%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n017.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 03:48:55 EDT 2022

% Result   : Theorem 8.00s 2.54s
% Output   : Proof 23.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO222+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.34  % Computer : n017.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 : Fri Jun 17 20:22:12 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.57/0.59          ____       _                          
% 0.57/0.59    ___  / __ \_____(_)___  ________  __________
% 0.57/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.57/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.57/0.59  
% 0.57/0.59  A Theorem Prover for First-Order Logic
% 0.57/0.59  (ePrincess v.1.0)
% 0.57/0.59  
% 0.57/0.59  (c) Philipp Rümmer, 2009-2015
% 0.57/0.59  (c) Peter Backeman, 2014-2015
% 0.57/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.59  Bug reports to peter@backeman.se
% 0.57/0.59  
% 0.57/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.59  
% 0.57/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.74/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/0.97  Prover 0: Preprocessing ...
% 2.29/1.19  Prover 0: Warning: ignoring some quantifiers
% 2.38/1.22  Prover 0: Constructing countermodel ...
% 3.50/1.50  Prover 0: gave up
% 3.50/1.50  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.64/1.54  Prover 1: Preprocessing ...
% 3.99/1.65  Prover 1: Constructing countermodel ...
% 3.99/1.67  Prover 1: gave up
% 3.99/1.67  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.27/1.69  Prover 2: Preprocessing ...
% 4.95/1.86  Prover 2: Warning: ignoring some quantifiers
% 4.95/1.87  Prover 2: Constructing countermodel ...
% 8.00/2.54  Prover 2: proved (873ms)
% 8.00/2.54  
% 8.00/2.54  No countermodel exists, formula is valid
% 8.00/2.54  % SZS status Theorem for theBenchmark
% 8.00/2.54  
% 8.00/2.54  Generating proof ... Warning: ignoring some quantifiers
% 22.56/6.21  found it (size 365)
% 22.56/6.21  
% 22.56/6.21  % SZS output start Proof for theBenchmark
% 22.56/6.21  Assumed formulas after preprocessing and simplification: 
% 22.56/6.21  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : (orthogonal_through_point(v2, v0) = v3 & orthogonal_through_point(v1, v0) = v2 & convergent_lines(v1, v3) = 0 &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (unorthogonal_lines(v6, v7) = v9) |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (distinct_lines(v5, v6) = 0) |  ? [v10] : ((v10 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v5) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (unorthogonal_lines(v6, v7) = v9) |  ~ (apart_point_and_line(v4, v5) = v8) |  ? [v10] : ((v10 = 0 & unorthogonal_lines(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (unorthogonal_lines(v5, v7) = v9) |  ~ (apart_point_and_line(v4, v6) = v8) |  ? [v10] : ((v10 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (unorthogonal_lines(v5, v7) = v9) |  ~ (apart_point_and_line(v4, v5) = v8) |  ~ (distinct_lines(v5, v6) = 0) |  ? [v10] : ((v10 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (apart_point_and_line(v5, v7) = v9) |  ~ (apart_point_and_line(v5, v6) = v8) |  ~ (distinct_points(v4, v5) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v4, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (apart_point_and_line(v5, v7) = v9) |  ~ (apart_point_and_line(v4, v7) = v8) |  ~ (distinct_lines(v6, v7) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (apart_point_and_line(v5, v7) = v9) |  ~ (apart_point_and_line(v4, v6) = v8) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | (v10 = 0 & apart_point_and_line(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (apart_point_and_line(v5, v6) = v9) |  ~ (apart_point_and_line(v4, v7) = v8) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (apart_point_and_line(v5, v6) = v9) |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (distinct_lines(v6, v7) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 | v8 = 0 |  ~ (apart_point_and_line(v4, v7) = v9) |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (distinct_points(v4, v5) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | (v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v6, v5) = v8) |  ~ (distinct_points(v4, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (apart_point_and_line(v4, v5) = v7) |  ? [v9] : ((v9 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v8) |  ~ (distinct_lines(v5, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v7) |  ~ (convergent_lines(v5, v6) = v8) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (apart_point_and_line(v4, v5) = v7) |  ~ (convergent_lines(v5, v6) = v8) |  ? [v9] : ((v9 = 0 & apart_point_and_line(v4, v6) = 0) | ( ~ (v9 = 0) & distinct_lines(v5, v6) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (convergent_lines(v5, v6) = v8) |  ~ (convergent_lines(v4, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (convergent_lines(v4, v6) = v8) |  ~ (distinct_lines(v5, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (distinct_lines(v5, v6) = v8) |  ~ (distinct_lines(v4, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 | v7 = 0 |  ~ (distinct_points(v5, v6) = v8) |  ~ (distinct_points(v4, v6) = v7) |  ? [v9] : ( ~ (v9 = 0) & distinct_points(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) |  ~ (unorthogonal_lines(v4, v6) = v7) |  ? [v9] : ((v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = v8) |  ~ (convergent_lines(v4, v6) = v7) |  ? [v9] : ((v9 = 0 & v8 = 0 & convergent_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (unorthogonal_lines(v4, v6) = v7) |  ~ (convergent_lines(v5, v6) = v8) |  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v5, v6) = v8) |  ~ (convergent_lines(v4, v6) = v7) |  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v4, v5) = v9) | ( ~ (v9 = 0) & convergent_lines(v4, v5) = v9))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v6, v5) = v7) |  ~ (apart_point_and_line(v4, v5) = 0) | distinct_points(v4, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v7) |  ~ (apart_point_and_line(v4, v5) = 0) | distinct_lines(v5, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v4, v6) = v7) |  ~ (distinct_lines(v5, v6) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v4, v5) = 0) | (v8 = 0 & convergent_lines(v5, v6) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v4, v5) = v7) |  ~ (distinct_lines(v5, v6) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v4, v6) = 0) | (v8 = 0 & convergent_lines(v5, v6) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v4, v5) = 0) |  ~ (distinct_lines(v5, v6) = v7) | apart_point_and_line(v4, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (apart_point_and_line(v4, v5) = 0) |  ~ (distinct_points(v4, v6) = v7) | apart_point_and_line(v6, v5) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (convergent_lines(v5, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v4, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (convergent_lines(v4, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) | convergent_lines(v5, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (convergent_lines(v4, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (convergent_lines(v4, v5) = 0) |  ~ (distinct_lines(v5, v6) = v7) | convergent_lines(v4, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (distinct_lines(v5, v6) = v7) |  ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v4, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (distinct_lines(v4, v6) = v7) |  ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (distinct_points(v5, v6) = v7) |  ~ (distinct_points(v4, v5) = 0) | distinct_points(v4, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v7 = 0 |  ~ (distinct_points(v4, v6) = v7) |  ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (orthogonal_through_point(v7, v6) = v5) |  ~ (orthogonal_through_point(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (unorthogonal_lines(v7, v6) = v5) |  ~ (unorthogonal_lines(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (parallel_through_point(v7, v6) = v5) |  ~ (parallel_through_point(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (intersection_point(v7, v6) = v5) |  ~ (intersection_point(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (line_connecting(v7, v6) = v5) |  ~ (line_connecting(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (apart_point_and_line(v7, v6) = v5) |  ~ (apart_point_and_line(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (convergent_lines(v7, v6) = v5) |  ~ (convergent_lines(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (distinct_lines(v7, v6) = v5) |  ~ (distinct_lines(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (distinct_points(v7, v6) = v5) |  ~ (distinct_points(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = v7) |  ~ (unorthogonal_lines(v4, v5) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v5, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) |  ~ (unorthogonal_lines(v4, v5) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v4, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & convergent_lines(v4, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = 0) |  ~ (convergent_lines(v5, v6) = v7) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (unorthogonal_lines(v4, v5) = 0) |  ~ (convergent_lines(v4, v6) = v7) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v5, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v4, v6) = 0 & convergent_lines(v4, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v4, v6) = v7) |  ~ (convergent_lines(v4, v5) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v6) = 0 & convergent_lines(v5, v6) = 0) | (v8 = 0 & v7 = 0 & unorthogonal_lines(v4, v6) = 0) | ( ~ (v8 = 0) & unorthogonal_lines(v4, v5) = v8))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) |  ~ (distinct_points(v4, v5) = 0) |  ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v7) = 0) | (v8 = 0 & apart_point_and_line(v5, v6) = 0) | (v8 = 0 & apart_point_and_line(v4, v7) = 0) | (v8 = 0 & apart_point_and_line(v4, v6) = 0))) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (unorthogonal_lines(v4, v5) = v6) | convergent_lines(v4, v5) = 0) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = 0 |  ~ (convergent_lines(v4, v5) = v6) | unorthogonal_lines(v4, v5) = 0) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) |  ? [v7] : ( ~ (v7 = 0) & unorthogonal_lines(v6, v5) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (orthogonal_through_point(v5, v4) = v6) |  ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) |  ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) |  ? [v7] : ( ~ (v7 = 0) & convergent_lines(v6, v5) = v7)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (intersection_point(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v6, v5) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (intersection_point(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v6, v4) = v7) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v5, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (line_connecting(v4, v5) = v6) |  ? [v7] : (( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) &  ! [v4] :  ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) |  ? [v6] :  ? [v7] : ( ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v5) = v7)) &  ! [v4] :  ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) |  ? [v6] :  ? [v7] : ( ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v4) = v7)) &  ! [v4] :  ! [v5] : ( ~ (distinct_points(v4, v5) = 0) |  ? [v6] :  ? [v7] : ( ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v5, v6) = v7)) &  ! [v4] :  ! [v5] : ( ~ (distinct_points(v4, v5) = 0) |  ? [v6] :  ? [v7] : ( ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v4, v6) = v7)) &  ! [v4] :  ~ (convergent_lines(v4, v4) = 0) &  ! [v4] :  ~ (distinct_lines(v4, v4) = 0) &  ! [v4] :  ~ (distinct_points(v4, v4) = 0) &  ? [v4] :  ? [v5] :  ? [v6] : orthogonal_through_point(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : unorthogonal_lines(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : parallel_through_point(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : intersection_point(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : line_connecting(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : apart_point_and_line(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : convergent_lines(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : distinct_lines(v5, v4) = v6 &  ? [v4] :  ? [v5] :  ? [v6] : distinct_points(v5, v4) = v6)
% 22.97/6.28  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 22.97/6.28  | (1) orthogonal_through_point(all_0_1_1, all_0_3_3) = all_0_0_0 & orthogonal_through_point(all_0_2_2, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_2_2, all_0_0_0) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) &  ! [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] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 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(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 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, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_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(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_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(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, 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(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 22.97/6.31  |
% 22.97/6.31  | Applying alpha-rule on (1) yields:
% 22.97/6.31  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 22.97/6.31  | (3)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 22.97/6.31  | (4)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 22.97/6.31  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 22.97/6.31  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 22.97/6.31  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 22.97/6.31  | (8)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 22.97/6.31  | (9)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 22.97/6.31  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 22.97/6.31  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 22.97/6.31  | (12)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 22.97/6.31  | (13)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 22.97/6.31  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 22.97/6.31  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 22.97/6.31  | (16)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 22.97/6.31  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 22.97/6.31  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 22.97/6.31  | (19)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 22.97/6.31  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 22.97/6.31  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 22.97/6.31  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 22.97/6.31  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5))
% 22.97/6.31  | (24)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 22.97/6.31  | (25)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 22.97/6.31  | (26)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 22.97/6.31  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 22.97/6.31  | (28)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 22.97/6.31  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 22.97/6.32  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 22.97/6.32  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 23.18/6.32  | (32) orthogonal_through_point(all_0_2_2, all_0_3_3) = all_0_1_1
% 23.18/6.32  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 23.18/6.32  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 23.18/6.32  | (35)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 23.18/6.32  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 23.18/6.32  | (37) orthogonal_through_point(all_0_1_1, all_0_3_3) = all_0_0_0
% 23.18/6.32  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 23.18/6.32  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 23.18/6.32  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 23.18/6.32  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 23.18/6.32  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 23.18/6.32  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 23.18/6.32  | (44)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 23.18/6.32  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 23.18/6.32  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 23.18/6.32  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 23.18/6.32  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 23.18/6.32  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 23.18/6.32  | (50)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 23.18/6.32  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 23.18/6.32  | (52)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.18/6.32  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.18/6.32  | (54)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 23.18/6.32  | (55)  ! [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)
