%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO221+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n016.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 03:48:54 EDT 2022

% Result   : Theorem 5.69s 1.94s
% Output   : Proof 9.19s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO221+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Fri Jun 17 16:31:51 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.56/0.60          ____       _                          
% 0.56/0.60    ___  / __ \_____(_)___  ________  __________
% 0.56/0.60   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.60  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.60  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.60  
% 0.56/0.60  A Theorem Prover for First-Order Logic
% 0.56/0.60  (ePrincess v.1.0)
% 0.56/0.60  
% 0.56/0.60  (c) Philipp Rümmer, 2009-2015
% 0.56/0.60  (c) Peter Backeman, 2014-2015
% 0.56/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.56/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.56/0.60  Bug reports to peter@backeman.se
% 0.56/0.60  
% 0.56/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.56/0.60  
% 0.62/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.95  Prover 0: Preprocessing ...
% 2.18/1.11  Prover 0: Warning: ignoring some quantifiers
% 2.18/1.13  Prover 0: Constructing countermodel ...
% 3.24/1.41  Prover 0: gave up
% 3.24/1.41  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.24/1.44  Prover 1: Preprocessing ...
% 3.92/1.55  Prover 1: Constructing countermodel ...
% 3.92/1.60  Prover 1: gave up
% 3.92/1.60  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.27/1.63  Prover 2: Preprocessing ...
% 5.04/1.79  Prover 2: Warning: ignoring some quantifiers
% 5.15/1.80  Prover 2: Constructing countermodel ...
% 5.69/1.94  Prover 2: proved (339ms)
% 5.69/1.94  
% 5.69/1.94  No countermodel exists, formula is valid
% 5.69/1.94  % SZS status Theorem for theBenchmark
% 5.69/1.94  
% 5.69/1.94  Generating proof ... Warning: ignoring some quantifiers
% 8.66/2.67  found it (size 182)
% 8.66/2.67  
% 8.66/2.67  % SZS output start Proof for theBenchmark
% 8.66/2.67  Assumed formulas after preprocessing and simplification: 
% 8.66/2.67  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v4 = 0) & orthogonal_through_point(v2, v1) = v5 & orthogonal_through_point(v2, v0) = v3 & apart_point_and_line(v1, v3) = v4 & distinct_lines(v3, v5) = 0 &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (unorthogonal_lines(v8, v9) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_lines(v7, v8) = 0) |  ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (unorthogonal_lines(v8, v9) = v11) |  ~ (apart_point_and_line(v6, v7) = v10) |  ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (unorthogonal_lines(v7, v9) = v11) |  ~ (apart_point_and_line(v6, v7) = v10) |  ~ (distinct_lines(v7, v8) = 0) |  ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v7, v8) = v10) |  ~ (distinct_points(v6, v7) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v6, v9) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v9) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v11) |  ~ (apart_point_and_line(v6, v9) = v10) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v7, v8) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_lines(v8, v9) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 | v10 = 0 |  ~ (apart_point_and_line(v6, v9) = v11) |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_points(v6, v7) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v8, v7) = v10) |  ~ (distinct_points(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (apart_point_and_line(v6, v7) = v9) |  ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v10) |  ~ (distinct_lines(v7, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v9) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (apart_point_and_line(v6, v7) = v9) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (convergent_lines(v7, v8) = v10) |  ~ (convergent_lines(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (convergent_lines(v6, v8) = v10) |  ~ (distinct_lines(v7, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = v10) |  ~ (distinct_lines(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_points(v7, v8) = v10) |  ~ (distinct_points(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (unorthogonal_lines(v6, v8) = v9) |  ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) |  ~ (convergent_lines(v6, v8) = v9) |  ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) |  ~ (convergent_lines(v7, v8) = v10) |  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) |  ~ (convergent_lines(v6, v8) = v9) |  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v8, v7) = v9) |  ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v9) |  ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v8) = v9) |  ~ (distinct_lines(v7, v8) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = v9) |  ~ (distinct_lines(v7, v8) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v7, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v6, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v7, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v6, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (orthogonal_through_point(v9, v8) = v7) |  ~ (orthogonal_through_point(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (unorthogonal_lines(v9, v8) = v7) |  ~ (unorthogonal_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (parallel_through_point(v9, v8) = v7) |  ~ (parallel_through_point(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (intersection_point(v9, v8) = v7) |  ~ (intersection_point(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (line_connecting(v9, v8) = v7) |  ~ (line_connecting(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (apart_point_and_line(v9, v8) = v7) |  ~ (apart_point_and_line(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (convergent_lines(v9, v8) = v7) |  ~ (convergent_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (distinct_lines(v9, v8) = v7) |  ~ (distinct_lines(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (distinct_points(v9, v8) = v7) |  ~ (distinct_points(v9, v8) = v6)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) |  ~ (unorthogonal_lines(v6, v7) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) |  ~ (unorthogonal_lines(v6, v7) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) |  ~ (convergent_lines(v7, v8) = v9) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) |  ~ (convergent_lines(v6, v8) = v9) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) |  ~ (distinct_points(v6, v7) = 0) |  ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] : (v8 = 0 |  ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) &  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) &  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) &  ! [v6] :  ! [v7] : ( ~ (distinct_points(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) &  ! [v6] :  ! [v7] : ( ~ (distinct_points(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) &  ! [v6] :  ~ (convergent_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_points(v6, v6) = 0) &  ? [v6] :  ? [v7] :  ? [v8] : orthogonal_through_point(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : unorthogonal_lines(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : parallel_through_point(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : intersection_point(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : line_connecting(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : apart_point_and_line(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : convergent_lines(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : distinct_lines(v7, v6) = v8 &  ? [v6] :  ? [v7] :  ? [v8] : distinct_points(v7, v6) = v8)
% 9.19/2.73  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields:
% 9.19/2.73  | (1)  ~ (all_0_1_1 = 0) & orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0 & orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2 & apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1 & distinct_lines(all_0_2_2, all_0_0_0) = 0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v2, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (unorthogonal_lines(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v1) = v4) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v2) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v0, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (apart_point_and_line(v0, v1) = v3) |  ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 9.19/2.75  |
% 9.19/2.75  | Applying alpha-rule on (1) yields:
% 9.19/2.75  | (2)  ! [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)
% 9.19/2.75  | (3) orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0
% 9.19/2.75  | (4)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 9.19/2.75  | (5)  ! [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)))
