%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n013.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 6.45s 2.09s
% Output   : Proof 120.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n013.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 07:11:44 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.51/0.58          ____       _                          
% 0.51/0.58    ___  / __ \_____(_)___  ________  __________
% 0.51/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.51/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.51/0.58  
% 0.51/0.58  A Theorem Prover for First-Order Logic
% 0.51/0.58  (ePrincess v.1.0)
% 0.51/0.58  
% 0.51/0.58  (c) Philipp Rümmer, 2009-2015
% 0.51/0.58  (c) Peter Backeman, 2014-2015
% 0.51/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.58  Bug reports to peter@backeman.se
% 0.51/0.58  
% 0.51/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.58  
% 0.51/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.51/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.53/0.90  Prover 0: Preprocessing ...
% 2.07/1.07  Prover 0: Warning: ignoring some quantifiers
% 2.20/1.09  Prover 0: Constructing countermodel ...
% 3.12/1.35  Prover 0: gave up
% 3.12/1.35  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.24/1.38  Prover 1: Preprocessing ...
% 3.72/1.48  Prover 1: Constructing countermodel ...
% 3.72/1.51  Prover 1: gave up
% 3.72/1.51  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.00/1.53  Prover 2: Preprocessing ...
% 4.68/1.69  Prover 2: Warning: ignoring some quantifiers
% 4.68/1.70  Prover 2: Constructing countermodel ...
% 6.45/2.08  Prover 2: proved (578ms)
% 6.45/2.09  
% 6.45/2.09  No countermodel exists, formula is valid
% 6.45/2.09  % SZS status Theorem for theBenchmark
% 6.45/2.09  
% 6.45/2.09  Generating proof ... Warning: ignoring some quantifiers
% 119.89/94.77  found it (size 310)
% 119.89/94.77  
% 119.89/94.77  % SZS output start Proof for theBenchmark
% 119.89/94.77  Assumed formulas after preprocessing and simplification: 
% 119.89/94.77  | (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 |  ~ (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] : (v8 = 0 |  ~ (intersection_point(v4, v5) = v7) |  ~ (distinct_points(v6, v7) = v8) |  ? [v9] :  ? [v10] : (( ~ (v10 = 0) &  ~ (v9 = 0) & apart_point_and_line(v6, v5) = v10 & apart_point_and_line(v6, v4) = v9) | ( ~ (v9 = 0) & convergent_lines(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 |  ~ (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] : ( ~ (line_connecting(v4, v5) = v7) |  ~ (apart_point_and_line(v6, v7) = 0) |  ? [v8] :  ? [v9] : ((v9 = 0 & v8 = 0 & distinct_points(v6, v5) = 0 & distinct_points(v6, v4) = 0) | ( ~ (v8 = 0) & distinct_points(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] : (v6 = 0 |  ~ (distinct_lines(v4, v5) = v6) |  ? [v7] : ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7)) &  ! [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] : ( ~ (convergent_lines(v4, v5) = 0) | distinct_lines(v4, v5) = 0) &  ! [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)
% 120.03/94.83  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 120.03/94.83  | (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 |  ~ (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] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) &  ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(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 |  ~ (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] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(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] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [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] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) &  ! [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
% 120.03/94.86  |
% 120.03/94.86  | Applying alpha-rule on (1) yields:
% 120.03/94.86  | (2)  ! [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))
% 120.03/94.86  | (3)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 120.03/94.86  | (4)  ! [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)))
% 120.03/94.86  | (5)  ! [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)))
% 120.03/94.86  | (6)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 120.03/94.86  | (7)  ! [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)))
% 120.03/94.86  | (8)  ! [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)))
% 120.03/94.86  | (9)  ! [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)
% 120.03/94.86  | (10)  ! [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)))
% 120.03/94.86  | (11)  ! [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)))
% 120.03/94.86  | (12) orthogonal_through_point(all_0_1_1, all_0_3_3) = all_0_0_0
% 120.03/94.86  | (13)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 120.03/94.86  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 120.03/94.86  | (15)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 120.03/94.86  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 120.03/94.86  | (17)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 120.03/94.86  | (18)  ! [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)))
% 120.03/94.86  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 120.03/94.86  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 120.03/94.86  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 120.03/94.86  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 120.03/94.86  | (23)  ! [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)))
% 120.03/94.86  | (24)  ! [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)))
% 120.03/94.86  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 120.03/94.86  | (26)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 120.03/94.86  | (27)  ! [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)))
% 120.03/94.87  | (28)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 120.03/94.87  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 120.03/94.87  | (30)  ! [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))
% 120.03/94.87  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) &  ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 120.03/94.87  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 120.03/94.87  | (33) orthogonal_through_point(all_0_2_2, all_0_3_3) = all_0_1_1
% 120.03/94.87  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 120.03/94.87  | (35)  ! [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)))
% 120.03/94.87  | (36)  ! [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)))
% 120.03/94.87  | (37)  ! [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)))
% 120.03/94.87  | (38)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 120.03/94.87  | (39)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 120.03/94.87  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 120.03/94.87  | (41)  ! [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)))
% 120.03/94.87  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 120.03/94.87  | (43)  ! [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)))
% 120.03/94.87  | (44)  ! [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)))
% 120.03/94.87  | (45)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 120.03/94.87  | (46)  ! [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)))
% 120.03/94.87  | (47)  ! [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)))
% 120.03/94.87  | (48)  ! [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)))
% 120.03/94.87  | (49)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 120.03/94.87  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 120.03/94.87  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 120.03/94.87  | (52) convergent_lines(all_0_2_2, all_0_0_0) = 0
% 120.03/94.87  | (53)  ! [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)
% 120.03/94.87  | (54)  ! [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)))
% 120.03/94.87  | (55)  ! [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)))
% 120.03/94.87  | (56)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 120.03/94.88  | (57)  ! [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)))
% 120.03/94.88  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 120.03/94.88  | (59)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 120.03/94.88  | (60)  ! [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)))
% 120.03/94.88  | (61)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 120.03/94.88  | (62)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 120.03/94.88  | (63)  ! [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)))
% 120.03/94.88  | (64)  ! [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)
% 120.03/94.88  | (65)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 120.03/94.88  | (66)  ! [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)
% 120.03/94.88  | (67)  ! [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)))
% 120.03/94.88  | (68)  ! [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))
% 120.49/94.88  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 120.49/94.88  | (70)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 120.49/94.88  | (71)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 120.49/94.88  | (72)  ! [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)))
% 120.49/94.88  | (73)  ! [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)))
% 120.49/94.88  | (74)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 120.49/94.88  | (75)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 120.49/94.88  | (76)  ! [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))
% 120.49/94.88  | (77)  ! [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)))
% 120.49/94.88  | (78)  ! [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))
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (17) 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:
% 120.49/94.88  | (79)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = v0)
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (50) 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:
% 120.49/94.88  | (80)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = v0)
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (17) 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:
% 120.49/94.88  | (81)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_1_1, all_0_2_2) = v0)
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (50) 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:
% 120.49/94.88  | (82)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = v0)
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (10) 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:
% 120.49/94.88  | (83)  ? [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))
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (54) 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:
% 120.49/94.88  | (84)  ? [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))
% 120.49/94.88  |
% 120.49/94.88  | Instantiating formula (45) with all_0_0_0, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.49/94.88  | (85) distinct_lines(all_0_2_2, all_0_0_0) = 0
% 120.49/94.88  |
% 120.49/94.88  | Instantiating (82) with all_27_0_31 yields:
% 120.49/94.88  | (86)  ~ (all_27_0_31 = 0) & apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31
% 120.49/94.88  |
% 120.49/94.89  | Applying alpha-rule on (86) yields:
% 120.49/94.89  | (87)  ~ (all_27_0_31 = 0)
% 120.49/94.89  | (88) apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31
% 120.49/94.89  |
% 120.49/94.89  | Instantiating (80) with all_29_0_32 yields:
% 120.49/94.89  | (89)  ~ (all_29_0_32 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32
% 120.49/94.89  |
% 120.49/94.89  | Applying alpha-rule on (89) yields:
% 120.49/94.89  | (90)  ~ (all_29_0_32 = 0)
% 120.49/94.89  | (91) apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32
% 120.49/94.89  |
% 120.49/94.89  | Instantiating (79) with all_31_0_33 yields:
% 120.49/94.89  | (92)  ~ (all_31_0_33 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33
% 120.49/94.89  |
% 120.49/94.89  | Applying alpha-rule on (92) yields:
% 120.49/94.89  | (93)  ~ (all_31_0_33 = 0)
% 120.49/94.89  | (94) unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33
% 120.49/94.89  |
% 120.49/94.89  | Instantiating (81) with all_33_0_34 yields:
% 120.49/94.89  | (95)  ~ (all_33_0_34 = 0) & unorthogonal_lines(all_0_1_1, all_0_2_2) = all_33_0_34
