TSTP Solution File: GEO197+2 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% 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 : Sat Jul 16 03:48:33 EDT 2022

% Result   : Theorem 18.15s 5.52s
% Output   : Proof 19.85s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n004.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 : Sat Jun 18 09:55:08 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.50/0.52          ____       _                          
% 0.50/0.52    ___  / __ \_____(_)___  ________  __________
% 0.50/0.52   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.52  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.50/0.52  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.50/0.52  
% 0.50/0.52  A Theorem Prover for First-Order Logic
% 0.50/0.52  (ePrincess v.1.0)
% 0.50/0.52  
% 0.50/0.52  (c) Philipp Rümmer, 2009-2015
% 0.50/0.52  (c) Peter Backeman, 2014-2015
% 0.50/0.52  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.52  Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.52  Bug reports to peter@backeman.se
% 0.50/0.52  
% 0.50/0.52  For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.52  
% 0.50/0.52  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.57  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.46/0.88  Prover 0: Preprocessing ...
% 1.89/1.02  Prover 0: Warning: ignoring some quantifiers
% 1.89/1.04  Prover 0: Constructing countermodel ...
% 18.15/5.51  Prover 0: proved (4944ms)
% 18.15/5.51  
% 18.15/5.51  No countermodel exists, formula is valid
% 18.15/5.52  % SZS status Theorem for theBenchmark
% 18.15/5.52  
% 18.15/5.52  Generating proof ... Warning: ignoring some quantifiers
% 19.51/5.76  found it (size 16)
% 19.51/5.76  
% 19.51/5.76  % SZS output start Proof for theBenchmark
% 19.51/5.76  Assumed formulas after preprocessing and simplification: 
% 19.51/5.76  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] : (intersection_point(v2, v1) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v0) & convergent_lines(v2, v1) & convergent_lines(v0, v2) & convergent_lines(v0, v1) &  ~ apart_point_and_line(v3, v2) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (intersection_point(v8, v7) = v6) |  ~ (intersection_point(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v6 = v5 |  ~ (line_connecting(v8, v7) = v6) |  ~ (line_connecting(v8, v7) = v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v5, v6) = v8) |  ~ apart_point_and_line(v7, v6) |  ~ convergent_lines(v5, v6) | distinct_points(v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v5, v6) = v8) |  ~ apart_point_and_line(v7, v5) |  ~ convergent_lines(v5, v6) | distinct_points(v7, v8)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v5, v6) = v8) |  ~ apart_point_and_line(v7, v8) |  ~ distinct_points(v5, v6) | distinct_points(v7, v6)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v5, v6) = v8) |  ~ apart_point_and_line(v7, v8) |  ~ distinct_points(v5, v6) | distinct_points(v7, v5)) &  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ distinct_lines(v7, v8) |  ~ distinct_points(v5, v6) | apart_point_and_line(v6, v8) | apart_point_and_line(v6, v7) | apart_point_and_line(v5, v8) | apart_point_and_line(v5, v7)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v6, v5) | distinct_lines(v7, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ apart_point_and_line(v6, v7) | apart_point_and_line(v5, v7) | distinct_points(v6, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ convergent_lines(v6, v7) | convergent_lines(v7, v5) | convergent_lines(v6, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ distinct_lines(v6, v7) | distinct_lines(v7, v5) | distinct_lines(v6, v5)) &  ? [v5] :  ! [v6] :  ! [v7] : ( ~ distinct_points(v6, v7) | distinct_points(v7, v5) | distinct_points(v6, v5)) &  ! [v5] :  ! [v6] : ( ~ convergent_lines(v5, v6) | distinct_lines(v5, v6)) &  ! [v5] :  ~ convergent_lines(v5, v5) &  ! [v5] :  ~ distinct_lines(v5, v5) &  ! [v5] :  ~ distinct_points(v5, v5))
