TSTP Solution File: SYN373+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : SYN373+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n004.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 05:01:54 EDT 2022

% Result   : Theorem 1.96s 1.12s
% Output   : Proof 2.46s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SYN373+1 : TPTP v8.1.0. Released v2.0.0.
% 0.08/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n004.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 : Tue Jul 12 05:55:22 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.59          ____       _                          
% 0.19/0.59    ___  / __ \_____(_)___  ________  __________
% 0.19/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.59  
% 0.19/0.59  A Theorem Prover for First-Order Logic
% 0.19/0.59  (ePrincess v.1.0)
% 0.19/0.59  
% 0.19/0.59  (c) Philipp Rümmer, 2009-2015
% 0.19/0.59  (c) Peter Backeman, 2014-2015
% 0.19/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.59  Bug reports to peter@backeman.se
% 0.19/0.59  
% 0.19/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.59  
% 0.19/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.17/0.88  Prover 0: Preprocessing ...
% 1.30/0.93  Prover 0: Warning: ignoring some quantifiers
% 1.30/0.94  Prover 0: Constructing countermodel ...
% 1.43/1.02  Prover 0: gave up
% 1.43/1.02  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 1.43/1.04  Prover 1: Preprocessing ...
% 1.79/1.08  Prover 1: Constructing countermodel ...
% 1.96/1.12  Prover 1: proved (97ms)
% 1.96/1.12  
% 1.96/1.12  No countermodel exists, formula is valid
% 1.96/1.12  % SZS status Theorem for theBenchmark
% 1.96/1.12  
% 1.96/1.12  Generating proof ... found it (size 20)
% 2.35/1.26  
% 2.35/1.26  % SZS output start Proof for theBenchmark
% 2.35/1.26  Assumed formulas after preprocessing and simplification: 
% 2.35/1.26  | (0)  ? [v0] :  ? [v1] :  ? [v2] : ( ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (big_p(v5) = v4) |  ~ (big_p(v5) = v3)) &  ! [v3] :  ! [v4] :  ! [v5] : (v4 = v3 |  ~ (big_q(v5) = v4) |  ~ (big_q(v5) = v3)) &  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (big_p(v3) = v4)) &  ! [v3] :  ~ (big_q(v3) = 0) & ((v1 = 0 & big_q(v0) = 0) | ( ~ (v1 = 0) & big_p(v0) = v1) | (big_p(v0) = v1 & big_q(v0) = v2 & ( ~ (v1 = 0) | v2 = 0))))
% 2.46/1.30  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2 yields:
% 2.46/1.30  | (1)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_p(v2) = v1) |  ~ (big_p(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_q(v2) = v1) |  ~ (big_q(v2) = v0)) &  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (big_p(v0) = v1)) &  ! [v0] :  ~ (big_q(v0) = 0) & ((all_0_1_1 = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1) | (big_p(all_0_2_2) = all_0_1_1 & big_q(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)))
% 2.46/1.30  |
% 2.46/1.30  | Applying alpha-rule on (1) yields:
% 2.46/1.30  | (2)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_p(v2) = v1) |  ~ (big_p(v2) = v0))
% 2.46/1.30  | (3) (all_0_1_1 = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1) | (big_p(all_0_2_2) = all_0_1_1 & big_q(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0))
% 2.46/1.30  | (4)  ! [v0] :  ~ (big_q(v0) = 0)
% 2.46/1.30  | (5)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (big_q(v2) = v1) |  ~ (big_q(v2) = v0))
% 2.46/1.30  | (6)  ! [v0] :  ! [v1] : (v1 = 0 |  ~ (big_p(v0) = v1))
% 2.46/1.30  |
% 2.46/1.30  +-Applying beta-rule and splitting (3), into two cases.
% 2.46/1.30  |-Branch one:
% 2.46/1.30  | (7) (all_0_1_1 = 0 & big_q(all_0_2_2) = 0) | ( ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1)
% 2.46/1.31  |
% 2.46/1.31  	+-Applying beta-rule and splitting (7), into two cases.