% 9.19/2.75  | (6)  ! [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))
% 9.19/2.75  | (7)  ! [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)))
% 9.19/2.75  | (8)  ! [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)))
% 9.19/2.75  | (9) distinct_lines(all_0_2_2, all_0_0_0) = 0
% 9.19/2.75  | (10)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 9.19/2.75  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 9.19/2.75  | (12)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 9.19/2.75  | (13)  ! [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)
% 9.19/2.75  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 9.19/2.75  | (15)  ! [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)))
% 9.19/2.75  | (16)  ! [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)))
% 9.19/2.75  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 9.19/2.75  | (18)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 9.19/2.75  | (19)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 9.19/2.75  | (20)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 9.19/2.75  | (21)  ! [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)))
% 9.19/2.75  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 9.19/2.75  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.19/2.75  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 9.19/2.76  | (25)  ! [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)))
% 9.19/2.76  | (26)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 9.19/2.76  | (27)  ! [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)))
% 9.19/2.76  | (28)  ! [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)))
% 9.19/2.76  | (29)  ! [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)))
% 9.19/2.76  | (30)  ! [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)))
% 9.19/2.76  | (31)  ! [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)))
% 9.19/2.76  | (32)  ! [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)))
% 9.19/2.76  | (33)  ! [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)))
% 9.19/2.76  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 9.19/2.76  | (35)  ! [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)))
% 9.19/2.76  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 9.19/2.76  | (37)  ! [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)))
% 9.19/2.76  | (38)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 9.19/2.76  | (39)  ! [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)))
% 9.19/2.76  | (40)  ! [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)))
% 9.19/2.76  | (41)  ! [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)))
% 9.19/2.76  | (42)  ! [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))
% 9.19/2.76  | (43)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 9.19/2.76  | (44) apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1
% 9.19/2.76  | (45)  ! [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)))
% 9.19/2.76  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 9.19/2.76  | (47)  ! [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))
% 9.19/2.76  | (48)  ! [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)))
% 9.19/2.76  | (49)  ! [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)))
% 9.19/2.76  | (50)  ~ (all_0_1_1 = 0)
% 9.19/2.76  | (51)  ! [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)))
% 9.19/2.76  | (52)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 9.19/2.76  | (53)  ! [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)))
% 9.19/2.76  | (54)  ! [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)))
% 9.19/2.76  | (55)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 9.19/2.76  | (56)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 9.19/2.76  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 9.19/2.76  | (58)  ! [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)))
% 9.19/2.76  | (59)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 9.19/2.76  | (60)  ! [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)))
% 9.19/2.76  | (61)  ! [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)
% 9.19/2.76  | (62)  ! [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))
% 9.19/2.77  | (63) orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2
% 9.19/2.77  | (64)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 9.19/2.77  | (65)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 9.19/2.77  | (66)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 9.19/2.77  | (67)  ! [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)))
% 9.19/2.77  | (68)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 9.19/2.77  | (69)  ! [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)))
% 9.19/2.77  | (70)  ! [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))
% 9.19/2.77  | (71)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 9.19/2.77  | (72)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.19/2.77  | (73)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 9.19/2.77  | (74)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 9.19/2.77  | (75)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 9.19/2.77  | (76)  ! [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)))
% 9.19/2.77  | (77)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 9.19/2.77  | (78)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.19/2.77  | (79)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 9.19/2.77  | (80)  ! [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)))
% 9.19/2.77  | (81)  ! [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))
% 9.19/2.77  | (82)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 9.19/2.77  | (83)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.19/2.77  | (84)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 9.19/2.77  | (85)  ! [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)))
% 9.19/2.77  | (86)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 9.19/2.77  | (87)  ! [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)
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (86) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields:
% 9.19/2.77  | (88)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_3_3) = v0)
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (83) with all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0, yields:
% 9.19/2.77  | (89)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = v0)
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (86) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 9.19/2.77  | (90)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (83) with all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2, yields:
% 9.19/2.77  | (91)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0)
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (7) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.77  | (92) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (40) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.77  | (93) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (41) with all_0_1_1, all_0_1_1, all_0_0_0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.77  | (94) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.77  |
% 9.19/2.77  | Instantiating formula (32) with all_0_1_1, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.77  | (95) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0))
% 9.19/2.77  |
% 9.19/2.77  | Instantiating (91) with all_26_0_33 yields:
% 9.19/2.77  | (96)  ~ (all_26_0_33 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33
% 9.19/2.77  |
% 9.19/2.77  | Applying alpha-rule on (96) yields:
% 9.19/2.77  | (97)  ~ (all_26_0_33 = 0)
% 9.19/2.77  | (98) apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33
% 9.19/2.77  |
% 9.19/2.77  | Instantiating (90) with all_28_0_34 yields:
% 9.19/2.77  | (99)  ~ (all_28_0_34 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34
% 9.19/2.77  |
% 9.19/2.77  | Applying alpha-rule on (99) yields:
% 9.19/2.77  | (100)  ~ (all_28_0_34 = 0)
% 9.19/2.77  | (101) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34
% 9.19/2.77  |
% 9.19/2.77  | Instantiating (89) with all_30_0_35 yields:
% 9.19/2.77  | (102)  ~ (all_30_0_35 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35
% 9.19/2.77  |
% 9.19/2.77  | Applying alpha-rule on (102) yields:
% 9.19/2.77  | (103)  ~ (all_30_0_35 = 0)
% 9.19/2.77  | (104) apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35
% 9.19/2.77  |
% 9.19/2.77  | Instantiating (88) with all_32_0_36 yields:
% 9.19/2.77  | (105)  ~ (all_32_0_36 = 0) & unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36
% 9.19/2.77  |
% 9.19/2.77  | Applying alpha-rule on (105) yields:
% 9.19/2.77  | (106)  ~ (all_32_0_36 = 0)
% 9.19/2.77  | (107) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36
% 9.19/2.77  |
% 9.19/2.77  +-Applying beta-rule and splitting (95), into two cases.
