%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO205+3 : TPTP v8.1.0. Released v4.0.0.
% 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 03:48:41 EDT 2022

% Result   : Theorem 20.85s 6.23s
% Output   : Proof 27.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO205+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n013.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jun 17 23:53:14 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.53/0.58          ____       _                          
% 0.53/0.58    ___  / __ \_____(_)___  ________  __________
% 0.53/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.53/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.53/0.59  
% 0.53/0.59  A Theorem Prover for First-Order Logic
% 0.53/0.59  (ePrincess v.1.0)
% 0.53/0.59  
% 0.53/0.59  (c) Philipp Rümmer, 2009-2015
% 0.53/0.59  (c) Peter Backeman, 2014-2015
% 0.53/0.59  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59  Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59  Bug reports to peter@backeman.se
% 0.53/0.59  
% 0.53/0.59  For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59  
% 0.53/0.59  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.75/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.88/0.94  Prover 0: Preprocessing ...
% 2.45/1.15  Prover 0: Warning: ignoring some quantifiers
% 2.45/1.18  Prover 0: Constructing countermodel ...
% 17.83/5.58  Prover 0: gave up
% 17.83/5.58  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.83/5.61  Prover 1: Preprocessing ...
% 18.47/5.74  Prover 1: Constructing countermodel ...
% 18.73/5.80  Prover 1: gave up
% 18.73/5.80  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 18.73/5.84  Prover 2: Preprocessing ...
% 19.90/6.00  Prover 2: Warning: ignoring some quantifiers
% 19.90/6.01  Prover 2: Constructing countermodel ...
% 20.85/6.23  Prover 2: proved (428ms)
% 20.85/6.23  
% 20.85/6.23  No countermodel exists, formula is valid
% 20.85/6.23  % SZS status Theorem for theBenchmark
% 20.85/6.23  
% 20.85/6.23  Generating proof ... Warning: ignoring some quantifiers
% 26.31/7.51  found it (size 297)
% 26.31/7.51  
% 26.31/7.51  % SZS output start Proof for theBenchmark
% 26.31/7.51  Assumed formulas after preprocessing and simplification: 
% 26.31/7.51  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] : (equal_lines(v1, v2) = 0 & convergent_lines(v0, v1) = 0 &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v9, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v8) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v9, v10) = v12) |  ~ (apart_point_and_line(v7, v8) = v11) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (unorthogonal_lines(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v8) = v11) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v13] : ((v13 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (apart_point_and_line(v8, v9) = v11) |  ~ (distinct_points(v7, v8) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v7, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v10) = v11) |  ~ (distinct_lines(v9, v10) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v9) = v12) |  ~ (apart_point_and_line(v7, v10) = v11) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v9) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_lines(v9, v10) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v7, v10) = 0) | ( ~ (v13 = 0) & distinct_points(v7, v8) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v7, v10) = v12) |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_points(v7, v8) = 0) |  ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | (v13 = 0 & apart_point_and_line(v8, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (unorthogonal_lines(v7, v8) = v10) |  ? [v12] : ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v9, v8) = v11) |  ~ (distinct_points(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (distinct_lines(v8, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & apart_point_and_line(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = v11) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v10) |  ~ (convergent_lines(v8, v9) = v11) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (convergent_lines(v8, v9) = v11) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (convergent_lines(v7, v9) = v11) |  ~ (distinct_lines(v8, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (distinct_lines(v8, v9) = v11) |  ~ (distinct_lines(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (distinct_points(v8, v9) = v11) |  ~ (distinct_points(v7, v9) = v10) |  ? [v12] : ( ~ (v12 = 0) & distinct_points(v7, v8) = v12)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) |  ~ (unorthogonal_lines(v7, v9) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (unorthogonal_lines(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & convergent_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = v11) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v7, v9) = v11) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (convergent_lines(v8, v9) = v11) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v7, v8) = v12) | ( ~ (v12 = 0) & convergent_lines(v7, v8) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (convergent_lines(v7, v9) = v11) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = 0) | unorthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v8, v9) = 0) | unorthogonal_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v9, v8) = v10) |  ~ (apart_point_and_line(v7, v8) = 0) | distinct_points(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v10) |  ~ (apart_point_and_line(v7, v8) = 0) | distinct_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v7, v8) = 0) | (v11 = 0 & convergent_lines(v8, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v7, v9) = 0) | (v11 = 0 & convergent_lines(v8, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v8) = 0) |  ~ (distinct_lines(v8, v9) = v10) | apart_point_and_line(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (apart_point_and_line(v7, v8) = 0) |  ~ (distinct_points(v7, v9) = v10) | apart_point_and_line(v9, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v8, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) | convergent_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (convergent_lines(v7, v8) = 0) |  ~ (distinct_lines(v8, v9) = v10) | convergent_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_lines(v8, v9) = v10) |  ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_lines(v7, v9) = v10) |  ~ (distinct_lines(v7, v8) = 0) | distinct_lines(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_points(v8, v9) = v10) |  ~ (distinct_points(v7, v8) = 0) | distinct_points(v7, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 |  ~ (distinct_points(v7, v9) = v10) |  ~ (distinct_points(v7, v8) = 0) | distinct_points(v8, v9) = 0) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (orthogonal_lines(v10, v9) = v8) |  ~ (orthogonal_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (incident_point_and_line(v10, v9) = v8) |  ~ (incident_point_and_line(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (parallel_lines(v10, v9) = v8) |  ~ (parallel_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (equal_lines(v10, v9) = v8) |  ~ (equal_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (equal_points(v10, v9) = v8) |  ~ (equal_points(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (orthogonal_through_point(v10, v9) = v8) |  ~ (orthogonal_through_point(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (unorthogonal_lines(v10, v9) = v8) |  ~ (unorthogonal_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (parallel_through_point(v10, v9) = v8) |  ~ (parallel_through_point(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (intersection_point(v10, v9) = v8) |  ~ (intersection_point(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (line_connecting(v10, v9) = v8) |  ~ (line_connecting(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (apart_point_and_line(v10, v9) = v8) |  ~ (apart_point_and_line(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (convergent_lines(v10, v9) = v8) |  ~ (convergent_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (distinct_lines(v10, v9) = v8) |  ~ (distinct_lines(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v8 = v7 |  ~ (distinct_points(v10, v9) = v8) |  ~ (distinct_points(v10, v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = v10) |  ~ (unorthogonal_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (unorthogonal_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (unorthogonal_lines(v7, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (unorthogonal_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v8, v9) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v8, v9) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = 0) |  ~ (convergent_lines(v8, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = 0) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v8, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v9) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v8, v9) = 0) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v7, v9) = 0 & convergent_lines(v7, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v8, v9) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v7, v9) = v10) |  ~ (convergent_lines(v7, v8) = 0) |  ? [v11] :  ? [v12] : ((v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v9) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11))) &  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (distinct_lines(v9, v10) = 0) |  ~ (distinct_points(v7, v8) = 0) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v8, v10) = 0) | (v11 = 0 & apart_point_and_line(v8, v9) = 0) | (v11 = 0 & apart_point_and_line(v7, v10) = 0) | (v11 = 0 & apart_point_and_line(v7, v9) = 0))) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (orthogonal_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (incident_point_and_line(v7, v8) = v9) | apart_point_and_line(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (parallel_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equal_lines(v7, v8) = v9) | distinct_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (equal_points(v7, v8) = v9) | distinct_points(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (unorthogonal_lines(v7, v8) = v9) | orthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (unorthogonal_lines(v7, v8) = v9) | convergent_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v7, v8) = v9) | incident_point_and_line(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) | parallel_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) | unorthogonal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) |  ? [v10] : ( ~ (v10 = 0) & distinct_lines(v7, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v7, v8) = v9) | equal_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v7, v8) = v9) | equal_points(v7, v8) = 0) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (point(v9) = v8) |  ~ (point(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : (v8 = v7 |  ~ (line(v9) = v8) |  ~ (line(v9) = v7)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & unorthogonal_lines(v9, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (orthogonal_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (orthogonal_through_point(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (parallel_through_point(v8, v7) = v9) |  ? [v10] : ( ~ (v10 = 0) & convergent_lines(v9, v8) = v10)) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (parallel_through_point(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection_point(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & point(v9) = 0) | ( ~ (v10 = 0) & line(v8) = v10) | ( ~ (v10 = 0) & line(v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection_point(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v8) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (intersection_point(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v9, v7) = v10) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v7, v8) = v9) |  ? [v10] : ((v10 = 0 & line(v9) = 0) | ( ~ (v10 = 0) & point(v8) = v10) | ( ~ (v10 = 0) & point(v7) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v8, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) &  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (line_connecting(v7, v8) = v9) |  ? [v10] : (( ~ (v10 = 0) & apart_point_and_line(v7, v9) = v10) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) &  ! [v7] :  ! [v8] : ( ~ (orthogonal_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (incident_point_and_line(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (parallel_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (equal_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & distinct_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (equal_points(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & distinct_points(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (unorthogonal_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & orthogonal_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (apart_point_and_line(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & incident_point_and_line(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v8) = v10)) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & intersection_point(v7, v8) = v9 & apart_point_and_line(v9, v7) = v10)) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & point(v9) = 0 & intersection_point(v7, v8) = v9) | ( ~ (v9 = 0) & line(v8) = v9) | ( ~ (v9 = 0) & line(v7) = v9))) &  ! [v7] :  ! [v8] : ( ~ (convergent_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & parallel_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | convergent_lines(v7, v8) = 0) &  ! [v7] :  ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & equal_lines(v7, v8) = v9)) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v8, v9) = v10)) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] :  ? [v10] : ( ~ (v10 = 0) & line_connecting(v7, v8) = v9 & apart_point_and_line(v7, v9) = v10)) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] :  ? [v10] : ((v10 = 0 & line(v9) = 0 & line_connecting(v7, v8) = v9) | ( ~ (v9 = 0) & point(v8) = v9) | ( ~ (v9 = 0) & point(v7) = v9))) &  ! [v7] :  ! [v8] : ( ~ (distinct_points(v7, v8) = 0) |  ? [v9] : ( ~ (v9 = 0) & equal_points(v7, v8) = v9)) &  ! [v7] :  ~ (convergent_lines(v7, v7) = 0) &  ! [v7] :  ~ (distinct_lines(v7, v7) = 0) &  ! [v7] :  ~ (distinct_points(v7, v7) = 0) &  ? [v7] :  ? [v8] :  ? [v9] : orthogonal_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : incident_point_and_line(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : parallel_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : equal_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : equal_points(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : orthogonal_through_point(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : unorthogonal_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : parallel_through_point(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : intersection_point(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : line_connecting(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : apart_point_and_line(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : convergent_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : distinct_lines(v8, v7) = v9 &  ? [v7] :  ? [v8] :  ? [v9] : distinct_points(v8, v7) = v9 &  ? [v7] :  ? [v8] : point(v7) = v8 &  ? [v7] :  ? [v8] : line(v7) = v8 & (( ~ (v6 = 0) & equal_points(v4, v5) = v6 & intersection_point(v0, v2) = v5 & intersection_point(v0, v1) = v4) | ( ~ (v3 = 0) & convergent_lines(v0, v2) = v3)))
% 26.73/7.58  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 26.73/7.58  | (1) equal_lines(all_0_5_5, all_0_4_4) = 0 & convergent_lines(all_0_6_6, all_0_5_5) = 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 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = 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] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v0, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = 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] :  ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0)) &  ! [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(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = 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(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = 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) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = 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 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0)) &  ! [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] : ( ~ (orthogonal_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2 &  ? [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 &  ? [v0] :  ? [v1] : point(v0) = v1 &  ? [v0] :  ? [v1] : line(v0) = v1 & (( ~ (all_0_0_0 = 0) & equal_points(all_0_2_2, all_0_1_1) = all_0_0_0 & intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1 & intersection_point(all_0_6_6, all_0_5_5) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_0_3_3))
% 26.95/7.62  |
% 26.95/7.62  | Applying alpha-rule on (1) yields:
% 26.95/7.62  | (2)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 26.95/7.62  | (3) convergent_lines(all_0_6_6, all_0_5_5) = 0
% 26.95/7.62  | (4)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 26.95/7.62  | (5)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 26.95/7.62  | (6)  ! [v0] :  ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 26.95/7.62  | (7)  ! [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)
% 26.95/7.62  | (8)  ! [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)
% 26.95/7.62  | (9)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 26.95/7.62  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 26.95/7.62  | (11)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 26.95/7.62  | (12)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 26.95/7.62  | (13)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 26.95/7.62  | (14)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 26.95/7.62  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 26.95/7.62  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_lines(v3, v2) = v1) |  ~ (parallel_lines(v3, v2) = v0))
% 26.95/7.62  | (17)  ! [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)))
% 26.95/7.62  | (18)  ! [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)))
% 26.95/7.62  | (19)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 26.95/7.62  | (20)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 26.95/7.62  | (21)  ! [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)))
% 26.95/7.62  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_lines(v3, v2) = v1) |  ~ (equal_lines(v3, v2) = v0))
% 26.95/7.62  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 26.95/7.62  | (24)  ! [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)))
% 26.95/7.62  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 26.95/7.62  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (incident_point_and_line(v3, v2) = v1) |  ~ (incident_point_and_line(v3, v2) = v0))
% 26.95/7.62  | (27)  ! [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)))
% 26.95/7.62  | (28)  ! [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)))
% 26.95/7.62  | (29)  ! [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)))
% 26.95/7.62  | (30)  ! [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)))
% 26.95/7.62  | (31)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 26.95/7.62  | (32)  ! [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)))
% 26.95/7.62  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 26.95/7.63  | (34)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 26.95/7.63  | (35)  ! [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)))
% 26.95/7.63  | (36)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 26.95/7.63  | (37)  ! [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)))
% 26.95/7.63  | (38) ( ~ (all_0_0_0 = 0) & equal_points(all_0_2_2, all_0_1_1) = all_0_0_0 & intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1 & intersection_point(all_0_6_6, all_0_5_5) = all_0_2_2) | ( ~ (all_0_3_3 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_0_3_3)
% 26.95/7.63  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 26.95/7.63  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 26.95/7.63  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (equal_points(v3, v2) = v1) |  ~ (equal_points(v3, v2) = v0))
% 26.95/7.63  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 26.95/7.63  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 26.95/7.63  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 26.95/7.63  | (45)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 26.95/7.63  | (46)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 26.95/7.63  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 26.95/7.63  | (48)  ! [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))
% 26.95/7.63  | (49)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 26.95/7.63  | (50)  ? [v0] :  ? [v1] :  ? [v2] : incident_point_and_line(v1, v0) = v2
% 26.95/7.63  | (51)  ! [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)))
% 26.95/7.63  | (52)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 26.95/7.63  | (53)  ! [v0] :  ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 26.95/7.63  | (54)  ! [v0] :  ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 26.95/7.63  | (55)  ! [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)))
% 26.95/7.63  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 26.95/7.63  | (57)  ! [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)))
% 26.95/7.63  | (58)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 26.95/7.63  | (59)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_lines(v1, v0) = v2
% 26.95/7.63  | (60)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 26.95/7.63  | (61)  ! [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)))
% 26.95/7.63  | (62)  ! [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)))
% 26.95/7.63  | (63)  ! [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)))
% 26.95/7.63  | (64)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 26.95/7.63  | (65)  ! [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)
% 26.95/7.63  | (66)  ! [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)))
% 26.95/7.63  | (67)  ! [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)))
% 26.95/7.64  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_lines(v3, v2) = v1) |  ~ (orthogonal_lines(v3, v2) = v0))
% 26.95/7.64  | (69)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 26.95/7.64  | (70)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 26.95/7.64  | (71)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 26.95/7.64  | (72)  ! [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))
% 26.95/7.64  | (73)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 26.95/7.64  | (74)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 26.95/7.64  | (75)  ! [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))
% 26.95/7.64  | (76)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 26.95/7.64  | (77)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (line(v2) = v1) |  ~ (line(v2) = v0))
% 26.95/7.64  | (78)  ! [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)))
% 26.95/7.64  | (79)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 26.95/7.64  | (80)  ! [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))
% 26.95/7.64  | (81)  ? [v0] :  ? [v1] :  ? [v2] : parallel_lines(v1, v0) = v2
% 26.95/7.64  | (82)  ? [v0] :  ? [v1] : point(v0) = v1
% 26.95/7.64  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 26.95/7.64  | (84)  ? [v0] :  ? [v1] :  ? [v2] : equal_lines(v1, v0) = v2
% 26.95/7.64  | (85)  ! [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))
% 26.95/7.64  | (86)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 26.95/7.64  | (87)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 26.95/7.64  | (88)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 26.95/7.64  | (89)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) |  ~ (unorthogonal_lines(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 27.07/7.64  | (90)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 27.07/7.64  | (91)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 27.07/7.64  | (92)  ? [v0] :  ? [v1] :  ? [v2] : equal_points(v1, v0) = v2
% 27.07/7.64  | (93)  ! [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)
% 27.07/7.64  | (94)  ! [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)))
% 27.07/7.64  | (95)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 27.07/7.64  | (96)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 27.07/7.64  | (97)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 27.07/7.64  | (98)  ! [v0] :  ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 27.07/7.64  | (99)  ! [v0] :  ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 27.07/7.64  | (100)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (point(v2) = v1) |  ~ (point(v2) = v0))
% 27.07/7.64  | (101)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 27.07/7.64  | (102)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v1) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 27.07/7.64  | (103)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 27.07/7.64  | (104) equal_lines(all_0_5_5, all_0_4_4) = 0
% 27.07/7.64  | (105)  ! [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)))
% 27.07/7.64  | (106)  ! [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)))
% 27.07/7.64  | (107)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 27.07/7.64  | (108)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 27.07/7.64  | (109)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 27.07/7.64  | (110)  ! [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)))