% 120.49/94.89  |
% 120.49/94.89  | Applying alpha-rule on (95) yields:
% 120.49/94.89  | (96)  ~ (all_33_0_34 = 0)
% 120.49/94.89  | (97) unorthogonal_lines(all_0_1_1, all_0_2_2) = all_33_0_34
% 120.49/94.89  |
% 120.49/94.89  | Instantiating (84) with all_35_0_35, all_35_1_36 yields:
% 120.49/94.89  | (98) (all_35_0_35 = 0 & all_35_1_36 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_35_1_36 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_35_1_36 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36)
% 120.49/94.89  |
% 120.49/94.89  | Instantiating (83) with all_36_0_37 yields:
% 120.49/94.89  | (99) (all_36_0_37 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_36_0_37 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = all_36_0_37) | ( ~ (all_36_0_37 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_36_0_37)
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (46) with all_31_0_33, all_31_0_33, all_0_1_1, all_0_0_0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, yields:
% 120.49/94.89  | (100)  ? [v0] : ((v0 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_0_0, all_0_0_0) = v0))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (23) with all_31_0_33, 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_31_0_33, convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.49/94.89  | (101)  ? [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_31_0_33 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (71) with all_31_0_33, all_0_1_1, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, yields:
% 120.49/94.89  | (102) all_31_0_33 = 0 | convergent_lines(all_0_0_0, all_0_1_1) = 0
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (7) with all_31_0_33, all_29_0_32, 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_31_0_33, apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, yields:
% 120.49/94.89  | (103) all_31_0_33 = 0 | all_29_0_32 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (7) with all_33_0_34, all_29_0_32, 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_33_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, yields:
% 120.49/94.89  | (104) all_33_0_34 = 0 | all_29_0_32 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (11) with all_33_0_34, all_29_0_32, 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_33_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, yields:
% 120.49/94.89  | (105) all_33_0_34 = 0 | all_29_0_32 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (60) with all_29_0_32, all_29_0_32, 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_29_0_32, yields:
% 120.49/94.89  | (106) all_29_0_32 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (37) with all_29_0_32, all_29_0_32, 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_29_0_32, yields:
% 120.49/94.89  | (107) all_29_0_32 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (7) with all_31_0_33, all_27_0_31, all_0_1_1, all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.49/94.89  | (108) all_31_0_33 = 0 | all_27_0_31 = 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_1_1, all_0_0_0) = v0))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (11) with all_31_0_33, all_27_0_31, 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_31_0_33, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.49/94.89  | (109) all_31_0_33 = 0 | all_27_0_31 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (7) with all_33_0_34, all_27_0_31, 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_33_0_34, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.49/94.89  | (110) all_33_0_34 = 0 | all_27_0_31 = 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))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (60) with all_27_0_31, all_29_0_32, all_0_1_1, all_0_0_0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.49/94.89  | (111) all_29_0_32 = 0 | all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 120.49/94.89  |
% 120.49/94.89  | Instantiating formula (60) with all_29_0_32, all_27_0_31, all_0_0_0, all_0_1_1, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.49/94.89  | (112) all_29_0_32 = 0 | all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 120.49/94.90  |
% 120.49/94.90  | Instantiating formula (37) with all_27_0_31, all_29_0_32, all_0_1_1, 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_29_0_32, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.49/94.90  | (113) all_29_0_32 = 0 | all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.90  |
% 120.59/94.90  | Instantiating formula (37) with all_29_0_32, all_27_0_31, all_0_0_0, 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_0_0) = all_29_0_32, apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, yields:
% 120.59/94.90  | (114) all_29_0_32 = 0 | all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.90  |
% 120.59/94.90  | Instantiating formula (60) with all_27_0_31, all_27_0_31, 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_27_0_31, yields:
% 120.59/94.90  | (115) all_27_0_31 = 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))
% 120.59/94.90  |
% 120.59/94.90  | Instantiating formula (37) with all_27_0_31, all_27_0_31, 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_27_0_31, yields:
% 120.59/94.90  | (116) all_27_0_31 = 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))
% 120.59/94.90  |
% 120.59/94.90  | Instantiating formula (8) with all_31_0_33, all_29_0_32, all_0_1_1, all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.59/94.90  | (117) all_31_0_33 = 0 | all_29_0_32 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0))
% 120.59/94.90  |
% 120.59/94.90  | Instantiating formula (67) with all_29_0_32, all_29_0_32, all_0_0_0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.59/94.90  | (118) all_29_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.90  |
% 120.59/94.90  | Instantiating (101) with all_43_0_39, all_43_1_40 yields:
% 120.59/94.90  | (119) (all_43_0_39 = 0 & all_43_1_40 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | (all_43_1_40 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (all_43_1_40 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_43_1_40)
% 120.59/94.90  |
% 120.59/94.90  | Instantiating (100) with all_44_0_41 yields:
% 120.59/94.90  | (120) (all_44_0_41 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (all_44_0_41 = 0) & unorthogonal_lines(all_0_0_0, all_0_0_0) = all_44_0_41) | ( ~ (all_44_0_41 = 0) & convergent_lines(all_0_0_0, all_0_0_0) = all_44_0_41)
% 120.59/94.90  |
% 120.59/94.90  +-Applying beta-rule and splitting (102), into two cases.
% 120.59/94.90  |-Branch one:
% 120.59/94.90  | (121) convergent_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.90  |
% 120.59/94.90  	+-Applying beta-rule and splitting (116), into two cases.
% 120.59/94.90  	|-Branch one:
% 120.59/94.90  	| (122) all_27_0_31 = 0
% 120.59/94.90  	|
% 120.59/94.90  		| Equations (122) can reduce 87 to:
% 120.59/94.90  		| (123) $false
% 120.59/94.90  		|
% 120.59/94.90  		|-The branch is then unsatisfiable
% 120.59/94.90  	|-Branch two:
% 120.59/94.90  	| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.90  	| (125)  ? [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))
% 120.59/94.90  	|
% 120.59/94.90  		+-Applying beta-rule and splitting (115), into two cases.
% 120.59/94.90  		|-Branch one:
% 120.59/94.90  		| (122) all_27_0_31 = 0
% 120.59/94.90  		|
% 120.59/94.90  			| Equations (122) can reduce 87 to:
% 120.59/94.90  			| (123) $false
% 120.59/94.90  			|
% 120.59/94.90  			|-The branch is then unsatisfiable
% 120.59/94.90  		|-Branch two:
% 120.59/94.90  		| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.90  		| (129)  ? [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))
% 120.59/94.90  		|
% 120.59/94.90  			+-Applying beta-rule and splitting (118), into two cases.
% 120.59/94.90  			|-Branch one:
% 120.59/94.90  			| (130) all_29_0_32 = 0
% 120.59/94.90  			|
% 120.59/94.90  				| Equations (130) can reduce 90 to:
% 120.59/94.90  				| (123) $false
% 120.59/94.90  				|
% 120.59/94.90  				|-The branch is then unsatisfiable
% 120.59/94.90  			|-Branch two:
% 120.59/94.90  			| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.90  			| (133)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.90  			|
% 120.59/94.90  				+-Applying beta-rule and splitting (106), into two cases.
% 120.59/94.90  				|-Branch one:
% 120.59/94.90  				| (130) all_29_0_32 = 0
% 120.59/94.90  				|
% 120.59/94.90  					| Equations (130) can reduce 90 to:
% 120.59/94.90  					| (123) $false
% 120.59/94.90  					|
% 120.59/94.90  					|-The branch is then unsatisfiable
% 120.59/94.90  				|-Branch two:
% 120.59/94.90  				| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.90  				| (137)  ? [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))
% 120.59/94.90  				|
% 120.59/94.90  					+-Applying beta-rule and splitting (107), into two cases.
% 120.59/94.90  					|-Branch one:
% 120.59/94.90  					| (130) all_29_0_32 = 0
% 120.59/94.90  					|
% 120.59/94.90  						| Equations (130) can reduce 90 to:
% 120.59/94.90  						| (123) $false
% 120.59/94.90  						|
% 120.59/94.90  						|-The branch is then unsatisfiable
% 120.59/94.90  					|-Branch two:
% 120.59/94.90  					| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.90  					| (141)  ? [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))
% 120.59/94.90  					|
% 120.59/94.90  						+-Applying beta-rule and splitting (105), into two cases.
% 120.59/94.90  						|-Branch one:
% 120.59/94.90  						| (142) all_33_0_34 = 0
% 120.59/94.90  						|
% 120.59/94.90  							| Equations (142) can reduce 96 to:
% 120.59/94.90  							| (123) $false
% 120.59/94.90  							|
% 120.59/94.90  							|-The branch is then unsatisfiable
% 120.59/94.90  						|-Branch two:
% 120.59/94.90  						| (96)  ~ (all_33_0_34 = 0)
% 120.59/94.90  						| (145) all_29_0_32 = 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))
% 120.59/94.90  						|
% 120.59/94.90  							+-Applying beta-rule and splitting (104), into two cases.
% 120.59/94.90  							|-Branch one:
% 120.59/94.90  							| (142) all_33_0_34 = 0
% 120.59/94.90  							|
% 120.59/94.90  								| Equations (142) can reduce 96 to:
% 120.59/94.90  								| (123) $false
% 120.59/94.90  								|
% 120.59/94.90  								|-The branch is then unsatisfiable
% 120.59/94.90  							|-Branch two:
% 120.59/94.90  							| (96)  ~ (all_33_0_34 = 0)
% 120.59/94.90  							| (149) all_29_0_32 = 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))
% 120.59/94.90  							|
% 120.59/94.90  								+-Applying beta-rule and splitting (103), into two cases.
% 120.59/94.90  								|-Branch one:
% 120.59/94.90  								| (150) all_31_0_33 = 0
% 120.59/94.90  								|
% 120.59/94.90  									| Equations (150) can reduce 93 to:
% 120.59/94.90  									| (123) $false
% 120.59/94.90  									|
% 120.59/94.90  									|-The branch is then unsatisfiable
% 120.59/94.90  								|-Branch two:
% 120.59/94.90  								| (93)  ~ (all_31_0_33 = 0)
% 120.59/94.90  								| (153) all_29_0_32 = 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))
% 120.59/94.90  								|
% 120.59/94.90  									+-Applying beta-rule and splitting (108), into two cases.
% 120.59/94.90  									|-Branch one:
% 120.59/94.90  									| (150) all_31_0_33 = 0
% 120.59/94.90  									|
% 120.59/94.90  										| Equations (150) can reduce 93 to:
% 120.59/94.90  										| (123) $false
% 120.59/94.90  										|
% 120.59/94.90  										|-The branch is then unsatisfiable
% 120.59/94.90  									|-Branch two:
% 120.59/94.90  									| (93)  ~ (all_31_0_33 = 0)
% 120.59/94.90  									| (157) all_27_0_31 = 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_1_1, all_0_0_0) = v0))
% 120.59/94.90  									|
% 120.59/94.90  										+-Applying beta-rule and splitting (109), into two cases.
% 120.59/94.90  										|-Branch one:
% 120.59/94.90  										| (150) all_31_0_33 = 0
% 120.59/94.90  										|
% 120.59/94.90  											| Equations (150) can reduce 93 to:
% 120.59/94.90  											| (123) $false
% 120.59/94.90  											|
% 120.59/94.90  											|-The branch is then unsatisfiable
% 120.59/94.90  										|-Branch two:
% 120.59/94.90  										| (93)  ~ (all_31_0_33 = 0)
% 120.59/94.90  										| (161) all_27_0_31 = 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))
% 120.59/94.91  										|
% 120.59/94.91  											+-Applying beta-rule and splitting (113), into two cases.