% 9.19/2.77  |-Branch one:
% 9.19/2.77  | (108) all_0_1_1 = 0
% 9.19/2.77  |
% 9.19/2.77  	| Equations (108) can reduce 50 to:
% 9.19/2.77  	| (109) $false
% 9.19/2.77  	|
% 9.19/2.77  	|-The branch is then unsatisfiable
% 9.19/2.77  |-Branch two:
% 9.19/2.77  | (50)  ~ (all_0_1_1 = 0)
% 9.19/2.77  | (111)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & convergent_lines(all_0_2_2, all_0_0_0) = 0))
% 9.19/2.77  |
% 9.19/2.77  	+-Applying beta-rule and splitting (92), into two cases.
% 9.19/2.77  	|-Branch one:
% 9.19/2.77  	| (108) all_0_1_1 = 0
% 9.19/2.77  	|
% 9.19/2.78  		| Equations (108) can reduce 50 to:
% 9.19/2.78  		| (109) $false
% 9.19/2.78  		|
% 9.19/2.78  		|-The branch is then unsatisfiable
% 9.19/2.78  	|-Branch two:
% 9.19/2.78  	| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.78  	| (115)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.78  	|
% 9.19/2.78  		+-Applying beta-rule and splitting (93), into two cases.
% 9.19/2.78  		|-Branch one:
% 9.19/2.78  		| (108) all_0_1_1 = 0
% 9.19/2.78  		|
% 9.19/2.78  			| Equations (108) can reduce 50 to:
% 9.19/2.78  			| (109) $false
% 9.19/2.78  			|
% 9.19/2.78  			|-The branch is then unsatisfiable
% 9.19/2.78  		|-Branch two:
% 9.19/2.78  		| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.78  		| (119)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.78  		|
% 9.19/2.78  			+-Applying beta-rule and splitting (94), into two cases.
% 9.19/2.78  			|-Branch one:
% 9.19/2.78  			| (108) all_0_1_1 = 0
% 9.19/2.78  			|
% 9.19/2.78  				| Equations (108) can reduce 50 to:
% 9.19/2.78  				| (109) $false
% 9.19/2.78  				|
% 9.19/2.78  				|-The branch is then unsatisfiable
% 9.19/2.78  			|-Branch two:
% 9.19/2.78  			| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.78  			| (123)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.78  			|
% 9.19/2.78  				| Instantiating formula (39) with all_32_0_36, all_0_1_1, all_0_3_3, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.78  				| (124) all_32_0_36 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (60) with all_32_0_36, all_0_1_1, all_0_3_3, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.78  				| (125) all_32_0_36 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (39) with all_28_0_34, all_0_1_1, all_0_3_3, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.78  				| (126) all_28_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (49) with all_32_0_36, all_30_0_35, all_0_3_3, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.78  				| (127) all_32_0_36 = 0 | all_30_0_35 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (39) with all_28_0_34, all_30_0_35, all_0_3_3, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields:
% 9.19/2.78  				| (128) all_30_0_35 = 0 | all_28_0_34 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (60) with all_28_0_34, all_30_0_35, all_0_3_3, all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields:
% 9.19/2.78  				| (129) all_30_0_35 = 0 | all_28_0_34 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (7) with all_0_1_1, all_30_0_35, all_0_2_2, all_0_0_0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.78  				| (130) all_30_0_35 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_0_1_1, all_30_0_35, all_0_2_2, all_0_0_0, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, yields:
% 9.19/2.78  				| (131) all_30_0_35 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (7) with all_30_0_35, all_30_0_35, all_0_0_0, all_0_0_0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields:
% 9.19/2.78  				| (132) all_30_0_35 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_30_0_35, all_30_0_35, all_0_0_0, all_0_0_0, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, yields:
% 9.19/2.78  				| (133) all_30_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (39) with all_32_0_36, all_26_0_33, all_0_3_3, all_0_0_0, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (134) all_32_0_36 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (60) with all_32_0_36, all_26_0_33, all_0_3_3, all_0_2_2, all_0_0_0, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (135) all_32_0_36 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (29) with all_28_0_34, all_26_0_33, all_0_3_3, all_0_0_0, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.78  				| (136) all_28_0_34 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (39) with all_28_0_34, all_26_0_33, all_0_3_3, all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (137) all_28_0_34 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (41) with all_26_0_33, all_0_1_1, all_0_0_0, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.78  				| (138) all_26_0_33 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (41) with all_0_1_1, all_26_0_33, all_0_0_0, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.78  				| (139) all_26_0_33 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_26_0_33, all_0_1_1, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (140) all_26_0_33 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_0_1_1, all_26_0_33, all_0_2_2, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (141) all_26_0_33 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_26_0_33, all_30_0_35, all_0_2_2, all_0_0_0, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (142) all_30_0_35 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_30_0_35, all_26_0_33, all_0_0_0, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (143) all_30_0_35 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (45) with all_26_0_33, all_30_0_35, all_0_0_0, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (144) all_30_0_35 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (45) with all_30_0_35, all_26_0_33, all_0_2_2, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35, apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (145) all_30_0_35 = 0 | all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (7) with all_26_0_33, all_26_0_33, all_0_2_2, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (146) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (41) with all_26_0_33, all_26_0_33, all_0_0_0, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.19/2.78  				| (147) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				| Instantiating formula (40) with all_26_0_33, all_26_0_33, all_0_2_2, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33, yields:
% 9.19/2.78  				| (148) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 9.19/2.78  				|
% 9.19/2.78  				+-Applying beta-rule and splitting (124), into two cases.
