%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n029.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 03:48:41 EDT 2022

% Result   : Theorem 3.54s 1.54s
% Output   : Proof 4.87s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.15/0.36  % Computer : n029.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Sat Jun 18 02:18:28 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.62/0.63          ____       _                          
% 0.62/0.63    ___  / __ \_____(_)___  ________  __________
% 0.62/0.63   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.63  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.62/0.63  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.62/0.63  
% 0.62/0.63  A Theorem Prover for First-Order Logic
% 0.62/0.63  (ePrincess v.1.0)
% 0.62/0.63  
% 0.62/0.63  (c) Philipp Rümmer, 2009-2015
% 0.62/0.63  (c) Peter Backeman, 2014-2015
% 0.62/0.63  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.63  Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.63  Bug reports to peter@backeman.se
% 0.62/0.63  
% 0.62/0.63  For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.63  
% 0.62/0.63  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.67/0.68  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/1.00  Prover 0: Preprocessing ...
% 1.99/1.15  Prover 0: Warning: ignoring some quantifiers
% 1.99/1.17  Prover 0: Constructing countermodel ...
% 2.84/1.34  Prover 0: gave up
% 2.84/1.34  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.84/1.37  Prover 1: Preprocessing ...
% 3.37/1.48  Prover 1: Constructing countermodel ...
% 3.54/1.54  Prover 1: proved (195ms)
% 3.54/1.54  
% 3.54/1.54  No countermodel exists, formula is valid
% 3.54/1.54  % SZS status Theorem for theBenchmark
% 3.54/1.54  
% 3.54/1.54  Generating proof ... found it (size 20)
% 4.63/1.78  
% 4.63/1.78  % SZS output start Proof for theBenchmark
% 4.63/1.78  Assumed formulas after preprocessing and simplification: 
% 4.63/1.78  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v4 = 0) &  ~ (v3 = 0) & parallel_through_point(v2, v0) = v5 & apart_point_and_line(v0, v1) = v3 & convergent_lines(v1, v2) = v4 & distinct_lines(v1, v5) = 0 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = v9) |  ~ (distinct_lines(v7, v8) = 0) |  ? [v10] :  ? [v11] : (apart_point_and_line(v6, v8) = v10 & convergent_lines(v7, v8) = v11 & (v11 = 0 | v10 = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v6, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v6, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (parallel_through_point(v9, v8) = v7) |  ~ (parallel_through_point(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (intersection_point(v9, v8) = v7) |  ~ (intersection_point(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (line_connecting(v9, v8) = v7) |  ~ (line_connecting(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (apart_point_and_line(v9, v8) = v7) |  ~ (apart_point_and_line(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (convergent_lines(v9, v8) = v7) |  ~ (convergent_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (distinct_lines(v9, v8) = v7) |  ~ (distinct_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (distinct_points(v9, v8) = v7) |  ~ (distinct_points(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) |  ~ (distinct_points(v6, v7) = 0) |  ? [v10] :  ? [v11] :  ? [v12] :  ? [v13] : (apart_point_and_line(v7, v9) = v13 & apart_point_and_line(v7, v8) = v12 & apart_point_and_line(v6, v9) = v11 & apart_point_and_line(v6, v8) = v10 & (v13 = 0 | v12 = 0 | v11 = 0 | v10 = 0))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) |  ~ (apart_point_and_line(v6, v8) = 0)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) |  ~ (convergent_lines(v8, v7) = 0)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ~ (apart_point_and_line(v8, v7) = 0) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ~ (apart_point_and_line(v8, v6) = 0) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ (apart_point_and_line(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ~ (apart_point_and_line(v6, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & distinct_points(v6, v7) = v9)) &  ! [v6] :  ~ (convergent_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_points(v6, v6) = 0))
% 4.78/1.82  | 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 yields:
% 4.78/1.82  | (1)  ~ (all_0_1_1 = 0) &  ~ (all_0_2_2 = 0) & parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0 & apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2 & convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1 & distinct_lines(all_0_4_4, all_0_0_0) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0)) &  ! [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] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ (apart_point_and_line(v0, v2) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ (convergent_lines(v2, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ (apart_point_and_line(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ (apart_point_and_line(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ (apart_point_and_line(v1, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ (apart_point_and_line(v0, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 4.78/1.83  |
% 4.78/1.83  | Applying alpha-rule on (1) yields:
% 4.78/1.83  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 4.78/1.83  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 4.78/1.83  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 4.78/1.83  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 4.78/1.83  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0)
% 4.78/1.83  | (7)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 4.78/1.83  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 4.78/1.83  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ (convergent_lines(v2, v1) = 0))
% 4.78/1.83  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 4.78/1.83  | (11)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 4.78/1.83  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ (apart_point_and_line(v1, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 4.78/1.83  | (13)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 4.78/1.83  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 4.78/1.83  | (15)  ~ (all_0_2_2 = 0)
% 4.78/1.83  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : (apart_point_and_line(v0, v2) = v4 & convergent_lines(v1, v2) = v5 & (v5 = 0 | v4 = 0)))
% 4.78/1.83  | (17)  ~ (all_0_1_1 = 0)
% 4.78/1.83  | (18)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ (apart_point_and_line(v0, v2) = 0))
% 4.78/1.83  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 4.78/1.83  | (20) apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2
% 4.78/1.83  | (21) distinct_lines(all_0_4_4, all_0_0_0) = 0
% 4.78/1.83  | (22) convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1
% 4.78/1.83  | (23) parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0
% 4.78/1.83  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 4.78/1.84  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v1, v3) = v7 & apart_point_and_line(v1, v2) = v6 & apart_point_and_line(v0, v3) = v5 & apart_point_and_line(v0, v2) = v4 & (v7 = 0 | v6 = 0 | v5 = 0 | v4 = 0)))
% 4.78/1.84  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 4.78/1.84  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ~ (apart_point_and_line(v0, v2) = 0) |  ? [v3] : ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))
% 4.78/1.84  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ (apart_point_and_line(v2, v1) = 0) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.87/1.84  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 4.87/1.84  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 4.87/1.84  | (31)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ~ (apart_point_and_line(v2, v0) = 0) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.87/1.84  |
% 4.87/1.84  | Instantiating formula (16) with all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_4_4) = all_0_2_2, distinct_lines(all_0_4_4, all_0_0_0) = 0, yields:
% 4.87/1.84  | (32) all_0_2_2 = 0 |  ? [v0] :  ? [v1] : (apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & convergent_lines(all_0_4_4, all_0_0_0) = v1 & (v1 = 0 | v0 = 0))
% 4.87/1.84  |
% 4.87/1.84  +-Applying beta-rule and splitting (32), into two cases.