% 23.18/6.32  | (56)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 23.18/6.33  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 23.18/6.33  | (58)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 23.18/6.33  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.18/6.33  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0)))
% 23.18/6.33  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 23.18/6.33  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 23.18/6.33  | (63)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 23.18/6.33  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 23.18/6.33  | (65)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 23.18/6.33  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 23.18/6.33  | (67)  ! [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)
% 23.18/6.33  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 23.18/6.33  | (69)  ! [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] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0)))
% 23.18/6.33  | (70)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 23.18/6.33  | (71)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 23.18/6.33  | (72)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 23.18/6.33  | (73)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 23.18/6.33  | (74) convergent_lines(all_0_2_2, all_0_0_0) = 0
% 23.18/6.33  | (75)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 23.18/6.33  | (76)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 23.18/6.33  | (77)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 23.18/6.33  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 23.18/6.33  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 23.18/6.33  | (80)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 23.18/6.33  | (81)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 23.18/6.33  | (82)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 23.18/6.33  | (83)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 23.18/6.33  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 23.18/6.33  | (85)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (70) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms orthogonal_through_point(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 23.18/6.34  | (86)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = v0)
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (80) with all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms orthogonal_through_point(all_0_1_1, all_0_3_3) = all_0_0_0, yields:
% 23.18/6.34  | (87)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = v0)
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (70) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms orthogonal_through_point(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.18/6.34  | (88)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_1_1, all_0_2_2) = v0)
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (80) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms orthogonal_through_point(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.18/6.34  | (89)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = v0)
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (46) with 0, all_0_0_0, all_0_0_0, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.18/6.34  | (90)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = v0))
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (15) with 0, 0, all_0_0_0, all_0_2_2, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.18/6.34  | (91)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = v0))
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (19) with all_0_0_0, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.18/6.34  | (92)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_2_2, all_0_0_0) = v0 & apart_point_and_line(v0, all_0_0_0) = v1)
% 23.18/6.34  |
% 23.18/6.34  | Instantiating formula (44) with all_0_0_0, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.18/6.34  | (93)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_2_2, all_0_0_0) = v0 & apart_point_and_line(v0, all_0_2_2) = v1)
% 23.18/6.34  |
% 23.18/6.34  | Instantiating (93) with all_26_0_31, all_26_1_32 yields:
% 23.18/6.34  | (94)  ~ (all_26_0_31 = 0) & intersection_point(all_0_2_2, all_0_0_0) = all_26_1_32 & apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31
% 23.18/6.34  |
% 23.18/6.34  | Applying alpha-rule on (94) yields:
% 23.18/6.34  | (95)  ~ (all_26_0_31 = 0)
% 23.18/6.34  | (96) intersection_point(all_0_2_2, all_0_0_0) = all_26_1_32
% 23.18/6.34  | (97) apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31
% 23.18/6.34  |
% 23.18/6.34  | Instantiating (92) with all_28_0_33, all_28_1_34 yields:
% 23.18/6.34  | (98)  ~ (all_28_0_33 = 0) & intersection_point(all_0_2_2, all_0_0_0) = all_28_1_34 & apart_point_and_line(all_28_1_34, all_0_0_0) = all_28_0_33
% 23.18/6.34  |
% 23.18/6.34  | Applying alpha-rule on (98) yields:
% 23.18/6.34  | (99)  ~ (all_28_0_33 = 0)
% 23.18/6.34  | (100) intersection_point(all_0_2_2, all_0_0_0) = all_28_1_34
% 23.18/6.34  | (101) apart_point_and_line(all_28_1_34, all_0_0_0) = all_28_0_33
% 23.18/6.34  |
% 23.18/6.34  | Instantiating (91) with all_30_0_35 yields:
% 23.31/6.34  | (102) (all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_30_0_35 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = all_30_0_35) | ( ~ (all_30_0_35 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_30_0_35)
% 23.31/6.34  |
% 23.31/6.34  | Instantiating (90) with all_31_0_36, all_31_1_37 yields:
% 23.31/6.34  | (103) (all_31_0_36 = 0 & all_31_1_37 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_31_1_37 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_31_1_37 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_31_1_37)
% 23.31/6.34  |
% 23.31/6.34  | Instantiating (89) with all_32_0_38 yields:
% 23.31/6.34  | (104)  ~ (all_32_0_38 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38
% 23.31/6.34  |
% 23.31/6.34  | Applying alpha-rule on (104) yields:
% 23.31/6.34  | (105)  ~ (all_32_0_38 = 0)
% 23.31/6.34  | (106) apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38
% 23.31/6.34  |
% 23.31/6.34  | Instantiating (87) with all_34_0_39 yields:
% 23.31/6.34  | (107)  ~ (all_34_0_39 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39
% 23.31/6.34  |
% 23.31/6.34  | Applying alpha-rule on (107) yields:
% 23.31/6.34  | (108)  ~ (all_34_0_39 = 0)
% 23.31/6.34  | (109) apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39
% 23.31/6.34  |
% 23.31/6.34  | Instantiating (86) with all_36_0_40 yields:
% 23.31/6.34  | (110)  ~ (all_36_0_40 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40
% 23.31/6.34  |
% 23.31/6.34  | Applying alpha-rule on (110) yields:
% 23.31/6.34  | (111)  ~ (all_36_0_40 = 0)
% 23.31/6.34  | (112) unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40
% 23.31/6.34  |
% 23.31/6.34  | Instantiating (88) with all_38_0_41 yields:
% 23.31/6.34  | (113)  ~ (all_38_0_41 = 0) & unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41
% 23.31/6.34  |
% 23.31/6.34  | Applying alpha-rule on (113) yields:
% 23.31/6.34  | (114)  ~ (all_38_0_41 = 0)
% 23.31/6.34  | (115) unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41
% 23.31/6.34  |
% 23.31/6.34  | Instantiating formula (36) with all_0_2_2, all_0_0_0, all_26_1_32, all_28_1_34 and discharging atoms intersection_point(all_0_2_2, all_0_0_0) = all_28_1_34, intersection_point(all_0_2_2, all_0_0_0) = all_26_1_32, yields:
% 23.31/6.34  | (116) all_28_1_34 = all_26_1_32
% 23.31/6.34  |
% 23.31/6.34  | From (116) and (101) follows:
% 23.31/6.34  | (117) apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33
% 23.31/6.34  |
% 23.31/6.34  | Instantiating formula (42) with all_36_0_40, all_0_1_1, all_0_0_0, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40, convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.31/6.34  | (118)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & all_36_0_40 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = v0))
% 23.31/6.34  |
% 23.31/6.34  | Instantiating formula (4) with all_38_0_41, all_0_2_2, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, yields:
% 23.31/6.34  | (119) all_38_0_41 = 0 | convergent_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.34  |
% 23.31/6.34  | Instantiating formula (29) with all_36_0_40, all_28_0_33, all_0_1_1, all_0_0_0, all_0_0_0, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40, apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, yields:
% 23.31/6.34  | (120) all_36_0_40 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (29) with all_38_0_41, all_28_0_33, all_0_2_2, all_0_1_1, all_0_0_0, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, yields:
% 23.31/6.35  | (121) all_38_0_41 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (31) with all_38_0_41, all_28_0_33, all_0_2_2, all_0_0_0, all_0_1_1, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, yields:
% 23.31/6.35  | (122) all_38_0_41 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (83) with all_28_0_33, all_28_0_33, all_0_0_0, all_0_0_0, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, yields:
% 23.31/6.35  | (123) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (20) with all_28_0_33, all_28_0_33, all_0_0_0, all_0_0_0, all_26_1_32, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, yields:
% 23.31/6.35  | (124) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (29) with all_36_0_40, all_26_0_31, all_0_1_1, all_0_0_0, all_0_2_2, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (125) all_36_0_40 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (31) with all_36_0_40, all_26_0_31, all_0_1_1, all_0_2_2, all_0_0_0, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (126) all_36_0_40 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (29) with all_38_0_41, all_26_0_31, all_0_2_2, all_0_1_1, all_0_2_2, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (127) all_38_0_41 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (31) with all_38_0_41, all_26_0_31, all_0_2_2, all_0_2_2, all_0_1_1, all_26_1_32 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (128) all_38_0_41 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (83) with all_26_0_31, all_28_0_33, all_0_2_2, all_0_0_0, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (129) all_28_0_33 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (83) with all_28_0_33, all_26_0_31, all_0_0_0, all_0_2_2, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (130) all_28_0_33 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (20) with all_26_0_31, all_28_0_33, all_0_2_2, all_0_0_0, all_26_1_32, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (131) all_28_0_33 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (20) with all_28_0_33, all_26_0_31, all_0_0_0, all_0_2_2, all_26_1_32, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (132) all_28_0_33 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (83) with all_26_0_31, all_26_0_31, all_0_2_2, all_0_2_2, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (133) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (20) with all_26_0_31, all_26_0_31, all_0_2_2, all_0_2_2, all_26_1_32, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, yields:
% 23.31/6.35  | (134) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (29) with all_36_0_40, all_34_0_39, all_0_1_1, all_0_0_0, all_0_0_0, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.35  | (135) all_36_0_40 = 0 | all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (29) with all_38_0_41, all_34_0_39, all_0_2_2, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.35  | (136) all_38_0_41 = 0 | all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.35  |
% 23.31/6.35  | Instantiating formula (31) with all_38_0_41, all_34_0_39, all_0_2_2, all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.35  | (137) all_38_0_41 = 0 | all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_34_0_39, all_28_0_33, all_0_0_0, all_0_0_0, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (138) all_34_0_39 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_28_0_33, all_34_0_39, all_0_0_0, all_0_0_0, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (139) all_34_0_39 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_34_0_39, all_26_0_31, all_0_0_0, all_0_2_2, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (140) all_34_0_39 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_26_0_31, all_34_0_39, all_0_2_2, all_0_0_0, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (141) all_34_0_39 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (10) with all_34_0_39, all_26_0_31, all_0_2_2, all_0_0_0, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (142) all_34_0_39 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (10) with all_26_0_31, all_34_0_39, all_0_0_0, all_0_2_2, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (143) all_34_0_39 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (83) with all_34_0_39, all_34_0_39, all_0_0_0, all_0_0_0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (144) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_34_0_39, all_34_0_39, all_0_0_0, all_0_0_0, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_39, yields:
% 23.31/6.36  | (145) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (31) with all_36_0_40, all_32_0_38, all_0_1_1, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_36_0_40, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (146) all_36_0_40 = 0 | all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (29) with all_38_0_41, all_32_0_38, all_0_2_2, all_0_1_1, all_0_1_1, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (147) all_38_0_41 = 0 | all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_32_0_38, all_28_0_33, all_0_1_1, all_0_0_0, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (148) all_32_0_38 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_28_0_33, all_32_0_38, all_0_0_0, all_0_1_1, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (149) all_32_0_38 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (10) with all_32_0_38, all_28_0_33, all_0_0_0, all_0_1_1, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (150) all_32_0_38 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (10) with all_28_0_33, all_32_0_38, all_0_1_1, all_0_0_0, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (151) all_32_0_38 = 0 | all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_32_0_38, all_26_0_31, all_0_1_1, all_0_2_2, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (152) all_32_0_38 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_26_0_31, all_32_0_38, all_0_2_2, all_0_1_1, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (153) all_32_0_38 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (10) with all_32_0_38, all_26_0_31, all_0_2_2, all_0_1_1, all_0_3_3, all_26_1_32 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (154) all_32_0_38 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (10) with all_26_0_31, all_32_0_38, all_0_1_1, all_0_2_2, all_26_1_32, all_0_3_3 and discharging atoms apart_point_and_line(all_26_1_32, all_0_2_2) = all_26_0_31, apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (155) all_32_0_38 = 0 | all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (83) with all_32_0_38, all_32_0_38, all_0_1_1, all_0_1_1, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (156) all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating formula (20) with all_32_0_38, all_32_0_38, all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_32_0_38, yields:
% 23.31/6.36  | (157) all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 23.31/6.36  |
% 23.31/6.36  | Instantiating (118) with all_50_0_43, all_50_1_44 yields:
% 23.31/6.36  | (158) (all_50_0_43 = 0 & all_50_1_44 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | (all_50_1_44 = 0 & all_36_0_40 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (all_50_1_44 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_50_1_44)
% 23.31/6.36  |
% 23.31/6.36  +-Applying beta-rule and splitting (102), into two cases.