% 120.59/94.91  											|-Branch one:
% 120.59/94.91  											| (130) all_29_0_32 = 0
% 120.59/94.91  											|
% 120.59/94.91  												| Equations (130) can reduce 90 to:
% 120.59/94.91  												| (123) $false
% 120.59/94.91  												|
% 120.59/94.91  												|-The branch is then unsatisfiable
% 120.59/94.91  											|-Branch two:
% 120.59/94.91  											| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  											| (165) all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.91  											|
% 120.59/94.91  												+-Applying beta-rule and splitting (117), into two cases.
% 120.59/94.91  												|-Branch one:
% 120.59/94.91  												| (150) all_31_0_33 = 0
% 120.59/94.91  												|
% 120.59/94.91  													| Equations (150) can reduce 93 to:
% 120.59/94.91  													| (123) $false
% 120.59/94.91  													|
% 120.59/94.91  													|-The branch is then unsatisfiable
% 120.59/94.91  												|-Branch two:
% 120.59/94.91  												| (93)  ~ (all_31_0_33 = 0)
% 120.59/94.91  												| (169) all_29_0_32 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0))
% 120.59/94.91  												|
% 120.59/94.91  													+-Applying beta-rule and splitting (114), into two cases.
% 120.59/94.91  													|-Branch one:
% 120.59/94.91  													| (130) all_29_0_32 = 0
% 120.59/94.91  													|
% 120.59/94.91  														| Equations (130) can reduce 90 to:
% 120.59/94.91  														| (123) $false
% 120.59/94.91  														|
% 120.59/94.91  														|-The branch is then unsatisfiable
% 120.59/94.91  													|-Branch two:
% 120.59/94.91  													| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  													| (173) all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.91  													|
% 120.59/94.91  														+-Applying beta-rule and splitting (110), into two cases.
% 120.59/94.91  														|-Branch one:
% 120.59/94.91  														| (142) all_33_0_34 = 0
% 120.59/94.91  														|
% 120.59/94.91  															| Equations (142) can reduce 96 to:
% 120.59/94.91  															| (123) $false
% 120.59/94.91  															|
% 120.59/94.91  															|-The branch is then unsatisfiable
% 120.59/94.91  														|-Branch two:
% 120.59/94.91  														| (96)  ~ (all_33_0_34 = 0)
% 120.59/94.91  														| (177) all_27_0_31 = 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))
% 120.59/94.91  														|
% 120.59/94.91  															+-Applying beta-rule and splitting (112), into two cases.
% 120.59/94.91  															|-Branch one:
% 120.59/94.91  															| (130) all_29_0_32 = 0
% 120.59/94.91  															|
% 120.59/94.91  																| Equations (130) can reduce 90 to:
% 120.59/94.91  																| (123) $false
% 120.59/94.91  																|
% 120.59/94.91  																|-The branch is then unsatisfiable
% 120.59/94.91  															|-Branch two:
% 120.59/94.91  															| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  															| (181) all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 120.59/94.91  															|
% 120.59/94.91  																+-Applying beta-rule and splitting (111), into two cases.
% 120.59/94.91  																|-Branch one:
% 120.59/94.91  																| (130) all_29_0_32 = 0
% 120.59/94.91  																|
% 120.59/94.91  																	| Equations (130) can reduce 90 to:
% 120.59/94.91  																	| (123) $false
% 120.59/94.91  																	|
% 120.59/94.91  																	|-The branch is then unsatisfiable
% 120.59/94.91  																|-Branch two:
% 120.59/94.91  																| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  																| (185) all_27_0_31 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 120.59/94.91  																|
% 120.59/94.91  																	+-Applying beta-rule and splitting (145), into two cases.
% 120.59/94.91  																	|-Branch one:
% 120.59/94.91  																	| (130) all_29_0_32 = 0
% 120.59/94.91  																	|
% 120.59/94.91  																		| Equations (130) can reduce 90 to:
% 120.59/94.91  																		| (123) $false
% 120.59/94.91  																		|
% 120.59/94.91  																		|-The branch is then unsatisfiable
% 120.59/94.91  																	|-Branch two:
% 120.59/94.91  																	| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  																	| (189)  ? [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))
% 120.59/94.91  																	|
% 120.59/94.91  																		+-Applying beta-rule and splitting (149), into two cases.
% 120.59/94.91  																		|-Branch one:
% 120.59/94.91  																		| (130) all_29_0_32 = 0
% 120.59/94.91  																		|
% 120.59/94.91  																			| Equations (130) can reduce 90 to:
% 120.59/94.91  																			| (123) $false
% 120.59/94.91  																			|
% 120.59/94.91  																			|-The branch is then unsatisfiable
% 120.59/94.91  																		|-Branch two:
% 120.59/94.91  																		| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  																		| (193)  ? [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))
% 120.59/94.91  																		|
% 120.59/94.91  																			| Instantiating (193) with all_113_0_48 yields:
% 120.59/94.91  																			| (194) (all_113_0_48 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (all_113_0_48 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0) | ( ~ (all_113_0_48 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = all_113_0_48)
% 120.59/94.91  																			|
% 120.59/94.91  																			+-Applying beta-rule and splitting (153), into two cases.
% 120.59/94.91  																			|-Branch one:
% 120.59/94.91  																			| (130) all_29_0_32 = 0
% 120.59/94.91  																			|
% 120.59/94.91  																				| Equations (130) can reduce 90 to:
% 120.59/94.91  																				| (123) $false
% 120.59/94.91  																				|
% 120.59/94.91  																				|-The branch is then unsatisfiable
% 120.59/94.91  																			|-Branch two:
% 120.59/94.91  																			| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  																			| (198)  ? [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))
% 120.59/94.91  																			|
% 120.59/94.91  																				| Instantiating (198) with all_117_0_49 yields:
% 120.59/94.91  																				| (199) (all_117_0_49 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (all_117_0_49 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (all_117_0_49 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = all_117_0_49)
% 120.59/94.91  																				|
% 120.59/94.91  																				+-Applying beta-rule and splitting (157), into two cases.
% 120.59/94.91  																				|-Branch one:
% 120.59/94.91  																				| (122) all_27_0_31 = 0
% 120.59/94.91  																				|
% 120.59/94.91  																					| Equations (122) can reduce 87 to:
% 120.59/94.91  																					| (123) $false
% 120.59/94.91  																					|
% 120.59/94.91  																					|-The branch is then unsatisfiable
% 120.59/94.91  																				|-Branch two:
% 120.59/94.91  																				| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																				| (203)  ? [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_1_1, all_0_0_0) = v0))
% 120.59/94.91  																				|
% 120.59/94.91  																					+-Applying beta-rule and splitting (161), into two cases.
% 120.59/94.91  																					|-Branch one:
% 120.59/94.91  																					| (122) all_27_0_31 = 0
% 120.59/94.91  																					|
% 120.59/94.91  																						| Equations (122) can reduce 87 to:
% 120.59/94.91  																						| (123) $false
% 120.59/94.91  																						|
% 120.59/94.91  																						|-The branch is then unsatisfiable
% 120.59/94.91  																					|-Branch two:
% 120.59/94.91  																					| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																					| (207)  ? [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))
% 120.59/94.91  																					|
% 120.59/94.91  																						+-Applying beta-rule and splitting (165), into two cases.
% 120.59/94.91  																						|-Branch one:
% 120.59/94.91  																						| (122) all_27_0_31 = 0
% 120.59/94.91  																						|
% 120.59/94.91  																							| Equations (122) can reduce 87 to:
% 120.59/94.91  																							| (123) $false
% 120.59/94.91  																							|
% 120.59/94.91  																							|-The branch is then unsatisfiable
% 120.59/94.91  																						|-Branch two:
% 120.59/94.91  																						| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																						| (211)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.91  																						|
% 120.59/94.91  																							+-Applying beta-rule and splitting (169), into two cases.
% 120.59/94.91  																							|-Branch one:
% 120.59/94.91  																							| (130) all_29_0_32 = 0
% 120.59/94.91  																							|
% 120.59/94.91  																								| Equations (130) can reduce 90 to:
% 120.59/94.91  																								| (123) $false
% 120.59/94.91  																								|
% 120.59/94.91  																								|-The branch is then unsatisfiable
% 120.59/94.91  																							|-Branch two:
% 120.59/94.91  																							| (90)  ~ (all_29_0_32 = 0)
% 120.59/94.91  																							| (215)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0))
% 120.59/94.91  																							|
% 120.59/94.91  																								+-Applying beta-rule and splitting (173), into two cases.
% 120.59/94.91  																								|-Branch one:
% 120.59/94.91  																								| (122) all_27_0_31 = 0
% 120.59/94.91  																								|
% 120.59/94.91  																									| Equations (122) can reduce 87 to:
% 120.59/94.91  																									| (123) $false
% 120.59/94.91  																									|
% 120.59/94.91  																									|-The branch is then unsatisfiable
% 120.59/94.91  																								|-Branch two:
% 120.59/94.91  																								| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																								| (219)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 120.59/94.91  																								|
% 120.59/94.91  																									+-Applying beta-rule and splitting (177), into two cases.
% 120.59/94.91  																									|-Branch one:
% 120.59/94.91  																									| (122) all_27_0_31 = 0
% 120.59/94.91  																									|
% 120.59/94.91  																										| Equations (122) can reduce 87 to:
% 120.59/94.91  																										| (123) $false
% 120.59/94.91  																										|
% 120.59/94.91  																										|-The branch is then unsatisfiable
% 120.59/94.91  																									|-Branch two:
% 120.59/94.91  																									| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																									| (223)  ? [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))
% 120.59/94.91  																									|
% 120.59/94.91  																										+-Applying beta-rule and splitting (181), into two cases.
