TSTP Solution File: SYN722+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN722+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n015.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 05:04:41 EDT 2022

% Result   : Theorem 2.18s 1.21s
% Output   : Proof 3.04s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SYN722+1 : TPTP v8.1.0. Released v2.5.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n015.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 : Mon Jul 11 14:33:54 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.59/0.58          ____       _                          
% 0.59/0.58    ___  / __ \_____(_)___  ________  __________
% 0.59/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.58  
% 0.59/0.58  A Theorem Prover for First-Order Logic
% 0.59/0.58  (ePrincess v.1.0)
% 0.59/0.58  
% 0.59/0.58  (c) Philipp Rümmer, 2009-2015
% 0.59/0.58  (c) Peter Backeman, 2014-2015
% 0.59/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.58  Bug reports to peter@backeman.se
% 0.59/0.58  
% 0.59/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.58  
% 0.59/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.77/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.30/0.88  Prover 0: Preprocessing ...
% 1.42/0.94  Prover 0: Warning: ignoring some quantifiers
% 1.45/0.95  Prover 0: Constructing countermodel ...
% 1.59/1.05  Prover 0: gave up
% 1.59/1.05  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.59/1.07  Prover 1: Preprocessing ...
% 1.86/1.12  Prover 1: Constructing countermodel ...
% 2.18/1.21  Prover 1: proved (156ms)
% 2.18/1.21  
% 2.18/1.21  No countermodel exists, formula is valid
% 2.18/1.21  % SZS status Theorem for theBenchmark
% 2.18/1.21  
% 2.18/1.21  Generating proof ... found it (size 43)
% 2.65/1.42  
% 2.65/1.42  % SZS output start Proof for theBenchmark
% 2.65/1.42  Assumed formulas after preprocessing and simplification: 
% 2.65/1.42  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (q(d) = v1 & q(c) = v0 & p(b) = v3 & p(a) = v2 &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (q(v6) = v5) |  ~ (q(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (r(v6) = v5) |  ~ (r(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (p(v6) = v5) |  ~ (p(v6) = v4)) &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (q(v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (r(v4) = v5) | p(v4) = 0) &  ! [v4] :  ! [v5] : ( ~ (p(v4) = v5) |  ? [v6] :  ? [v7] :  ? [v8] : (q(v7) = v8 & q(v4) = v6 & ( ~ (v8 = 0) |  ~ (v6 = 0) |  ~ (v1 = 0) |  ~ (v0 = 0) | v5 = 0))) & ( ~ (v3 = 0) |  ~ (v2 = 0)))
% 2.65/1.45  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 2.65/1.45  | (1) q(d) = all_0_2_2 & q(c) = all_0_3_3 & p(b) = all_0_0_0 & p(a) = all_0_1_1 &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (r(v2) = v1) |  ~ (r(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (q(v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (r(v0) = v1) | p(v0) = 0) &  ! [v0] :  ! [v1] : ( ~ (p(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (q(v3) = v4 & q(v0) = v2 & ( ~ (v4 = 0) |  ~ (v2 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | v1 = 0))) & ( ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0))
% 2.65/1.46  |
% 2.65/1.46  | Applying alpha-rule on (1) yields:
% 2.65/1.46  | (2) q(c) = all_0_3_3
% 2.65/1.46  | (3) p(a) = all_0_1_1
% 2.65/1.46  | (4)  ~ (all_0_0_0 = 0) |  ~ (all_0_1_1 = 0)
% 2.65/1.46  | (5) p(b) = all_0_0_0
% 2.65/1.46  | (6) q(d) = all_0_2_2
% 2.65/1.46  | (7)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (q(v2) = v1) |  ~ (q(v2) = v0))
% 3.04/1.46  | (8)  ! [v0] :  ! [v1] : ( ~ (p(v0) = v1) |  ? [v2] :  ? [v3] :  ? [v4] : (q(v3) = v4 & q(v0) = v2 & ( ~ (v4 = 0) |  ~ (v2 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | v1 = 0)))
% 3.04/1.46  | (9)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (r(v2) = v1) |  ~ (r(v2) = v0))
% 3.04/1.46  | (10)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (r(v0) = v1) | p(v0) = 0)
% 3.04/1.46  | (11)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (p(v2) = v1) |  ~ (p(v2) = v0))