% 23.31/6.36  |-Branch one:
% 23.31/6.36  | (159) (all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_30_0_35 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = all_30_0_35)
% 23.31/6.36  |
% 23.31/6.36  	+-Applying beta-rule and splitting (159), into two cases.
% 23.31/6.36  	|-Branch one:
% 23.31/6.36  	| (160) all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 23.31/6.36  	|
% 23.31/6.36  		| Applying alpha-rule on (160) yields:
% 23.31/6.36  		| (161) all_30_0_35 = 0
% 23.31/6.36  		| (162) unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 23.31/6.36  		|
% 23.31/6.37  		+-Applying beta-rule and splitting (103), into two cases.
% 23.31/6.37  		|-Branch one:
% 23.31/6.37  		| (163) (all_31_0_36 = 0 & all_31_1_37 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_31_1_37 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0)
% 23.31/6.37  		|
% 23.31/6.37  			+-Applying beta-rule and splitting (163), into two cases.
% 23.31/6.37  			|-Branch one:
% 23.31/6.37  			| (164) all_31_0_36 = 0 & all_31_1_37 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0
% 23.31/6.37  			|
% 23.31/6.37  				| Applying alpha-rule on (164) yields:
% 23.31/6.37  				| (165) all_31_0_36 = 0
% 23.31/6.37  				| (166) all_31_1_37 = 0
% 23.31/6.37  				| (167) unorthogonal_lines(all_0_0_0, all_0_0_0) = 0
% 23.31/6.37  				| (168) convergent_lines(all_0_0_0, all_0_0_0) = 0
% 23.31/6.37  				|
% 23.31/6.37  				| Instantiating formula (82) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = 0, yields:
% 23.31/6.37  				| (169) $false
% 23.31/6.37  				|
% 23.31/6.37  				|-The branch is then unsatisfiable
% 23.31/6.37  			|-Branch two:
% 23.31/6.37  			| (170) all_31_1_37 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 23.31/6.37  			|
% 23.31/6.37  				| Applying alpha-rule on (170) yields:
% 23.31/6.37  				| (166) all_31_1_37 = 0
% 23.31/6.37  				| (162) unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 23.31/6.37  				|
% 23.31/6.37  				+-Applying beta-rule and splitting (158), into two cases.
% 23.31/6.37  				|-Branch one:
% 23.31/6.37  				| (173) (all_50_0_43 = 0 & all_50_1_44 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | (all_50_1_44 = 0 & all_36_0_40 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0)
% 23.31/6.37  				|
% 23.31/6.37  					+-Applying beta-rule and splitting (173), into two cases.
% 23.31/6.37  					|-Branch one:
% 23.31/6.37  					| (174) all_50_0_43 = 0 & all_50_1_44 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 23.31/6.37  					|
% 23.31/6.37  						| Applying alpha-rule on (174) yields:
% 23.31/6.37  						| (175) all_50_0_43 = 0
% 23.31/6.37  						| (176) all_50_1_44 = 0
% 23.31/6.37  						| (177) unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 23.31/6.37  						| (178) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 23.31/6.37  						|
% 23.31/6.37  						+-Applying beta-rule and splitting (122), into two cases.
% 23.31/6.37  						|-Branch one:
% 23.31/6.37  						| (179) all_38_0_41 = 0
% 23.31/6.37  						|
% 23.31/6.37  							| Equations (179) can reduce 114 to:
% 23.31/6.37  							| (180) $false
% 23.31/6.37  							|
% 23.31/6.37  							|-The branch is then unsatisfiable
% 23.31/6.37  						|-Branch two:
% 23.31/6.37  						| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  						| (182) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.37  						|
% 23.31/6.37  							+-Applying beta-rule and splitting (127), into two cases.
% 23.31/6.37  							|-Branch one:
% 23.31/6.37  							| (179) all_38_0_41 = 0
% 23.31/6.37  							|
% 23.31/6.37  								| Equations (179) can reduce 114 to:
% 23.31/6.37  								| (180) $false
% 23.31/6.37  								|
% 23.31/6.37  								|-The branch is then unsatisfiable
% 23.31/6.37  							|-Branch two:
% 23.31/6.37  							| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  							| (186) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 23.31/6.37  							|
% 23.31/6.37  								+-Applying beta-rule and splitting (128), into two cases.
% 23.31/6.37  								|-Branch one:
% 23.31/6.37  								| (179) all_38_0_41 = 0
% 23.31/6.37  								|
% 23.31/6.37  									| Equations (179) can reduce 114 to:
% 23.31/6.37  									| (180) $false
% 23.31/6.37  									|
% 23.31/6.37  									|-The branch is then unsatisfiable
% 23.31/6.37  								|-Branch two:
% 23.31/6.37  								| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  								| (190) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 23.31/6.37  								|
% 23.31/6.37  									+-Applying beta-rule and splitting (136), into two cases.
% 23.31/6.37  									|-Branch one:
% 23.31/6.37  									| (179) all_38_0_41 = 0
% 23.31/6.37  									|
% 23.31/6.37  										| Equations (179) can reduce 114 to:
% 23.31/6.37  										| (180) $false
% 23.31/6.37  										|
% 23.31/6.37  										|-The branch is then unsatisfiable
% 23.31/6.37  									|-Branch two:
% 23.31/6.37  									| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  									| (194) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.37  									|
% 23.31/6.37  										+-Applying beta-rule and splitting (137), into two cases.
% 23.31/6.37  										|-Branch one:
% 23.31/6.37  										| (179) all_38_0_41 = 0
% 23.31/6.37  										|
% 23.31/6.37  											| Equations (179) can reduce 114 to:
% 23.31/6.37  											| (180) $false
% 23.31/6.37  											|
% 23.31/6.37  											|-The branch is then unsatisfiable
% 23.31/6.37  										|-Branch two:
% 23.31/6.37  										| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  										| (198) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.37  										|
% 23.31/6.37  											+-Applying beta-rule and splitting (121), into two cases.
% 23.31/6.37  											|-Branch one:
% 23.31/6.37  											| (179) all_38_0_41 = 0
% 23.31/6.37  											|
% 23.31/6.37  												| Equations (179) can reduce 114 to:
% 23.31/6.37  												| (180) $false
% 23.31/6.37  												|
% 23.31/6.37  												|-The branch is then unsatisfiable
% 23.31/6.37  											|-Branch two:
% 23.31/6.37  											| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  											| (202) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.37  											|
% 23.31/6.37  												+-Applying beta-rule and splitting (147), into two cases.
% 23.31/6.37  												|-Branch one:
% 23.31/6.37  												| (179) all_38_0_41 = 0
% 23.31/6.37  												|
% 23.31/6.37  													| Equations (179) can reduce 114 to:
% 23.31/6.37  													| (180) $false
% 23.31/6.37  													|
% 23.31/6.37  													|-The branch is then unsatisfiable
% 23.31/6.37  												|-Branch two:
% 23.31/6.37  												| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.37  												| (206) all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 23.31/6.37  												|
% 23.31/6.37  													| Instantiating formula (42) with all_38_0_41, all_0_2_2, all_0_1_1, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 23.31/6.37  													| (207)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = v0))
% 23.31/6.37  													|
% 23.31/6.37  													| Instantiating (207) with all_381_0_145, all_381_1_146 yields:
% 23.31/6.37  													| (208) (all_381_0_145 = 0 & all_381_1_146 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_381_1_146 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (all_381_1_146 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_381_1_146)
% 23.31/6.37  													|
% 23.31/6.37  													+-Applying beta-rule and splitting (208), into two cases.
% 23.31/6.37  													|-Branch one:
% 23.31/6.37  													| (209) (all_381_0_145 = 0 & all_381_1_146 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_381_1_146 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0)
% 23.31/6.37  													|
% 23.31/6.37  														+-Applying beta-rule and splitting (209), into two cases.