% 9.19/2.78  				|-Branch one:
% 9.19/2.78  				| (149) all_32_0_36 = 0
% 9.19/2.78  				|
% 9.19/2.78  					| Equations (149) can reduce 106 to:
% 9.19/2.78  					| (109) $false
% 9.19/2.78  					|
% 9.19/2.78  					|-The branch is then unsatisfiable
% 9.19/2.78  				|-Branch two:
% 9.19/2.78  				| (106)  ~ (all_32_0_36 = 0)
% 9.19/2.78  				| (152) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.78  				|
% 9.19/2.78  					+-Applying beta-rule and splitting (148), into two cases.
% 9.19/2.78  					|-Branch one:
% 9.19/2.78  					| (153) all_26_0_33 = 0
% 9.19/2.78  					|
% 9.19/2.78  						| Equations (153) can reduce 97 to:
% 9.19/2.78  						| (109) $false
% 9.19/2.78  						|
% 9.19/2.78  						|-The branch is then unsatisfiable
% 9.19/2.78  					|-Branch two:
% 9.19/2.78  					| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.78  					| (156)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 9.19/2.79  					|
% 9.19/2.79  						+-Applying beta-rule and splitting (125), into two cases.
% 9.19/2.79  						|-Branch one:
% 9.19/2.79  						| (149) all_32_0_36 = 0
% 9.19/2.79  						|
% 9.19/2.79  							| Equations (149) can reduce 106 to:
% 9.19/2.79  							| (109) $false
% 9.19/2.79  							|
% 9.19/2.79  							|-The branch is then unsatisfiable
% 9.19/2.79  						|-Branch two:
% 9.19/2.79  						| (106)  ~ (all_32_0_36 = 0)
% 9.19/2.79  						| (160) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.79  						|
% 9.19/2.79  							+-Applying beta-rule and splitting (152), into two cases.
% 9.19/2.79  							|-Branch one:
% 9.19/2.79  							| (108) all_0_1_1 = 0
% 9.19/2.79  							|
% 9.19/2.79  								| Equations (108) can reduce 50 to:
% 9.19/2.79  								| (109) $false
% 9.19/2.79  								|
% 9.19/2.79  								|-The branch is then unsatisfiable
% 9.19/2.79  							|-Branch two:
% 9.19/2.79  							| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.79  							| (164)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.79  							|
% 9.19/2.79  								+-Applying beta-rule and splitting (147), into two cases.
% 9.19/2.79  								|-Branch one:
% 9.19/2.79  								| (153) all_26_0_33 = 0
% 9.19/2.79  								|
% 9.19/2.79  									| Equations (153) can reduce 97 to:
% 9.19/2.79  									| (109) $false
% 9.19/2.79  									|
% 9.19/2.79  									|-The branch is then unsatisfiable
% 9.19/2.79  								|-Branch two:
% 9.19/2.79  								| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  								| (168)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 9.19/2.79  								|
% 9.19/2.79  									+-Applying beta-rule and splitting (146), into two cases.
% 9.19/2.79  									|-Branch one:
% 9.19/2.79  									| (153) all_26_0_33 = 0
% 9.19/2.79  									|
% 9.19/2.79  										| Equations (153) can reduce 97 to:
% 9.19/2.79  										| (109) $false
% 9.19/2.79  										|
% 9.19/2.79  										|-The branch is then unsatisfiable
% 9.19/2.79  									|-Branch two:
% 9.19/2.79  									| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  									| (115)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.79  									|
% 9.19/2.79  										+-Applying beta-rule and splitting (160), into two cases.
% 9.19/2.79  										|-Branch one:
% 9.19/2.79  										| (108) all_0_1_1 = 0
% 9.19/2.79  										|
% 9.19/2.79  											| Equations (108) can reduce 50 to:
% 9.19/2.79  											| (109) $false
% 9.19/2.79  											|
% 9.19/2.79  											|-The branch is then unsatisfiable
% 9.19/2.79  										|-Branch two:
% 9.19/2.79  										| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.79  										| (176)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.79  										|
% 9.19/2.79  											+-Applying beta-rule and splitting (129), into two cases.