% 120.59/94.91  																										|-Branch one:
% 120.59/94.91  																										| (122) all_27_0_31 = 0
% 120.59/94.91  																										|
% 120.59/94.91  																											| Equations (122) can reduce 87 to:
% 120.59/94.91  																											| (123) $false
% 120.59/94.91  																											|
% 120.59/94.91  																											|-The branch is then unsatisfiable
% 120.59/94.91  																										|-Branch two:
% 120.59/94.91  																										| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																										| (227)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_1_1, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_1_1, all_0_0_0) = v0))
% 120.59/94.91  																										|
% 120.59/94.91  																											+-Applying beta-rule and splitting (185), into two cases.
% 120.59/94.91  																											|-Branch one:
% 120.59/94.91  																											| (122) all_27_0_31 = 0
% 120.59/94.91  																											|
% 120.59/94.91  																												| Equations (122) can reduce 87 to:
% 120.59/94.91  																												| (123) $false
% 120.59/94.91  																												|
% 120.59/94.91  																												|-The branch is then unsatisfiable
% 120.59/94.91  																											|-Branch two:
% 120.59/94.91  																											| (87)  ~ (all_27_0_31 = 0)
% 120.59/94.91  																											| (231)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = v0))
% 120.59/94.91  																											|
% 120.59/94.91  																												+-Applying beta-rule and splitting (199), into two cases.
% 120.59/94.91  																												|-Branch one:
% 120.59/94.91  																												| (232) (all_117_0_49 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | (all_117_0_49 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0)
% 120.59/94.91  																												|
% 120.59/94.91  																													+-Applying beta-rule and splitting (232), into two cases.
% 120.59/94.91  																													|-Branch one:
% 120.59/94.91  																													| (233) all_117_0_49 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.92  																													|
% 120.59/94.92  																														| Applying alpha-rule on (233) yields:
% 120.59/94.92  																														| (234) all_117_0_49 = 0
% 120.59/94.92  																														| (235) unorthogonal_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.92  																														|
% 120.59/94.92  																														| Instantiating formula (58) with all_0_0_0, all_0_1_1, 0, all_31_0_33 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, unorthogonal_lines(all_0_0_0, all_0_1_1) = 0, yields:
% 120.59/94.92  																														| (150) all_31_0_33 = 0
% 120.59/94.92  																														|
% 120.59/94.92  																														| Equations (150) can reduce 93 to:
% 120.59/94.92  																														| (123) $false
% 120.59/94.92  																														|
% 120.59/94.92  																														|-The branch is then unsatisfiable
% 120.59/94.92  																													|-Branch two:
% 120.59/94.92  																													| (238) all_117_0_49 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 120.59/94.92  																													|
% 120.59/94.92  																														| Applying alpha-rule on (238) yields:
% 120.59/94.92  																														| (234) all_117_0_49 = 0
% 120.59/94.92  																														| (240) apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 120.59/94.92  																														|
% 120.59/94.92  																														| Instantiating formula (32) with all_0_3_3, all_0_0_0, 0, all_29_0_32 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, apart_point_and_line(all_0_3_3, all_0_0_0) = 0, yields:
% 120.59/94.92  																														| (130) all_29_0_32 = 0
% 120.59/94.92  																														|
% 120.59/94.92  																														| Equations (130) can reduce 90 to:
% 120.59/94.92  																														| (123) $false
% 120.59/94.92  																														|
% 120.59/94.92  																														|-The branch is then unsatisfiable
% 120.59/94.92  																												|-Branch two:
% 120.59/94.92  																												| (243)  ~ (all_117_0_49 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = all_117_0_49
% 120.59/94.92  																												|
% 120.59/94.92  																													| Applying alpha-rule on (243) yields:
% 120.59/94.92  																													| (244)  ~ (all_117_0_49 = 0)
% 120.59/94.92  																													| (245) distinct_lines(all_0_0_0, all_0_0_0) = all_117_0_49
% 120.59/94.92  																													|
% 120.59/94.92  																													| Instantiating formula (54) with 0, all_0_1_1, all_0_1_1, all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_1_1) = 0, yields:
% 120.59/94.92  																													| (246)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = v0))
% 120.59/94.92  																													|
% 120.59/94.92  																													| Instantiating formula (72) with all_31_0_33, all_0_1_1, all_0_1_1, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, convergent_lines(all_0_0_0, all_0_1_1) = 0, yields:
% 120.59/94.92  																													| (247)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (v0 = 0 & all_31_0_33 = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = v0))
% 120.59/94.92  																													|
% 120.59/94.92  																													| Instantiating formula (45) with all_0_1_1, all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_1_1) = 0, yields:
% 120.59/94.92  																													| (248) distinct_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.92  																													|
% 120.59/94.92  																													| Instantiating formula (39) with all_117_0_49, all_0_0_0, all_0_0_0 and discharging atoms distinct_lines(all_0_0_0, all_0_0_0) = all_117_0_49, yields:
% 120.59/94.92  																													| (249) all_117_0_49 = 0 |  ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_0_0, all_0_0_0) = v0)
% 120.59/94.92  																													|
% 120.59/94.92  																													| Instantiating (247) with all_170_0_68, all_170_1_69 yields:
% 120.59/94.92  																													| (250) (all_170_0_68 = 0 & all_170_1_69 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_170_1_69 = 0 & all_31_0_33 = 0) | ( ~ (all_170_1_69 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69)
% 120.59/94.92  																													|
% 120.59/94.92  																													| Instantiating (246) with all_173_0_73, all_173_1_74 yields:
% 120.59/94.92  																													| (251) (all_173_0_73 = 0 & all_173_1_74 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_173_1_74 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (all_173_1_74 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_173_1_74)
% 120.59/94.92  																													|
% 120.59/94.92  																													+-Applying beta-rule and splitting (251), into two cases.
% 120.59/94.92  																													|-Branch one:
% 120.59/94.92  																													| (252) (all_173_0_73 = 0 & all_173_1_74 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_173_1_74 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0)
% 120.59/94.92  																													|
% 120.59/94.92  																														+-Applying beta-rule and splitting (252), into two cases.
% 120.59/94.92  																														|-Branch one:
% 120.59/94.92  																														| (253) all_173_0_73 = 0 & all_173_1_74 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																														|
% 120.59/94.92  																															| Applying alpha-rule on (253) yields:
% 120.59/94.92  																															| (254) all_173_0_73 = 0
% 120.59/94.92  																															| (255) all_173_1_74 = 0
% 120.59/94.92  																															| (256) unorthogonal_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																															| (257) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																															|
% 120.59/94.92  																															| Instantiating formula (49) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 120.59/94.92  																															| (258) $false
% 120.59/94.92  																															|
% 120.59/94.92  																															|-The branch is then unsatisfiable
% 120.59/94.92  																														|-Branch two:
% 120.59/94.92  																														| (259) all_173_1_74 = 0 & unorthogonal_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.92  																														|
% 120.59/94.92  																															| Applying alpha-rule on (259) yields:
% 120.59/94.92  																															| (255) all_173_1_74 = 0
% 120.59/94.92  																															| (235) unorthogonal_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.92  																															|
% 120.59/94.92  																															+-Applying beta-rule and splitting (250), into two cases.
% 120.59/94.92  																															|-Branch one:
% 120.59/94.92  																															| (262) (all_170_0_68 = 0 & all_170_1_69 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_170_1_69 = 0 & all_31_0_33 = 0)
% 120.59/94.92  																															|
% 120.59/94.92  																																+-Applying beta-rule and splitting (262), into two cases.
% 120.59/94.92  																																|-Branch one:
% 120.59/94.92  																																| (263) all_170_0_68 = 0 & all_170_1_69 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																																|
% 120.59/94.92  																																	| Applying alpha-rule on (263) yields:
% 120.59/94.92  																																	| (264) all_170_0_68 = 0
% 120.59/94.92  																																	| (265) all_170_1_69 = 0
% 120.59/94.92  																																	| (256) unorthogonal_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																																	| (257) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																																	|
% 120.59/94.92  																																	| Instantiating formula (49) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 120.59/94.92  																																	| (258) $false
% 120.59/94.92  																																	|
% 120.59/94.92  																																	|-The branch is then unsatisfiable
% 120.59/94.92  																																|-Branch two:
% 120.59/94.92  																																| (269) all_170_1_69 = 0 & all_31_0_33 = 0
% 120.59/94.92  																																|
% 120.59/94.92  																																	| Applying alpha-rule on (269) yields:
% 120.59/94.92  																																	| (265) all_170_1_69 = 0
% 120.59/94.92  																																	| (150) all_31_0_33 = 0
% 120.59/94.92  																																	|
% 120.59/94.92  																																	| Equations (150) can reduce 93 to:
% 120.59/94.92  																																	| (123) $false
% 120.59/94.92  																																	|
% 120.59/94.92  																																	|-The branch is then unsatisfiable
% 120.59/94.92  																															|-Branch two:
% 120.59/94.92  																															| (273)  ~ (all_170_1_69 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69
% 120.59/94.92  																															|
% 120.59/94.92  																																| Applying alpha-rule on (273) yields:
% 120.59/94.92  																																| (274)  ~ (all_170_1_69 = 0)
% 120.59/94.92  																																| (275) unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69
% 120.59/94.92  																																|
% 120.59/94.92  																																| Instantiating formula (58) with all_0_0_0, all_0_1_1, all_170_1_69, all_31_0_33 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69, unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, yields:
% 120.59/94.92  																																| (276) all_170_1_69 = all_31_0_33
% 120.59/94.92  																																|
% 120.59/94.92  																																| Instantiating formula (58) with all_0_0_0, all_0_1_1, 0, all_170_1_69 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69, unorthogonal_lines(all_0_0_0, all_0_1_1) = 0, yields:
% 120.59/94.92  																																| (265) all_170_1_69 = 0
% 120.59/94.92  																																|
% 120.59/94.92  																																| Combining equations (276,265) yields a new equation:
% 120.59/94.92  																																| (278) all_31_0_33 = 0
% 120.59/94.92  																																|
% 120.59/94.92  																																| Simplifying 278 yields:
% 120.59/94.92  																																| (150) all_31_0_33 = 0
% 120.59/94.92  																																|
% 120.59/94.92  																																| Equations (150) can reduce 93 to:
% 120.59/94.92  																																| (123) $false
% 120.59/94.92  																																|
% 120.59/94.92  																																|-The branch is then unsatisfiable
% 120.59/94.92  																													|-Branch two:
% 120.59/94.92  																													| (281)  ~ (all_173_1_74 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_173_1_74
% 120.59/94.92  																													|
% 120.59/94.92  																														| Applying alpha-rule on (281) yields:
% 120.59/94.92  																														| (282)  ~ (all_173_1_74 = 0)
% 120.59/94.92  																														| (283) unorthogonal_lines(all_0_0_0, all_0_1_1) = all_173_1_74
% 120.59/94.92  																														|
% 120.59/94.92  																														+-Applying beta-rule and splitting (194), into two cases.