% 23.31/6.37  														|-Branch one:
% 23.31/6.37  														| (210) all_381_0_145 = 0 & all_381_1_146 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.37  														|
% 23.31/6.37  															| Applying alpha-rule on (210) yields:
% 23.31/6.37  															| (211) all_381_0_145 = 0
% 23.31/6.37  															| (212) all_381_1_146 = 0
% 23.31/6.37  															| (213) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.37  															| (214) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.37  															|
% 23.31/6.37  															| Instantiating formula (82) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 23.31/6.37  															| (169) $false
% 23.31/6.37  															|
% 23.31/6.37  															|-The branch is then unsatisfiable
% 23.31/6.37  														|-Branch two:
% 23.31/6.37  														| (216) all_381_1_146 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.37  														|
% 23.31/6.37  															| Applying alpha-rule on (216) yields:
% 23.31/6.37  															| (212) all_381_1_146 = 0
% 23.31/6.37  															| (179) all_38_0_41 = 0
% 23.31/6.37  															| (219) convergent_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.37  															|
% 23.31/6.37  															| Equations (179) can reduce 114 to:
% 23.31/6.38  															| (180) $false
% 23.31/6.38  															|
% 23.31/6.38  															|-The branch is then unsatisfiable
% 23.31/6.38  													|-Branch two:
% 23.31/6.38  													| (221)  ~ (all_381_1_146 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_381_1_146
% 23.31/6.38  													|
% 23.31/6.38  														| Applying alpha-rule on (221) yields:
% 23.31/6.38  														| (222)  ~ (all_381_1_146 = 0)
% 23.31/6.38  														| (223) unorthogonal_lines(all_0_2_2, all_0_1_1) = all_381_1_146
% 23.31/6.38  														|
% 23.31/6.38  														| Instantiating formula (79) with all_0_2_2, all_0_1_1, all_381_1_146, 0 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = all_381_1_146, unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 23.31/6.38  														| (212) all_381_1_146 = 0
% 23.31/6.38  														|
% 23.31/6.38  														| Equations (212) can reduce 222 to:
% 23.31/6.38  														| (180) $false
% 23.31/6.38  														|
% 23.31/6.38  														|-The branch is then unsatisfiable
% 23.31/6.38  					|-Branch two:
% 23.31/6.38  					| (226) all_50_1_44 = 0 & all_36_0_40 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0
% 23.31/6.38  					|
% 23.31/6.38  						| Applying alpha-rule on (226) yields:
% 23.31/6.38  						| (176) all_50_1_44 = 0
% 23.31/6.38  						| (228) all_36_0_40 = 0
% 23.31/6.38  						| (229) convergent_lines(all_0_0_0, all_0_1_1) = 0
% 23.31/6.38  						|
% 23.31/6.38  						| Equations (228) can reduce 111 to:
% 23.31/6.38  						| (180) $false
% 23.31/6.38  						|
% 23.31/6.38  						|-The branch is then unsatisfiable
% 23.31/6.38  				|-Branch two:
% 23.31/6.38  				| (231)  ~ (all_50_1_44 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_50_1_44
% 23.31/6.38  				|
% 23.31/6.38  					| Applying alpha-rule on (231) yields:
% 23.31/6.38  					| (232)  ~ (all_50_1_44 = 0)
% 23.31/6.38  					| (233) unorthogonal_lines(all_0_2_2, all_0_0_0) = all_50_1_44
% 23.31/6.38  					|
% 23.31/6.38  					| Instantiating formula (79) with all_0_2_2, all_0_0_0, 0, all_50_1_44 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_50_1_44, unorthogonal_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.31/6.38  					| (176) all_50_1_44 = 0
% 23.31/6.38  					|
% 23.31/6.38  					| Equations (176) can reduce 232 to:
% 23.31/6.38  					| (180) $false
% 23.31/6.38  					|
% 23.31/6.38  					|-The branch is then unsatisfiable
% 23.31/6.38  		|-Branch two:
% 23.31/6.38  		| (236)  ~ (all_31_1_37 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_31_1_37
% 23.31/6.38  		|
% 23.31/6.38  			| Applying alpha-rule on (236) yields:
% 23.31/6.38  			| (237)  ~ (all_31_1_37 = 0)
% 23.31/6.38  			| (238) unorthogonal_lines(all_0_2_2, all_0_0_0) = all_31_1_37
% 23.31/6.38  			|
% 23.31/6.38  			| Instantiating formula (79) with all_0_2_2, all_0_0_0, 0, all_31_1_37 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_31_1_37, unorthogonal_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 23.31/6.38  			| (166) all_31_1_37 = 0
% 23.31/6.38  			|
% 23.31/6.38  			| Equations (166) can reduce 237 to:
% 23.31/6.38  			| (180) $false
% 23.31/6.38  			|
% 23.31/6.38  			|-The branch is then unsatisfiable
% 23.31/6.38  	|-Branch two:
% 23.31/6.38  	| (241)  ~ (all_30_0_35 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = all_30_0_35
% 23.31/6.38  	|
% 23.31/6.38  		| Applying alpha-rule on (241) yields:
% 23.31/6.38  		| (242)  ~ (all_30_0_35 = 0)
% 23.31/6.38  		| (243) unorthogonal_lines(all_0_2_2, all_0_2_2) = all_30_0_35
% 23.31/6.38  		|
% 23.31/6.38  		| Instantiating formula (4) with all_30_0_35, all_0_2_2, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_2_2) = all_30_0_35, yields:
% 23.31/6.38  		| (244) all_30_0_35 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.38  		|
% 23.31/6.38  		+-Applying beta-rule and splitting (244), into two cases.
% 23.31/6.38  		|-Branch one:
% 23.31/6.38  		| (214) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.38  		|
% 23.31/6.38  			| Instantiating formula (82) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 23.31/6.38  			| (169) $false
% 23.31/6.38  			|
% 23.31/6.38  			|-The branch is then unsatisfiable
% 23.31/6.38  		|-Branch two:
% 23.31/6.38  		| (247)  ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 23.31/6.38  		| (161) all_30_0_35 = 0
% 23.31/6.38  		|
% 23.31/6.38  			| Equations (161) can reduce 242 to:
% 23.31/6.38  			| (180) $false
% 23.31/6.38  			|
% 23.31/6.38  			|-The branch is then unsatisfiable
% 23.31/6.38  |-Branch two:
% 23.31/6.38  | (250)  ~ (all_30_0_35 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_30_0_35
% 23.31/6.38  |
% 23.31/6.38  	| Applying alpha-rule on (250) yields:
% 23.31/6.38  	| (242)  ~ (all_30_0_35 = 0)
% 23.31/6.38  	| (252) convergent_lines(all_0_2_2, all_0_2_2) = all_30_0_35
% 23.31/6.38  	|
% 23.31/6.38  	+-Applying beta-rule and splitting (119), into two cases.
% 23.31/6.38  	|-Branch one:
% 23.31/6.38  	| (219) convergent_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.38  	|
% 23.31/6.38  		+-Applying beta-rule and splitting (123), into two cases.
% 23.31/6.38  		|-Branch one:
% 23.31/6.38  		| (254) all_28_0_33 = 0
% 23.31/6.38  		|
% 23.31/6.38  			| Equations (254) can reduce 99 to:
% 23.31/6.38  			| (180) $false
% 23.31/6.38  			|
% 23.31/6.38  			|-The branch is then unsatisfiable
% 23.31/6.38  		|-Branch two:
% 23.31/6.38  		| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.38  		| (257)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.38  		|
% 23.31/6.38  			+-Applying beta-rule and splitting (124), into two cases.
% 23.31/6.38  			|-Branch one:
% 23.31/6.38  			| (254) all_28_0_33 = 0
% 23.31/6.38  			|
% 23.31/6.38  				| Equations (254) can reduce 99 to:
% 23.31/6.38  				| (180) $false
% 23.31/6.38  				|
% 23.31/6.38  				|-The branch is then unsatisfiable
% 23.31/6.38  			|-Branch two:
% 23.31/6.38  			| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.38  			| (261)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.38  			|
% 23.31/6.38  				+-Applying beta-rule and splitting (133), into two cases.
% 23.31/6.38  				|-Branch one:
% 23.31/6.38  				| (262) all_26_0_31 = 0
% 23.31/6.38  				|
% 23.31/6.38  					| Equations (262) can reduce 95 to:
% 23.31/6.38  					| (180) $false
% 23.31/6.38  					|
% 23.31/6.38  					|-The branch is then unsatisfiable
% 23.31/6.38  				|-Branch two:
% 23.31/6.38  				| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.38  				| (265)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 23.31/6.38  				|
% 23.31/6.38  					+-Applying beta-rule and splitting (156), into two cases.
% 23.31/6.38  					|-Branch one:
% 23.31/6.38  					| (266) all_32_0_38 = 0
% 23.31/6.38  					|
% 23.31/6.38  						| Equations (266) can reduce 105 to:
% 23.31/6.38  						| (180) $false
% 23.31/6.38  						|
% 23.31/6.38  						|-The branch is then unsatisfiable
% 23.31/6.38  					|-Branch two:
% 23.31/6.38  					| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.38  					| (269)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 23.31/6.38  					|
% 23.31/6.38  						+-Applying beta-rule and splitting (144), into two cases.
% 23.31/6.38  						|-Branch one:
% 23.31/6.38  						| (270) all_34_0_39 = 0
% 23.31/6.38  						|
% 23.31/6.38  							| Equations (270) can reduce 108 to:
% 23.31/6.38  							| (180) $false
% 23.31/6.38  							|
% 23.31/6.38  							|-The branch is then unsatisfiable
% 23.31/6.38  						|-Branch two:
% 23.31/6.38  						| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.38  						| (257)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.38  						|
% 23.31/6.38  							+-Applying beta-rule and splitting (134), into two cases.
% 23.31/6.38  							|-Branch one:
% 23.31/6.38  							| (262) all_26_0_31 = 0
% 23.31/6.38  							|
% 23.31/6.38  								| Equations (262) can reduce 95 to:
% 23.31/6.38  								| (180) $false
% 23.31/6.38  								|
% 23.31/6.38  								|-The branch is then unsatisfiable
% 23.31/6.38  							|-Branch two:
% 23.31/6.38  							| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.38  							| (277)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.38  							|
% 23.31/6.38  								+-Applying beta-rule and splitting (145), into two cases.
% 23.31/6.38  								|-Branch one:
% 23.31/6.38  								| (270) all_34_0_39 = 0
% 23.31/6.38  								|
% 23.31/6.38  									| Equations (270) can reduce 108 to:
% 23.31/6.38  									| (180) $false
% 23.31/6.38  									|
% 23.31/6.38  									|-The branch is then unsatisfiable
% 23.31/6.38  								|-Branch two:
% 23.31/6.38  								| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.38  								| (281)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 23.31/6.38  								|
% 23.31/6.38  									+-Applying beta-rule and splitting (157), into two cases.
% 23.31/6.38  									|-Branch one:
% 23.31/6.38  									| (266) all_32_0_38 = 0
% 23.31/6.38  									|
% 23.31/6.38  										| Equations (266) can reduce 105 to:
% 23.31/6.38  										| (180) $false
% 23.31/6.38  										|
% 23.31/6.38  										|-The branch is then unsatisfiable
% 23.31/6.38  									|-Branch two:
% 23.31/6.38  									| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.38  									| (285)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 23.31/6.38  									|
% 23.31/6.38  										+-Applying beta-rule and splitting (146), into two cases.
% 23.31/6.38  										|-Branch one:
% 23.31/6.38  										| (228) all_36_0_40 = 0
% 23.31/6.38  										|
% 23.31/6.38  											| Equations (228) can reduce 111 to:
% 23.31/6.38  											| (180) $false
% 23.31/6.38  											|
% 23.31/6.38  											|-The branch is then unsatisfiable
% 23.31/6.38  										|-Branch two:
% 23.31/6.38  										| (111)  ~ (all_36_0_40 = 0)
% 23.31/6.38  										| (289) all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.38  										|
% 23.31/6.38  											+-Applying beta-rule and splitting (147), into two cases.