% 27.07/7.64  | (111)  ! [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)))
% 27.07/7.65  | (112)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 27.07/7.65  | (113)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 27.07/7.65  | (114)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 27.07/7.65  | (115)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 27.07/7.65  | (116)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 27.07/7.65  | (117)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 27.07/7.65  | (118)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 27.07/7.65  | (119)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 27.07/7.65  | (120)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 27.07/7.65  | (121)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 27.07/7.65  | (122)  ! [v0] :  ! [v1] : ( ~ (equal_points(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 27.07/7.65  | (123)  ! [v0] :  ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 27.07/7.65  | (124)  ! [v0] :  ! [v1] : ( ~ (equal_lines(v0, v1) = 0) |  ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 27.07/7.65  | (125)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 27.07/7.65  | (126)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 27.07/7.65  | (127)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 27.07/7.65  | (128)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 27.07/7.65  | (129)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 27.07/7.65  | (130)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 27.07/7.65  | (131)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 27.07/7.65  | (132)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 27.07/7.65  | (133)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) |  ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 27.07/7.65  | (134)  ! [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)))
% 27.07/7.65  | (135)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 27.07/7.65  | (136)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 27.07/7.65  | (137)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) |  ~ (convergent_lines(v0, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 27.07/7.65  | (138)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 27.07/7.65  | (139)  ! [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)))
% 27.07/7.65  | (140)  ! [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)))
% 27.07/7.65  | (141)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 27.07/7.65  | (142)  ? [v0] :  ? [v1] : line(v0) = v1
% 27.07/7.65  |
% 27.07/7.65  | Instantiating formula (124) with all_0_4_4, all_0_5_5 and discharging atoms equal_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 27.07/7.65  | (143)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)
% 27.07/7.65  |
% 27.07/7.65  | Instantiating formula (46) with all_0_5_5, all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_5_5) = 0, yields:
% 27.07/7.65  | (144)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_6_6, all_0_5_5) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 27.07/7.65  |
% 27.07/7.65  | Instantiating formula (4) with all_0_5_5, all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_5_5) = 0, yields:
% 27.07/7.65  | (145)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_6_6, all_0_5_5) = v0 & apart_point_and_line(v0, all_0_6_6) = v1)
% 27.07/7.65  |
% 27.07/7.65  | Instantiating (145) with all_42_0_54, all_42_1_55 yields:
% 27.07/7.65  | (146)  ~ (all_42_0_54 = 0) & intersection_point(all_0_6_6, all_0_5_5) = all_42_1_55 & apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54
% 27.07/7.65  |
% 27.07/7.65  | Applying alpha-rule on (146) yields:
% 27.07/7.65  | (147)  ~ (all_42_0_54 = 0)
% 27.07/7.65  | (148) intersection_point(all_0_6_6, all_0_5_5) = all_42_1_55
% 27.07/7.65  | (149) apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54
% 27.07/7.65  |
% 27.07/7.65  | Instantiating (144) with all_44_0_56, all_44_1_57 yields:
% 27.07/7.65  | (150)  ~ (all_44_0_56 = 0) & intersection_point(all_0_6_6, all_0_5_5) = all_44_1_57 & apart_point_and_line(all_44_1_57, all_0_5_5) = all_44_0_56
% 27.07/7.65  |
% 27.07/7.65  | Applying alpha-rule on (150) yields:
% 27.07/7.65  | (151)  ~ (all_44_0_56 = 0)
% 27.07/7.65  | (152) intersection_point(all_0_6_6, all_0_5_5) = all_44_1_57
% 27.07/7.65  | (153) apart_point_and_line(all_44_1_57, all_0_5_5) = all_44_0_56
% 27.07/7.65  |
% 27.07/7.65  | Instantiating (143) with all_51_0_66 yields:
% 27.07/7.65  | (154)  ~ (all_51_0_66 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = all_51_0_66
% 27.07/7.66  |
% 27.07/7.66  | Applying alpha-rule on (154) yields:
% 27.07/7.66  | (155)  ~ (all_51_0_66 = 0)
% 27.07/7.66  | (156) distinct_lines(all_0_5_5, all_0_4_4) = all_51_0_66
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (114) with all_0_6_6, all_0_5_5, all_42_1_55, all_44_1_57 and discharging atoms intersection_point(all_0_6_6, all_0_5_5) = all_44_1_57, intersection_point(all_0_6_6, all_0_5_5) = all_42_1_55, yields:
% 27.07/7.66  | (157) all_44_1_57 = all_42_1_55
% 27.07/7.66  |
% 27.07/7.66  | From (157) and (152) follows:
% 27.07/7.66  | (148) intersection_point(all_0_6_6, all_0_5_5) = all_42_1_55
% 27.07/7.66  |
% 27.07/7.66  | From (157) and (153) follows:
% 27.07/7.66  | (159) apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (37) with all_44_0_56, all_44_0_56, all_0_5_5, all_0_5_5, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.66  | (160) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (61) with all_44_0_56, all_44_0_56, all_0_5_5, all_0_5_5, all_42_1_55, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.66  | (161) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (37) with all_42_0_54, all_44_0_56, all_0_6_6, all_0_5_5, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56, apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.66  | (162) all_44_0_56 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (37) with all_44_0_56, all_42_0_54, all_0_5_5, all_0_6_6, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56, apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.66  | (163) all_44_0_56 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (61) with all_42_0_54, all_44_0_56, all_0_6_6, all_0_5_5, all_42_1_55, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56, apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.66  | (164) all_44_0_56 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (61) with all_44_0_56, all_42_0_54, all_0_5_5, all_0_6_6, all_42_1_55, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_5_5) = all_44_0_56, apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.66  | (165) all_44_0_56 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (37) with all_42_0_54, all_42_0_54, all_0_6_6, all_0_6_6, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.66  | (166) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (61) with all_42_0_54, all_42_0_54, all_0_6_6, all_0_6_6, all_42_1_55, all_42_1_55 and discharging atoms apart_point_and_line(all_42_1_55, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.66  | (167) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (107) with all_51_0_66, all_0_4_4, all_0_5_5, all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_5_5) = 0, distinct_lines(all_0_5_5, all_0_4_4) = all_51_0_66, yields:
% 27.07/7.66  | (168) all_51_0_66 = 0 | convergent_lines(all_0_6_6, all_0_4_4) = 0
% 27.07/7.66  |
% 27.07/7.66  | Instantiating formula (72) with all_51_0_66, all_51_0_66, all_0_4_4, all_0_5_5, all_0_5_5 and discharging atoms distinct_lines(all_0_5_5, all_0_4_4) = all_51_0_66, yields:
% 27.07/7.66  | (169) all_51_0_66 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)
% 27.07/7.66  |
% 27.07/7.66  +-Applying beta-rule and splitting (38), into two cases.
% 27.07/7.66  |-Branch one:
% 27.07/7.66  | (170)  ~ (all_0_0_0 = 0) & equal_points(all_0_2_2, all_0_1_1) = all_0_0_0 & intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1 & intersection_point(all_0_6_6, all_0_5_5) = all_0_2_2
% 27.07/7.66  |
% 27.07/7.66  	| Applying alpha-rule on (170) yields:
% 27.07/7.66  	| (171)  ~ (all_0_0_0 = 0)
% 27.07/7.66  	| (172) equal_points(all_0_2_2, all_0_1_1) = all_0_0_0
% 27.07/7.66  	| (173) intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1
% 27.07/7.66  	| (174) intersection_point(all_0_6_6, all_0_5_5) = all_0_2_2
% 27.07/7.66  	|
% 27.07/7.66  	+-Applying beta-rule and splitting (168), into two cases.
% 27.07/7.66  	|-Branch one:
% 27.07/7.66  	| (175) convergent_lines(all_0_6_6, all_0_4_4) = 0
% 27.07/7.66  	|
% 27.07/7.66  		+-Applying beta-rule and splitting (160), into two cases.
% 27.07/7.66  		|-Branch one:
% 27.07/7.66  		| (176) all_44_0_56 = 0
% 27.07/7.66  		|
% 27.07/7.66  			| Equations (176) can reduce 151 to:
% 27.07/7.66  			| (177) $false
% 27.07/7.66  			|
% 27.07/7.66  			|-The branch is then unsatisfiable
% 27.07/7.66  		|-Branch two:
% 27.07/7.66  		| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.66  		| (179)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 27.07/7.66  		|
% 27.07/7.66  			+-Applying beta-rule and splitting (166), into two cases.
% 27.07/7.66  			|-Branch one:
% 27.07/7.66  			| (180) all_42_0_54 = 0
% 27.07/7.66  			|
% 27.07/7.66  				| Equations (180) can reduce 147 to:
% 27.07/7.66  				| (177) $false
% 27.07/7.66  				|
% 27.07/7.66  				|-The branch is then unsatisfiable
% 27.07/7.66  			|-Branch two:
% 27.07/7.66  			| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.66  			| (183)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.66  			|
% 27.07/7.66  				+-Applying beta-rule and splitting (163), into two cases.
% 27.07/7.66  				|-Branch one:
% 27.07/7.66  				| (176) all_44_0_56 = 0
% 27.07/7.66  				|
% 27.07/7.66  					| Equations (176) can reduce 151 to:
% 27.07/7.66  					| (177) $false
% 27.07/7.66  					|
% 27.07/7.66  					|-The branch is then unsatisfiable
% 27.07/7.66  				|-Branch two:
% 27.07/7.66  				| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.66  				| (187) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0))
% 27.07/7.66  				|
% 27.07/7.66  					+-Applying beta-rule and splitting (167), into two cases.
% 27.07/7.66  					|-Branch one:
% 27.07/7.66  					| (180) all_42_0_54 = 0
% 27.07/7.66  					|
% 27.07/7.66  						| Equations (180) can reduce 147 to:
% 27.07/7.66  						| (177) $false
% 27.07/7.66  						|
% 27.07/7.66  						|-The branch is then unsatisfiable
% 27.07/7.66  					|-Branch two:
% 27.07/7.66  					| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.66  					| (191)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.66  					|
% 27.07/7.66  						+-Applying beta-rule and splitting (162), into two cases.
% 27.07/7.66  						|-Branch one:
% 27.07/7.66  						| (176) all_44_0_56 = 0
% 27.07/7.66  						|
% 27.07/7.66  							| Equations (176) can reduce 151 to:
% 27.07/7.66  							| (177) $false
% 27.07/7.66  							|
% 27.07/7.66  							|-The branch is then unsatisfiable
% 27.07/7.66  						|-Branch two:
% 27.07/7.66  						| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.66  						| (195) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0))
% 27.07/7.66  						|
% 27.07/7.66  							+-Applying beta-rule and splitting (165), into two cases.
% 27.07/7.66  							|-Branch one:
% 27.07/7.66  							| (176) all_44_0_56 = 0
% 27.07/7.66  							|
% 27.07/7.66  								| Equations (176) can reduce 151 to:
% 27.07/7.66  								| (177) $false
% 27.07/7.66  								|
% 27.07/7.66  								|-The branch is then unsatisfiable
% 27.07/7.66  							|-Branch two:
% 27.07/7.66  							| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.66  							| (199) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.66  							|
% 27.07/7.66  								+-Applying beta-rule and splitting (164), into two cases.
% 27.07/7.66  								|-Branch one:
% 27.07/7.66  								| (176) all_44_0_56 = 0
% 27.07/7.66  								|
% 27.07/7.66  									| Equations (176) can reduce 151 to:
% 27.07/7.66  									| (177) $false
% 27.07/7.67  									|
% 27.07/7.67  									|-The branch is then unsatisfiable
% 27.07/7.67  								|-Branch two:
% 27.07/7.67  								| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.67  								| (203) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.67  								|
% 27.07/7.67  									+-Applying beta-rule and splitting (169), into two cases.
% 27.07/7.67  									|-Branch one:
% 27.07/7.67  									| (204) all_51_0_66 = 0
% 27.07/7.67  									|
% 27.07/7.67  										| Equations (204) can reduce 155 to:
% 27.07/7.67  										| (177) $false
% 27.07/7.67  										|
% 27.07/7.67  										|-The branch is then unsatisfiable
% 27.07/7.67  									|-Branch two:
% 27.07/7.67  									| (155)  ~ (all_51_0_66 = 0)
% 27.07/7.67  									| (207)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)
% 27.07/7.67  									|
% 27.07/7.67  										+-Applying beta-rule and splitting (161), into two cases.