% 19.51/5.81  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 19.51/5.81  | (1) intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0 & intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1 & apart_point_and_line(all_0_0_0, all_0_4_4) & convergent_lines(all_0_2_2, all_0_3_3) & convergent_lines(all_0_4_4, all_0_2_2) & convergent_lines(all_0_4_4, all_0_3_3) &  ~ apart_point_and_line(all_0_1_1, all_0_2_2) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection_point(v0, v1) = v3) |  ~ apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection_point(v0, v1) = v3) |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) | distinct_points(v2, v3)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ apart_point_and_line(v2, v3) |  ~ distinct_points(v0, v1) | distinct_points(v2, v1)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ apart_point_and_line(v2, v3) |  ~ distinct_points(v0, v1) | distinct_points(v2, v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ distinct_lines(v2, v3) |  ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0)) &  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0)) &  ! [v0] :  ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1)) &  ! [v0] :  ~ convergent_lines(v0, v0) &  ! [v0] :  ~ distinct_lines(v0, v0) &  ! [v0] :  ~ distinct_points(v0, v0)
% 19.85/5.82  |
% 19.85/5.82  | Applying alpha-rule on (1) yields:
% 19.85/5.82  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection_point(v0, v1) = v3) |  ~ apart_point_and_line(v2, v0) |  ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 19.85/5.82  | (3)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_points(v1, v2) | distinct_points(v2, v0) | distinct_points(v1, v0))
% 19.85/5.82  | (4) apart_point_and_line(all_0_0_0, all_0_4_4)
% 19.85/5.82  | (5) convergent_lines(all_0_4_4, all_0_3_3)
% 19.85/5.82  | (6) convergent_lines(all_0_2_2, all_0_3_3)
% 19.85/5.82  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ apart_point_and_line(v2, v3) |  ~ distinct_points(v0, v1) | distinct_points(v2, v1))
% 19.85/5.82  | (8) intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0
% 19.85/5.82  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ apart_point_and_line(v2, v3) |  ~ distinct_points(v0, v1) | distinct_points(v2, v0))
% 19.85/5.82  | (10) intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1
% 19.85/5.82  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 19.85/5.83  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 19.85/5.83  | (13)  ! [v0] :  ~ convergent_lines(v0, v0)
% 19.85/5.83  | (14)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v1, v0) | distinct_lines(v2, v0))
% 19.85/5.83  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ distinct_lines(v2, v3) |  ~ distinct_points(v0, v1) | apart_point_and_line(v1, v3) | apart_point_and_line(v1, v2) | apart_point_and_line(v0, v3) | apart_point_and_line(v0, v2))
% 19.85/5.83  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (intersection_point(v0, v1) = v3) |  ~ apart_point_and_line(v2, v1) |  ~ convergent_lines(v0, v1) | distinct_points(v2, v3))
% 19.85/5.83  | (17)  ! [v0] :  ~ distinct_points(v0, v0)
% 19.85/5.83  | (18)  ! [v0] :  ~ distinct_lines(v0, v0)
% 19.85/5.83  | (19)  ~ apart_point_and_line(all_0_1_1, all_0_2_2)
% 19.85/5.83  | (20)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ distinct_lines(v1, v2) | distinct_lines(v2, v0) | distinct_lines(v1, v0))
% 19.85/5.83  | (21)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ apart_point_and_line(v1, v2) | apart_point_and_line(v0, v2) | distinct_points(v1, v0))
% 19.85/5.83  | (22)  ? [v0] :  ! [v1] :  ! [v2] : ( ~ convergent_lines(v1, v2) | convergent_lines(v2, v0) | convergent_lines(v1, v0))
% 19.85/5.83  | (23)  ! [v0] :  ! [v1] : ( ~ convergent_lines(v0, v1) | distinct_lines(v0, v1))
% 19.85/5.83  | (24) convergent_lines(all_0_4_4, all_0_2_2)
% 19.85/5.83  |
% 19.85/5.83  | Instantiating formula (23) with all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3), yields:
% 19.85/5.83  | (25) distinct_lines(all_0_2_2, all_0_3_3)
% 19.85/5.83  |
% 19.85/5.83  | Instantiating formula (2) with all_0_1_1, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_0_0, all_0_4_4), convergent_lines(all_0_4_4, all_0_3_3), yields:
% 19.85/5.83  | (26) distinct_points(all_0_0_0, all_0_1_1)
% 19.85/5.83  |
% 19.85/5.83  | Instantiating formula (15) with all_0_3_3, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3), distinct_points(all_0_0_0, all_0_1_1),  ~ apart_point_and_line(all_0_1_1, all_0_2_2), yields:
% 19.85/5.83  | (27) apart_point_and_line(all_0_0_0, all_0_2_2) | apart_point_and_line(all_0_0_0, all_0_3_3) | apart_point_and_line(all_0_1_1, all_0_3_3)
% 19.85/5.83  |
% 19.85/5.83  +-Applying beta-rule and splitting (27), into two cases.