% 4.87/1.84  |-Branch one:
% 4.87/1.84  | (33) all_0_2_2 = 0
% 4.87/1.84  |
% 4.87/1.84  	| Equations (33) can reduce 15 to:
% 4.87/1.84  	| (34) $false
% 4.87/1.84  	|
% 4.87/1.84  	|-The branch is then unsatisfiable
% 4.87/1.84  |-Branch two:
% 4.87/1.84  | (15)  ~ (all_0_2_2 = 0)
% 4.87/1.84  | (36)  ? [v0] :  ? [v1] : (apart_point_and_line(all_0_5_5, all_0_0_0) = v0 & convergent_lines(all_0_4_4, all_0_0_0) = v1 & (v1 = 0 | v0 = 0))
% 4.87/1.84  |
% 4.87/1.84  	| Instantiating (36) with all_18_0_6, all_18_1_7 yields:
% 4.87/1.84  	| (37) apart_point_and_line(all_0_5_5, all_0_0_0) = all_18_1_7 & convergent_lines(all_0_4_4, all_0_0_0) = all_18_0_6 & (all_18_0_6 = 0 | all_18_1_7 = 0)
% 4.87/1.84  	|
% 4.87/1.84  	| Applying alpha-rule on (37) yields:
% 4.87/1.84  	| (38) apart_point_and_line(all_0_5_5, all_0_0_0) = all_18_1_7
% 4.87/1.84  	| (39) convergent_lines(all_0_4_4, all_0_0_0) = all_18_0_6
% 4.87/1.84  	| (40) all_18_0_6 = 0 | all_18_1_7 = 0
% 4.87/1.84  	|
% 4.87/1.84  	| Instantiating formula (18) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, yields:
% 4.87/1.84  	| (41)  ~ (apart_point_and_line(all_0_5_5, all_0_0_0) = 0)
% 4.87/1.84  	|
% 4.87/1.85  	| Using (38) and (41) yields:
% 4.87/1.85  	| (42)  ~ (all_18_1_7 = 0)
% 4.87/1.85  	|
% 4.87/1.85  	+-Applying beta-rule and splitting (40), into two cases.
% 4.87/1.85  	|-Branch one:
% 4.87/1.85  	| (43) all_18_0_6 = 0
% 4.87/1.85  	|
% 4.87/1.85  		| From (43) and (39) follows:
% 4.87/1.85  		| (44) convergent_lines(all_0_4_4, all_0_0_0) = 0
% 4.87/1.85  		|
% 4.87/1.85  		| Instantiating formula (3) with all_0_1_1, all_0_3_3, all_0_0_0, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_0_0) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_0_1_1, yields:
% 4.87/1.85  		| (45) all_0_1_1 = 0 | convergent_lines(all_0_0_0, all_0_3_3) = 0
% 4.87/1.85  		|
% 4.87/1.85  		+-Applying beta-rule and splitting (45), into two cases.
% 4.87/1.85  		|-Branch one:
% 4.87/1.85  		| (46) convergent_lines(all_0_0_0, all_0_3_3) = 0
% 4.87/1.85  		|
% 4.87/1.85  			| Instantiating formula (9) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms parallel_through_point(all_0_3_3, all_0_5_5) = all_0_0_0, convergent_lines(all_0_0_0, all_0_3_3) = 0, yields:
% 4.87/1.85  			| (47) $false
% 4.87/1.85  			|
% 4.87/1.85  			|-The branch is then unsatisfiable
% 4.87/1.85  		|-Branch two:
% 4.87/1.85  		| (48)  ~ (convergent_lines(all_0_0_0, all_0_3_3) = 0)
% 4.87/1.85  		| (49) all_0_1_1 = 0
% 4.87/1.85  		|
% 4.87/1.85  			| Equations (49) can reduce 17 to:
% 4.87/1.85  			| (34) $false
% 4.87/1.85  			|
% 4.87/1.85  			|-The branch is then unsatisfiable
% 4.87/1.85  	|-Branch two:
% 4.87/1.85  	| (51)  ~ (all_18_0_6 = 0)
% 4.87/1.85  	| (52) all_18_1_7 = 0
% 4.87/1.85  	|
% 4.87/1.85  		| Equations (52) can reduce 42 to:
% 4.87/1.85  		| (34) $false
% 4.87/1.85  		|
% 4.87/1.85  		|-The branch is then unsatisfiable
% 4.87/1.85  % SZS output end Proof for theBenchmark
% 4.87/1.85  
% 4.87/1.85  1206ms
%------------------------------------------------------------------------------