applying beta-rule and splitting (19), into two cases.
% 3.43/1.64  		|-Branch one:
% 3.43/1.64  		| (29)  ~ (p(all_0_3_3) = 0)
% 3.43/1.64  		|
% 3.43/1.64  			| Using (28) and (29) yields:
% 3.43/1.64  			| (30) $false
% 3.43/1.64  			|
% 3.43/1.64  			|-The branch is then unsatisfiable
% 3.43/1.64  		|-Branch two:
% 3.43/1.64  		| (28) p(all_0_3_3) = 0
% 3.43/1.64  		| (32)  ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0)
% 3.43/1.64  		|
% 3.43/1.64  			+-Applying beta-rule and splitting (32), into two cases.
% 3.43/1.64  			|-Branch one:
% 3.43/1.64  			| (33)  ~ (all_0_0_0 = 0)
% 3.43/1.64  			|
% 3.43/1.64  				+-Applying beta-rule and splitting (21), into two cases.
% 3.43/1.64  				|-Branch one:
% 3.43/1.64  				| (34) q(all_0_2_2) = 0
% 3.43/1.64  				|
% 3.43/1.64  					+-Applying beta-rule and splitting (22), into two cases.
% 3.43/1.64  					|-Branch one:
% 3.43/1.64  					| (35) all_0_0_0 = 0
% 3.43/1.64  					|
% 3.43/1.64  						| Equations (35) can reduce 33 to:
% 3.43/1.64  						| (36) $false
% 3.43/1.64  						|
% 3.43/1.64  						|-The branch is then unsatisfiable
% 3.43/1.64  					|-Branch two:
% 3.43/1.64  					| (33)  ~ (all_0_0_0 = 0)
% 3.43/1.64  					| (38)  ? [v0] : ( ~ (v0 = 0) & q(all_0_2_2) = v0)
% 3.43/1.64  					|
% 3.43/1.64  						| Instantiating (38) with all_45_0_8 yields:
% 3.43/1.64  						| (39)  ~ (all_45_0_8 = 0) & q(all_0_2_2) = all_45_0_8
% 3.43/1.64  						|
% 3.43/1.64  						| Applying alpha-rule on (39) yields:
% 3.43/1.64  						| (40)  ~ (all_45_0_8 = 0)
% 3.43/1.64  						| (41) q(all_0_2_2) = all_45_0_8
% 3.43/1.64  						|
% 3.43/1.64  						| Instantiating formula (17) with all_0_2_2, 0, all_45_0_8 and discharging atoms q(all_0_2_2) = all_45_0_8, q(all_0_2_2) = 0, yields:
% 3.43/1.64  						| (42) all_45_0_8 = 0
% 3.43/1.64  						|
% 3.43/1.64  						| Equations (42) can reduce 40 to:
% 3.43/1.64  						| (36) $false
% 3.43/1.64  						|
% 3.43/1.64  						|-The branch is then unsatisfiable
% 3.43/1.64  				|-Branch two:
% 3.43/1.64  				| (44)  ~ (q(all_0_2_2) = 0)
% 3.43/1.64  				| (45)  ~ (all_0_1_1 = 0)
% 3.43/1.64  				|
% 3.43/1.64  					| Equations (27) can reduce 45 to:
% 3.43/1.64  					| (36) $false
% 3.43/1.64  					|
% 3.43/1.64  					|-The branch is then unsatisfiable
% 3.43/1.64  			|-Branch two:
% 3.43/1.64  			| (35) all_0_0_0 = 0
% 3.43/1.64  			| (45)  ~ (all_0_1_1 = 0)
% 3.43/1.64  			|
% 3.43/1.64  				| Equations (27) can reduce 45 to:
% 3.43/1.64  				| (36) $false
% 3.43/1.64  				|
% 3.43/1.64  				|-The branch is then unsatisfiable
% 3.43/1.64  	|-Branch two:
% 3.43/1.64  	| (45)  ~ (all_0_1_1 = 0)
% 3.43/1.65  	| (51)  ? [v0] : ( ~ (v0 = 0) & q(all_0_3_3) = v0)
% 3.43/1.65  	|
% 3.43/1.65  		| Instantiating (51) with all_25_0_9 yields:
% 3.43/1.65  		| (52)  ~ (all_25_0_9 = 0) & q(all_0_3_3) = all_25_0_9