% 23.31/6.38  											|-Branch one:
% 23.31/6.38  											| (179) all_38_0_41 = 0
% 23.31/6.38  											|
% 23.31/6.38  												| Equations (179) can reduce 114 to:
% 23.31/6.38  												| (180) $false
% 23.31/6.38  												|
% 23.31/6.38  												|-The branch is then unsatisfiable
% 23.31/6.38  											|-Branch two:
% 23.31/6.38  											| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.38  											| (206) all_32_0_38 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_1_1) = v0))
% 23.31/6.38  											|
% 23.31/6.38  												+-Applying beta-rule and splitting (152), into two cases.
% 23.31/6.38  												|-Branch one:
% 23.31/6.38  												| (266) all_32_0_38 = 0
% 23.31/6.38  												|
% 23.31/6.38  													| Equations (266) can reduce 105 to:
% 23.31/6.38  													| (180) $false
% 23.31/6.38  													|
% 23.31/6.38  													|-The branch is then unsatisfiable
% 23.31/6.38  												|-Branch two:
% 23.31/6.38  												| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.38  												| (297) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.38  												|
% 23.31/6.38  													+-Applying beta-rule and splitting (149), into two cases.
% 23.31/6.38  													|-Branch one:
% 23.31/6.38  													| (266) all_32_0_38 = 0
% 23.31/6.38  													|
% 23.31/6.38  														| Equations (266) can reduce 105 to:
% 23.31/6.38  														| (180) $false
% 23.31/6.38  														|
% 23.31/6.38  														|-The branch is then unsatisfiable
% 23.31/6.38  													|-Branch two:
% 23.31/6.38  													| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.38  													| (301) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.39  													|
% 23.31/6.39  														+-Applying beta-rule and splitting (135), into two cases.
% 23.31/6.39  														|-Branch one:
% 23.31/6.39  														| (228) all_36_0_40 = 0
% 23.31/6.39  														|
% 23.31/6.39  															| Equations (228) can reduce 111 to:
% 23.31/6.39  															| (180) $false
% 23.31/6.39  															|
% 23.31/6.39  															|-The branch is then unsatisfiable
% 23.31/6.39  														|-Branch two:
% 23.31/6.39  														| (111)  ~ (all_36_0_40 = 0)
% 23.31/6.39  														| (305) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.39  														|
% 23.31/6.39  															+-Applying beta-rule and splitting (131), into two cases.
% 23.31/6.39  															|-Branch one:
% 23.31/6.39  															| (254) all_28_0_33 = 0
% 23.31/6.39  															|
% 23.31/6.39  																| Equations (254) can reduce 99 to:
% 23.31/6.39  																| (180) $false
% 23.31/6.39  																|
% 23.31/6.39  																|-The branch is then unsatisfiable
% 23.31/6.39  															|-Branch two:
% 23.31/6.39  															| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.39  															| (309) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.39  															|
% 23.31/6.39  																+-Applying beta-rule and splitting (132), into two cases.
% 23.31/6.39  																|-Branch one:
% 23.31/6.39  																| (254) all_28_0_33 = 0
% 23.31/6.39  																|
% 23.31/6.39  																	| Equations (254) can reduce 99 to:
% 23.31/6.39  																	| (180) $false
% 23.31/6.39  																	|
% 23.31/6.39  																	|-The branch is then unsatisfiable
% 23.31/6.39  																|-Branch two:
% 23.31/6.39  																| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.39  																| (313) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.39  																|
% 23.31/6.39  																	+-Applying beta-rule and splitting (136), into two cases.
% 23.31/6.39  																	|-Branch one:
% 23.31/6.39  																	| (179) all_38_0_41 = 0
% 23.31/6.39  																	|
% 23.31/6.39  																		| Equations (179) can reduce 114 to:
% 23.31/6.39  																		| (180) $false
% 23.31/6.39  																		|
% 23.31/6.39  																		|-The branch is then unsatisfiable
% 23.31/6.39  																	|-Branch two:
% 23.31/6.39  																	| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.39  																	| (194) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.39  																	|
% 23.31/6.39  																		+-Applying beta-rule and splitting (141), into two cases.
% 23.31/6.39  																		|-Branch one:
% 23.31/6.39  																		| (270) all_34_0_39 = 0
% 23.31/6.39  																		|
% 23.31/6.39  																			| Equations (270) can reduce 108 to:
% 23.31/6.39  																			| (180) $false
% 23.31/6.39  																			|
% 23.31/6.39  																			|-The branch is then unsatisfiable
% 23.31/6.39  																		|-Branch two:
% 23.31/6.39  																		| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.39  																		| (321) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.39  																		|
% 23.31/6.39  																			+-Applying beta-rule and splitting (142), into two cases.
% 23.31/6.39  																			|-Branch one:
% 23.31/6.39  																			| (270) all_34_0_39 = 0
% 23.31/6.39  																			|
% 23.31/6.39  																				| Equations (270) can reduce 108 to:
% 23.31/6.39  																				| (180) $false
% 23.31/6.39  																				|
% 23.31/6.39  																				|-The branch is then unsatisfiable
% 23.31/6.39  																			|-Branch two:
% 23.31/6.39  																			| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.39  																			| (325) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.39  																			|
% 23.31/6.39  																				+-Applying beta-rule and splitting (140), into two cases.
% 23.31/6.39  																				|-Branch one:
% 23.31/6.39  																				| (270) all_34_0_39 = 0
% 23.31/6.39  																				|
% 23.31/6.39  																					| Equations (270) can reduce 108 to:
% 23.31/6.39  																					| (180) $false
% 23.31/6.39  																					|
% 23.31/6.39  																					|-The branch is then unsatisfiable
% 23.31/6.39  																				|-Branch two:
% 23.31/6.39  																				| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.39  																				| (329) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.39  																				|
% 23.31/6.39  																					+-Applying beta-rule and splitting (120), into two cases.
% 23.31/6.39  																					|-Branch one:
% 23.31/6.39  																					| (228) all_36_0_40 = 0
% 23.31/6.39  																					|
% 23.31/6.39  																						| Equations (228) can reduce 111 to:
% 23.31/6.39  																						| (180) $false
% 23.31/6.39  																						|
% 23.31/6.39  																						|-The branch is then unsatisfiable
% 23.31/6.39  																					|-Branch two:
% 23.31/6.39  																					| (111)  ~ (all_36_0_40 = 0)
% 23.31/6.39  																					| (333) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.39  																					|
% 23.31/6.39  																						+-Applying beta-rule and splitting (137), into two cases.
% 23.31/6.39  																						|-Branch one:
% 23.31/6.39  																						| (179) all_38_0_41 = 0
% 23.31/6.39  																						|
% 23.31/6.39  																							| Equations (179) can reduce 114 to:
% 23.31/6.39  																							| (180) $false
% 23.31/6.39  																							|
% 23.31/6.39  																							|-The branch is then unsatisfiable
% 23.31/6.39  																						|-Branch two:
% 23.31/6.39  																						| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.39  																						| (198) all_34_0_39 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.39  																						|
% 23.31/6.39  																							+-Applying beta-rule and splitting (122), into two cases.
% 23.31/6.39  																							|-Branch one:
% 23.31/6.39  																							| (179) all_38_0_41 = 0
% 23.31/6.39  																							|
% 23.31/6.39  																								| Equations (179) can reduce 114 to:
% 23.31/6.39  																								| (180) $false
% 23.31/6.39  																								|
% 23.31/6.39  																								|-The branch is then unsatisfiable
% 23.31/6.39  																							|-Branch two:
% 23.31/6.39  																							| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.39  																							| (182) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.39  																							|
% 23.31/6.39  																								+-Applying beta-rule and splitting (125), into two cases.
% 23.31/6.39  																								|-Branch one:
% 23.31/6.39  																								| (228) all_36_0_40 = 0
% 23.31/6.39  																								|
% 23.31/6.39  																									| Equations (228) can reduce 111 to:
% 23.31/6.39  																									| (180) $false
% 23.31/6.39  																									|
% 23.31/6.39  																									|-The branch is then unsatisfiable
% 23.31/6.39  																								|-Branch two:
% 23.31/6.39  																								| (111)  ~ (all_36_0_40 = 0)
% 23.31/6.39  																								| (345) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 23.31/6.39  																								|
% 23.31/6.39  																									+-Applying beta-rule and splitting (138), into two cases.
% 23.31/6.39  																									|-Branch one:
% 23.31/6.39  																									| (270) all_34_0_39 = 0
% 23.31/6.39  																									|
% 23.31/6.39  																										| Equations (270) can reduce 108 to:
% 23.31/6.39  																										| (180) $false
% 23.31/6.39  																										|
% 23.31/6.39  																										|-The branch is then unsatisfiable
% 23.31/6.39  																									|-Branch two:
% 23.31/6.39  																									| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.39  																									| (349) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.39  																									|
% 23.31/6.39  																										+-Applying beta-rule and splitting (139), into two cases.
% 23.31/6.39  																										|-Branch one:
% 23.31/6.39  																										| (270) all_34_0_39 = 0
% 23.31/6.39  																										|
% 23.31/6.39  																											| Equations (270) can reduce 108 to:
% 23.31/6.39  																											| (180) $false
% 23.31/6.39  																											|
% 23.31/6.39  																											|-The branch is then unsatisfiable
% 23.31/6.39  																										|-Branch two:
% 23.31/6.39  																										| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.39  																										| (353) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.39  																										|
% 23.31/6.39  																											+-Applying beta-rule and splitting (143), into two cases.
% 23.31/6.39  																											|-Branch one:
% 23.31/6.39  																											| (270) all_34_0_39 = 0
% 23.31/6.39  																											|
% 23.31/6.39  																												| Equations (270) can reduce 108 to:
% 23.31/6.39  																												| (180) $false
% 23.31/6.39  																												|
% 23.31/6.39  																												|-The branch is then unsatisfiable
% 23.31/6.39  																											|-Branch two:
% 23.31/6.39  																											| (108)  ~ (all_34_0_39 = 0)
% 23.31/6.39  																											| (357) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.39  																											|
% 23.31/6.39  																												+-Applying beta-rule and splitting (126), into two cases.
% 23.31/6.39  																												|-Branch one:
% 23.31/6.39  																												| (228) all_36_0_40 = 0
% 23.31/6.39  																												|
% 23.31/6.39  																													| Equations (228) can reduce 111 to:
% 23.31/6.39  																													| (180) $false
% 23.31/6.39  																													|
% 23.31/6.39  																													|-The branch is then unsatisfiable
% 23.31/6.39  																												|-Branch two:
% 23.31/6.39  																												| (111)  ~ (all_36_0_40 = 0)
% 23.31/6.39  																												| (361) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 23.31/6.39  																												|
% 23.31/6.39  																													+-Applying beta-rule and splitting (153), into two cases.
% 23.31/6.39  																													|-Branch one:
% 23.31/6.39  																													| (266) all_32_0_38 = 0
% 23.31/6.39  																													|
% 23.31/6.39  																														| Equations (266) can reduce 105 to:
% 23.31/6.39  																														| (180) $false
% 23.31/6.39  																														|
% 23.31/6.39  																														|-The branch is then unsatisfiable
% 23.31/6.39  																													|-Branch two:
% 23.31/6.39  																													| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.39  																													| (365) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.39  																													|
% 23.31/6.39  																														+-Applying beta-rule and splitting (154), into two cases.