% 27.07/7.67  										|-Branch one:
% 27.07/7.67  										| (176) all_44_0_56 = 0
% 27.07/7.67  										|
% 27.07/7.67  											| Equations (176) can reduce 151 to:
% 27.07/7.67  											| (177) $false
% 27.07/7.67  											|
% 27.07/7.67  											|-The branch is then unsatisfiable
% 27.07/7.67  										|-Branch two:
% 27.07/7.67  										| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.67  										| (211)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.67  										|
% 27.07/7.67  											+-Applying beta-rule and splitting (187), into two cases.
% 27.07/7.67  											|-Branch one:
% 27.07/7.67  											| (180) all_42_0_54 = 0
% 27.07/7.67  											|
% 27.07/7.67  												| Equations (180) can reduce 147 to:
% 27.07/7.67  												| (177) $false
% 27.07/7.67  												|
% 27.07/7.67  												|-The branch is then unsatisfiable
% 27.07/7.67  											|-Branch two:
% 27.07/7.67  											| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.67  											| (215)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0))
% 27.07/7.67  											|
% 27.07/7.67  												+-Applying beta-rule and splitting (195), into two cases.
% 27.07/7.67  												|-Branch one:
% 27.07/7.67  												| (180) all_42_0_54 = 0
% 27.07/7.67  												|
% 27.07/7.67  													| Equations (180) can reduce 147 to:
% 27.07/7.67  													| (177) $false
% 27.07/7.67  													|
% 27.07/7.67  													|-The branch is then unsatisfiable
% 27.07/7.67  												|-Branch two:
% 27.07/7.67  												| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.67  												| (219)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0))
% 27.07/7.67  												|
% 27.07/7.67  													+-Applying beta-rule and splitting (199), into two cases.
% 27.07/7.67  													|-Branch one:
% 27.07/7.67  													| (180) all_42_0_54 = 0
% 27.07/7.67  													|
% 27.07/7.67  														| Equations (180) can reduce 147 to:
% 27.07/7.67  														| (177) $false
% 27.07/7.67  														|
% 27.07/7.67  														|-The branch is then unsatisfiable
% 27.07/7.67  													|-Branch two:
% 27.07/7.67  													| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.67  													| (223)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.67  													|
% 27.07/7.67  														+-Applying beta-rule and splitting (203), into two cases.
% 27.07/7.67  														|-Branch one:
% 27.07/7.67  														| (180) all_42_0_54 = 0
% 27.07/7.67  														|
% 27.07/7.67  															| Equations (180) can reduce 147 to:
% 27.07/7.67  															| (177) $false
% 27.07/7.67  															|
% 27.07/7.67  															|-The branch is then unsatisfiable
% 27.07/7.67  														|-Branch two:
% 27.07/7.67  														| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.67  														| (227)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_42_1_55, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_42_1_55, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_42_1_55, all_42_1_55) = v0))
% 27.07/7.67  														|
% 27.07/7.67  															| Instantiating formula (114) with all_0_6_6, all_0_5_5, all_0_2_2, all_42_1_55 and discharging atoms intersection_point(all_0_6_6, all_0_5_5) = all_42_1_55, intersection_point(all_0_6_6, all_0_5_5) = all_0_2_2, yields:
% 27.07/7.67  															| (228) all_42_1_55 = all_0_2_2
% 27.07/7.67  															|
% 27.07/7.67  															| From (228) and (159) follows:
% 27.07/7.67  															| (229) apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56
% 27.07/7.67  															|
% 27.07/7.67  															| From (228) and (149) follows:
% 27.07/7.67  															| (230) apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating formula (96) with all_0_0_0, all_0_1_1, all_0_2_2 and discharging atoms equal_points(all_0_2_2, all_0_1_1) = all_0_0_0, yields:
% 27.07/7.67  															| (231) all_0_0_0 = 0 | distinct_points(all_0_2_2, all_0_1_1) = 0
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating formula (40) with all_0_1_1, all_0_4_4, all_0_6_6 and discharging atoms intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 27.07/7.67  															| (232)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = v0))
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating formula (116) with all_0_1_1, all_0_4_4, all_0_6_6 and discharging atoms intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 27.07/7.67  															| (233)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = v0))
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating formula (46) with all_0_4_4, all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 27.07/7.67  															| (234)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_6_6, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating formula (4) with all_0_4_4, all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 27.07/7.67  															| (235)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_6_6, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_6_6) = v1)
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating (235) with all_141_0_83, all_141_1_84 yields:
% 27.07/7.67  															| (236)  ~ (all_141_0_83 = 0) & intersection_point(all_0_6_6, all_0_4_4) = all_141_1_84 & apart_point_and_line(all_141_1_84, all_0_6_6) = all_141_0_83
% 27.07/7.67  															|
% 27.07/7.67  															| Applying alpha-rule on (236) yields:
% 27.07/7.67  															| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.67  															| (238) intersection_point(all_0_6_6, all_0_4_4) = all_141_1_84
% 27.07/7.67  															| (239) apart_point_and_line(all_141_1_84, all_0_6_6) = all_141_0_83
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating (234) with all_143_0_85, all_143_1_86 yields:
% 27.07/7.67  															| (240)  ~ (all_143_0_85 = 0) & intersection_point(all_0_6_6, all_0_4_4) = all_143_1_86 & apart_point_and_line(all_143_1_86, all_0_4_4) = all_143_0_85
% 27.07/7.67  															|
% 27.07/7.67  															| Applying alpha-rule on (240) yields:
% 27.07/7.67  															| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.67  															| (242) intersection_point(all_0_6_6, all_0_4_4) = all_143_1_86
% 27.07/7.67  															| (243) apart_point_and_line(all_143_1_86, all_0_4_4) = all_143_0_85
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating (233) with all_149_0_93 yields:
% 27.07/7.67  															| (244) ( ~ (all_149_0_93 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = all_149_0_93) | ( ~ (all_149_0_93 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_149_0_93)
% 27.07/7.67  															|
% 27.07/7.67  															| Instantiating (232) with all_150_0_94 yields:
% 27.07/7.67  															| (245) ( ~ (all_150_0_94 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_150_0_94) | ( ~ (all_150_0_94 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_150_0_94)
% 27.07/7.67  															|
% 27.07/7.67  															+-Applying beta-rule and splitting (231), into two cases.
% 27.07/7.67  															|-Branch one:
% 27.07/7.67  															| (246) distinct_points(all_0_2_2, all_0_1_1) = 0
% 27.07/7.67  															|
% 27.07/7.67  																+-Applying beta-rule and splitting (244), into two cases.
% 27.07/7.67  																|-Branch one:
% 27.07/7.67  																| (247)  ~ (all_149_0_93 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = all_149_0_93
% 27.07/7.67  																|
% 27.07/7.67  																	| Applying alpha-rule on (247) yields:
% 27.07/7.67  																	| (248)  ~ (all_149_0_93 = 0)
% 27.07/7.67  																	| (249) apart_point_and_line(all_0_1_1, all_0_6_6) = all_149_0_93
% 27.07/7.67  																	|
% 27.07/7.67  																	+-Applying beta-rule and splitting (245), into two cases.
% 27.07/7.67  																	|-Branch one:
% 27.07/7.67  																	| (250)  ~ (all_150_0_94 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_150_0_94
% 27.07/7.67  																	|
% 27.07/7.67  																		| Applying alpha-rule on (250) yields:
% 27.07/7.67  																		| (251)  ~ (all_150_0_94 = 0)
% 27.07/7.67  																		| (252) apart_point_and_line(all_0_1_1, all_0_4_4) = all_150_0_94
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (114) with all_0_6_6, all_0_4_4, all_143_1_86, all_0_1_1 and discharging atoms intersection_point(all_0_6_6, all_0_4_4) = all_143_1_86, intersection_point(all_0_6_6, all_0_4_4) = all_0_1_1, yields:
% 27.07/7.67  																		| (253) all_143_1_86 = all_0_1_1
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (114) with all_0_6_6, all_0_4_4, all_141_1_84, all_143_1_86 and discharging atoms intersection_point(all_0_6_6, all_0_4_4) = all_143_1_86, intersection_point(all_0_6_6, all_0_4_4) = all_141_1_84, yields:
% 27.07/7.67  																		| (254) all_143_1_86 = all_141_1_84
% 27.07/7.67  																		|
% 27.07/7.67  																		| Combining equations (253,254) yields a new equation:
% 27.07/7.67  																		| (255) all_141_1_84 = all_0_1_1
% 27.07/7.67  																		|
% 27.07/7.67  																		| Combining equations (255,254) yields a new equation:
% 27.07/7.67  																		| (253) all_143_1_86 = all_0_1_1
% 27.07/7.67  																		|
% 27.07/7.67  																		| From (253) and (243) follows:
% 27.07/7.67  																		| (257) apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85
% 27.07/7.67  																		|
% 27.07/7.67  																		| From (255) and (239) follows:
% 27.07/7.67  																		| (258) apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (47) with all_0_1_1, all_0_4_4, all_143_0_85, all_150_0_94 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_150_0_94, apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, yields:
% 27.07/7.67  																		| (259) all_150_0_94 = all_143_0_85
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (47) with all_0_1_1, all_0_6_6, all_141_0_83, all_149_0_93 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_149_0_93, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.67  																		| (260) all_149_0_93 = all_141_0_83
% 27.07/7.67  																		|
% 27.07/7.67  																		| Equations (259) can reduce 251 to:
% 27.07/7.67  																		| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.67  																		|
% 27.07/7.67  																		| Equations (260) can reduce 248 to:
% 27.07/7.67  																		| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.67  																		|
% 27.07/7.67  																		| From (259) and (252) follows:
% 27.07/7.67  																		| (257) apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85
% 27.07/7.67  																		|
% 27.07/7.67  																		| From (260) and (249) follows:
% 27.07/7.67  																		| (258) apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (61) with all_143_0_85, all_44_0_56, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.67  																		| (265) all_143_0_85 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (61) with all_44_0_56, all_143_0_85, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.67  																		| (266) all_143_0_85 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.67  																		|
% 27.07/7.67  																		| Instantiating formula (30) with all_143_0_85, all_44_0_56, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.67  																		| (267) all_143_0_85 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (30) with all_44_0_56, all_143_0_85, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.68  																		| (268) all_143_0_85 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_143_0_85, all_42_0_54, all_0_4_4, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.68  																		| (269) all_143_0_85 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_42_0_54, all_143_0_85, all_0_6_6, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.68  																		| (270) all_143_0_85 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (30) with all_143_0_85, all_42_0_54, all_0_6_6, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.68  																		| (271) all_143_0_85 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (30) with all_42_0_54, all_143_0_85, all_0_4_4, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.68  																		| (272) all_143_0_85 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (37) with all_143_0_85, all_143_0_85, all_0_4_4, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, yields:
% 27.07/7.68  																		| (273) all_143_0_85 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_143_0_85, all_143_0_85, all_0_4_4, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, yields:
% 27.07/7.68  																		| (274) all_143_0_85 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (75) with all_143_0_85, all_51_0_66, all_0_4_4, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, distinct_lines(all_0_5_5, all_0_4_4) = all_51_0_66, yields:
% 27.07/7.68  																		| (275) all_143_0_85 = 0 | all_51_0_66 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0)
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_141_0_83, all_44_0_56, all_0_6_6, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.68  																		| (276) all_141_0_83 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_44_0_56, all_141_0_83, all_0_5_5, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.68  																		| (277) all_141_0_83 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (30) with all_44_0_56, all_141_0_83, all_0_6_6, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, yields:
% 27.07/7.68  																		| (278) all_141_0_83 = 0 | all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_141_0_83, all_42_0_54, all_0_6_6, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.68  																		| (279) all_141_0_83 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_42_0_54, all_141_0_83, all_0_6_6, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, yields:
% 27.07/7.68  																		| (280) all_141_0_83 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (37) with all_141_0_83, all_143_0_85, all_0_6_6, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.68  																		| (281) all_143_0_85 = 0 | all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (37) with all_143_0_85, all_141_0_83, all_0_4_4, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.68  																		| (282) all_143_0_85 = 0 | all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_141_0_83, all_143_0_85, all_0_6_6, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.68  																		| (283) all_143_0_85 = 0 | all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_143_0_85, all_141_0_83, all_0_4_4, all_0_6_6, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.68  																		| (284) all_143_0_85 = 0 | all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (37) with all_141_0_83, all_141_0_83, all_0_6_6, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.68  																		| (285) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (61) with all_141_0_83, all_141_0_83, all_0_6_6, all_0_6_6, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, yields:
% 27.07/7.68  																		| (286) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (140) with all_44_0_56, all_44_0_56, all_0_5_5, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (287) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (140) with all_44_0_56, all_42_0_54, all_0_5_5, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (288) all_44_0_56 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (140) with all_42_0_54, all_44_0_56, all_0_6_6, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_44_0_56, apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (289) all_44_0_56 = 0 | all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (140) with all_42_0_54, all_42_0_54, all_0_6_6, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (290) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (51) with all_143_0_85, all_143_0_85, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (291) all_143_0_85 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (51) with all_143_0_85, all_141_0_83, all_0_4_4, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (292) all_143_0_85 = 0 | all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (51) with all_141_0_83, all_143_0_85, all_0_6_6, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_143_0_85, apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (293) all_143_0_85 = 0 | all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		| Instantiating formula (51) with all_141_0_83, all_141_0_83, all_0_6_6, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_141_0_83, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.68  																		| (294) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																		+-Applying beta-rule and splitting (285), into two cases.
% 27.07/7.68  																		|-Branch one:
% 27.07/7.68  																		| (295) all_141_0_83 = 0
% 27.07/7.68  																		|
% 27.07/7.68  																			| Equations (295) can reduce 237 to:
% 27.07/7.68  																			| (177) $false
% 27.07/7.68  																			|
% 27.07/7.68  																			|-The branch is then unsatisfiable
% 27.07/7.68  																		|-Branch two:
% 27.07/7.68  																		| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.68  																		| (183)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.68  																		|
% 27.07/7.68  																			+-Applying beta-rule and splitting (273), into two cases.
% 27.07/7.68  																			|-Branch one:
% 27.07/7.68  																			| (299) all_143_0_85 = 0
% 27.07/7.68  																			|
% 27.07/7.68  																				| Equations (299) can reduce 241 to:
% 27.07/7.68  																				| (177) $false
% 27.07/7.68  																				|
% 27.07/7.68  																				|-The branch is then unsatisfiable
% 27.07/7.68  																			|-Branch two:
% 27.07/7.68  																			| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																			| (302)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 27.07/7.69  																			|
% 27.07/7.69  																				+-Applying beta-rule and splitting (294), into two cases.
% 27.07/7.69  																				|-Branch one:
% 27.07/7.69  																				| (295) all_141_0_83 = 0
% 27.07/7.69  																				|
% 27.07/7.69  																					| Equations (295) can reduce 237 to:
% 27.07/7.69  																					| (177) $false
% 27.07/7.69  																					|
% 27.07/7.69  																					|-The branch is then unsatisfiable
% 27.07/7.69  																				|-Branch two:
% 27.07/7.69  																				| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																				| (306)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.69  																				|
% 27.07/7.69  																					+-Applying beta-rule and splitting (281), into two cases.
% 27.07/7.69  																					|-Branch one:
% 27.07/7.69  																					| (299) all_143_0_85 = 0
% 27.07/7.69  																					|
% 27.07/7.69  																						| Equations (299) can reduce 241 to:
% 27.07/7.69  																						| (177) $false
% 27.07/7.69  																						|
% 27.07/7.69  																						|-The branch is then unsatisfiable
% 27.07/7.69  																					|-Branch two:
% 27.07/7.69  																					| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																					| (310) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0))
% 27.07/7.69  																					|
% 27.07/7.69  																						+-Applying beta-rule and splitting (282), into two cases.
% 27.07/7.69  																						|-Branch one:
% 27.07/7.69  																						| (299) all_143_0_85 = 0
% 27.07/7.69  																						|
% 27.07/7.69  																							| Equations (299) can reduce 241 to:
% 27.07/7.69  																							| (177) $false
% 27.07/7.69  																							|
% 27.07/7.69  																							|-The branch is then unsatisfiable
% 27.07/7.69  																						|-Branch two:
% 27.07/7.69  																						| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																						| (314) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_6_6, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0))
% 27.07/7.69  																						|
% 27.07/7.69  																							+-Applying beta-rule and splitting (274), into two cases.
% 27.07/7.69  																							|-Branch one:
% 27.07/7.69  																							| (299) all_143_0_85 = 0
% 27.07/7.69  																							|
% 27.07/7.69  																								| Equations (299) can reduce 241 to:
% 27.07/7.69  																								| (177) $false
% 27.07/7.69  																								|
% 27.07/7.69  																								|-The branch is then unsatisfiable
% 27.07/7.69  																							|-Branch two:
% 27.07/7.69  																							| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																							| (318)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.69  																							|
% 27.07/7.69  																								+-Applying beta-rule and splitting (286), into two cases.
% 27.07/7.69  																								|-Branch one:
% 27.07/7.69  																								| (295) all_141_0_83 = 0
% 27.07/7.69  																								|
% 27.07/7.69  																									| Equations (295) can reduce 237 to:
% 27.07/7.69  																									| (177) $false
% 27.07/7.69  																									|
% 27.07/7.69  																									|-The branch is then unsatisfiable
% 27.07/7.69  																								|-Branch two:
% 27.07/7.69  																								| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																								| (322)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.69  																								|
% 27.07/7.69  																									+-Applying beta-rule and splitting (283), into two cases.
% 27.07/7.69  																									|-Branch one:
% 27.07/7.69  																									| (299) all_143_0_85 = 0
% 27.07/7.69  																									|
% 27.07/7.69  																										| Equations (299) can reduce 241 to:
% 27.07/7.69  																										| (177) $false
% 27.07/7.69  																										|
% 27.07/7.69  																										|-The branch is then unsatisfiable
% 27.07/7.69  																									|-Branch two:
% 27.07/7.69  																									| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																									| (326) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.69  																									|
% 27.07/7.69  																										+-Applying beta-rule and splitting (279), into two cases.
% 27.07/7.69  																										|-Branch one:
% 27.07/7.69  																										| (295) all_141_0_83 = 0
% 27.07/7.69  																										|
% 27.07/7.69  																											| Equations (295) can reduce 237 to:
% 27.07/7.69  																											| (177) $false
% 27.07/7.69  																											|
% 27.07/7.69  																											|-The branch is then unsatisfiable
% 27.07/7.69  																										|-Branch two:
% 27.07/7.69  																										| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																										| (330) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.69  																										|
% 27.07/7.69  																											+-Applying beta-rule and splitting (280), into two cases.
% 27.07/7.69  																											|-Branch one:
% 27.07/7.69  																											| (295) all_141_0_83 = 0
% 27.07/7.69  																											|
% 27.07/7.69  																												| Equations (295) can reduce 237 to:
% 27.07/7.69  																												| (177) $false
% 27.07/7.69  																												|
% 27.07/7.69  																												|-The branch is then unsatisfiable
% 27.07/7.69  																											|-Branch two:
% 27.07/7.69  																											| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																											| (334) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.69  																											|
% 27.07/7.69  																												+-Applying beta-rule and splitting (277), into two cases.
% 27.07/7.69  																												|-Branch one:
% 27.07/7.69  																												| (295) all_141_0_83 = 0
% 27.07/7.69  																												|
% 27.07/7.69  																													| Equations (295) can reduce 237 to:
% 27.07/7.69  																													| (177) $false
% 27.07/7.69  																													|
% 27.07/7.69  																													|-The branch is then unsatisfiable
% 27.07/7.69  																												|-Branch two:
% 27.07/7.69  																												| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																												| (338) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.69  																												|
% 27.07/7.69  																													+-Applying beta-rule and splitting (278), into two cases.
% 27.07/7.69  																													|-Branch one:
% 27.07/7.69  																													| (295) all_141_0_83 = 0
% 27.07/7.69  																													|
% 27.07/7.69  																														| Equations (295) can reduce 237 to:
% 27.07/7.69  																														| (177) $false
% 27.07/7.69  																														|
% 27.07/7.69  																														|-The branch is then unsatisfiable
% 27.07/7.69  																													|-Branch two:
% 27.07/7.69  																													| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																													| (342) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.69  																													|
% 27.07/7.69  																														+-Applying beta-rule and splitting (276), into two cases.