% 9.19/2.79  											|-Branch one:
% 9.19/2.79  											| (177) all_30_0_35 = 0
% 9.19/2.79  											|
% 9.19/2.79  												| Equations (177) can reduce 103 to:
% 9.19/2.79  												| (109) $false
% 9.19/2.79  												|
% 9.19/2.79  												|-The branch is then unsatisfiable
% 9.19/2.79  											|-Branch two:
% 9.19/2.79  											| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  											| (180) all_28_0_34 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.79  											|
% 9.19/2.79  												+-Applying beta-rule and splitting (126), into two cases.
% 9.19/2.79  												|-Branch one:
% 9.19/2.79  												| (181) all_28_0_34 = 0
% 9.19/2.79  												|
% 9.19/2.79  													| Equations (181) can reduce 100 to:
% 9.19/2.79  													| (109) $false
% 9.19/2.79  													|
% 9.19/2.79  													|-The branch is then unsatisfiable
% 9.19/2.79  												|-Branch two:
% 9.19/2.79  												| (100)  ~ (all_28_0_34 = 0)
% 9.19/2.79  												| (184) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.79  												|
% 9.19/2.79  													+-Applying beta-rule and splitting (132), into two cases.
% 9.19/2.79  													|-Branch one:
% 9.19/2.79  													| (177) all_30_0_35 = 0
% 9.19/2.79  													|
% 9.19/2.79  														| Equations (177) can reduce 103 to:
% 9.19/2.79  														| (109) $false
% 9.19/2.79  														|
% 9.19/2.79  														|-The branch is then unsatisfiable
% 9.19/2.79  													|-Branch two:
% 9.19/2.79  													| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  													| (188)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 9.19/2.79  													|
% 9.19/2.79  														+-Applying beta-rule and splitting (133), into two cases.
% 9.19/2.79  														|-Branch one:
% 9.19/2.79  														| (177) all_30_0_35 = 0
% 9.19/2.79  														|
% 9.19/2.79  															| Equations (177) can reduce 103 to:
% 9.19/2.79  															| (109) $false
% 9.19/2.79  															|
% 9.19/2.79  															|-The branch is then unsatisfiable
% 9.19/2.79  														|-Branch two:
% 9.19/2.79  														| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  														| (192)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.79  														|
% 9.19/2.79  															+-Applying beta-rule and splitting (136), into two cases.
% 9.19/2.79  															|-Branch one:
% 9.19/2.79  															| (181) all_28_0_34 = 0
% 9.19/2.79  															|
% 9.19/2.79  																| Equations (181) can reduce 100 to:
% 9.19/2.79  																| (109) $false
% 9.19/2.79  																|
% 9.19/2.79  																|-The branch is then unsatisfiable
% 9.19/2.79  															|-Branch two:
% 9.19/2.79  															| (100)  ~ (all_28_0_34 = 0)
% 9.19/2.79  															| (196) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0))
% 9.19/2.79  															|
% 9.19/2.79  																+-Applying beta-rule and splitting (137), into two cases.
% 9.19/2.79  																|-Branch one:
% 9.19/2.79  																| (181) all_28_0_34 = 0
% 9.19/2.79  																|
% 9.19/2.79  																	| Equations (181) can reduce 100 to:
% 9.19/2.79  																	| (109) $false
% 9.19/2.79  																	|
% 9.19/2.79  																	|-The branch is then unsatisfiable
% 9.19/2.79  																|-Branch two:
% 9.19/2.79  																| (100)  ~ (all_28_0_34 = 0)
% 9.19/2.79  																| (200) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.79  																|
% 9.19/2.79  																	+-Applying beta-rule and splitting (134), into two cases.
% 9.19/2.79  																	|-Branch one:
% 9.19/2.79  																	| (149) all_32_0_36 = 0
% 9.19/2.79  																	|
% 9.19/2.79  																		| Equations (149) can reduce 106 to:
% 9.19/2.79  																		| (109) $false
% 9.19/2.79  																		|
% 9.19/2.79  																		|-The branch is then unsatisfiable
% 9.19/2.79  																	|-Branch two:
% 9.19/2.79  																	| (106)  ~ (all_32_0_36 = 0)
% 9.19/2.79  																	| (204) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.79  																	|
% 9.19/2.79  																		+-Applying beta-rule and splitting (135), into two cases.
% 9.19/2.79  																		|-Branch one:
% 9.19/2.79  																		| (149) all_32_0_36 = 0
% 9.19/2.79  																		|
% 9.19/2.79  																			| Equations (149) can reduce 106 to:
% 9.19/2.79  																			| (109) $false
% 9.19/2.79  																			|
% 9.19/2.79  																			|-The branch is then unsatisfiable
% 9.19/2.79  																		|-Branch two:
% 9.19/2.79  																		| (106)  ~ (all_32_0_36 = 0)
% 9.19/2.79  																		| (208) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.79  																		|
% 9.19/2.79  																			+-Applying beta-rule and splitting (204), into two cases.
% 9.19/2.79  																			|-Branch one:
% 9.19/2.79  																			| (153) all_26_0_33 = 0
% 9.19/2.79  																			|
% 9.19/2.79  																				| Equations (153) can reduce 97 to:
% 9.19/2.79  																				| (109) $false
% 9.19/2.79  																				|
% 9.19/2.79  																				|-The branch is then unsatisfiable
% 9.19/2.79  																			|-Branch two:
% 9.19/2.79  																			| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  																			| (212)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.79  																			|
% 9.19/2.79  																				+-Applying beta-rule and splitting (208), into two cases.
