%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO211+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.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 03:48:46 EDT 2022

% Result   : Theorem 3.26s 1.42s
% Output   : Proof 4.70s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : GEO211+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.11/0.33  % Computer : n023.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 600
% 0.11/0.33  % DateTime : Sat Jun 18 10:48:34 EDT 2022
% 0.11/0.33  % CPUTime  : 
% 0.54/0.56          ____       _                          
% 0.54/0.56    ___  / __ \_____(_)___  ________  __________
% 0.54/0.56   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.56  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.54/0.56  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.54/0.56  
% 0.54/0.56  A Theorem Prover for First-Order Logic
% 0.54/0.57  (ePrincess v.1.0)
% 0.54/0.57  
% 0.54/0.57  (c) Philipp Rümmer, 2009-2015
% 0.54/0.57  (c) Peter Backeman, 2014-2015
% 0.54/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.57  Bug reports to peter@backeman.se
% 0.54/0.57  
% 0.54/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.57  
% 0.54/0.57  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.54/0.61  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.90  Prover 0: Preprocessing ...
% 2.10/1.05  Prover 0: Warning: ignoring some quantifiers
% 2.10/1.07  Prover 0: Constructing countermodel ...
% 2.81/1.27  Prover 0: gave up
% 2.81/1.27  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.81/1.30  Prover 1: Preprocessing ...
% 3.26/1.40  Prover 1: Constructing countermodel ...
% 3.26/1.41  Prover 1: proved (146ms)
% 3.26/1.42  
% 3.26/1.42  No countermodel exists, formula is valid
% 3.26/1.42  % SZS status Theorem for theBenchmark
% 3.26/1.42  
% 3.26/1.42  Generating proof ... found it (size 8)
% 4.16/1.61  
% 4.16/1.61  % SZS output start Proof for theBenchmark
% 4.16/1.61  Assumed formulas after preprocessing and simplification: 
% 4.16/1.61  | (0)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & unorthogonal_lines(v0, v0) = v1 &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 | v6 = 0 |  ~ (unorthogonal_lines(v3, v5) = v7) |  ~ (apart_point_and_line(v2, v3) = v6) |  ~ (distinct_lines(v3, v4) = 0) |  ? [v8] :  ? [v9] : (unorthogonal_lines(v4, v5) = v9 & apart_point_and_line(v2, v4) = v8 & (v9 = 0 | v8 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (intersection_point(v2, v3) = v5) |  ~ (distinct_points(v4, v5) = v6) |  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v4, v3) = v9 & apart_point_and_line(v4, v2) = v8 & convergent_lines(v2, v3) = v7 & ( ~ (v7 = 0) | ( ~ (v9 = 0) &  ~ (v8 = 0))))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = v5) |  ~ (distinct_lines(v3, v4) = 0) |  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v4) = v6 & convergent_lines(v3, v4) = v7 & (v7 = 0 | v6 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = 0) |  ~ (distinct_lines(v3, v4) = v5) | apart_point_and_line(v2, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (apart_point_and_line(v2, v3) = 0) |  ~ (distinct_points(v2, v4) = v5) | apart_point_and_line(v4, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (convergent_lines(v2, v4) = v5) |  ~ (convergent_lines(v2, v3) = 0) | convergent_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_lines(v2, v4) = v5) |  ~ (distinct_lines(v2, v3) = 0) | distinct_lines(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 |  ~ (distinct_points(v2, v4) = v5) |  ~ (distinct_points(v2, v3) = 0) | distinct_points(v3, v4) = 0) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (orthogonal_through_point(v5, v4) = v3) |  ~ (orthogonal_through_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (unorthogonal_lines(v5, v4) = v3) |  ~ (unorthogonal_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (parallel_through_point(v5, v4) = v3) |  ~ (parallel_through_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (intersection_point(v5, v4) = v3) |  ~ (intersection_point(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (line_connecting(v5, v4) = v3) |  ~ (line_connecting(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (apart_point_and_line(v5, v4) = v3) |  ~ (apart_point_and_line(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (convergent_lines(v5, v4) = v3) |  ~ (convergent_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (distinct_lines(v5, v4) = v3) |  ~ (distinct_lines(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v3 = v2 |  ~ (distinct_points(v5, v4) = v3) |  ~ (distinct_points(v5, v4) = v2)) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (unorthogonal_lines(v2, v4) = v5) |  ~ (unorthogonal_lines(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (unorthogonal_lines(v3, v4) = v9 & convergent_lines(v3, v4) = v8 & convergent_lines(v2, v4) = v7 & convergent_lines(v2, v3) = v6 & ( ~ (v6 = 0) | (v9 = 0 & v8 = 0) | (v7 = 0 & v5 = 0)))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (line_connecting(v2, v3) = v5) |  ~ (apart_point_and_line(v4, v5) = 0) |  ? [v6] :  ? [v7] :  ? [v8] : (distinct_points(v4, v3) = v8 & distinct_points(v4, v2) = v7 & distinct_points(v2, v3) = v6 & ( ~ (v6 = 0) | (v8 = 0 & v7 = 0)))) &  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (distinct_lines(v4, v5) = 0) |  ~ (distinct_points(v2, v3) = 0) |  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : (apart_point_and_line(v3, v5) = v9 & apart_point_and_line(v3, v4) = v8 & apart_point_and_line(v2, v5) = v7 & apart_point_and_line(v2, v4) = v6 & (v9 = 0 | v8 = 0 | v7 = 0 | v6 = 0))) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v4) | convergent_lines(v2, v3) = 0) &  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (distinct_lines(v2, v3) = v4) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v2, v3) = v5)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) |  ~ (unorthogonal_lines(v4, v3) = 0)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (orthogonal_through_point(v3, v2) = v4) |  ~ (apart_point_and_line(v2, v4) = 0)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) |  ~ (apart_point_and_line(v2, v4) = 0)) &  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (parallel_through_point(v3, v2) = v4) |  ~ (convergent_lines(v4, v3) = 0)) &  ! [v2] :  ~ (convergent_lines(v2, v2) = 0) &  ! [v2] :  ~ (distinct_lines(v2, v2) = 0) &  ! [v2] :  ~ (distinct_points(v2, v2) = 0))