% 23.31/6.39  																														|-Branch one:
% 23.31/6.39  																														| (266) all_32_0_38 = 0
% 23.31/6.39  																														|
% 23.31/6.39  																															| Equations (266) can reduce 105 to:
% 23.31/6.39  																															| (180) $false
% 23.31/6.39  																															|
% 23.31/6.39  																															|-The branch is then unsatisfiable
% 23.31/6.39  																														|-Branch two:
% 23.31/6.39  																														| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.39  																														| (369) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.39  																														|
% 23.31/6.39  																															+-Applying beta-rule and splitting (155), into two cases.
% 23.31/6.39  																															|-Branch one:
% 23.31/6.39  																															| (266) all_32_0_38 = 0
% 23.31/6.39  																															|
% 23.31/6.39  																																| Equations (266) can reduce 105 to:
% 23.31/6.39  																																| (180) $false
% 23.31/6.39  																																|
% 23.31/6.39  																																|-The branch is then unsatisfiable
% 23.31/6.39  																															|-Branch two:
% 23.31/6.39  																															| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.39  																															| (373) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.39  																															|
% 23.31/6.39  																																+-Applying beta-rule and splitting (150), into two cases.
% 23.31/6.39  																																|-Branch one:
% 23.31/6.39  																																| (266) all_32_0_38 = 0
% 23.31/6.39  																																|
% 23.31/6.39  																																	| Equations (266) can reduce 105 to:
% 23.31/6.39  																																	| (180) $false
% 23.31/6.39  																																	|
% 23.31/6.39  																																	|-The branch is then unsatisfiable
% 23.31/6.39  																																|-Branch two:
% 23.31/6.39  																																| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.39  																																| (377) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.39  																																|
% 23.31/6.39  																																	+-Applying beta-rule and splitting (127), into two cases.
% 23.31/6.39  																																	|-Branch one:
% 23.31/6.39  																																	| (179) all_38_0_41 = 0
% 23.31/6.39  																																	|
% 23.31/6.39  																																		| Equations (179) can reduce 114 to:
% 23.31/6.39  																																		| (180) $false
% 23.31/6.39  																																		|
% 23.31/6.39  																																		|-The branch is then unsatisfiable
% 23.31/6.39  																																	|-Branch two:
% 23.31/6.39  																																	| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.39  																																	| (186) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0))
% 23.31/6.39  																																	|
% 23.31/6.39  																																		+-Applying beta-rule and splitting (121), into two cases.
% 23.31/6.39  																																		|-Branch one:
% 23.31/6.39  																																		| (179) all_38_0_41 = 0
% 23.31/6.39  																																		|
% 23.31/6.39  																																			| Equations (179) can reduce 114 to:
% 23.31/6.39  																																			| (180) $false
% 23.31/6.39  																																			|
% 23.31/6.39  																																			|-The branch is then unsatisfiable
% 23.31/6.39  																																		|-Branch two:
% 23.31/6.39  																																		| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.39  																																		| (202) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.39  																																		|
% 23.31/6.39  																																			+-Applying beta-rule and splitting (128), into two cases.
% 23.31/6.39  																																			|-Branch one:
% 23.31/6.39  																																			| (179) all_38_0_41 = 0
% 23.31/6.39  																																			|
% 23.31/6.39  																																				| Equations (179) can reduce 114 to:
% 23.31/6.39  																																				| (180) $false
% 23.31/6.39  																																				|
% 23.31/6.39  																																				|-The branch is then unsatisfiable
% 23.31/6.39  																																			|-Branch two:
% 23.31/6.39  																																			| (114)  ~ (all_38_0_41 = 0)
% 23.31/6.39  																																			| (190) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 23.31/6.39  																																			|
% 23.31/6.39  																																				+-Applying beta-rule and splitting (148), into two cases.
% 23.31/6.39  																																				|-Branch one:
% 23.31/6.39  																																				| (266) all_32_0_38 = 0
% 23.31/6.39  																																				|
% 23.31/6.39  																																					| Equations (266) can reduce 105 to:
% 23.31/6.39  																																					| (180) $false
% 23.31/6.39  																																					|
% 23.31/6.39  																																					|-The branch is then unsatisfiable
% 23.31/6.39  																																				|-Branch two:
% 23.31/6.39  																																				| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.39  																																				| (393) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.39  																																				|
% 23.31/6.39  																																					+-Applying beta-rule and splitting (151), into two cases.
% 23.31/6.39  																																					|-Branch one:
% 23.31/6.39  																																					| (266) all_32_0_38 = 0
% 23.31/6.39  																																					|
% 23.31/6.39  																																						| Equations (266) can reduce 105 to:
% 23.31/6.39  																																						| (180) $false
% 23.31/6.39  																																						|
% 23.31/6.39  																																						|-The branch is then unsatisfiable
% 23.31/6.39  																																					|-Branch two:
% 23.31/6.39  																																					| (105)  ~ (all_32_0_38 = 0)
% 23.31/6.39  																																					| (397) all_28_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.40  																																					|
% 23.31/6.40  																																						+-Applying beta-rule and splitting (130), into two cases.
% 23.31/6.40  																																						|-Branch one:
% 23.31/6.40  																																						| (254) all_28_0_33 = 0
% 23.31/6.40  																																						|
% 23.31/6.40  																																							| Equations (254) can reduce 99 to:
% 23.31/6.40  																																							| (180) $false
% 23.31/6.40  																																							|
% 23.31/6.40  																																							|-The branch is then unsatisfiable
% 23.31/6.40  																																						|-Branch two:
% 23.31/6.40  																																						| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																						| (401) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 23.31/6.40  																																						|
% 23.31/6.40  																																							+-Applying beta-rule and splitting (129), into two cases.
% 23.31/6.40  																																							|-Branch one:
% 23.31/6.40  																																							| (254) all_28_0_33 = 0
% 23.31/6.40  																																							|
% 23.31/6.40  																																								| Equations (254) can reduce 99 to:
% 23.31/6.40  																																								| (180) $false
% 23.31/6.40  																																								|
% 23.31/6.40  																																								|-The branch is then unsatisfiable
% 23.31/6.40  																																							|-Branch two:
% 23.31/6.40  																																							| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																							| (405) all_26_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 23.31/6.40  																																							|
% 23.31/6.40  																																								+-Applying beta-rule and splitting (309), into two cases.
% 23.31/6.40  																																								|-Branch one:
% 23.31/6.40  																																								| (262) all_26_0_31 = 0
% 23.31/6.40  																																								|
% 23.31/6.40  																																									| Equations (262) can reduce 95 to:
% 23.31/6.40  																																									| (180) $false
% 23.31/6.40  																																									|
% 23.31/6.40  																																									|-The branch is then unsatisfiable
% 23.31/6.40  																																								|-Branch two:
% 23.31/6.40  																																								| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																								| (409)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.40  																																								|
% 23.31/6.40  																																									+-Applying beta-rule and splitting (321), into two cases.
% 23.31/6.40  																																									|-Branch one:
% 23.31/6.40  																																									| (262) all_26_0_31 = 0
% 23.31/6.40  																																									|
% 23.31/6.40  																																										| Equations (262) can reduce 95 to:
% 23.31/6.40  																																										| (180) $false
% 23.31/6.40  																																										|
% 23.31/6.40  																																										|-The branch is then unsatisfiable
% 23.31/6.40  																																									|-Branch two:
% 23.31/6.40  																																									| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																									| (413)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.40  																																									|
% 23.31/6.40  																																										+-Applying beta-rule and splitting (329), into two cases.
% 23.31/6.40  																																										|-Branch one:
% 23.31/6.40  																																										| (262) all_26_0_31 = 0
% 23.31/6.40  																																										|
% 23.31/6.40  																																											| Equations (262) can reduce 95 to:
% 23.31/6.40  																																											| (180) $false
% 23.31/6.40  																																											|
% 23.31/6.40  																																											|-The branch is then unsatisfiable
% 23.31/6.40  																																										|-Branch two:
% 23.31/6.40  																																										| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																										| (417)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.40  																																										|
% 23.31/6.40  																																											+-Applying beta-rule and splitting (333), into two cases.
% 23.31/6.40  																																											|-Branch one:
% 23.31/6.40  																																											| (254) all_28_0_33 = 0
% 23.31/6.40  																																											|
% 23.31/6.40  																																												| Equations (254) can reduce 99 to:
% 23.31/6.40  																																												| (180) $false
% 23.31/6.40  																																												|
% 23.31/6.40  																																												|-The branch is then unsatisfiable
% 23.31/6.40  																																											|-Branch two:
% 23.31/6.40  																																											| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																											| (421)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 23.31/6.40  																																											|
% 23.31/6.40  																																												+-Applying beta-rule and splitting (182), into two cases.
% 23.31/6.40  																																												|-Branch one:
% 23.31/6.40  																																												| (254) all_28_0_33 = 0
% 23.31/6.40  																																												|
% 23.31/6.40  																																													| Equations (254) can reduce 99 to:
% 23.31/6.40  																																													| (180) $false
% 23.31/6.40  																																													|
% 23.31/6.40  																																													|-The branch is then unsatisfiable
% 23.31/6.40  																																												|-Branch two:
% 23.31/6.40  																																												| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																												| (425)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 23.31/6.40  																																												|
% 23.31/6.40  																																													+-Applying beta-rule and splitting (345), into two cases.
% 23.31/6.40  																																													|-Branch one:
% 23.31/6.40  																																													| (262) all_26_0_31 = 0
% 23.31/6.40  																																													|
% 23.31/6.40  																																														| Equations (262) can reduce 95 to:
% 23.31/6.40  																																														| (180) $false
% 23.31/6.40  																																														|
% 23.31/6.40  																																														|-The branch is then unsatisfiable
% 23.31/6.40  																																													|-Branch two:
% 23.31/6.40  																																													| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																													| (429)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 23.31/6.40  																																													|
% 23.31/6.40  																																														+-Applying beta-rule and splitting (349), into two cases.
% 23.31/6.40  																																														|-Branch one:
% 23.31/6.40  																																														| (254) all_28_0_33 = 0
% 23.31/6.40  																																														|
% 23.31/6.40  																																															| Equations (254) can reduce 99 to:
% 23.31/6.40  																																															| (180) $false
% 23.31/6.40  																																															|
% 23.31/6.40  																																															|-The branch is then unsatisfiable
% 23.31/6.40  																																														|-Branch two:
% 23.31/6.40  																																														| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																														| (433)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.40  																																														|
% 23.31/6.40  																																															+-Applying beta-rule and splitting (353), into two cases.
% 23.31/6.40  																																															|-Branch one:
% 23.31/6.40  																																															| (254) all_28_0_33 = 0
% 23.31/6.40  																																															|
% 23.31/6.40  																																																| Equations (254) can reduce 99 to:
% 23.31/6.40  																																																| (180) $false
% 23.31/6.40  																																																|
% 23.31/6.40  																																																|-The branch is then unsatisfiable
% 23.31/6.40  																																															|-Branch two:
% 23.31/6.40  																																															| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																															| (437)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.40  																																															|
% 23.31/6.40  																																																+-Applying beta-rule and splitting (377), into two cases.