% 9.19/2.79  																				|-Branch one:
% 9.19/2.79  																				| (153) all_26_0_33 = 0
% 9.19/2.79  																				|
% 9.19/2.79  																					| Equations (153) can reduce 97 to:
% 9.19/2.79  																					| (109) $false
% 9.19/2.79  																					|
% 9.19/2.79  																					|-The branch is then unsatisfiable
% 9.19/2.79  																				|-Branch two:
% 9.19/2.79  																				| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  																				| (216)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.79  																				|
% 9.19/2.79  																					+-Applying beta-rule and splitting (180), into two cases.
% 9.19/2.79  																					|-Branch one:
% 9.19/2.79  																					| (181) all_28_0_34 = 0
% 9.19/2.79  																					|
% 9.19/2.79  																						| Equations (181) can reduce 100 to:
% 9.19/2.79  																						| (109) $false
% 9.19/2.79  																						|
% 9.19/2.79  																						|-The branch is then unsatisfiable
% 9.19/2.79  																					|-Branch two:
% 9.19/2.79  																					| (100)  ~ (all_28_0_34 = 0)
% 9.19/2.79  																					| (220)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 9.19/2.79  																					|
% 9.19/2.79  																						+-Applying beta-rule and splitting (128), into two cases.
% 9.19/2.79  																						|-Branch one:
% 9.19/2.79  																						| (177) all_30_0_35 = 0
% 9.19/2.79  																						|
% 9.19/2.79  																							| Equations (177) can reduce 103 to:
% 9.19/2.79  																							| (109) $false
% 9.19/2.79  																							|
% 9.19/2.79  																							|-The branch is then unsatisfiable
% 9.19/2.79  																						|-Branch two:
% 9.19/2.79  																						| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  																						| (224) all_28_0_34 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.79  																						|
% 9.19/2.79  																							+-Applying beta-rule and splitting (138), into two cases.
% 9.19/2.79  																							|-Branch one:
% 9.19/2.79  																							| (153) all_26_0_33 = 0
% 9.19/2.79  																							|
% 9.19/2.79  																								| Equations (153) can reduce 97 to:
% 9.19/2.79  																								| (109) $false
% 9.19/2.79  																								|
% 9.19/2.79  																								|-The branch is then unsatisfiable
% 9.19/2.79  																							|-Branch two:
% 9.19/2.79  																							| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  																							| (228) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.79  																							|
% 9.19/2.79  																								+-Applying beta-rule and splitting (139), into two cases.
% 9.19/2.79  																								|-Branch one:
% 9.19/2.79  																								| (153) all_26_0_33 = 0
% 9.19/2.79  																								|
% 9.19/2.79  																									| Equations (153) can reduce 97 to:
% 9.19/2.79  																									| (109) $false
% 9.19/2.79  																									|
% 9.19/2.79  																									|-The branch is then unsatisfiable
% 9.19/2.79  																								|-Branch two:
% 9.19/2.79  																								| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  																								| (232) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.79  																								|
% 9.19/2.79  																									+-Applying beta-rule and splitting (140), into two cases.
% 9.19/2.79  																									|-Branch one:
% 9.19/2.79  																									| (153) all_26_0_33 = 0
% 9.19/2.79  																									|
% 9.19/2.79  																										| Equations (153) can reduce 97 to:
% 9.19/2.79  																										| (109) $false
% 9.19/2.79  																										|
% 9.19/2.79  																										|-The branch is then unsatisfiable
% 9.19/2.79  																									|-Branch two:
% 9.19/2.79  																									| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  																									| (236) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.79  																									|
% 9.19/2.79  																										+-Applying beta-rule and splitting (141), into two cases.
% 9.19/2.79  																										|-Branch one:
% 9.19/2.79  																										| (153) all_26_0_33 = 0
% 9.19/2.79  																										|
% 9.19/2.79  																											| Equations (153) can reduce 97 to:
% 9.19/2.79  																											| (109) $false
% 9.19/2.79  																											|
% 9.19/2.79  																											|-The branch is then unsatisfiable
% 9.19/2.79  																										|-Branch two:
% 9.19/2.79  																										| (97)  ~ (all_26_0_33 = 0)
% 9.19/2.79  																										| (240) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.79  																										|
% 9.19/2.79  																											+-Applying beta-rule and splitting (144), into two cases.
% 9.19/2.79  																											|-Branch one:
% 9.19/2.79  																											| (177) all_30_0_35 = 0
% 9.19/2.79  																											|
% 9.19/2.79  																												| Equations (177) can reduce 103 to:
% 9.19/2.79  																												| (109) $false
% 9.19/2.79  																												|
% 9.19/2.79  																												|-The branch is then unsatisfiable
% 9.19/2.79  																											|-Branch two:
% 9.19/2.79  																											| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  																											| (244) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.79  																											|
% 9.19/2.79  																												+-Applying beta-rule and splitting (130), into two cases.
% 9.19/2.79  																												|-Branch one:
% 9.19/2.79  																												| (177) all_30_0_35 = 0
% 9.19/2.79  																												|
% 9.19/2.79  																													| Equations (177) can reduce 103 to:
% 9.19/2.79  																													| (109) $false
% 9.19/2.79  																													|
% 9.19/2.79  																													|-The branch is then unsatisfiable
% 9.19/2.79  																												|-Branch two:
% 9.19/2.79  																												| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  																												| (248) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.79  																												|
% 9.19/2.79  																													+-Applying beta-rule and splitting (131), into two cases.