% 120.59/94.92  																														|-Branch one:
% 120.59/94.92  																														| (284) (all_113_0_48 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0) | (all_113_0_48 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0)
% 120.59/94.92  																														|
% 120.59/94.92  																															+-Applying beta-rule and splitting (284), into two cases.
% 120.59/94.92  																															|-Branch one:
% 120.59/94.92  																															| (285) all_113_0_48 = 0 & unorthogonal_lines(all_0_0_0, all_0_2_2) = 0
% 120.59/94.92  																															|
% 120.59/94.92  																																| Applying alpha-rule on (285) yields:
% 120.59/94.92  																																| (286) all_113_0_48 = 0
% 120.59/94.92  																																| (287) unorthogonal_lines(all_0_0_0, all_0_2_2) = 0
% 120.59/94.92  																																|
% 120.59/94.92  																																+-Applying beta-rule and splitting (250), into two cases.
% 120.59/94.92  																																|-Branch one:
% 120.59/94.92  																																| (262) (all_170_0_68 = 0 & all_170_1_69 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0) | (all_170_1_69 = 0 & all_31_0_33 = 0)
% 120.59/94.92  																																|
% 120.59/94.92  																																	+-Applying beta-rule and splitting (262), into two cases.
% 120.59/94.92  																																	|-Branch one:
% 120.59/94.92  																																	| (263) all_170_0_68 = 0 & all_170_1_69 = 0 & unorthogonal_lines(all_0_1_1, all_0_1_1) = 0 & convergent_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																																	|
% 120.59/94.92  																																		| Applying alpha-rule on (263) yields:
% 120.59/94.92  																																		| (264) all_170_0_68 = 0
% 120.59/94.92  																																		| (265) all_170_1_69 = 0
% 120.59/94.92  																																		| (256) unorthogonal_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																																		| (257) convergent_lines(all_0_1_1, all_0_1_1) = 0
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Instantiating formula (49) with all_0_1_1 and discharging atoms convergent_lines(all_0_1_1, all_0_1_1) = 0, yields:
% 120.59/94.92  																																		| (258) $false
% 120.59/94.92  																																		|
% 120.59/94.92  																																		|-The branch is then unsatisfiable
% 120.59/94.92  																																	|-Branch two:
% 120.59/94.92  																																	| (269) all_170_1_69 = 0 & all_31_0_33 = 0
% 120.59/94.92  																																	|
% 120.59/94.92  																																		| Applying alpha-rule on (269) yields:
% 120.59/94.92  																																		| (265) all_170_1_69 = 0
% 120.59/94.92  																																		| (150) all_31_0_33 = 0
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Equations (150) can reduce 93 to:
% 120.59/94.92  																																		| (123) $false
% 120.59/94.92  																																		|
% 120.59/94.92  																																		|-The branch is then unsatisfiable
% 120.59/94.92  																																|-Branch two:
% 120.59/94.92  																																| (273)  ~ (all_170_1_69 = 0) & unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69
% 120.59/94.92  																																|
% 120.59/94.92  																																	| Applying alpha-rule on (273) yields:
% 120.59/94.92  																																	| (274)  ~ (all_170_1_69 = 0)
% 120.59/94.92  																																	| (275) unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69
% 120.59/94.92  																																	|
% 120.59/94.92  																																	+-Applying beta-rule and splitting (249), into two cases.
% 120.59/94.92  																																	|-Branch one:
% 120.59/94.92  																																	| (234) all_117_0_49 = 0
% 120.59/94.92  																																	|
% 120.59/94.92  																																		| Equations (234) can reduce 244 to:
% 120.59/94.92  																																		| (123) $false
% 120.59/94.92  																																		|
% 120.59/94.92  																																		|-The branch is then unsatisfiable
% 120.59/94.92  																																	|-Branch two:
% 120.59/94.92  																																	| (244)  ~ (all_117_0_49 = 0)
% 120.59/94.92  																																	| (305)  ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_0_0, all_0_0_0) = v0)
% 120.59/94.92  																																	|
% 120.59/94.92  																																		| Instantiating (305) with all_219_0_123 yields:
% 120.59/94.92  																																		| (306)  ~ (all_219_0_123 = 0) & convergent_lines(all_0_0_0, all_0_0_0) = all_219_0_123
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Applying alpha-rule on (306) yields:
% 120.59/94.92  																																		| (307)  ~ (all_219_0_123 = 0)
% 120.59/94.92  																																		| (308) convergent_lines(all_0_0_0, all_0_0_0) = all_219_0_123
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Instantiating formula (58) with all_0_0_0, all_0_1_1, all_173_1_74, all_31_0_33 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_173_1_74, unorthogonal_lines(all_0_0_0, all_0_1_1) = all_31_0_33, yields:
% 120.59/94.92  																																		| (309) all_173_1_74 = all_31_0_33
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Instantiating formula (58) with all_0_0_0, all_0_1_1, all_170_1_69, all_173_1_74 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_1_1) = all_173_1_74, unorthogonal_lines(all_0_0_0, all_0_1_1) = all_170_1_69, yields:
% 120.59/94.92  																																		| (310) all_173_1_74 = all_170_1_69
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Combining equations (309,310) yields a new equation:
% 120.59/94.92  																																		| (276) all_170_1_69 = all_31_0_33
% 120.59/94.92  																																		|
% 120.59/94.92  																																		| Equations (276) can reduce 274 to:
% 120.59/94.92  																																		| (93)  ~ (all_31_0_33 = 0)
% 120.59/94.92  																																		|
% 120.59/94.92  																																		+-Applying beta-rule and splitting (98), into two cases.
% 120.59/94.92  																																		|-Branch one:
% 120.59/94.92  																																		| (313) (all_35_0_35 = 0 & all_35_1_36 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_35_1_36 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0)
% 120.59/94.92  																																		|
% 120.59/94.92  																																			+-Applying beta-rule and splitting (313), into two cases.
% 120.59/94.92  																																			|-Branch one:
% 120.59/94.92  																																			| (314) all_35_0_35 = 0 & all_35_1_36 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.59/94.92  																																			|
% 120.59/94.92  																																				| Applying alpha-rule on (314) yields:
% 120.59/94.92  																																				| (315) all_35_0_35 = 0
% 120.59/94.92  																																				| (316) all_35_1_36 = 0
% 120.59/94.92  																																				| (317) unorthogonal_lines(all_0_0_0, all_0_0_0) = 0
% 120.59/94.92  																																				| (318) convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.59/94.92  																																				|
% 120.59/94.92  																																				| Instantiating formula (49) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = 0, yields:
% 120.59/94.92  																																				| (258) $false
% 120.59/94.92  																																				|
% 120.59/94.92  																																				|-The branch is then unsatisfiable
% 120.59/94.92  																																			|-Branch two:
% 120.59/94.92  																																			| (320) all_35_1_36 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.59/94.92  																																			|
% 120.59/94.92  																																				| Applying alpha-rule on (320) yields:
% 120.59/94.92  																																				| (316) all_35_1_36 = 0
% 120.59/94.92  																																				| (322) unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.59/94.92  																																				|
% 120.59/94.92  																																				+-Applying beta-rule and splitting (119), into two cases.
% 120.59/94.92  																																				|-Branch one:
% 120.59/94.92  																																				| (323) (all_43_0_39 = 0 & all_43_1_40 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0) | (all_43_1_40 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0)
% 120.59/94.92  																																				|
% 120.59/94.92  																																					+-Applying beta-rule and splitting (323), into two cases.
% 120.59/94.92  																																					|-Branch one:
% 120.59/94.92  																																					| (324) all_43_0_39 = 0 & all_43_1_40 = 0 & unorthogonal_lines(all_0_2_2, all_0_1_1) = 0 & convergent_lines(all_0_2_2, all_0_1_1) = 0
% 120.59/94.92  																																					|
% 120.59/94.93  																																						| Applying alpha-rule on (324) yields:
% 120.59/94.93  																																						| (325) all_43_0_39 = 0
% 120.59/94.93  																																						| (326) all_43_1_40 = 0
% 120.59/94.93  																																						| (327) unorthogonal_lines(all_0_2_2, all_0_1_1) = 0
% 120.59/94.93  																																						| (328) convergent_lines(all_0_2_2, all_0_1_1) = 0
% 120.59/94.93  																																						|
% 120.59/94.93  																																						| Instantiating formula (23) with all_33_0_34, 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_33_0_34, convergent_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 120.59/94.93  																																						| (329)  ? [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_33_0_34 = 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))
% 120.59/94.93  																																						|
% 120.59/94.93  																																						| Instantiating (329) with all_279_0_391, all_279_1_392 yields:
% 120.59/94.93  																																						| (330) (all_279_0_391 = 0 & all_279_1_392 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_279_1_392 = 0 & all_33_0_34 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0) | ( ~ (all_279_1_392 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_279_1_392)
% 120.59/94.93  																																						|
% 120.59/94.93  																																						+-Applying beta-rule and splitting (330), into two cases.
% 120.59/94.93  																																						|-Branch one:
% 120.59/94.93  																																						| (331) (all_279_0_391 = 0 & all_279_1_392 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_279_1_392 = 0 & all_33_0_34 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0)
% 120.59/94.93  																																						|
% 120.59/94.93  																																							+-Applying beta-rule and splitting (331), into two cases.