% 27.07/7.69  																														|-Branch one:
% 27.07/7.69  																														| (295) all_141_0_83 = 0
% 27.07/7.69  																														|
% 27.07/7.69  																															| Equations (295) can reduce 237 to:
% 27.07/7.69  																															| (177) $false
% 27.07/7.69  																															|
% 27.07/7.69  																															|-The branch is then unsatisfiable
% 27.07/7.69  																														|-Branch two:
% 27.07/7.69  																														| (237)  ~ (all_141_0_83 = 0)
% 27.07/7.69  																														| (346) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.69  																														|
% 27.07/7.69  																															+-Applying beta-rule and splitting (284), into two cases.
% 27.07/7.69  																															|-Branch one:
% 27.07/7.69  																															| (299) all_143_0_85 = 0
% 27.07/7.69  																															|
% 27.07/7.69  																																| Equations (299) can reduce 241 to:
% 27.07/7.69  																																| (177) $false
% 27.07/7.69  																																|
% 27.07/7.69  																																|-The branch is then unsatisfiable
% 27.07/7.69  																															|-Branch two:
% 27.07/7.69  																															| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																															| (350) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 27.07/7.69  																															|
% 27.07/7.69  																																+-Applying beta-rule and splitting (288), into two cases.
% 27.07/7.69  																																|-Branch one:
% 27.07/7.69  																																| (176) all_44_0_56 = 0
% 27.07/7.69  																																|
% 27.07/7.69  																																	| Equations (176) can reduce 151 to:
% 27.07/7.69  																																	| (177) $false
% 27.07/7.69  																																	|
% 27.07/7.69  																																	|-The branch is then unsatisfiable
% 27.07/7.69  																																|-Branch two:
% 27.07/7.69  																																| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.69  																																| (354) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0))
% 27.07/7.69  																																|
% 27.07/7.69  																																	+-Applying beta-rule and splitting (289), into two cases.
% 27.07/7.69  																																	|-Branch one:
% 27.07/7.69  																																	| (176) all_44_0_56 = 0
% 27.07/7.69  																																	|
% 27.07/7.69  																																		| Equations (176) can reduce 151 to:
% 27.07/7.69  																																		| (177) $false
% 27.07/7.69  																																		|
% 27.07/7.69  																																		|-The branch is then unsatisfiable
% 27.07/7.69  																																	|-Branch two:
% 27.07/7.69  																																	| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.69  																																	| (358) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0))
% 27.07/7.69  																																	|
% 27.07/7.69  																																		+-Applying beta-rule and splitting (287), into two cases.
% 27.07/7.69  																																		|-Branch one:
% 27.07/7.69  																																		| (176) all_44_0_56 = 0
% 27.07/7.69  																																		|
% 27.07/7.69  																																			| Equations (176) can reduce 151 to:
% 27.07/7.69  																																			| (177) $false
% 27.07/7.69  																																			|
% 27.07/7.69  																																			|-The branch is then unsatisfiable
% 27.07/7.69  																																		|-Branch two:
% 27.07/7.69  																																		| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.69  																																		| (362)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 27.07/7.69  																																		|
% 27.07/7.69  																																			+-Applying beta-rule and splitting (290), into two cases.
% 27.07/7.69  																																			|-Branch one:
% 27.07/7.69  																																			| (180) all_42_0_54 = 0
% 27.07/7.69  																																			|
% 27.07/7.69  																																				| Equations (180) can reduce 147 to:
% 27.07/7.69  																																				| (177) $false
% 27.07/7.69  																																				|
% 27.07/7.69  																																				|-The branch is then unsatisfiable
% 27.07/7.69  																																			|-Branch two:
% 27.07/7.69  																																			| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.69  																																			| (366)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 27.07/7.69  																																			|
% 27.07/7.69  																																				+-Applying beta-rule and splitting (291), into two cases.
% 27.07/7.69  																																				|-Branch one:
% 27.07/7.69  																																				| (299) all_143_0_85 = 0
% 27.07/7.69  																																				|
% 27.07/7.69  																																					| Equations (299) can reduce 241 to:
% 27.07/7.69  																																					| (177) $false
% 27.07/7.69  																																					|
% 27.07/7.69  																																					|-The branch is then unsatisfiable
% 27.07/7.69  																																				|-Branch two:
% 27.07/7.69  																																				| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																																				| (370)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0))
% 27.07/7.69  																																				|
% 27.07/7.69  																																					+-Applying beta-rule and splitting (272), into two cases.
% 27.07/7.69  																																					|-Branch one:
% 27.07/7.69  																																					| (299) all_143_0_85 = 0
% 27.07/7.69  																																					|
% 27.07/7.69  																																						| Equations (299) can reduce 241 to:
% 27.07/7.69  																																						| (177) $false
% 27.07/7.69  																																						|
% 27.07/7.69  																																						|-The branch is then unsatisfiable
% 27.07/7.69  																																					|-Branch two:
% 27.07/7.69  																																					| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																																					| (374) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.69  																																					|
% 27.07/7.69  																																						+-Applying beta-rule and splitting (292), into two cases.
% 27.07/7.69  																																						|-Branch one:
% 27.07/7.69  																																						| (299) all_143_0_85 = 0
% 27.07/7.69  																																						|
% 27.07/7.69  																																							| Equations (299) can reduce 241 to:
% 27.07/7.69  																																							| (177) $false
% 27.07/7.69  																																							|
% 27.07/7.69  																																							|-The branch is then unsatisfiable
% 27.07/7.69  																																						|-Branch two:
% 27.07/7.69  																																						| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																																						| (378) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0))
% 27.07/7.69  																																						|
% 27.07/7.69  																																							+-Applying beta-rule and splitting (275), into two cases.
% 27.07/7.69  																																							|-Branch one:
% 27.07/7.69  																																							| (299) all_143_0_85 = 0
% 27.07/7.69  																																							|
% 27.07/7.69  																																								| Equations (299) can reduce 241 to:
% 27.07/7.69  																																								| (177) $false
% 27.07/7.69  																																								|
% 27.07/7.69  																																								|-The branch is then unsatisfiable
% 27.07/7.69  																																							|-Branch two:
% 27.07/7.69  																																							| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																																							| (382) all_51_0_66 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0)
% 27.07/7.69  																																							|
% 27.07/7.69  																																								+-Applying beta-rule and splitting (293), into two cases.
% 27.07/7.69  																																								|-Branch one:
% 27.07/7.69  																																								| (299) all_143_0_85 = 0
% 27.07/7.69  																																								|
% 27.07/7.69  																																									| Equations (299) can reduce 241 to:
% 27.07/7.69  																																									| (177) $false
% 27.07/7.69  																																									|
% 27.07/7.69  																																									|-The branch is then unsatisfiable
% 27.07/7.69  																																								|-Branch two:
% 27.07/7.69  																																								| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.69  																																								| (386) all_141_0_83 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0))
% 27.07/7.70  																																								|
% 27.07/7.70  																																									+-Applying beta-rule and splitting (265), into two cases.
% 27.07/7.70  																																									|-Branch one:
% 27.07/7.70  																																									| (299) all_143_0_85 = 0
% 27.07/7.70  																																									|
% 27.07/7.70  																																										| Equations (299) can reduce 241 to:
% 27.07/7.70  																																										| (177) $false
% 27.07/7.70  																																										|
% 27.07/7.70  																																										|-The branch is then unsatisfiable
% 27.07/7.70  																																									|-Branch two:
% 27.07/7.70  																																									| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																									| (390) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																									|
% 27.07/7.70  																																										+-Applying beta-rule and splitting (266), into two cases.
% 27.07/7.70  																																										|-Branch one:
% 27.07/7.70  																																										| (299) all_143_0_85 = 0
% 27.07/7.70  																																										|
% 27.07/7.70  																																											| Equations (299) can reduce 241 to:
% 27.07/7.70  																																											| (177) $false
% 27.07/7.70  																																											|
% 27.07/7.70  																																											|-The branch is then unsatisfiable
% 27.07/7.70  																																										|-Branch two:
% 27.07/7.70  																																										| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																										| (394) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																										|
% 27.07/7.70  																																											+-Applying beta-rule and splitting (267), into two cases.
% 27.07/7.70  																																											|-Branch one:
% 27.07/7.70  																																											| (299) all_143_0_85 = 0
% 27.07/7.70  																																											|
% 27.07/7.70  																																												| Equations (299) can reduce 241 to:
% 27.07/7.70  																																												| (177) $false
% 27.07/7.70  																																												|
% 27.07/7.70  																																												|-The branch is then unsatisfiable
% 27.07/7.70  																																											|-Branch two:
% 27.07/7.70  																																											| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																											| (398) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																											|
% 27.07/7.70  																																												+-Applying beta-rule and splitting (268), into two cases.
% 27.07/7.70  																																												|-Branch one:
% 27.07/7.70  																																												| (299) all_143_0_85 = 0
% 27.07/7.70  																																												|
% 27.07/7.70  																																													| Equations (299) can reduce 241 to:
% 27.07/7.70  																																													| (177) $false
% 27.07/7.70  																																													|
% 27.07/7.70  																																													|-The branch is then unsatisfiable
% 27.07/7.70  																																												|-Branch two:
% 27.07/7.70  																																												| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																												| (402) all_44_0_56 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																												|
% 27.07/7.70  																																													+-Applying beta-rule and splitting (271), into two cases.
% 27.07/7.70  																																													|-Branch one:
% 27.07/7.70  																																													| (299) all_143_0_85 = 0
% 27.07/7.70  																																													|
% 27.07/7.70  																																														| Equations (299) can reduce 241 to:
% 27.07/7.70  																																														| (177) $false
% 27.07/7.70  																																														|
% 27.07/7.70  																																														|-The branch is then unsatisfiable
% 27.07/7.70  																																													|-Branch two:
% 27.07/7.70  																																													| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																													| (406) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																													|
% 27.07/7.70  																																														+-Applying beta-rule and splitting (269), into two cases.
% 27.07/7.70  																																														|-Branch one:
% 27.07/7.70  																																														| (299) all_143_0_85 = 0
% 27.07/7.70  																																														|
% 27.07/7.70  																																															| Equations (299) can reduce 241 to:
% 27.07/7.70  																																															| (177) $false
% 27.07/7.70  																																															|
% 27.07/7.70  																																															|-The branch is then unsatisfiable
% 27.07/7.70  																																														|-Branch two:
% 27.07/7.70  																																														| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																														| (410) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																														|
% 27.07/7.70  																																															+-Applying beta-rule and splitting (270), into two cases.