% 2.46/1.31  	|-Branch one:
% 2.46/1.31  	| (8) all_0_1_1 = 0 & big_q(all_0_2_2) = 0
% 2.46/1.31  	|
% 2.46/1.31  		| Applying alpha-rule on (8) yields:
% 2.46/1.31  		| (9) all_0_1_1 = 0
% 2.46/1.31  		| (10) big_q(all_0_2_2) = 0
% 2.46/1.31  		|
% 2.46/1.31  		| Instantiating formula (4) with all_0_2_2 and discharging atoms big_q(all_0_2_2) = 0, yields:
% 2.46/1.31  		| (11) $false
% 2.46/1.31  		|
% 2.46/1.31  		|-The branch is then unsatisfiable
% 2.46/1.31  	|-Branch two:
% 2.46/1.31  	| (12)  ~ (all_0_1_1 = 0) & big_p(all_0_2_2) = all_0_1_1
% 2.46/1.31  	|
% 2.46/1.31  		| Applying alpha-rule on (12) yields:
% 2.46/1.31  		| (13)  ~ (all_0_1_1 = 0)
% 2.46/1.31  		| (14) big_p(all_0_2_2) = all_0_1_1
% 2.46/1.31  		|
% 2.46/1.31  		| Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms big_p(all_0_2_2) = all_0_1_1, yields:
% 2.46/1.31  		| (9) all_0_1_1 = 0
% 2.46/1.31  		|
% 2.46/1.31  		| Equations (9) can reduce 13 to:
% 2.46/1.31  		| (16) $false
% 2.46/1.31  		|
% 2.46/1.31  		|-The branch is then unsatisfiable
% 2.46/1.31  |-Branch two:
% 2.46/1.31  | (17) big_p(all_0_2_2) = all_0_1_1 & big_q(all_0_2_2) = all_0_0_0 & ( ~ (all_0_1_1 = 0) | all_0_0_0 = 0)
% 2.46/1.31  |
% 2.46/1.31  	| Applying alpha-rule on (17) yields:
% 2.46/1.31  	| (14) big_p(all_0_2_2) = all_0_1_1
% 2.46/1.31  	| (19) big_q(all_0_2_2) = all_0_0_0
% 2.46/1.31  	| (20)  ~ (all_0_1_1 = 0) | all_0_0_0 = 0
% 2.46/1.31  	|
% 2.46/1.31  	| Instantiating formula (6) with all_0_1_1, all_0_2_2 and discharging atoms big_p(all_0_2_2) = all_0_1_1, yields:
% 2.46/1.31  	| (9) all_0_1_1 = 0
% 2.46/1.31  	|
% 2.46/1.31  	| Instantiating formula (4) with all_0_2_2 yields:
% 2.46/1.31  	| (22)  ~ (big_q(all_0_2_2) = 0)
% 2.46/1.31  	|
% 2.46/1.31  	+-Applying beta-rule and splitting (20), into two cases.
% 2.46/1.31  	|-Branch one:
% 2.46/1.31  	| (13)  ~ (all_0_1_1 = 0)
% 2.46/1.31  	|
% 2.46/1.31  		| Equations (9) can reduce 13 to:
% 2.46/1.31  		| (16) $false
% 2.46/1.31  		|
% 2.46/1.31  		|-The branch is then unsatisfiable
% 2.46/1.31  	|-Branch two:
% 2.46/1.31  	| (9) all_0_1_1 = 0
% 2.46/1.31  	| (26) all_0_0_0 = 0
% 2.46/1.31  	|
% 2.46/1.31  		| From (26) and (19) follows:
% 2.46/1.31  		| (10) big_q(all_0_2_2) = 0
% 2.46/1.31  		|
% 2.46/1.31  		| Using (10) and (22) yields:
% 2.46/1.31  		| (11) $false
% 2.46/1.31  		|
% 2.46/1.31  		|-The branch is then unsatisfiable
% 2.46/1.31  % SZS output end Proof for theBenchmark
% 2.46/1.31  
% 2.46/1.31  712ms
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