TSTP Solution File: LCL650+1.001 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : LCL650+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 09:37:43 EDT 2022

% Result   : Theorem 2.24s 1.14s
% Output   : Proof 3.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem  : LCL650+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.08  % Command  : ePrincess-casc -timeout=%d %s
% 0.07/0.28  % Computer : n024.cluster.edu
% 0.07/0.28  % Model    : x86_64 x86_64
% 0.07/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.28  % Memory   : 8042.1875MB
% 0.07/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.28  % CPULimit : 300
% 0.07/0.28  % WCLimit  : 600
% 0.07/0.28  % DateTime : Sun Jul  3 10:34:29 EDT 2022
% 0.07/0.28  % CPUTime  : 
% 0.12/0.48          ____       _                          
% 0.12/0.48    ___  / __ \_____(_)___  ________  __________
% 0.12/0.48   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.12/0.48  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.12/0.48  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.12/0.48  
% 0.12/0.48  A Theorem Prover for First-Order Logic
% 0.12/0.48  (ePrincess v.1.0)
% 0.12/0.48  
% 0.12/0.48  (c) Philipp Rümmer, 2009-2015
% 0.12/0.48  (c) Peter Backeman, 2014-2015
% 0.12/0.48  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.12/0.48  Free software under GNU Lesser General Public License (LGPL).
% 0.12/0.48  Bug reports to peter@backeman.se
% 0.12/0.48  
% 0.12/0.48  For more information, visit http://user.uu.se/~petba168/breu/
% 0.12/0.48  
% 0.12/0.48  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.12/0.53  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.42/0.83  Prover 0: Preprocessing ...
% 1.66/0.96  Prover 0: Constructing countermodel ...
% 2.24/1.13  Prover 0: proved (602ms)
% 2.24/1.14  
% 2.24/1.14  No countermodel exists, formula is valid
% 2.24/1.14  % SZS status Theorem for theBenchmark
% 2.24/1.14  
% 2.24/1.14  Generating proof ... found it (size 19)
% 3.18/1.35  
% 3.18/1.35  % SZS output start Proof for theBenchmark
% 3.18/1.35  Assumed formulas after preprocessing and simplification: 
% 3.18/1.35  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (r1(v8, v9) & r1(v7, v8) & r1(v6, v7) & r1(v3, v4) & r1(v2, v3) & r1(v1, v2) & r1(v0, v6) & r1(v0, v5) & r1(v0, v1) &  ~ p5(v5) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ p1(v13) |  ~ p3(v13) |  ~ r1(v12, v13) |  ~ r1(v11, v12) |  ~ r1(v10, v11) |  ~ r1(v0, v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ p1(v13) |  ~ p2(v13) |  ~ r1(v12, v13) |  ~ r1(v11, v12) |  ~ r1(v10, v11) |  ~ r1(v0, v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ p3(v13) |  ~ p2(v13) |  ~ r1(v12, v13) |  ~ r1(v11, v12) |  ~ r1(v10, v11) |  ~ r1(v0, v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ r1(v12, v13) |  ~ r1(v11, v12) |  ~ r1(v10, v11) |  ~ r1(v0, v10) | p1(v13) | p3(v13)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ r1(v12, v13) |  ~ r1(v11, v12) |  ~ r1(v10, v11) |  ~ r1(v0, v10) | p1(v13) | p2(v13)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ r1(v12, v13) |  ~ r1(v11, v12) |  ~ r1(v10, v11) |  ~ r1(v0, v10) | p3(v13) | p2(v13)) &  ! [v10] :  ! [v11] : ( ~ r1(v10, v11) |  ~ r1(v0, v10) |  ? [v12] : (r1(v11, v12) &  ~ p3(v12))) &  ! [v10] : ( ~ r1(v0, v10) |  ? [v11] : (r1(v10, v11) &  ~ p4(v11))) & ( ~ p1(v4) |  ~ p3(v4) |  ~ p2(v4) |  ~ p4(v4)) & (p2(v9) | p4(v9) | p6(v9) | p8(v9)))