% 27.07/7.70  																																															|-Branch one:
% 27.07/7.70  																																															| (299) all_143_0_85 = 0
% 27.07/7.70  																																															|
% 27.07/7.70  																																																| Equations (299) can reduce 241 to:
% 27.07/7.70  																																																| (177) $false
% 27.07/7.70  																																																|
% 27.07/7.70  																																																|-The branch is then unsatisfiable
% 27.07/7.70  																																															|-Branch two:
% 27.07/7.70  																																															| (241)  ~ (all_143_0_85 = 0)
% 27.07/7.70  																																															| (414) all_42_0_54 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																															|
% 27.07/7.70  																																																+-Applying beta-rule and splitting (330), into two cases.
% 27.07/7.70  																																																|-Branch one:
% 27.07/7.70  																																																| (180) all_42_0_54 = 0
% 27.07/7.70  																																																|
% 27.07/7.70  																																																	| Equations (180) can reduce 147 to:
% 27.07/7.70  																																																	| (177) $false
% 27.07/7.70  																																																	|
% 27.07/7.70  																																																	|-The branch is then unsatisfiable
% 27.07/7.70  																																																|-Branch two:
% 27.07/7.70  																																																| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.70  																																																| (418)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																																|
% 27.07/7.70  																																																	+-Applying beta-rule and splitting (338), into two cases.
% 27.07/7.70  																																																	|-Branch one:
% 27.07/7.70  																																																	| (176) all_44_0_56 = 0
% 27.07/7.70  																																																	|
% 27.07/7.70  																																																		| Equations (176) can reduce 151 to:
% 27.07/7.70  																																																		| (177) $false
% 27.07/7.70  																																																		|
% 27.07/7.70  																																																		|-The branch is then unsatisfiable
% 27.07/7.70  																																																	|-Branch two:
% 27.07/7.70  																																																	| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.70  																																																	| (422)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																																	|
% 27.07/7.70  																																																		+-Applying beta-rule and splitting (342), into two cases.
% 27.07/7.70  																																																		|-Branch one:
% 27.07/7.70  																																																		| (176) all_44_0_56 = 0
% 27.07/7.70  																																																		|
% 27.07/7.70  																																																			| Equations (176) can reduce 151 to:
% 27.07/7.70  																																																			| (177) $false
% 27.07/7.70  																																																			|
% 27.07/7.70  																																																			|-The branch is then unsatisfiable
% 27.07/7.70  																																																		|-Branch two:
% 27.07/7.70  																																																		| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.70  																																																		| (426)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																																		|
% 27.07/7.70  																																																			+-Applying beta-rule and splitting (346), into two cases.
% 27.07/7.70  																																																			|-Branch one:
% 27.07/7.70  																																																			| (176) all_44_0_56 = 0
% 27.07/7.70  																																																			|
% 27.07/7.70  																																																				| Equations (176) can reduce 151 to:
% 27.07/7.70  																																																				| (177) $false
% 27.07/7.70  																																																				|
% 27.07/7.70  																																																				|-The branch is then unsatisfiable
% 27.07/7.70  																																																			|-Branch two:
% 27.07/7.70  																																																			| (151)  ~ (all_44_0_56 = 0)
% 27.07/7.70  																																																			| (430)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																																			|
% 27.07/7.70  																																																				| Instantiating (430) with all_324_0_144 yields:
% 27.07/7.70  																																																				| (431) (all_324_0_144 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_324_0_144 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (all_324_0_144 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = all_324_0_144) | ( ~ (all_324_0_144 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_324_0_144)
% 27.07/7.70  																																																				|
% 27.07/7.70  																																																				+-Applying beta-rule and splitting (382), into two cases.
% 27.07/7.70  																																																				|-Branch one:
% 27.07/7.70  																																																				| (204) all_51_0_66 = 0
% 27.07/7.70  																																																				|
% 27.07/7.70  																																																					| Equations (204) can reduce 155 to:
% 27.07/7.70  																																																					| (177) $false
% 27.07/7.70  																																																					|
% 27.07/7.70  																																																					|-The branch is then unsatisfiable
% 27.07/7.70  																																																				|-Branch two:
% 27.07/7.70  																																																				| (155)  ~ (all_51_0_66 = 0)
% 27.07/7.70  																																																				| (435)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0)
% 27.07/7.70  																																																				|
% 27.07/7.70  																																																					| Instantiating (435) with all_340_0_162 yields:
% 27.07/7.70  																																																					| (436)  ~ (all_340_0_162 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_340_0_162
% 27.07/7.70  																																																					|
% 27.07/7.70  																																																					| Applying alpha-rule on (436) yields:
% 27.07/7.70  																																																					| (437)  ~ (all_340_0_162 = 0)
% 27.07/7.70  																																																					| (438) apart_point_and_line(all_0_1_1, all_0_5_5) = all_340_0_162
% 27.07/7.70  																																																					|
% 27.07/7.70  																																																					+-Applying beta-rule and splitting (410), into two cases.
% 27.07/7.70  																																																					|-Branch one:
% 27.07/7.70  																																																					| (180) all_42_0_54 = 0
% 27.07/7.70  																																																					|
% 27.07/7.70  																																																						| Equations (180) can reduce 147 to:
% 27.07/7.70  																																																						| (177) $false
% 27.07/7.70  																																																						|
% 27.07/7.70  																																																						|-The branch is then unsatisfiable
% 27.07/7.70  																																																					|-Branch two:
% 27.07/7.70  																																																					| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.70  																																																					| (442)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.70  																																																					|
% 27.07/7.70  																																																						+-Applying beta-rule and splitting (431), into two cases.
% 27.07/7.70  																																																						|-Branch one:
% 27.07/7.70  																																																						| (443) (all_324_0_144 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_324_0_144 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (all_324_0_144 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = all_324_0_144)
% 27.07/7.70  																																																						|
% 27.07/7.70  																																																							+-Applying beta-rule and splitting (443), into two cases.
% 27.07/7.70  																																																							|-Branch one:
% 27.07/7.70  																																																							| (444) (all_324_0_144 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_324_0_144 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0)
% 27.07/7.70  																																																							|
% 27.07/7.70  																																																								+-Applying beta-rule and splitting (444), into two cases.
% 27.07/7.70  																																																								|-Branch one:
% 27.07/7.70  																																																								| (445) all_324_0_144 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 27.07/7.70  																																																								|
% 27.07/7.70  																																																									| Applying alpha-rule on (445) yields:
% 27.07/7.70  																																																									| (446) all_324_0_144 = 0
% 27.07/7.70  																																																									| (447) apart_point_and_line(all_0_1_1, all_0_5_5) = 0
% 27.07/7.70  																																																									|
% 27.07/7.70  																																																									| Instantiating formula (47) with all_0_1_1, all_0_5_5, 0, all_340_0_162 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_340_0_162, apart_point_and_line(all_0_1_1, all_0_5_5) = 0, yields:
% 27.07/7.70  																																																									| (448) all_340_0_162 = 0
% 27.07/7.70  																																																									|
% 27.07/7.70  																																																									| Equations (448) can reduce 437 to:
% 27.07/7.70  																																																									| (177) $false
% 27.07/7.70  																																																									|
% 27.07/7.70  																																																									|-The branch is then unsatisfiable
% 27.07/7.70  																																																								|-Branch two:
% 27.07/7.70  																																																								| (450) all_324_0_144 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 27.07/7.70  																																																								|
% 27.07/7.70  																																																									| Applying alpha-rule on (450) yields:
% 27.07/7.70  																																																									| (446) all_324_0_144 = 0
% 27.07/7.70  																																																									| (452) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 27.07/7.70  																																																									|
% 27.07/7.70  																																																									+-Applying beta-rule and splitting (414), into two cases.
% 27.07/7.70  																																																									|-Branch one:
% 27.07/7.70  																																																									| (180) all_42_0_54 = 0
% 27.07/7.70  																																																									|
% 27.07/7.70  																																																										| Equations (180) can reduce 147 to:
% 27.07/7.70  																																																										| (177) $false
% 27.07/7.70  																																																										|
% 27.07/7.70  																																																										|-The branch is then unsatisfiable
% 27.07/7.70  																																																									|-Branch two:
% 27.07/7.70  																																																									| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.70  																																																									| (456)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																																									|
% 27.07/7.70  																																																										+-Applying beta-rule and splitting (334), into two cases.
% 27.07/7.70  																																																										|-Branch one:
% 27.07/7.70  																																																										| (180) all_42_0_54 = 0
% 27.07/7.70  																																																										|
% 27.07/7.70  																																																											| Equations (180) can reduce 147 to:
% 27.07/7.70  																																																											| (177) $false
% 27.07/7.70  																																																											|
% 27.07/7.70  																																																											|-The branch is then unsatisfiable
% 27.07/7.70  																																																										|-Branch two:
% 27.07/7.70  																																																										| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.70  																																																										| (460)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.70  																																																										|
% 27.07/7.70  																																																											+-Applying beta-rule and splitting (354), into two cases.
% 27.07/7.70  																																																											|-Branch one:
% 27.07/7.70  																																																											| (180) all_42_0_54 = 0
% 27.07/7.70  																																																											|
% 27.07/7.70  																																																												| Equations (180) can reduce 147 to:
% 27.07/7.70  																																																												| (177) $false
% 27.07/7.70  																																																												|
% 27.07/7.70  																																																												|-The branch is then unsatisfiable
% 27.07/7.70  																																																											|-Branch two:
% 27.07/7.70  																																																											| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.70  																																																											| (464)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0))
% 27.07/7.71  																																																											|
% 27.07/7.71  																																																												+-Applying beta-rule and splitting (358), into two cases.