% 3.43/1.65  		|
% 3.43/1.65  		| Applying alpha-rule on (52) yields:
% 3.43/1.65  		| (53)  ~ (all_25_0_9 = 0)
% 3.43/1.65  		| (54) q(all_0_3_3) = all_25_0_9
% 3.43/1.65  		|
% 3.43/1.65  		| Instantiating formula (17) with all_0_3_3, 0, all_25_0_9 and discharging atoms q(all_0_3_3) = all_25_0_9, q(all_0_3_3) = 0, yields:
% 3.43/1.65  		| (55) all_25_0_9 = 0
% 3.43/1.65  		|
% 3.43/1.65  		| Equations (55) can reduce 53 to:
% 3.43/1.65  		| (36) $false
% 3.43/1.65  		|
% 3.43/1.65  		|-The branch is then unsatisfiable
% 3.43/1.65  |-Branch two:
% 3.43/1.65  | (57)  ~ (q(all_0_3_3) = 0)
% 3.43/1.65  | (27) all_0_1_1 = 0
% 3.43/1.65  |
% 3.43/1.65  	| From (27) and (11) follows:
% 3.43/1.65  	| (28) p(all_0_3_3) = 0
% 3.43/1.65  	|
% 3.43/1.65  	+-Applying beta-rule and splitting (20), into two cases.
% 3.43/1.65  	|-Branch one:
% 3.43/1.65  	| (45)  ~ (all_0_1_1 = 0)
% 3.43/1.65  	|
% 3.43/1.65  		| Equations (27) can reduce 45 to:
% 3.43/1.65  		| (36) $false
% 3.43/1.65  		|
% 3.43/1.65  		|-The branch is then unsatisfiable
% 3.43/1.65  	|-Branch two:
% 3.43/1.65  	| (27) all_0_1_1 = 0
% 3.43/1.65  	| (63) all_3_0_4 = 0
% 3.43/1.65  	|
% 3.43/1.65  		+-Applying beta-rule and splitting (19), into two cases.
% 3.43/1.65  		|-Branch one:
% 3.43/1.65  		| (29)  ~ (p(all_0_3_3) = 0)
% 3.43/1.65  		|
% 3.43/1.65  			| Using (28) and (29) yields:
% 3.43/1.65  			| (30) $false
% 3.43/1.65  			|
% 3.43/1.65  			|-The branch is then unsatisfiable
% 3.43/1.65  		|-Branch two:
% 3.43/1.65  		| (28) p(all_0_3_3) = 0
% 3.43/1.65  		| (32)  ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0)
% 3.43/1.65  		|
% 3.43/1.65  			+-Applying beta-rule and splitting (23), into two cases.
% 3.43/1.65  			|-Branch one:
% 3.43/1.65  			| (29)  ~ (p(all_0_3_3) = 0)
% 3.43/1.65  			|
% 3.43/1.65  				| Using (28) and (29) yields:
% 3.43/1.65  				| (30) $false
% 3.43/1.65  				|
% 3.43/1.65  				|-The branch is then unsatisfiable
% 3.43/1.65  			|-Branch two:
% 3.43/1.65  			| (28) p(all_0_3_3) = 0
% 3.43/1.65  			| (71)  ~ (all_0_1_1 = 0) | q(all_0_3_3) = 0
% 3.43/1.65  			|
% 3.43/1.65  				+-Applying beta-rule and splitting (71), into two cases.
% 3.43/1.65  				|-Branch one:
% 3.43/1.65  				| (26) q(all_0_3_3) = 0
% 3.43/1.65  				|
% 3.43/1.65  					| Using (26) and (57) yields:
% 3.43/1.65  					| (30) $false
% 3.43/1.65  					|
% 3.43/1.65  					|-The branch is then unsatisfiable
% 3.43/1.65  				|-Branch two:
% 3.43/1.65  				| (57)  ~ (q(all_0_3_3) = 0)
% 3.43/1.65  				| (45)  ~ (all_0_1_1 = 0)
% 3.43/1.65  				|
% 3.43/1.65  					| Equations (27) can reduce 45 to:
% 3.43/1.65  					| (36) $false
% 3.43/1.65  					|
% 3.43/1.65  					|-The branch is then unsatisfiable
% 3.43/1.65  % SZS output end Proof for theBenchmark
% 3.43/1.65  
% 3.43/1.65  1035ms
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