% 3.18/1.37  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 3.18/1.37  | (1) r1(all_0_1_1, all_0_0_0) & r1(all_0_2_2, all_0_1_1) & r1(all_0_3_3, all_0_2_2) & r1(all_0_6_6, all_0_5_5) & r1(all_0_7_7, all_0_6_6) & r1(all_0_8_8, all_0_7_7) & r1(all_0_9_9, all_0_3_3) & r1(all_0_9_9, all_0_4_4) & r1(all_0_9_9, all_0_8_8) &  ~ p5(all_0_4_4) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ p1(v3) |  ~ p3(v3) |  ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ p1(v3) |  ~ p2(v3) |  ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ p3(v3) |  ~ p2(v3) |  ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) | p1(v3) | p3(v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) | p1(v3) | p2(v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) | p3(v3) | p2(v3)) &  ! [v0] :  ! [v1] : ( ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) |  ? [v2] : (r1(v1, v2) &  ~ p3(v2))) &  ! [v0] : ( ~ r1(all_0_9_9, v0) |  ? [v1] : (r1(v0, v1) &  ~ p4(v1))) & ( ~ p1(all_0_5_5) |  ~ p3(all_0_5_5) |  ~ p2(all_0_5_5) |  ~ p4(all_0_5_5)) & (p2(all_0_0_0) | p4(all_0_0_0) | p6(all_0_0_0) | p8(all_0_0_0))
% 3.37/1.37  |
% 3.37/1.37  | Applying alpha-rule on (1) yields:
% 3.37/1.37  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) | p1(v3) | p2(v3))
% 3.37/1.37  | (3) r1(all_0_8_8, all_0_7_7)
% 3.37/1.37  | (4) r1(all_0_2_2, all_0_1_1)
% 3.37/1.37  | (5) r1(all_0_9_9, all_0_4_4)
% 3.37/1.37  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ p1(v3) |  ~ p3(v3) |  ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0))
% 3.37/1.37  | (7) r1(all_0_7_7, all_0_6_6)
% 3.37/1.37  | (8) r1(all_0_6_6, all_0_5_5)
% 3.37/1.38  | (9)  ! [v0] : ( ~ r1(all_0_9_9, v0) |  ? [v1] : (r1(v0, v1) &  ~ p4(v1)))
% 3.37/1.38  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) | p1(v3) | p3(v3))
% 3.37/1.38  | (11) r1(all_0_9_9, all_0_3_3)
% 3.37/1.38  | (12)  ~ p5(all_0_4_4)
% 3.37/1.38  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ p1(v3) |  ~ p2(v3) |  ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0))
% 3.37/1.38  | (14) r1(all_0_3_3, all_0_2_2)
% 3.37/1.38  | (15)  ~ p1(all_0_5_5) |  ~ p3(all_0_5_5) |  ~ p2(all_0_5_5) |  ~ p4(all_0_5_5)
% 3.37/1.38  | (16) r1(all_0_9_9, all_0_8_8)
% 3.37/1.38  | (17)  ! [v0] :  ! [v1] : ( ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) |  ? [v2] : (r1(v1, v2) &  ~ p3(v2)))
% 3.37/1.38  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ p3(v3) |  ~ p2(v3) |  ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0))
% 3.37/1.38  | (19) p2(all_0_0_0) | p4(all_0_0_0) | p6(all_0_0_0) | p8(all_0_0_0)
% 3.37/1.38  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ r1(v2, v3) |  ~ r1(v1, v2) |  ~ r1(v0, v1) |  ~ r1(all_0_9_9, v0) | p3(v3) | p2(v3))
% 3.37/1.38  | (21) r1(all_0_1_1, all_0_0_0)
% 3.37/1.38  |
% 3.37/1.38  | Instantiating formula (10) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.38  | (22) p1(all_0_5_5) | p3(all_0_5_5)
% 3.37/1.38  |
% 3.37/1.38  | Instantiating formula (2) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.38  | (23) p1(all_0_5_5) | p2(all_0_5_5)
% 3.37/1.38  |
% 3.37/1.38  | Instantiating formula (20) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.38  | (24) p3(all_0_5_5) | p2(all_0_5_5)
% 3.37/1.38  |
% 3.37/1.38  +-Applying beta-rule and splitting (15), into two cases.