% 27.07/7.71  																																																												|-Branch one:
% 27.07/7.71  																																																												| (180) all_42_0_54 = 0
% 27.07/7.71  																																																												|
% 27.07/7.71  																																																													| Equations (180) can reduce 147 to:
% 27.07/7.71  																																																													| (177) $false
% 27.07/7.71  																																																													|
% 27.07/7.71  																																																													|-The branch is then unsatisfiable
% 27.07/7.71  																																																												|-Branch two:
% 27.07/7.71  																																																												| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.71  																																																												| (468)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0))
% 27.07/7.71  																																																												|
% 27.07/7.71  																																																													+-Applying beta-rule and splitting (374), into two cases.
% 27.07/7.71  																																																													|-Branch one:
% 27.07/7.71  																																																													| (180) all_42_0_54 = 0
% 27.07/7.71  																																																													|
% 27.07/7.71  																																																														| Equations (180) can reduce 147 to:
% 27.07/7.71  																																																														| (177) $false
% 27.07/7.71  																																																														|
% 27.07/7.71  																																																														|-The branch is then unsatisfiable
% 27.07/7.71  																																																													|-Branch two:
% 27.07/7.71  																																																													| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.71  																																																													| (472)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 27.07/7.71  																																																													|
% 27.07/7.71  																																																														+-Applying beta-rule and splitting (406), into two cases.
% 27.07/7.71  																																																														|-Branch one:
% 27.07/7.71  																																																														| (180) all_42_0_54 = 0
% 27.07/7.71  																																																														|
% 27.07/7.71  																																																															| Equations (180) can reduce 147 to:
% 27.07/7.71  																																																															| (177) $false
% 27.07/7.71  																																																															|
% 27.07/7.71  																																																															|-The branch is then unsatisfiable
% 27.07/7.71  																																																														|-Branch two:
% 27.07/7.71  																																																														| (147)  ~ (all_42_0_54 = 0)
% 27.07/7.71  																																																														| (476)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 27.07/7.71  																																																														|
% 27.07/7.71  																																																															| Instantiating formula (47) with all_0_2_2, all_0_6_6, 0, all_42_0_54 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_42_0_54, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 27.07/7.71  																																																															| (180) all_42_0_54 = 0
% 27.07/7.71  																																																															|
% 27.07/7.71  																																																															| Equations (180) can reduce 147 to:
% 27.07/7.71  																																																															| (177) $false
% 27.07/7.71  																																																															|
% 27.07/7.71  																																																															|-The branch is then unsatisfiable
% 27.07/7.71  																																																							|-Branch two:
% 27.07/7.71  																																																							| (479)  ~ (all_324_0_144 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = all_324_0_144
% 27.07/7.71  																																																							|
% 27.07/7.71  																																																								| Applying alpha-rule on (479) yields:
% 27.07/7.71  																																																								| (480)  ~ (all_324_0_144 = 0)
% 27.07/7.71  																																																								| (481) distinct_lines(all_0_5_5, all_0_6_6) = all_324_0_144
% 27.07/7.71  																																																								|
% 27.07/7.71  																																																								| Instantiating formula (107) with all_324_0_144, all_0_6_6, all_0_5_5, all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_5_5) = 0, distinct_lines(all_0_5_5, all_0_6_6) = all_324_0_144, yields:
% 27.07/7.71  																																																								| (482) all_324_0_144 = 0 | convergent_lines(all_0_6_6, all_0_6_6) = 0
% 27.07/7.71  																																																								|
% 27.07/7.71  																																																								+-Applying beta-rule and splitting (482), into two cases.
% 27.07/7.71  																																																								|-Branch one:
% 27.07/7.71  																																																								| (483) convergent_lines(all_0_6_6, all_0_6_6) = 0
% 27.07/7.71  																																																								|
% 27.07/7.71  																																																									| Instantiating formula (101) with all_0_6_6 and discharging atoms convergent_lines(all_0_6_6, all_0_6_6) = 0, yields:
% 27.07/7.71  																																																									| (484) $false
% 27.07/7.71  																																																									|
% 27.07/7.71  																																																									|-The branch is then unsatisfiable
% 27.07/7.71  																																																								|-Branch two:
% 27.07/7.71  																																																								| (485)  ~ (convergent_lines(all_0_6_6, all_0_6_6) = 0)
% 27.07/7.71  																																																								| (446) all_324_0_144 = 0
% 27.07/7.71  																																																								|
% 27.07/7.71  																																																									| Equations (446) can reduce 480 to:
% 27.07/7.71  																																																									| (177) $false
% 27.07/7.71  																																																									|
% 27.07/7.71  																																																									|-The branch is then unsatisfiable
% 27.07/7.71  																																																						|-Branch two:
% 27.07/7.71  																																																						| (488)  ~ (all_324_0_144 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_324_0_144
% 27.07/7.71  																																																						|
% 27.07/7.71  																																																							| Applying alpha-rule on (488) yields:
% 27.07/7.71  																																																							| (480)  ~ (all_324_0_144 = 0)
% 27.07/7.71  																																																							| (490) distinct_points(all_0_2_2, all_0_1_1) = all_324_0_144
% 27.07/7.71  																																																							|
% 27.07/7.71  																																																							| Instantiating formula (9) with all_0_2_2, all_0_1_1, all_324_0_144, 0 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_324_0_144, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 27.07/7.71  																																																							| (446) all_324_0_144 = 0
% 27.07/7.71  																																																							|
% 27.07/7.71  																																																							| Equations (446) can reduce 480 to:
% 27.07/7.71  																																																							| (177) $false
% 27.07/7.71  																																																							|
% 27.07/7.71  																																																							|-The branch is then unsatisfiable
% 27.07/7.71  																	|-Branch two:
% 27.07/7.71  																	| (493)  ~ (all_150_0_94 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_150_0_94
% 27.07/7.71  																	|
% 27.07/7.71  																		| Applying alpha-rule on (493) yields:
% 27.07/7.71  																		| (251)  ~ (all_150_0_94 = 0)
% 27.07/7.71  																		| (495) convergent_lines(all_0_6_6, all_0_4_4) = all_150_0_94
% 27.07/7.71  																		|
% 27.07/7.71  																		| Instantiating formula (44) with all_0_6_6, all_0_4_4, all_150_0_94, 0 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = all_150_0_94, convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 27.07/7.71  																		| (496) all_150_0_94 = 0
% 27.07/7.71  																		|
% 27.07/7.71  																		| Equations (496) can reduce 251 to:
% 27.07/7.71  																		| (177) $false
% 27.07/7.71  																		|
% 27.07/7.71  																		|-The branch is then unsatisfiable
% 27.07/7.71  																|-Branch two:
% 27.07/7.71  																| (498)  ~ (all_149_0_93 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_149_0_93
% 27.07/7.71  																|
% 27.07/7.71  																	| Applying alpha-rule on (498) yields:
% 27.07/7.71  																	| (248)  ~ (all_149_0_93 = 0)
% 27.07/7.71  																	| (500) convergent_lines(all_0_6_6, all_0_4_4) = all_149_0_93
% 27.07/7.71  																	|
% 27.07/7.71  																	| Instantiating formula (44) with all_0_6_6, all_0_4_4, all_149_0_93, 0 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = all_149_0_93, convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 27.07/7.71  																	| (501) all_149_0_93 = 0
% 27.07/7.71  																	|
% 27.07/7.71  																	| Equations (501) can reduce 248 to:
% 27.07/7.71  																	| (177) $false
% 27.07/7.71  																	|
% 27.07/7.71  																	|-The branch is then unsatisfiable
% 27.07/7.71  															|-Branch two:
% 27.07/7.71  															| (503)  ~ (distinct_points(all_0_2_2, all_0_1_1) = 0)
% 27.07/7.71  															| (504) all_0_0_0 = 0
% 27.07/7.71  															|
% 27.07/7.71  																| Equations (504) can reduce 171 to:
% 27.07/7.71  																| (177) $false
% 27.07/7.71  																|
% 27.07/7.71  																|-The branch is then unsatisfiable
% 27.07/7.71  	|-Branch two:
% 27.07/7.71  	| (506)  ~ (convergent_lines(all_0_6_6, all_0_4_4) = 0)
% 27.07/7.71  	| (204) all_51_0_66 = 0
% 27.07/7.71  	|
% 27.07/7.71  		| Equations (204) can reduce 155 to:
% 27.07/7.71  		| (177) $false
% 27.07/7.71  		|
% 27.07/7.71  		|-The branch is then unsatisfiable
% 27.07/7.71  |-Branch two:
% 27.07/7.71  | (509)  ~ (all_0_3_3 = 0) & convergent_lines(all_0_6_6, all_0_4_4) = all_0_3_3
% 27.07/7.71  |
% 27.07/7.71  	| Applying alpha-rule on (509) yields:
% 27.07/7.71  	| (510)  ~ (all_0_3_3 = 0)
% 27.07/7.71  	| (511) convergent_lines(all_0_6_6, all_0_4_4) = all_0_3_3
% 27.07/7.71  	|
% 27.07/7.71  	+-Applying beta-rule and splitting (168), into two cases.
% 27.07/7.71  	|-Branch one:
% 27.07/7.71  	| (175) convergent_lines(all_0_6_6, all_0_4_4) = 0
% 27.07/7.71  	|
% 27.07/7.71  		| Instantiating formula (44) with all_0_6_6, all_0_4_4, 0, all_0_3_3 and discharging atoms convergent_lines(all_0_6_6, all_0_4_4) = all_0_3_3, convergent_lines(all_0_6_6, all_0_4_4) = 0, yields:
% 27.07/7.71  		| (513) all_0_3_3 = 0
% 27.07/7.71  		|
% 27.07/7.71  		| Equations (513) can reduce 510 to:
% 27.07/7.71  		| (177) $false
% 27.07/7.71  		|
% 27.07/7.71  		|-The branch is then unsatisfiable
% 27.07/7.71  	|-Branch two:
% 27.07/7.71  	| (506)  ~ (convergent_lines(all_0_6_6, all_0_4_4) = 0)
% 27.07/7.71  	| (204) all_51_0_66 = 0
% 27.07/7.71  	|
% 27.07/7.71  		| Equations (204) can reduce 155 to:
% 27.07/7.71  		| (177) $false
% 27.07/7.71  		|
% 27.07/7.71  		|-The branch is then unsatisfiable
% 27.07/7.71  % SZS output end Proof for theBenchmark
% 27.07/7.72  
% 27.07/7.72  7118ms
%------------------------------------------------------------------------------