% 9.19/2.79  																													|-Branch one:
% 9.19/2.79  																													| (177) all_30_0_35 = 0
% 9.19/2.79  																													|
% 9.19/2.79  																														| Equations (177) can reduce 103 to:
% 9.19/2.79  																														| (109) $false
% 9.19/2.79  																														|
% 9.19/2.79  																														|-The branch is then unsatisfiable
% 9.19/2.79  																													|-Branch two:
% 9.19/2.79  																													| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  																													| (252) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.79  																													|
% 9.19/2.79  																														+-Applying beta-rule and splitting (142), into two cases.
% 9.19/2.79  																														|-Branch one:
% 9.19/2.79  																														| (177) all_30_0_35 = 0
% 9.19/2.79  																														|
% 9.19/2.79  																															| Equations (177) can reduce 103 to:
% 9.19/2.79  																															| (109) $false
% 9.19/2.79  																															|
% 9.19/2.79  																															|-The branch is then unsatisfiable
% 9.19/2.79  																														|-Branch two:
% 9.19/2.79  																														| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  																														| (256) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.79  																														|
% 9.19/2.79  																															+-Applying beta-rule and splitting (143), into two cases.
% 9.19/2.79  																															|-Branch one:
% 9.19/2.79  																															| (177) all_30_0_35 = 0
% 9.19/2.79  																															|
% 9.19/2.79  																																| Equations (177) can reduce 103 to:
% 9.19/2.79  																																| (109) $false
% 9.19/2.79  																																|
% 9.19/2.79  																																|-The branch is then unsatisfiable
% 9.19/2.79  																															|-Branch two:
% 9.19/2.79  																															| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.79  																															| (260) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.80  																															|
% 9.19/2.80  																																+-Applying beta-rule and splitting (145), into two cases.
% 9.19/2.80  																																|-Branch one:
% 9.19/2.80  																																| (177) all_30_0_35 = 0
% 9.19/2.80  																																|
% 9.19/2.80  																																	| Equations (177) can reduce 103 to:
% 9.19/2.80  																																	| (109) $false
% 9.19/2.80  																																	|
% 9.19/2.80  																																	|-The branch is then unsatisfiable
% 9.19/2.80  																																|-Branch two:
% 9.19/2.80  																																| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.80  																																| (264) all_26_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.80  																																|
% 9.19/2.80  																																	+-Applying beta-rule and splitting (127), into two cases.
% 9.19/2.80  																																	|-Branch one:
% 9.19/2.80  																																	| (149) all_32_0_36 = 0
% 9.19/2.80  																																	|
% 9.19/2.80  																																		| Equations (149) can reduce 106 to:
% 9.19/2.80  																																		| (109) $false
% 9.19/2.80  																																		|
% 9.19/2.80  																																		|-The branch is then unsatisfiable
% 9.19/2.80  																																	|-Branch two:
% 9.19/2.80  																																	| (106)  ~ (all_32_0_36 = 0)
% 9.19/2.80  																																	| (268) all_30_0_35 = 0 |  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0))
% 9.19/2.80  																																	|
% 9.19/2.80  																																		+-Applying beta-rule and splitting (268), into two cases.
% 9.19/2.80  																																		|-Branch one:
% 9.19/2.80  																																		| (177) all_30_0_35 = 0
% 9.19/2.80  																																		|
% 9.19/2.80  																																			| Equations (177) can reduce 103 to:
% 9.19/2.80  																																			| (109) $false
% 9.19/2.80  																																			|
% 9.19/2.80  																																			|-The branch is then unsatisfiable
% 9.19/2.80  																																		|-Branch two:
% 9.19/2.80  																																		| (103)  ~ (all_30_0_35 = 0)
% 9.19/2.80  																																		| (272)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0))
% 9.19/2.80  																																		|
% 9.19/2.80  																																			| Instantiating (272) with all_219_0_127 yields:
% 9.19/2.80  																																			| (273) (all_219_0_127 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_219_0_127 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 9.19/2.80  																																			|
% 9.19/2.80  																																			+-Applying beta-rule and splitting (273), into two cases.
% 9.19/2.80  																																			|-Branch one:
% 9.19/2.80  																																			| (274) all_219_0_127 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0
% 9.19/2.80  																																			|
% 9.19/2.80  																																				| Applying alpha-rule on (274) yields:
% 9.19/2.80  																																				| (275) all_219_0_127 = 0
% 9.19/2.80  																																				| (276) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0
% 9.19/2.80  																																				|
% 9.19/2.80  																																				+-Applying beta-rule and splitting (224), into two cases.
% 9.19/2.80  																																				|-Branch one:
% 9.19/2.80  																																				| (181) all_28_0_34 = 0
% 9.19/2.80  																																				|
% 9.19/2.80  																																					| Equations (181) can reduce 100 to:
% 9.19/2.80  																																					| (109) $false
% 9.19/2.80  																																					|
% 9.19/2.80  																																					|-The branch is then unsatisfiable
% 9.19/2.80  																																				|-Branch two:
% 9.19/2.80  																																				| (100)  ~ (all_28_0_34 = 0)
% 9.19/2.80  																																				| (280)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.80  																																				|
% 9.19/2.80  																																					| Instantiating formula (36) with all_0_2_2, all_0_3_3, 0, all_28_0_34 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields:
% 9.19/2.80  																																					| (181) all_28_0_34 = 0
% 9.19/2.80  																																					|
% 9.19/2.80  																																					| Equations (181) can reduce 100 to:
% 9.19/2.80  																																					| (109) $false
% 9.19/2.80  																																					|
% 9.19/2.80  																																					|-The branch is then unsatisfiable
% 9.19/2.80  																																			|-Branch two:
% 9.19/2.80  																																			| (283) all_219_0_127 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 9.19/2.80  																																			|
% 9.19/2.80  																																				| Applying alpha-rule on (283) yields:
% 9.19/2.80  																																				| (275) all_219_0_127 = 0
% 9.19/2.80  																																				| (285) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 9.19/2.80  																																				|
% 9.19/2.80  																																				+-Applying beta-rule and splitting (236), into two cases.