% 4.51/1.66  | Instantiating (0) with all_0_0_0, all_0_1_1 yields:
% 4.51/1.66  | (1)  ~ (all_0_0_0 = 0) & unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] :  ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 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 |  ~ (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 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [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] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0)))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0)))) &  ! [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] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ~ (unorthogonal_lines(v2, v1) = 0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ~ (apart_point_and_line(v0, v2) = 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] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 4.51/1.67  |
% 4.51/1.67  | Applying alpha-rule on (1) yields:
% 4.51/1.67  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 4.51/1.67  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 4.51/1.67  | (4)  ! [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)))
% 4.51/1.67  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 4.51/1.67  | (6)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 4.51/1.67  | (7)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ (apart_point_and_line(v0, v2) = 0))
% 4.51/1.67  | (8)  ~ (all_0_0_0 = 0)
% 4.51/1.67  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 4.51/1.67  | (10)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ~ (convergent_lines(v2, v1) = 0))
% 4.51/1.67  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 4.51/1.67  | (12)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ~ (unorthogonal_lines(v2, v1) = 0))
% 4.51/1.67  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] :  ? [v6] : (distinct_points(v2, v1) = v6 & distinct_points(v2, v0) = v5 & distinct_points(v0, v1) = v4 & ( ~ (v4 = 0) | (v6 = 0 & v5 = 0))))
% 4.51/1.67  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 4.51/1.67  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 4.51/1.67  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 4.51/1.67  | (17)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 4.51/1.67  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 4.51/1.67  | (19)  ! [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)
% 4.51/1.67  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 4.51/1.68  | (21)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 4.51/1.68  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] :  ? [v7] : (apart_point_and_line(v2, v1) = v7 & apart_point_and_line(v2, v0) = v6 & convergent_lines(v0, v1) = v5 & ( ~ (v5 = 0) | ( ~ (v7 = 0) &  ~ (v6 = 0)))))
% 4.51/1.68  | (23) unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0
% 4.51/1.68  | (24)  ! [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)
% 4.51/1.68  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ~ (apart_point_and_line(v0, v2) = 0))
% 4.51/1.68  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 4.51/1.68  | (27)  ! [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)))
% 4.51/1.68  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] :  ? [v7] : (unorthogonal_lines(v2, v3) = v7 & apart_point_and_line(v0, v2) = v6 & (v7 = 0 | v6 = 0)))
% 4.51/1.68  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : (unorthogonal_lines(v1, v2) = v7 & convergent_lines(v1, v2) = v6 & convergent_lines(v0, v2) = v5 & convergent_lines(v0, v1) = v4 & ( ~ (v4 = 0) | (v7 = 0 & v6 = 0) | (v5 = 0 & v3 = 0))))
% 4.51/1.68  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 4.51/1.68  | (31)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 4.51/1.68  | (32)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 4.51/1.68  |
% 4.70/1.68  | Instantiating formula (17) with all_0_0_0, all_0_1_1, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_1_1) = all_0_0_0, yields:
% 4.70/1.68  | (33) all_0_0_0 = 0 | convergent_lines(all_0_1_1, all_0_1_1) = 0
% 4.70/1.68  |
% 4.70/1.68  +-Applying beta-rule and splitting (33), into two cases.
% 4.70/1.68  |-Branch one:
% 4.70/1.68  | (34) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 4.70/1.68  |
% 4.70/1.68  	| Instantiating formula (21) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 4.70/1.68  	| (35) $false
% 4.70/1.68  	|
% 4.70/1.68  	|-The branch is then unsatisfiable
% 4.70/1.68  |-Branch two:
% 4.70/1.68  | (36)  ~ (convergent_lines(all_0_1_1, all_0_1_1) = 0)
% 4.70/1.68  | (37) all_0_0_0 = 0
% 4.70/1.68  |
% 4.70/1.68  	| Equations (37) can reduce 8 to:
% 4.70/1.68  	| (38) $false
% 4.70/1.68  	|
% 4.70/1.68  	|-The branch is then unsatisfiable
% 4.70/1.68  % SZS output end Proof for theBenchmark
% 4.70/1.68  
% 4.70/1.68  1108ms
%------------------------------------------------------------------------------