% 120.59/94.93  																																							|-Branch one:
% 120.59/94.93  																																							| (332) all_279_0_391 = 0 & all_279_1_392 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0
% 120.59/94.93  																																							|
% 120.59/94.93  																																								| Applying alpha-rule on (332) yields:
% 120.59/94.93  																																								| (333) all_279_0_391 = 0
% 120.59/94.93  																																								| (334) all_279_1_392 = 0
% 120.59/94.93  																																								| (335) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0
% 120.59/94.93  																																								| (336) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 120.59/94.93  																																								|
% 120.59/94.93  																																								| Instantiating formula (49) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 120.59/94.93  																																								| (258) $false
% 120.59/94.93  																																								|
% 120.59/94.93  																																								|-The branch is then unsatisfiable
% 120.59/94.93  																																							|-Branch two:
% 120.59/94.93  																																							| (338) all_279_1_392 = 0 & all_33_0_34 = 0 & convergent_lines(all_0_1_1, all_0_2_2) = 0
% 120.59/94.93  																																							|
% 120.59/94.93  																																								| Applying alpha-rule on (338) yields:
% 120.59/94.93  																																								| (334) all_279_1_392 = 0
% 120.59/94.93  																																								| (142) all_33_0_34 = 0
% 120.59/94.93  																																								| (341) convergent_lines(all_0_1_1, all_0_2_2) = 0
% 120.59/94.93  																																								|
% 120.59/94.93  																																								| Equations (142) can reduce 96 to:
% 120.59/94.93  																																								| (123) $false
% 120.59/94.93  																																								|
% 120.59/94.93  																																								|-The branch is then unsatisfiable
% 120.59/94.93  																																						|-Branch two:
% 120.59/94.93  																																						| (343)  ~ (all_279_1_392 = 0) & unorthogonal_lines(all_0_2_2, all_0_1_1) = all_279_1_392
% 120.59/94.93  																																						|
% 120.59/94.93  																																							| Applying alpha-rule on (343) yields:
% 120.59/94.93  																																							| (344)  ~ (all_279_1_392 = 0)
% 120.59/94.93  																																							| (345) unorthogonal_lines(all_0_2_2, all_0_1_1) = all_279_1_392
% 120.59/94.93  																																							|
% 120.59/94.93  																																							| Instantiating formula (58) with all_0_2_2, all_0_1_1, all_279_1_392, 0 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_1_1) = all_279_1_392, unorthogonal_lines(all_0_2_2, all_0_1_1) = 0, yields:
% 120.59/94.93  																																							| (334) all_279_1_392 = 0
% 120.59/94.93  																																							|
% 120.59/94.93  																																							| Equations (334) can reduce 344 to:
% 120.59/94.93  																																							| (123) $false
% 120.59/94.93  																																							|
% 120.59/94.93  																																							|-The branch is then unsatisfiable
% 120.59/94.93  																																					|-Branch two:
% 120.59/94.93  																																					| (348) all_43_1_40 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.93  																																					|
% 120.59/94.93  																																						| Applying alpha-rule on (348) yields:
% 120.59/94.93  																																						| (326) all_43_1_40 = 0
% 120.59/94.93  																																						| (150) all_31_0_33 = 0
% 120.59/94.93  																																						| (121) convergent_lines(all_0_0_0, all_0_1_1) = 0
% 120.59/94.93  																																						|
% 120.59/94.93  																																						| Equations (150) can reduce 93 to:
% 120.59/94.93  																																						| (123) $false
% 120.59/94.93  																																						|
% 120.59/94.93  																																						|-The branch is then unsatisfiable
% 120.59/94.93  																																				|-Branch two:
% 120.59/94.93  																																				| (353)  ~ (all_43_1_40 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_43_1_40
% 120.59/94.93  																																				|
% 120.59/94.93  																																					| Applying alpha-rule on (353) yields:
% 120.59/94.93  																																					| (354)  ~ (all_43_1_40 = 0)
% 120.59/94.93  																																					| (355) unorthogonal_lines(all_0_2_2, all_0_0_0) = all_43_1_40
% 120.59/94.93  																																					|
% 120.59/94.93  																																					| Instantiating formula (58) with all_0_2_2, all_0_0_0, 0, all_43_1_40 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_43_1_40, unorthogonal_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.59/94.93  																																					| (326) all_43_1_40 = 0
% 120.59/94.93  																																					|
% 120.59/94.93  																																					| Equations (326) can reduce 354 to:
% 120.59/94.93  																																					| (123) $false
% 120.59/94.93  																																					|
% 120.59/94.93  																																					|-The branch is then unsatisfiable
% 120.59/94.93  																																		|-Branch two:
% 120.59/94.93  																																		| (358)  ~ (all_35_1_36 = 0) & unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36
% 120.59/94.93  																																		|
% 120.59/94.93  																																			| Applying alpha-rule on (358) yields:
% 120.59/94.93  																																			| (359)  ~ (all_35_1_36 = 0)
% 120.59/94.93  																																			| (360) unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36
% 120.59/94.93  																																			|
% 120.59/94.93  																																			+-Applying beta-rule and splitting (99), into two cases.
% 120.59/94.93  																																			|-Branch one:
% 120.59/94.93  																																			| (361) (all_36_0_37 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_36_0_37 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = all_36_0_37)
% 120.59/94.93  																																			|
% 120.59/94.93  																																				+-Applying beta-rule and splitting (361), into two cases.
% 120.59/94.93  																																				|-Branch one:
% 120.59/94.93  																																				| (362) all_36_0_37 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.59/94.93  																																				|
% 120.59/94.93  																																					| Applying alpha-rule on (362) yields:
% 120.59/94.93  																																					| (363) all_36_0_37 = 0
% 120.59/94.93  																																					| (322) unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.59/94.93  																																					|
% 120.59/94.93  																																					| Instantiating formula (58) with all_0_2_2, all_0_0_0, 0, all_35_1_36 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36, unorthogonal_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.59/94.93  																																					| (316) all_35_1_36 = 0
% 120.59/94.93  																																					|
% 120.59/94.93  																																					| Equations (316) can reduce 359 to:
% 120.59/94.93  																																					| (123) $false
% 120.59/94.93  																																					|
% 120.59/94.93  																																					|-The branch is then unsatisfiable
% 120.59/94.93  																																				|-Branch two:
% 120.59/94.93  																																				| (367)  ~ (all_36_0_37 = 0) & unorthogonal_lines(all_0_2_2, all_0_2_2) = all_36_0_37
% 120.59/94.93  																																				|
% 120.59/94.93  																																					| Applying alpha-rule on (367) yields:
% 120.59/94.93  																																					| (368)  ~ (all_36_0_37 = 0)
% 120.59/94.93  																																					| (369) unorthogonal_lines(all_0_2_2, all_0_2_2) = all_36_0_37
% 120.59/94.93  																																					|
% 120.59/94.93  																																					| Instantiating formula (7) with all_36_0_37, all_29_0_32, all_0_2_2, all_0_2_2, all_0_0_0, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_2_2) = all_36_0_37, apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, yields:
% 120.59/94.93  																																					| (370) all_36_0_37 = 0 | all_29_0_32 = 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_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 120.59/94.93  																																					|
% 120.59/94.93  																																					| Instantiating formula (71) with all_36_0_37, all_0_2_2, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_2_2) = all_36_0_37, yields:
% 120.59/94.93  																																					| (371) all_36_0_37 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0
% 120.59/94.93  																																					|
% 120.59/94.93  																																					+-Applying beta-rule and splitting (370), into two cases.
% 120.59/94.93  																																					|-Branch one:
% 120.59/94.93  																																					| (363) all_36_0_37 = 0
% 120.59/94.93  																																					|
% 120.59/94.93  																																						| Equations (363) can reduce 368 to:
% 120.59/94.93  																																						| (123) $false
% 120.59/94.93  																																						|
% 120.59/94.93  																																						|-The branch is then unsatisfiable
% 120.59/94.93  																																					|-Branch two:
% 120.59/94.93  																																					| (368)  ~ (all_36_0_37 = 0)
% 120.59/94.93  																																					| (375) all_29_0_32 = 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_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 120.59/94.93  																																					|
% 120.59/94.93  																																						+-Applying beta-rule and splitting (371), into two cases.
% 120.59/94.93  																																						|-Branch one:
% 120.59/94.93  																																						| (336) convergent_lines(all_0_2_2, all_0_2_2) = 0
% 120.59/94.93  																																						|
% 120.59/94.93  																																							| Instantiating formula (49) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields:
% 120.59/94.93  																																							| (258) $false
% 120.59/94.93  																																							|
% 120.59/94.93  																																							|-The branch is then unsatisfiable
% 120.59/94.93  																																						|-Branch two:
% 120.59/94.93  																																						| (378)  ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0)
% 120.59/94.93  																																						| (363) all_36_0_37 = 0
% 120.59/94.93  																																						|
% 120.59/94.93  																																							| Equations (363) can reduce 368 to:
% 120.59/94.93  																																							| (123) $false
% 120.59/94.93  																																							|
% 120.59/94.93  																																							|-The branch is then unsatisfiable
% 120.59/94.93  																																			|-Branch two:
% 120.59/94.93  																																			| (381)  ~ (all_36_0_37 = 0) & convergent_lines(all_0_2_2, all_0_2_2) = all_36_0_37
% 120.76/94.93  																																			|
% 120.76/94.93  																																				| Applying alpha-rule on (381) yields:
% 120.76/94.93  																																				| (368)  ~ (all_36_0_37 = 0)
% 120.76/94.93  																																				| (383) convergent_lines(all_0_2_2, all_0_2_2) = all_36_0_37
% 120.76/94.93  																																				|
% 120.76/94.93  																																				+-Applying beta-rule and splitting (120), into two cases.
% 120.76/94.93  																																				|-Branch one:
% 120.76/94.93  																																				| (384) (all_44_0_41 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0) | ( ~ (all_44_0_41 = 0) & unorthogonal_lines(all_0_0_0, all_0_0_0) = all_44_0_41)
% 120.76/94.93  																																				|
% 120.76/94.93  																																					+-Applying beta-rule and splitting (384), into two cases.