% 19.85/5.83  |-Branch one:
% 19.85/5.83  | (28) apart_point_and_line(all_0_0_0, all_0_2_2)
% 19.85/5.83  |
% 19.85/5.83  	| Instantiating formula (2) with all_0_0_0, all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_2_2), convergent_lines(all_0_2_2, all_0_3_3), yields:
% 19.85/5.83  	| (29) distinct_points(all_0_0_0, all_0_0_0)
% 19.85/5.83  	|
% 19.85/5.83  	| Instantiating formula (17) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 19.85/5.83  	| (30) $false
% 19.85/5.83  	|
% 19.85/5.83  	|-The branch is then unsatisfiable
% 19.85/5.83  |-Branch two:
% 19.85/5.83  | (31)  ~ apart_point_and_line(all_0_0_0, all_0_2_2)
% 19.85/5.83  | (32) apart_point_and_line(all_0_0_0, all_0_3_3) | apart_point_and_line(all_0_1_1, all_0_3_3)
% 19.85/5.83  |
% 19.85/5.83  	+-Applying beta-rule and splitting (32), into two cases.
% 19.85/5.83  	|-Branch one:
% 19.85/5.83  	| (33) apart_point_and_line(all_0_0_0, all_0_3_3)
% 19.85/5.83  	|
% 19.85/5.83  		| Instantiating formula (16) with all_0_0_0, all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms intersection_point(all_0_2_2, all_0_3_3) = all_0_0_0, apart_point_and_line(all_0_0_0, all_0_3_3), convergent_lines(all_0_2_2, all_0_3_3), yields:
% 19.85/5.83  		| (29) distinct_points(all_0_0_0, all_0_0_0)
% 19.85/5.83  		|
% 19.85/5.83  		| Instantiating formula (17) with all_0_0_0 and discharging atoms distinct_points(all_0_0_0, all_0_0_0), yields:
% 19.85/5.83  		| (30) $false
% 19.85/5.83  		|
% 19.85/5.83  		|-The branch is then unsatisfiable
% 19.85/5.83  	|-Branch two:
% 19.85/5.83  	| (36)  ~ apart_point_and_line(all_0_0_0, all_0_3_3)
% 19.85/5.83  	| (37) apart_point_and_line(all_0_1_1, all_0_3_3)
% 19.85/5.83  	|
% 19.85/5.83  		| Instantiating formula (16) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_4_4 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_1_1, all_0_3_3), convergent_lines(all_0_4_4, all_0_3_3), yields:
% 19.85/5.83  		| (38) distinct_points(all_0_1_1, all_0_1_1)
% 19.85/5.83  		|
% 19.85/5.83  		| Instantiating formula (17) with all_0_1_1 and discharging atoms distinct_points(all_0_1_1, all_0_1_1), yields:
% 19.85/5.83  		| (30) $false
% 19.85/5.83  		|
% 19.85/5.83  		|-The branch is then unsatisfiable
% 19.85/5.83  % SZS output end Proof for theBenchmark
% 19.85/5.83  
% 19.85/5.83  5302ms
%------------------------------------------------------------------------------