% 9.19/2.80  																																				|-Branch one:
% 9.19/2.80  																																				| (108) all_0_1_1 = 0
% 9.19/2.80  																																				|
% 9.19/2.80  																																					| Equations (108) can reduce 50 to:
% 9.19/2.80  																																					| (109) $false
% 9.19/2.80  																																					|
% 9.19/2.80  																																					|-The branch is then unsatisfiable
% 9.19/2.80  																																				|-Branch two:
% 9.19/2.80  																																				| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																				| (289)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.80  																																				|
% 9.19/2.80  																																					+-Applying beta-rule and splitting (248), into two cases.
% 9.19/2.80  																																					|-Branch one:
% 9.19/2.80  																																					| (108) all_0_1_1 = 0
% 9.19/2.80  																																					|
% 9.19/2.80  																																						| Equations (108) can reduce 50 to:
% 9.19/2.80  																																						| (109) $false
% 9.19/2.80  																																						|
% 9.19/2.80  																																						|-The branch is then unsatisfiable
% 9.19/2.80  																																					|-Branch two:
% 9.19/2.80  																																					| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																					| (293)  ? [v0] : ((v0 = 0 & convergent_lines(all_0_0_0, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 9.19/2.80  																																					|
% 9.19/2.80  																																						+-Applying beta-rule and splitting (184), into two cases.
% 9.19/2.80  																																						|-Branch one:
% 9.19/2.80  																																						| (108) all_0_1_1 = 0
% 9.19/2.80  																																						|
% 9.19/2.80  																																							| Equations (108) can reduce 50 to:
% 9.19/2.80  																																							| (109) $false
% 9.19/2.80  																																							|
% 9.19/2.80  																																							|-The branch is then unsatisfiable
% 9.19/2.80  																																						|-Branch two:
% 9.19/2.80  																																						| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																						| (297)  ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 9.19/2.80  																																						|
% 9.19/2.80  																																							+-Applying beta-rule and splitting (228), into two cases.
% 9.19/2.80  																																							|-Branch one:
% 9.19/2.80  																																							| (108) all_0_1_1 = 0
% 9.19/2.80  																																							|
% 9.19/2.80  																																								| Equations (108) can reduce 50 to:
% 9.19/2.80  																																								| (109) $false
% 9.19/2.80  																																								|
% 9.19/2.80  																																								|-The branch is then unsatisfiable
% 9.19/2.80  																																							|-Branch two:
% 9.19/2.80  																																							| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																							| (301)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 9.19/2.80  																																							|
% 9.19/2.80  																																								+-Applying beta-rule and splitting (232), into two cases.
% 9.19/2.80  																																								|-Branch one:
% 9.19/2.80  																																								| (108) all_0_1_1 = 0
% 9.19/2.80  																																								|
% 9.19/2.80  																																									| Equations (108) can reduce 50 to:
% 9.19/2.80  																																									| (109) $false
% 9.19/2.80  																																									|
% 9.19/2.80  																																									|-The branch is then unsatisfiable
% 9.19/2.80  																																								|-Branch two:
% 9.19/2.80  																																								| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																								| (305)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.80  																																								|
% 9.19/2.80  																																									+-Applying beta-rule and splitting (240), into two cases.
% 9.19/2.80  																																									|-Branch one:
% 9.19/2.80  																																									| (108) all_0_1_1 = 0
% 9.19/2.80  																																									|
% 9.19/2.80  																																										| Equations (108) can reduce 50 to:
% 9.19/2.80  																																										| (109) $false
% 9.19/2.80  																																										|
% 9.19/2.80  																																										|-The branch is then unsatisfiable
% 9.19/2.80  																																									|-Branch two:
% 9.19/2.80  																																									| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																									| (309)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 9.19/2.80  																																									|
% 9.19/2.80  																																										+-Applying beta-rule and splitting (252), into two cases.
% 9.19/2.80  																																										|-Branch one:
% 9.19/2.80  																																										| (108) all_0_1_1 = 0
% 9.19/2.80  																																										|
% 9.19/2.80  																																											| Equations (108) can reduce 50 to:
% 9.19/2.80  																																											| (109) $false
% 9.19/2.80  																																											|
% 9.19/2.80  																																											|-The branch is then unsatisfiable
% 9.19/2.80  																																										|-Branch two:
% 9.19/2.80  																																										| (50)  ~ (all_0_1_1 = 0)
% 9.19/2.80  																																										| (313)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 9.19/2.80  																																										|
% 9.19/2.80  																																											| Instantiating formula (24) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 9.19/2.80  																																											| (108) all_0_1_1 = 0
% 9.19/2.80  																																											|
% 9.19/2.80  																																											| Equations (108) can reduce 50 to:
% 9.19/2.80  																																											| (109) $false
% 9.19/2.80  																																											|
% 9.19/2.80  																																											|-The branch is then unsatisfiable
% 9.19/2.80  % SZS output end Proof for theBenchmark
% 9.19/2.80  
% 9.19/2.80  2187ms
%------------------------------------------------------------------------------