% 120.76/94.93  																																					|-Branch one:
% 120.76/94.93  																																					| (385) all_44_0_41 = 0 & all_31_0_33 = 0 & convergent_lines(all_0_0_0, all_0_1_1) = 0
% 120.76/94.93  																																					|
% 120.76/94.93  																																						| Applying alpha-rule on (385) yields:
% 120.76/94.93  																																						| (386) all_44_0_41 = 0
% 120.76/94.93  																																						| (150) all_31_0_33 = 0
% 120.76/94.93  																																						| (121) convergent_lines(all_0_0_0, all_0_1_1) = 0
% 120.76/94.93  																																						|
% 120.76/94.93  																																						| Equations (150) can reduce 93 to:
% 120.76/94.93  																																						| (123) $false
% 120.76/94.93  																																						|
% 120.76/94.93  																																						|-The branch is then unsatisfiable
% 120.76/94.93  																																					|-Branch two:
% 120.76/94.93  																																					| (390)  ~ (all_44_0_41 = 0) & unorthogonal_lines(all_0_0_0, all_0_0_0) = all_44_0_41
% 120.76/94.93  																																					|
% 120.76/94.93  																																						| Applying alpha-rule on (390) yields:
% 120.76/94.93  																																						| (391)  ~ (all_44_0_41 = 0)
% 120.76/94.93  																																						| (392) unorthogonal_lines(all_0_0_0, all_0_0_0) = all_44_0_41
% 120.76/94.93  																																						|
% 120.76/94.93  																																						| Instantiating formula (71) with all_44_0_41, all_0_0_0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_0_0) = all_44_0_41, yields:
% 120.76/94.93  																																						| (393) all_44_0_41 = 0 | convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.93  																																						|
% 120.77/94.93  																																						+-Applying beta-rule and splitting (393), into two cases.
% 120.77/94.93  																																						|-Branch one:
% 120.77/94.93  																																						| (318) convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.93  																																						|
% 120.77/94.93  																																							| Instantiating formula (49) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = 0, yields:
% 120.77/94.93  																																							| (258) $false
% 120.77/94.93  																																							|
% 120.77/94.93  																																							|-The branch is then unsatisfiable
% 120.77/94.93  																																						|-Branch two:
% 120.77/94.93  																																						| (396)  ~ (convergent_lines(all_0_0_0, all_0_0_0) = 0)
% 120.77/94.93  																																						| (386) all_44_0_41 = 0
% 120.77/94.93  																																						|
% 120.77/94.93  																																							| Equations (386) can reduce 391 to:
% 120.77/94.93  																																							| (123) $false
% 120.77/94.93  																																							|
% 120.77/94.93  																																							|-The branch is then unsatisfiable
% 120.77/94.93  																																				|-Branch two:
% 120.77/94.93  																																				| (399)  ~ (all_44_0_41 = 0) & convergent_lines(all_0_0_0, all_0_0_0) = all_44_0_41
% 120.77/94.93  																																				|
% 120.77/94.93  																																					| Applying alpha-rule on (399) yields:
% 120.77/94.93  																																					| (391)  ~ (all_44_0_41 = 0)
% 120.77/94.93  																																					| (401) convergent_lines(all_0_0_0, all_0_0_0) = all_44_0_41
% 120.77/94.93  																																					|
% 120.77/94.93  																																					| Instantiating formula (34) with all_0_0_0, all_0_0_0, all_44_0_41, all_219_0_123 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = all_219_0_123, convergent_lines(all_0_0_0, all_0_0_0) = all_44_0_41, yields:
% 120.77/94.93  																																					| (402) all_219_0_123 = all_44_0_41
% 120.77/94.93  																																					|
% 120.77/94.93  																																					| Equations (402) can reduce 307 to:
% 120.77/94.93  																																					| (391)  ~ (all_44_0_41 = 0)
% 120.77/94.93  																																					|
% 120.77/94.93  																																					| From (402) and (308) follows:
% 120.77/94.93  																																					| (401) convergent_lines(all_0_0_0, all_0_0_0) = all_44_0_41
% 120.77/94.93  																																					|
% 120.77/94.93  																																					| Instantiating formula (27) with 0, all_0_0_0, all_0_2_2, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_2_2) = 0, convergent_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.77/94.93  																																					| (405)  ? [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) & convergent_lines(all_0_0_0, all_0_2_2) = v0))
% 120.77/94.93  																																					|
% 120.77/94.94  																																					| Instantiating formula (7) with all_35_1_36, all_29_0_32, all_0_0_0, all_0_2_2, all_0_0_0, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36, apart_point_and_line(all_0_3_3, all_0_0_0) = all_29_0_32, yields:
% 120.77/94.94  																																					| (406) all_35_1_36 = 0 | all_29_0_32 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, 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))
% 120.77/94.94  																																					|
% 120.77/94.94  																																					| Instantiating formula (24) with all_35_1_36, all_0_0_0, all_0_2_2, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_2_2) = 0, unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36, yields:
% 120.77/94.94  																																					| (407)  ? [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 & all_35_1_36 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = v0))
% 120.77/94.94  																																					|
% 120.77/94.94  																																					| Instantiating formula (57) with all_44_0_41, all_0_0_0, all_0_2_2, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_2_2) = 0, convergent_lines(all_0_0_0, all_0_0_0) = all_44_0_41, yields:
% 120.77/94.94  																																					| (408)  ? [v0] :  ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | (v0 = 0 & all_44_0_41 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = v0))
% 120.77/94.94  																																					|
% 120.77/94.94  																																					| Instantiating formula (69) with all_36_0_37, 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_36_0_37, yields:
% 120.77/94.94  																																					| (409) all_36_0_37 = 0 | convergent_lines(all_0_0_0, all_0_2_2) = 0
% 120.77/94.94  																																					|
% 120.77/94.94  																																					| Instantiating (405) with all_304_0_784, all_304_1_785 yields:
% 120.77/94.94  																																					| (410) (all_304_0_784 = 0 & all_304_1_785 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_304_1_785 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_304_1_785 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = all_304_1_785)
% 120.77/94.94  																																					|
% 120.77/94.94  																																					| Instantiating (408) with all_348_0_849, all_348_1_850 yields:
% 120.77/94.94  																																					| (411) (all_348_0_849 = 0 & all_348_1_850 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | (all_348_1_850 = 0 & all_44_0_41 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (all_348_1_850 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = all_348_1_850)
% 120.77/94.94  																																					|
% 120.77/94.94  																																					| Instantiating (407) with all_358_0_863, all_358_1_864 yields:
% 120.77/94.94  																																					| (412) (all_358_0_863 = 0 & all_358_1_864 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_358_1_864 = 0 & all_35_1_36 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | ( ~ (all_358_1_864 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = all_358_1_864)
% 120.77/94.94  																																					|
% 120.77/94.94  																																					+-Applying beta-rule and splitting (409), into two cases.
% 120.77/94.94  																																					|-Branch one:
% 120.77/94.94  																																					| (413) convergent_lines(all_0_0_0, all_0_2_2) = 0
% 120.77/94.94  																																					|
% 120.77/94.94  																																						+-Applying beta-rule and splitting (406), into two cases.
% 120.77/94.94  																																						|-Branch one:
% 120.77/94.94  																																						| (316) all_35_1_36 = 0
% 120.77/94.94  																																						|
% 120.77/94.94  																																							| Equations (316) can reduce 359 to:
% 120.77/94.94  																																							| (123) $false
% 120.77/94.94  																																							|
% 120.77/94.94  																																							|-The branch is then unsatisfiable
% 120.77/94.94  																																						|-Branch two:
% 120.77/94.94  																																						| (359)  ~ (all_35_1_36 = 0)
% 120.77/94.94  																																						| (417) all_29_0_32 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, 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))
% 120.77/94.94  																																						|
% 120.77/94.94  																																							+-Applying beta-rule and splitting (411), into two cases.
% 120.77/94.94  																																							|-Branch one:
% 120.77/94.94  																																							| (418) (all_348_0_849 = 0 & all_348_1_850 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0) | (all_348_1_850 = 0 & all_44_0_41 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0)
% 120.77/94.94  																																							|
% 120.77/94.94  																																								+-Applying beta-rule and splitting (418), into two cases.
% 120.77/94.94  																																								|-Branch one:
% 120.77/94.94  																																								| (419) all_348_0_849 = 0 & all_348_1_850 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																								|
% 120.77/94.94  																																									| Applying alpha-rule on (419) yields:
% 120.77/94.94  																																									| (420) all_348_0_849 = 0
% 120.77/94.94  																																									| (421) all_348_1_850 = 0
% 120.77/94.94  																																									| (322) unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																									| (52) convergent_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																									|
% 120.77/94.94  																																									| Instantiating formula (58) with all_0_2_2, all_0_0_0, 0, all_35_1_36 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36, unorthogonal_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.77/94.94  																																									| (316) all_35_1_36 = 0
% 120.77/94.94  																																									|
% 120.77/94.94  																																									| Equations (316) can reduce 359 to:
% 120.77/94.94  																																									| (123) $false
% 120.77/94.94  																																									|
% 120.77/94.94  																																									|-The branch is then unsatisfiable
% 120.77/94.94  																																								|-Branch two:
% 120.77/94.94  																																								| (426) all_348_1_850 = 0 & all_44_0_41 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																								|
% 120.77/94.94  																																									| Applying alpha-rule on (426) yields:
% 120.77/94.94  																																									| (421) all_348_1_850 = 0
% 120.77/94.94  																																									| (386) all_44_0_41 = 0
% 120.77/94.94  																																									| (317) unorthogonal_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																									|
% 120.77/94.94  																																									| Equations (386) can reduce 391 to:
% 120.77/94.94  																																									| (123) $false
% 120.77/94.94  																																									|
% 120.77/94.94  																																									|-The branch is then unsatisfiable
% 120.77/94.94  																																							|-Branch two:
% 120.77/94.94  																																							| (431)  ~ (all_348_1_850 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = all_348_1_850
% 120.77/94.94  																																							|
% 120.77/94.94  																																								| Applying alpha-rule on (431) yields:
% 120.77/94.94  																																								| (432)  ~ (all_348_1_850 = 0)
% 120.77/94.94  																																								| (433) convergent_lines(all_0_0_0, all_0_2_2) = all_348_1_850
% 120.77/94.94  																																								|
% 120.77/94.94  																																								+-Applying beta-rule and splitting (412), into two cases.