% 23.31/6.40  																																																|-Branch one:
% 23.31/6.40  																																																| (254) all_28_0_33 = 0
% 23.31/6.40  																																																|
% 23.31/6.40  																																																	| Equations (254) can reduce 99 to:
% 23.31/6.40  																																																	| (180) $false
% 23.31/6.40  																																																	|
% 23.31/6.40  																																																	|-The branch is then unsatisfiable
% 23.31/6.40  																																																|-Branch two:
% 23.31/6.40  																																																| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																																| (441)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.40  																																																|
% 23.31/6.40  																																																	+-Applying beta-rule and splitting (190), into two cases.
% 23.31/6.40  																																																	|-Branch one:
% 23.31/6.40  																																																	| (262) all_26_0_31 = 0
% 23.31/6.40  																																																	|
% 23.31/6.40  																																																		| Equations (262) can reduce 95 to:
% 23.31/6.40  																																																		| (180) $false
% 23.31/6.40  																																																		|
% 23.31/6.40  																																																		|-The branch is then unsatisfiable
% 23.31/6.40  																																																	|-Branch two:
% 23.31/6.40  																																																	| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																																	| (445)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_2_2) = v0))
% 23.31/6.40  																																																	|
% 23.31/6.40  																																																		+-Applying beta-rule and splitting (393), into two cases.
% 23.31/6.40  																																																		|-Branch one:
% 23.31/6.40  																																																		| (254) all_28_0_33 = 0
% 23.31/6.40  																																																		|
% 23.31/6.40  																																																			| Equations (254) can reduce 99 to:
% 23.31/6.40  																																																			| (180) $false
% 23.31/6.40  																																																			|
% 23.31/6.40  																																																			|-The branch is then unsatisfiable
% 23.31/6.40  																																																		|-Branch two:
% 23.31/6.40  																																																		| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																																		| (449)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.40  																																																		|
% 23.31/6.40  																																																			+-Applying beta-rule and splitting (297), into two cases.
% 23.31/6.40  																																																			|-Branch one:
% 23.31/6.40  																																																			| (262) all_26_0_31 = 0
% 23.31/6.40  																																																			|
% 23.31/6.40  																																																				| Equations (262) can reduce 95 to:
% 23.31/6.40  																																																				| (180) $false
% 23.31/6.40  																																																				|
% 23.31/6.40  																																																				|-The branch is then unsatisfiable
% 23.31/6.40  																																																			|-Branch two:
% 23.31/6.40  																																																			| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																																			| (453)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.40  																																																			|
% 23.31/6.40  																																																				+-Applying beta-rule and splitting (301), into two cases.
% 23.31/6.40  																																																				|-Branch one:
% 23.31/6.40  																																																				| (254) all_28_0_33 = 0
% 23.31/6.40  																																																				|
% 23.31/6.40  																																																					| Equations (254) can reduce 99 to:
% 23.31/6.40  																																																					| (180) $false
% 23.31/6.40  																																																					|
% 23.31/6.40  																																																					|-The branch is then unsatisfiable
% 23.31/6.40  																																																				|-Branch two:
% 23.31/6.40  																																																				| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																																				| (457)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.40  																																																				|
% 23.31/6.40  																																																					+-Applying beta-rule and splitting (313), into two cases.
% 23.31/6.40  																																																					|-Branch one:
% 23.31/6.40  																																																					| (262) all_26_0_31 = 0
% 23.31/6.40  																																																					|
% 23.31/6.40  																																																						| Equations (262) can reduce 95 to:
% 23.31/6.40  																																																						| (180) $false
% 23.31/6.40  																																																						|
% 23.31/6.40  																																																						|-The branch is then unsatisfiable
% 23.31/6.40  																																																					|-Branch two:
% 23.31/6.40  																																																					| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																																					| (461)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_26_1_32) = v0))
% 23.31/6.40  																																																					|
% 23.31/6.40  																																																						+-Applying beta-rule and splitting (325), into two cases.
% 23.31/6.40  																																																						|-Branch one:
% 23.31/6.40  																																																						| (262) all_26_0_31 = 0
% 23.31/6.40  																																																						|
% 23.31/6.40  																																																							| Equations (262) can reduce 95 to:
% 23.31/6.40  																																																							| (180) $false
% 23.31/6.40  																																																							|
% 23.31/6.40  																																																							|-The branch is then unsatisfiable
% 23.31/6.40  																																																						|-Branch two:
% 23.31/6.40  																																																						| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																																						| (465)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_32, all_0_3_3) = v0))
% 23.31/6.40  																																																						|
% 23.31/6.40  																																																							+-Applying beta-rule and splitting (357), into two cases.
% 23.31/6.40  																																																							|-Branch one:
% 23.31/6.40  																																																							| (262) all_26_0_31 = 0
% 23.31/6.40  																																																							|
% 23.31/6.40  																																																								| Equations (262) can reduce 95 to:
% 23.31/6.40  																																																								| (180) $false
% 23.31/6.40  																																																								|
% 23.31/6.40  																																																								|-The branch is then unsatisfiable
% 23.31/6.40  																																																							|-Branch two:
% 23.31/6.40  																																																							| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																																							| (469)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.40  																																																							|
% 23.31/6.40  																																																								+-Applying beta-rule and splitting (361), into two cases.
% 23.31/6.40  																																																								|-Branch one:
% 23.31/6.40  																																																								| (262) all_26_0_31 = 0
% 23.31/6.40  																																																								|
% 23.31/6.40  																																																									| Equations (262) can reduce 95 to:
% 23.31/6.40  																																																									| (180) $false
% 23.31/6.40  																																																									|
% 23.31/6.40  																																																									|-The branch is then unsatisfiable
% 23.31/6.40  																																																								|-Branch two:
% 23.31/6.40  																																																								| (95)  ~ (all_26_0_31 = 0)
% 23.31/6.40  																																																								| (473)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 23.31/6.40  																																																								|
% 23.31/6.40  																																																									| Instantiating (473) with all_316_0_485 yields:
% 23.31/6.40  																																																									| (474) (all_316_0_485 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (all_316_0_485 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0) | ( ~ (all_316_0_485 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_316_0_485)
% 23.31/6.40  																																																									|
% 23.31/6.40  																																																									+-Applying beta-rule and splitting (202), into two cases.
% 23.31/6.40  																																																									|-Branch one:
% 23.31/6.40  																																																									| (254) all_28_0_33 = 0
% 23.31/6.40  																																																									|
% 23.31/6.40  																																																										| Equations (254) can reduce 99 to:
% 23.31/6.40  																																																										| (180) $false
% 23.31/6.40  																																																										|
% 23.31/6.40  																																																										|-The branch is then unsatisfiable
% 23.31/6.40  																																																									|-Branch two:
% 23.31/6.40  																																																									| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																																									| (478)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 23.31/6.40  																																																									|
% 23.31/6.40  																																																										+-Applying beta-rule and splitting (397), into two cases.
% 23.31/6.40  																																																										|-Branch one:
% 23.31/6.40  																																																										| (254) all_28_0_33 = 0
% 23.31/6.40  																																																										|
% 23.31/6.40  																																																											| Equations (254) can reduce 99 to:
% 23.31/6.40  																																																											| (180) $false
% 23.31/6.40  																																																											|
% 23.31/6.40  																																																											|-The branch is then unsatisfiable
% 23.31/6.40  																																																										|-Branch two:
% 23.31/6.40  																																																										| (99)  ~ (all_28_0_33 = 0)
% 23.31/6.40  																																																										| (482)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_32, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_26_1_32) = v0))
% 23.31/6.40  																																																										|
% 23.31/6.40  																																																											| Instantiating formula (59) with all_30_0_35, all_0_2_2, all_0_0_0, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_0_0) = 0, convergent_lines(all_0_2_2, all_0_2_2) = all_30_0_35, yields:
% 23.31/6.40  																																																											| (483) all_30_0_35 = 0 | distinct_lines(all_0_0_0, all_0_2_2) = 0
% 23.31/6.40  																																																											|
% 23.31/6.40  																																																											| Instantiating formula (15) with 0, all_30_0_35, all_0_2_2, all_0_1_1, all_0_2_2 and discharging atoms convergent_lines(all_0_1_1, all_0_2_2) = 0, convergent_lines(all_0_2_2, all_0_2_2) = all_30_0_35, yields:
% 23.31/6.40  																																																											| (484)  ? [v0] : ((v0 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 23.31/6.40  																																																											|
% 23.31/6.40  																																																											| Instantiating formula (2) with all_38_0_41, all_30_0_35, all_0_2_2, all_0_1_1, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, convergent_lines(all_0_2_2, all_0_2_2) = all_30_0_35, yields:
% 23.31/6.40  																																																											| (485)  ? [v0] : ((v0 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | (v0 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = v0))
% 23.31/6.40  																																																											|
% 23.31/6.40  																																																											| Instantiating (485) with all_366_0_495 yields:
% 23.31/6.40  																																																											| (486) (all_366_0_495 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | (all_366_0_495 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (all_366_0_495 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_366_0_495) | ( ~ (all_366_0_495 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_366_0_495)
% 23.31/6.41  																																																											|
% 23.31/6.41  																																																											| Instantiating (484) with all_368_0_497 yields:
% 23.31/6.41  																																																											| (487) (all_368_0_497 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (all_368_0_497 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (all_368_0_497 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_368_0_497) | ( ~ (all_368_0_497 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_368_0_497)
% 23.31/6.41  																																																											|
% 23.31/6.41  																																																											+-Applying beta-rule and splitting (483), into two cases.
% 23.31/6.41  																																																											|-Branch one:
% 23.31/6.41  																																																											| (488) distinct_lines(all_0_0_0, all_0_2_2) = 0
% 23.31/6.41  																																																											|
% 23.31/6.41  																																																												+-Applying beta-rule and splitting (474), into two cases.
% 23.31/6.41  																																																												|-Branch one:
% 23.31/6.41  																																																												| (489) (all_316_0_485 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (all_316_0_485 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0)
% 23.31/6.41  																																																												|
% 23.31/6.41  																																																													+-Applying beta-rule and splitting (489), into two cases.
% 23.31/6.41  																																																													|-Branch one:
% 23.31/6.41  																																																													| (490) all_316_0_485 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 23.31/6.41  																																																													|
% 23.31/6.41  																																																														| Applying alpha-rule on (490) yields:
% 23.31/6.41  																																																														| (491) all_316_0_485 = 0
% 23.31/6.41  																																																														| (177) unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 23.31/6.41  																																																														|
% 23.31/6.41  																																																														+-Applying beta-rule and splitting (486), into two cases.
% 23.31/6.41  																																																														|-Branch one:
% 23.31/6.41  																																																														| (493) (all_366_0_495 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | (all_366_0_495 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (all_366_0_495 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_366_0_495)
% 23.31/6.41  																																																														|
% 23.31/6.41  																																																															+-Applying beta-rule and splitting (493), into two cases.
% 23.31/6.41  																																																															|-Branch one:
% 23.31/6.41  																																																															| (494) (all_366_0_495 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | (all_366_0_495 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0)
% 23.31/6.41  																																																															|
% 23.31/6.41  																																																																+-Applying beta-rule and splitting (494), into two cases.