% 3.04/1.46  | (12)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (q(v0) = v1))
% 3.04/1.46  |
% 3.04/1.46  | Instantiating formula (12) with all_0_2_2, d and discharging atoms q(d) = all_0_2_2, yields:
% 3.04/1.47  | (13) all_0_2_2 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (12) with all_0_3_3, c and discharging atoms q(c) = all_0_3_3, yields:
% 3.04/1.47  | (14) all_0_3_3 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (8) with all_0_0_0, b and discharging atoms p(b) = all_0_0_0, yields:
% 3.04/1.47  | (15)  ? [v0] :  ? [v1] :  ? [v2] : (q(v1) = v2 & q(b) = v0 & ( ~ (v2 = 0) |  ~ (v0 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_0_0 = 0))
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (8) with all_0_1_1, a and discharging atoms p(a) = all_0_1_1, yields:
% 3.04/1.47  | (16)  ? [v0] :  ? [v1] :  ? [v2] : (q(v1) = v2 & q(a) = v0 & ( ~ (v2 = 0) |  ~ (v0 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_1_1 = 0))
% 3.04/1.47  |
% 3.04/1.47  | Instantiating (16) with all_12_0_4, all_12_1_5, all_12_2_6 yields:
% 3.04/1.47  | (17) q(all_12_1_5) = all_12_0_4 & q(a) = all_12_2_6 & ( ~ (all_12_0_4 = 0) |  ~ (all_12_2_6 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_1_1 = 0)
% 3.04/1.47  |
% 3.04/1.47  | Applying alpha-rule on (17) yields:
% 3.04/1.47  | (18) q(all_12_1_5) = all_12_0_4
% 3.04/1.47  | (19) q(a) = all_12_2_6
% 3.04/1.47  | (20)  ~ (all_12_0_4 = 0) |  ~ (all_12_2_6 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating (15) with all_14_0_7, all_14_1_8, all_14_2_9 yields:
% 3.04/1.47  | (21) q(all_14_1_8) = all_14_0_7 & q(b) = all_14_2_9 & ( ~ (all_14_0_7 = 0) |  ~ (all_14_2_9 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_0_0 = 0)
% 3.04/1.47  |
% 3.04/1.47  | Applying alpha-rule on (21) yields:
% 3.04/1.47  | (22) q(all_14_1_8) = all_14_0_7
% 3.04/1.47  | (23) q(b) = all_14_2_9
% 3.04/1.47  | (24)  ~ (all_14_0_7 = 0) |  ~ (all_14_2_9 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (12) with all_14_0_7, all_14_1_8 and discharging atoms q(all_14_1_8) = all_14_0_7, yields:
% 3.04/1.47  | (25) all_14_0_7 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (12) with all_12_0_4, all_12_1_5 and discharging atoms q(all_12_1_5) = all_12_0_4, yields:
% 3.04/1.47  | (26) all_12_0_4 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (12) with all_14_2_9, b and discharging atoms q(b) = all_14_2_9, yields:
% 3.04/1.47  | (27) all_14_2_9 = 0
% 3.04/1.47  |
% 3.04/1.47  | Instantiating formula (12) with all_12_2_6, a and discharging atoms q(a) = all_12_2_6, yields:
% 3.04/1.47  | (28) all_12_2_6 = 0
% 3.04/1.47  |
% 3.04/1.47  +-Applying beta-rule and splitting (24), into two cases.
% 3.04/1.47  |-Branch one:
% 3.04/1.47  | (29)  ~ (all_14_0_7 = 0)
% 3.04/1.47  |
% 3.04/1.47  	| Equations (25) can reduce 29 to:
% 3.04/1.47  	| (30) $false
% 3.04/1.47  	|
% 3.04/1.47  	|-The branch is then unsatisfiable
% 3.04/1.47  |-Branch two:
% 3.04/1.47  | (25) all_14_0_7 = 0
% 3.04/1.47  | (32)  ~ (all_14_2_9 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.47  |
% 3.04/1.47  	+-Applying beta-rule and splitting (32), into two cases.
% 3.04/1.47  	|-Branch one:
% 3.04/1.47  	| (33)  ~ (all_14_2_9 = 0)
% 3.04/1.47  	|
% 3.04/1.47  		| Equations (27) can reduce 33 to:
% 3.04/1.47  		| (30) $false
% 3.04/1.47  		|
% 3.04/1.47  		|-The branch is then unsatisfiable
% 3.04/1.47  	|-Branch two:
% 3.04/1.47  	| (27) all_14_2_9 = 0
% 3.04/1.47  	| (36)  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.48  	|
% 3.04/1.48  		+-Applying beta-rule and splitting (36), into two cases.
% 3.04/1.48  		|-Branch one:
% 3.04/1.48  		| (37)  ~ (all_0_2_2 = 0)
% 3.04/1.48  		|
% 3.04/1.48  			| Equations (13) can reduce 37 to:
% 3.04/1.48  			| (30) $false
% 3.04/1.48  			|
% 3.04/1.48  			|-The branch is then unsatisfiable
% 3.04/1.48  		|-Branch two:
% 3.04/1.48  		| (13) all_0_2_2 = 0
% 3.04/1.48  		| (40)  ~ (all_0_3_3 = 0) | all_0_0_0 = 0
% 3.04/1.48  		|
% 3.04/1.48  			+-Applying beta-rule and splitting (40), into two cases.