% 120.77/94.94  																																								|-Branch one:
% 120.77/94.94  																																								| (434) (all_358_0_863 = 0 & all_358_1_864 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_358_1_864 = 0 & all_35_1_36 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0)
% 120.77/94.94  																																								|
% 120.77/94.94  																																									+-Applying beta-rule and splitting (434), into two cases.
% 120.77/94.94  																																									|-Branch one:
% 120.77/94.94  																																									| (435) all_358_0_863 = 0 & all_358_1_864 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																									|
% 120.77/94.94  																																										| Applying alpha-rule on (435) yields:
% 120.77/94.94  																																										| (436) all_358_0_863 = 0
% 120.77/94.94  																																										| (437) all_358_1_864 = 0
% 120.77/94.94  																																										| (317) unorthogonal_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																										| (318) convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Instantiating formula (49) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = 0, yields:
% 120.77/94.94  																																										| (258) $false
% 120.77/94.94  																																										|
% 120.77/94.94  																																										|-The branch is then unsatisfiable
% 120.77/94.94  																																									|-Branch two:
% 120.77/94.94  																																									| (441) all_358_1_864 = 0 & all_35_1_36 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																									|
% 120.77/94.94  																																										| Applying alpha-rule on (441) yields:
% 120.77/94.94  																																										| (437) all_358_1_864 = 0
% 120.77/94.94  																																										| (316) all_35_1_36 = 0
% 120.77/94.94  																																										| (52) convergent_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Equations (316) can reduce 359 to:
% 120.77/94.94  																																										| (123) $false
% 120.77/94.94  																																										|
% 120.77/94.94  																																										|-The branch is then unsatisfiable
% 120.77/94.94  																																								|-Branch two:
% 120.77/94.94  																																								| (446)  ~ (all_358_1_864 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = all_358_1_864
% 120.77/94.94  																																								|
% 120.77/94.94  																																									| Applying alpha-rule on (446) yields:
% 120.77/94.94  																																									| (447)  ~ (all_358_1_864 = 0)
% 120.77/94.94  																																									| (448) convergent_lines(all_0_0_0, all_0_2_2) = all_358_1_864
% 120.77/94.94  																																									|
% 120.77/94.94  																																									+-Applying beta-rule and splitting (410), into two cases.
% 120.77/94.94  																																									|-Branch one:
% 120.77/94.94  																																									| (449) (all_304_0_784 = 0 & all_304_1_785 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | (all_304_1_785 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0)
% 120.77/94.94  																																									|
% 120.77/94.94  																																										+-Applying beta-rule and splitting (449), into two cases.
% 120.77/94.94  																																										|-Branch one:
% 120.77/94.94  																																										| (450) all_304_0_784 = 0 & all_304_1_785 = 0 & unorthogonal_lines(all_0_0_0, all_0_0_0) = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																											| Applying alpha-rule on (450) yields:
% 120.77/94.94  																																											| (451) all_304_0_784 = 0
% 120.77/94.94  																																											| (452) all_304_1_785 = 0
% 120.77/94.94  																																											| (317) unorthogonal_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																											| (318) convergent_lines(all_0_0_0, all_0_0_0) = 0
% 120.77/94.94  																																											|
% 120.77/94.94  																																											| Instantiating formula (49) with all_0_0_0 and discharging atoms convergent_lines(all_0_0_0, all_0_0_0) = 0, yields:
% 120.77/94.94  																																											| (258) $false
% 120.77/94.94  																																											|
% 120.77/94.94  																																											|-The branch is then unsatisfiable
% 120.77/94.94  																																										|-Branch two:
% 120.77/94.94  																																										| (456) all_304_1_785 = 0 & unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																											| Applying alpha-rule on (456) yields:
% 120.77/94.94  																																											| (452) all_304_1_785 = 0
% 120.77/94.94  																																											| (322) unorthogonal_lines(all_0_2_2, all_0_0_0) = 0
% 120.77/94.94  																																											|
% 120.77/94.94  																																											| Instantiating formula (58) with all_0_2_2, all_0_0_0, 0, all_35_1_36 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_0_0) = all_35_1_36, unorthogonal_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 120.77/94.94  																																											| (316) all_35_1_36 = 0
% 120.77/94.94  																																											|
% 120.77/94.94  																																											| Equations (316) can reduce 359 to:
% 120.77/94.94  																																											| (123) $false
% 120.77/94.94  																																											|
% 120.77/94.94  																																											|-The branch is then unsatisfiable
% 120.77/94.94  																																									|-Branch two:
% 120.77/94.94  																																									| (461)  ~ (all_304_1_785 = 0) & convergent_lines(all_0_0_0, all_0_2_2) = all_304_1_785
% 120.77/94.94  																																									|
% 120.77/94.94  																																										| Applying alpha-rule on (461) yields:
% 120.77/94.94  																																										| (462)  ~ (all_304_1_785 = 0)
% 120.77/94.94  																																										| (463) convergent_lines(all_0_0_0, all_0_2_2) = all_304_1_785
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Instantiating formula (34) with all_0_0_0, all_0_2_2, all_348_1_850, all_358_1_864 and discharging atoms convergent_lines(all_0_0_0, all_0_2_2) = all_358_1_864, convergent_lines(all_0_0_0, all_0_2_2) = all_348_1_850, yields:
% 120.77/94.94  																																										| (464) all_358_1_864 = all_348_1_850
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Instantiating formula (34) with all_0_0_0, all_0_2_2, all_304_1_785, all_358_1_864 and discharging atoms convergent_lines(all_0_0_0, all_0_2_2) = all_358_1_864, convergent_lines(all_0_0_0, all_0_2_2) = all_304_1_785, yields:
% 120.77/94.94  																																										| (465) all_358_1_864 = all_304_1_785
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Instantiating formula (34) with all_0_0_0, all_0_2_2, 0, all_358_1_864 and discharging atoms convergent_lines(all_0_0_0, all_0_2_2) = all_358_1_864, convergent_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 120.77/94.94  																																										| (437) all_358_1_864 = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Combining equations (437,464) yields a new equation:
% 120.77/94.94  																																										| (421) all_348_1_850 = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Combining equations (465,464) yields a new equation:
% 120.77/94.94  																																										| (468) all_348_1_850 = all_304_1_785
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Combining equations (421,468) yields a new equation:
% 120.77/94.94  																																										| (452) all_304_1_785 = 0
% 120.77/94.94  																																										|
% 120.77/94.94  																																										| Equations (452) can reduce 462 to:
% 120.77/94.94  																																										| (123) $false
% 120.77/94.94  																																										|
% 120.77/94.94  																																										|-The branch is then unsatisfiable
% 120.77/94.94  																																					|-Branch two:
% 120.77/94.94  																																					| (471)  ~ (convergent_lines(all_0_0_0, all_0_2_2) = 0)
% 120.77/94.94  																																					| (363) all_36_0_37 = 0
% 120.77/94.94  																																					|
% 120.77/94.94  																																						| Equations (363) can reduce 368 to:
% 120.77/94.94  																																						| (123) $false
% 120.77/94.94  																																						|
% 120.77/94.94  																																						|-The branch is then unsatisfiable
% 120.77/94.94  																															|-Branch two:
% 120.77/94.94  																															| (474) all_113_0_48 = 0 & apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 120.77/94.94  																															|
% 120.77/94.94  																																| Applying alpha-rule on (474) yields:
% 120.77/94.94  																																| (286) all_113_0_48 = 0
% 120.77/94.94  																																| (476) apart_point_and_line(all_0_3_3, all_0_1_1) = 0
% 120.77/94.94  																																|
% 120.77/94.94  																																| Instantiating formula (32) with all_0_3_3, all_0_1_1, 0, all_27_0_31 and discharging atoms apart_point_and_line(all_0_3_3, all_0_1_1) = all_27_0_31, apart_point_and_line(all_0_3_3, all_0_1_1) = 0, yields:
% 120.77/94.94  																																| (122) all_27_0_31 = 0
% 120.77/94.94  																																|
% 120.77/94.94  																																| Equations (122) can reduce 87 to:
% 120.77/94.94  																																| (123) $false
% 120.77/94.94  																																|
% 120.77/94.94  																																|-The branch is then unsatisfiable
% 120.77/94.94  																														|-Branch two:
% 120.77/94.94  																														| (479)  ~ (all_113_0_48 = 0) & distinct_lines(all_0_0_0, all_0_1_1) = all_113_0_48
% 120.77/94.94  																														|
% 120.77/94.94  																															| Applying alpha-rule on (479) yields:
% 120.77/94.94  																															| (480)  ~ (all_113_0_48 = 0)
% 120.77/94.94  																															| (481) distinct_lines(all_0_0_0, all_0_1_1) = all_113_0_48
% 120.77/94.94  																															|
% 120.77/94.94  																															| Instantiating formula (20) with all_0_0_0, all_0_1_1, 0, all_113_0_48 and discharging atoms distinct_lines(all_0_0_0, all_0_1_1) = all_113_0_48, distinct_lines(all_0_0_0, all_0_1_1) = 0, yields:
% 120.77/94.94  																															| (286) all_113_0_48 = 0
% 120.77/94.94  																															|
% 120.77/94.94  																															| Equations (286) can reduce 480 to:
% 120.77/94.94  																															| (123) $false
% 120.77/94.94  																															|
% 120.77/94.94  																															|-The branch is then unsatisfiable
% 120.77/94.94  |-Branch two:
% 120.77/94.94  | (484)  ~ (convergent_lines(all_0_0_0, all_0_1_1) = 0)
% 120.77/94.94  | (150) all_31_0_33 = 0
% 120.77/94.94  |
% 120.77/94.94  	| Equations (150) can reduce 93 to:
% 120.77/94.94  	| (123) $false
% 120.77/94.94  	|
% 120.77/94.94  	|-The branch is then unsatisfiable
% 120.77/94.94  % SZS output end Proof for theBenchmark
% 120.77/94.94  
% 120.77/94.94  94355ms
%------------------------------------------------------------------------------