% 3.37/1.38  |-Branch one:
% 3.37/1.38  | (25)  ~ p1(all_0_5_5)
% 3.37/1.38  |
% 3.37/1.38  	+-Applying beta-rule and splitting (23), into two cases.
% 3.37/1.38  	|-Branch one:
% 3.37/1.38  	| (26) p1(all_0_5_5)
% 3.37/1.38  	|
% 3.37/1.38  		| Using (26) and (25) yields:
% 3.37/1.38  		| (27) $false
% 3.37/1.38  		|
% 3.37/1.38  		|-The branch is then unsatisfiable
% 3.37/1.38  	|-Branch two:
% 3.37/1.38  	| (25)  ~ p1(all_0_5_5)
% 3.37/1.38  	| (29) p2(all_0_5_5)
% 3.37/1.38  	|
% 3.37/1.38  		+-Applying beta-rule and splitting (22), into two cases.
% 3.37/1.38  		|-Branch one:
% 3.37/1.38  		| (26) p1(all_0_5_5)
% 3.37/1.38  		|
% 3.37/1.38  			| Using (26) and (25) yields:
% 3.37/1.39  			| (27) $false
% 3.37/1.39  			|
% 3.37/1.39  			|-The branch is then unsatisfiable
% 3.37/1.39  		|-Branch two:
% 3.37/1.39  		| (25)  ~ p1(all_0_5_5)
% 3.37/1.39  		| (33) p3(all_0_5_5)
% 3.37/1.39  		|
% 3.37/1.39  			| Instantiating formula (18) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms p3(all_0_5_5), p2(all_0_5_5), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.39  			| (27) $false
% 3.37/1.39  			|
% 3.37/1.39  			|-The branch is then unsatisfiable
% 3.37/1.39  |-Branch two:
% 3.37/1.39  | (26) p1(all_0_5_5)
% 3.37/1.39  | (36)  ~ p3(all_0_5_5) |  ~ p2(all_0_5_5) |  ~ p4(all_0_5_5)
% 3.37/1.39  |
% 3.37/1.39  	+-Applying beta-rule and splitting (24), into two cases.
% 3.37/1.39  	|-Branch one:
% 3.37/1.39  	| (33) p3(all_0_5_5)
% 3.37/1.39  	|
% 3.37/1.39  		| Instantiating formula (6) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms p1(all_0_5_5), p3(all_0_5_5), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.39  		| (27) $false
% 3.37/1.39  		|
% 3.37/1.39  		|-The branch is then unsatisfiable
% 3.37/1.39  	|-Branch two:
% 3.37/1.39  	| (39)  ~ p3(all_0_5_5)
% 3.37/1.39  	| (29) p2(all_0_5_5)
% 3.37/1.39  	|
% 3.37/1.39  		| Instantiating formula (13) with all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8 and discharging atoms p1(all_0_5_5), p2(all_0_5_5), r1(all_0_6_6, all_0_5_5), r1(all_0_7_7, all_0_6_6), r1(all_0_8_8, all_0_7_7), r1(all_0_9_9, all_0_8_8), yields:
% 3.37/1.39  		| (27) $false
% 3.37/1.39  		|
% 3.37/1.39  		|-The branch is then unsatisfiable
% 3.37/1.39  % SZS output end Proof for theBenchmark
% 3.37/1.39  
% 3.37/1.39  900ms
%------------------------------------------------------------------------------