% 23.31/6.41  																																																																|-Branch one:
% 23.31/6.41  																																																																| (495) all_366_0_495 = 0 & all_38_0_41 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																	| Applying alpha-rule on (495) yields:
% 23.31/6.41  																																																																	| (496) all_366_0_495 = 0
% 23.31/6.41  																																																																	| (179) all_38_0_41 = 0
% 23.31/6.41  																																																																	| (219) convergent_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	| Equations (179) can reduce 114 to:
% 23.31/6.41  																																																																	| (180) $false
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	|-The branch is then unsatisfiable
% 23.31/6.41  																																																																|-Branch two:
% 23.31/6.41  																																																																| (500) all_366_0_495 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																	| Applying alpha-rule on (500) yields:
% 23.31/6.41  																																																																	| (496) all_366_0_495 = 0
% 23.31/6.41  																																																																	| (161) all_30_0_35 = 0
% 23.31/6.41  																																																																	| (213) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	| Equations (161) can reduce 242 to:
% 23.31/6.41  																																																																	| (180) $false
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	|-The branch is then unsatisfiable
% 23.31/6.41  																																																															|-Branch two:
% 23.31/6.41  																																																															| (505)  ~ (all_366_0_495 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_366_0_495
% 23.31/6.41  																																																															|
% 23.31/6.41  																																																																| Applying alpha-rule on (505) yields:
% 23.31/6.41  																																																																| (506)  ~ (all_366_0_495 = 0)
% 23.31/6.41  																																																																| (507) unorthogonal_lines(all_0_2_2, all_0_1_1) = all_366_0_495
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																| Instantiating formula (79) with all_0_2_2, all_0_1_1, 0, all_366_0_495 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = all_366_0_495, unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 23.31/6.41  																																																																| (496) all_366_0_495 = 0
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																| Equations (496) can reduce 506 to:
% 23.31/6.41  																																																																| (180) $false
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																|-The branch is then unsatisfiable
% 23.31/6.41  																																																														|-Branch two:
% 23.31/6.41  																																																														| (510)  ~ (all_366_0_495 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_366_0_495
% 23.31/6.41  																																																														|
% 23.31/6.41  																																																															| Applying alpha-rule on (510) yields:
% 23.31/6.41  																																																															| (506)  ~ (all_366_0_495 = 0)
% 23.31/6.41  																																																															| (512) convergent_lines(all_0_2_2, all_0_1_1) = all_366_0_495
% 23.31/6.41  																																																															|
% 23.31/6.41  																																																															+-Applying beta-rule and splitting (487), into two cases.
% 23.31/6.41  																																																															|-Branch one:
% 23.31/6.41  																																																															| (513) (all_368_0_497 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (all_368_0_497 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (all_368_0_497 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_368_0_497)
% 23.31/6.41  																																																															|
% 23.31/6.41  																																																																+-Applying beta-rule and splitting (513), into two cases.
% 23.31/6.41  																																																																|-Branch one:
% 23.31/6.41  																																																																| (514) (all_368_0_497 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0) | (all_368_0_497 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0)
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																	+-Applying beta-rule and splitting (514), into two cases.
% 23.31/6.41  																																																																	|-Branch one:
% 23.31/6.41  																																																																	| (515) all_368_0_497 = 0 & all_30_0_35 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																		| Applying alpha-rule on (515) yields:
% 23.31/6.41  																																																																		| (516) all_368_0_497 = 0
% 23.31/6.41  																																																																		| (161) all_30_0_35 = 0
% 23.31/6.41  																																																																		| (213) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 23.31/6.41  																																																																		|
% 23.31/6.41  																																																																		| Equations (161) can reduce 242 to:
% 23.31/6.41  																																																																		| (180) $false
% 23.31/6.41  																																																																		|
% 23.31/6.41  																																																																		|-The branch is then unsatisfiable
% 23.31/6.41  																																																																	|-Branch two:
% 23.31/6.41  																																																																	| (520) all_368_0_497 = 0 & unorthogonal_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																		| Applying alpha-rule on (520) yields:
% 23.31/6.41  																																																																		| (516) all_368_0_497 = 0
% 23.31/6.41  																																																																		| (522) unorthogonal_lines(all_0_1_1, all_0_2_2) = 0
% 23.31/6.41  																																																																		|
% 23.31/6.41  																																																																		| Instantiating formula (79) with all_0_1_1, all_0_2_2, 0, all_38_0_41 and discharging atoms unorthogonal_lines(all_0_1_1, all_0_2_2) = all_38_0_41, unorthogonal_lines(all_0_1_1, all_0_2_2) = 0, yields:
% 23.31/6.41  																																																																		| (179) all_38_0_41 = 0
% 23.31/6.41  																																																																		|
% 23.31/6.41  																																																																		| Equations (179) can reduce 114 to:
% 23.31/6.41  																																																																		| (180) $false
% 23.31/6.41  																																																																		|
% 23.31/6.41  																																																																		|-The branch is then unsatisfiable
% 23.31/6.41  																																																																|-Branch two:
% 23.31/6.41  																																																																| (525)  ~ (all_368_0_497 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_368_0_497
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																	| Applying alpha-rule on (525) yields:
% 23.31/6.41  																																																																	| (526)  ~ (all_368_0_497 = 0)
% 23.31/6.41  																																																																	| (527) unorthogonal_lines(all_0_2_2, all_0_1_1) = all_368_0_497
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	| Instantiating formula (79) with all_0_2_2, all_0_1_1, 0, all_368_0_497 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = all_368_0_497, unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 23.31/6.41  																																																																	| (516) all_368_0_497 = 0
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	| Equations (516) can reduce 526 to:
% 23.31/6.41  																																																																	| (180) $false
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	|-The branch is then unsatisfiable
% 23.31/6.41  																																																															|-Branch two:
% 23.31/6.41  																																																															| (530)  ~ (all_368_0_497 = 0) & convergent_lines(all_0_2_2, all_0_1_1) = all_368_0_497
% 23.31/6.41  																																																															|
% 23.31/6.41  																																																																| Applying alpha-rule on (530) yields:
% 23.31/6.41  																																																																| (526)  ~ (all_368_0_497 = 0)
% 23.31/6.41  																																																																| (532) convergent_lines(all_0_2_2, all_0_1_1) = all_368_0_497
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																| Instantiating formula (27) with all_0_2_2, all_0_1_1, all_366_0_495, all_368_0_497 and discharging atoms convergent_lines(all_0_2_2, all_0_1_1) = all_368_0_497, convergent_lines(all_0_2_2, all_0_1_1) = all_366_0_495, yields:
% 23.31/6.41  																																																																| (533) all_368_0_497 = all_366_0_495
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																| Equations (533) can reduce 526 to:
% 23.31/6.41  																																																																| (506)  ~ (all_366_0_495 = 0)
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																| From (533) and (532) follows:
% 23.31/6.41  																																																																| (512) convergent_lines(all_0_2_2, all_0_1_1) = all_366_0_495
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																| Instantiating formula (51) with all_366_0_495, all_0_1_1, all_0_2_2, all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_2_2) = 0, convergent_lines(all_0_2_2, all_0_1_1) = all_366_0_495, yields:
% 23.31/6.41  																																																																| (536) all_366_0_495 = 0 | convergent_lines(all_0_1_1, all_0_1_1) = 0
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																+-Applying beta-rule and splitting (536), into two cases.
% 23.31/6.41  																																																																|-Branch one:
% 23.31/6.41  																																																																| (537) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																	| Instantiating formula (82) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 23.31/6.41  																																																																	| (169) $false
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	|-The branch is then unsatisfiable
% 23.31/6.41  																																																																|-Branch two:
% 23.31/6.41  																																																																| (539)  ~ (convergent_lines(all_0_1_1, all_0_1_1) = 0)
% 23.31/6.41  																																																																| (496) all_366_0_495 = 0
% 23.31/6.41  																																																																|
% 23.31/6.41  																																																																	| Equations (496) can reduce 506 to:
% 23.31/6.41  																																																																	| (180) $false
% 23.31/6.41  																																																																	|
% 23.31/6.41  																																																																	|-The branch is then unsatisfiable
% 23.31/6.41  																																																													|-Branch two:
% 23.31/6.41  																																																													| (542) all_316_0_485 = 0 & apart_point_and_line(all_26_1_32, all_0_0_0) = 0
% 23.31/6.41  																																																													|
% 23.31/6.41  																																																														| Applying alpha-rule on (542) yields:
% 23.31/6.41  																																																														| (491) all_316_0_485 = 0
% 23.31/6.41  																																																														| (544) apart_point_and_line(all_26_1_32, all_0_0_0) = 0
% 23.31/6.41  																																																														|
% 23.31/6.41  																																																														| Instantiating formula (11) with all_26_1_32, all_0_0_0, 0, all_28_0_33 and discharging atoms apart_point_and_line(all_26_1_32, all_0_0_0) = all_28_0_33, apart_point_and_line(all_26_1_32, all_0_0_0) = 0, yields:
% 23.31/6.41  																																																														| (254) all_28_0_33 = 0
% 23.31/6.41  																																																														|
% 23.31/6.41  																																																														| Equations (254) can reduce 99 to:
% 23.31/6.41  																																																														| (180) $false
% 23.31/6.41  																																																														|
% 23.31/6.41  																																																														|-The branch is then unsatisfiable
% 23.31/6.41  																																																												|-Branch two:
% 23.31/6.41  																																																												| (547)  ~ (all_316_0_485 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_316_0_485
% 23.31/6.41  																																																												|
% 23.31/6.41  																																																													| Applying alpha-rule on (547) yields:
% 23.31/6.41  																																																													| (548)  ~ (all_316_0_485 = 0)
% 23.31/6.41  																																																													| (549) distinct_lines(all_0_0_0, all_0_2_2) = all_316_0_485
% 23.31/6.41  																																																													|
% 23.31/6.41  																																																													| Instantiating formula (50) with all_0_0_0, all_0_2_2, 0, all_316_0_485 and discharging atoms distinct_lines(all_0_0_0, all_0_2_2) = all_316_0_485, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 23.31/6.41  																																																													| (491) all_316_0_485 = 0
% 23.31/6.41  																																																													|
% 23.31/6.41  																																																													| Equations (491) can reduce 548 to:
% 23.31/6.41  																																																													| (180) $false
% 23.31/6.41  																																																													|
% 23.31/6.41  																																																													|-The branch is then unsatisfiable
% 23.31/6.41  																																																											|-Branch two:
% 23.31/6.41  																																																											| (552)  ~ (distinct_lines(all_0_0_0, all_0_2_2) = 0)
% 23.31/6.41  																																																											| (161) all_30_0_35 = 0
% 23.31/6.41  																																																											|
% 23.31/6.41  																																																												| Equations (161) can reduce 242 to:
% 23.31/6.41  																																																												| (180) $false
% 23.31/6.41  																																																												|
% 23.31/6.41  																																																												|-The branch is then unsatisfiable
% 23.31/6.42  	|-Branch two:
% 23.31/6.42  	| (555)  ~ (convergent_lines(all_0_1_1, all_0_2_2) = 0)
% 23.31/6.42  	| (179) all_38_0_41 = 0
% 23.31/6.42  	|
% 23.31/6.42  		| Equations (179) can reduce 114 to:
% 23.31/6.42  		| (180) $false
% 23.31/6.42  		|
% 23.31/6.42  		|-The branch is then unsatisfiable
% 23.31/6.42  % SZS output end Proof for theBenchmark
% 23.31/6.42  
% 23.31/6.42  5813ms
%------------------------------------------------------------------------------