% 3.04/1.48  			|-Branch one:
% 3.04/1.48  			| (41)  ~ (all_0_3_3 = 0)
% 3.04/1.48  			|
% 3.04/1.48  				| Equations (14) can reduce 41 to:
% 3.04/1.48  				| (30) $false
% 3.04/1.48  				|
% 3.04/1.48  				|-The branch is then unsatisfiable
% 3.04/1.48  			|-Branch two:
% 3.04/1.48  			| (14) all_0_3_3 = 0
% 3.04/1.48  			| (44) all_0_0_0 = 0
% 3.04/1.48  			|
% 3.04/1.48  				+-Applying beta-rule and splitting (4), into two cases.
% 3.04/1.48  				|-Branch one:
% 3.04/1.48  				| (45)  ~ (all_0_0_0 = 0)
% 3.04/1.48  				|
% 3.04/1.48  					| Equations (44) can reduce 45 to:
% 3.04/1.48  					| (30) $false
% 3.04/1.48  					|
% 3.04/1.48  					|-The branch is then unsatisfiable
% 3.04/1.48  				|-Branch two:
% 3.04/1.48  				| (44) all_0_0_0 = 0
% 3.04/1.48  				| (48)  ~ (all_0_1_1 = 0)
% 3.04/1.48  				|
% 3.04/1.48  					+-Applying beta-rule and splitting (20), into two cases.
% 3.04/1.48  					|-Branch one:
% 3.04/1.48  					| (49)  ~ (all_12_0_4 = 0)
% 3.04/1.48  					|
% 3.04/1.48  						| Equations (26) can reduce 49 to:
% 3.04/1.48  						| (30) $false
% 3.04/1.48  						|
% 3.04/1.48  						|-The branch is then unsatisfiable
% 3.04/1.48  					|-Branch two:
% 3.04/1.48  					| (26) all_12_0_4 = 0
% 3.04/1.48  					| (52)  ~ (all_12_2_6 = 0) |  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.48  					|
% 3.04/1.48  						+-Applying beta-rule and splitting (52), into two cases.
% 3.04/1.48  						|-Branch one:
% 3.04/1.48  						| (53)  ~ (all_12_2_6 = 0)
% 3.04/1.48  						|
% 3.04/1.48  							| Equations (28) can reduce 53 to:
% 3.04/1.48  							| (30) $false
% 3.04/1.48  							|
% 3.04/1.48  							|-The branch is then unsatisfiable
% 3.04/1.48  						|-Branch two:
% 3.04/1.48  						| (28) all_12_2_6 = 0
% 3.04/1.48  						| (56)  ~ (all_0_2_2 = 0) |  ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.48  						|
% 3.04/1.48  							+-Applying beta-rule and splitting (56), into two cases.
% 3.04/1.48  							|-Branch one:
% 3.04/1.48  							| (37)  ~ (all_0_2_2 = 0)
% 3.04/1.48  							|
% 3.04/1.48  								| Equations (13) can reduce 37 to:
% 3.04/1.48  								| (30) $false
% 3.04/1.48  								|
% 3.04/1.48  								|-The branch is then unsatisfiable
% 3.04/1.48  							|-Branch two:
% 3.04/1.48  							| (13) all_0_2_2 = 0
% 3.04/1.48  							| (60)  ~ (all_0_3_3 = 0) | all_0_1_1 = 0
% 3.04/1.48  							|
% 3.04/1.48  								+-Applying beta-rule and splitting (60), into two cases.
% 3.04/1.48  								|-Branch one:
% 3.04/1.48  								| (41)  ~ (all_0_3_3 = 0)
% 3.04/1.48  								|
% 3.04/1.48  									| Equations (14) can reduce 41 to:
% 3.04/1.48  									| (30) $false
% 3.04/1.48  									|
% 3.04/1.48  									|-The branch is then unsatisfiable
% 3.04/1.48  								|-Branch two:
% 3.04/1.48  								| (14) all_0_3_3 = 0
% 3.04/1.48  								| (64) all_0_1_1 = 0
% 3.04/1.48  								|
% 3.04/1.48  									| Equations (64) can reduce 48 to:
% 3.04/1.48  									| (30) $false
% 3.04/1.48  									|
% 3.04/1.48  									|-The branch is then unsatisfiable
% 3.04/1.48  % SZS output end Proof for theBenchmark
% 3.04/1.48  
% 3.04/1.48  889ms
%------------------------------------------------------------------------------