%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO221+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n015.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 5.81s 1.99s
% Output   : Proof 9.50s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GEO221+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jun 18 14:22:13 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.62/0.61          ____       _                          
% 0.62/0.61    ___  / __ \_____(_)___  ________  __________
% 0.62/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.62/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.62/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.62/0.61  
% 0.62/0.61  A Theorem Prover for First-Order Logic
% 0.62/0.61  (ePrincess v.1.0)
% 0.62/0.61  
% 0.62/0.61  (c) Philipp Rümmer, 2009-2015
% 0.62/0.61  (c) Peter Backeman, 2014-2015
% 0.62/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.62/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.62/0.61  Bug reports to peter@backeman.se
% 0.62/0.61  
% 0.62/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.62/0.61  
% 0.62/0.62  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.66/0.69  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.62/1.00  Prover 0: Preprocessing ...
% 2.01/1.16  Prover 0: Warning: ignoring some quantifiers
% 2.28/1.19  Prover 0: Constructing countermodel ...
% 3.02/1.46  Prover 0: gave up
% 3.02/1.46  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.53/1.50  Prover 1: Preprocessing ...
% 4.04/1.60  Prover 1: Constructing countermodel ...
% 4.04/1.65  Prover 1: gave up
% 4.04/1.65  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 4.04/1.68  Prover 2: Preprocessing ...
% 5.08/1.84  Prover 2: Warning: ignoring some quantifiers
% 5.08/1.85  Prover 2: Constructing countermodel ...
% 5.81/1.99  Prover 2: proved (340ms)
% 5.81/1.99  
% 5.81/1.99  No countermodel exists, formula is valid
% 5.81/1.99  % SZS status Theorem for theBenchmark
% 5.81/1.99  
% 5.81/1.99  Generating proof ... Warning: ignoring some quantifiers
% 8.51/2.68  found it (size 165)
% 8.51/2.68  
% 8.51/2.68  % SZS output start Proof for theBenchmark
% 8.51/2.68  Assumed formulas after preprocessing and simplification: 
% 8.51/2.68  | (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 |  ~ (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] : (v10 = 0 |  ~ (intersection_point(v6, v7) = v9) |  ~ (distinct_points(v8, v9) = v10) |  ? [v11] :  ? [v12] : (( ~ (v12 = 0) &  ~ (v11 = 0) & apart_point_and_line(v8, v7) = v12 & apart_point_and_line(v8, v6) = v11) | ( ~ (v11 = 0) & convergent_lines(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 |  ~ (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] : ( ~ (line_connecting(v6, v7) = v9) |  ~ (apart_point_and_line(v8, v9) = 0) |  ? [v10] :  ? [v11] : ((v11 = 0 & v10 = 0 & distinct_points(v8, v7) = 0 & distinct_points(v8, v6) = 0) | ( ~ (v10 = 0) & distinct_points(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] : (v8 = 0 |  ~ (distinct_lines(v6, v7) = v8) |  ? [v9] : ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9)) &  ! [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] : ( ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v6, v7) = 0) &  ! [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)
% 9.03/2.74  | 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:
% 9.03/2.74  | (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 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) &  ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (unorthogonal_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v1, v2) = v4) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v2) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = v3) |  ~ (distinct_lines(v1, v2) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (unorthogonal_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v1, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) |  ~ (distinct_points(v0, v1) = 0) |  ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2 &  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 9.03/2.77  |
% 9.03/2.77  | Applying alpha-rule on (1) yields:
% 9.03/2.77  | (2)  ! [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)))
% 9.03/2.77  | (3)  ! [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)))
% 9.03/2.77  | (4)  ! [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)))
% 9.03/2.77  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 9.03/2.77  | (6)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 9.03/2.77  | (7)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v3) = v4) |  ~ (distinct_lines(v2, v3) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 9.03/2.77  | (8)  ! [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))
% 9.03/2.77  | (9)  ! [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))
% 9.03/2.77  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 9.03/2.77  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 9.03/2.77  | (12)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 9.03/2.77  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 |  ~ (intersection_point(v0, v1) = v3) |  ~ (distinct_points(v2, v3) = v4) |  ? [v5] :  ? [v6] : (( ~ (v6 = 0) &  ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 9.03/2.77  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 9.03/2.77  | (15)  ! [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)))
% 9.03/2.77  | (16)  ! [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)))
% 9.03/2.77  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 9.03/2.77  | (18)  ! [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)))
% 9.03/2.77  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 9.03/2.77  | (20)  ! [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)))
% 9.03/2.77  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 9.03/2.77  | (22)  ! [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)))
% 9.03/2.77  | (23)  ! [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)
% 9.03/2.77  | (24)  ! [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)))
% 9.03/2.77  | (25) distinct_lines(all_0_2_2, all_0_0_0) = 0
% 9.03/2.77  | (26)  ! [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)))
% 9.03/2.78  | (27)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.03/2.78  | (28)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 9.03/2.78  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (unorthogonal_lines(v3, v2) = v1) |  ~ (unorthogonal_lines(v3, v2) = v0))
% 9.03/2.78  | (30)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 9.03/2.78  | (31) orthogonal_through_point(all_0_3_3, all_0_4_4) = all_0_0_0
% 9.03/2.78  | (32)  ! [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)))
% 9.03/2.78  | (33)  ! [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))
% 9.03/2.78  | (34)  ! [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)))
% 9.03/2.78  | (35)  ! [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)))
% 9.03/2.78  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (line_connecting(v0, v1) = v3) |  ~ (apart_point_and_line(v2, v3) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4)))
% 9.03/2.78  | (37)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 9.03/2.78  | (38)  ! [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)
% 9.03/2.78  | (39)  ? [v0] :  ? [v1] :  ? [v2] : unorthogonal_lines(v1, v0) = v2
% 9.03/2.78  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 9.03/2.78  | (41)  ! [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)))
% 9.03/2.78  | (42)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 9.03/2.78  | (43)  ? [v0] :  ? [v1] :  ? [v2] : parallel_through_point(v1, v0) = v2
% 9.03/2.78  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 9.03/2.78  | (45)  ! [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)
% 9.03/2.78  | (46)  ! [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)))
% 9.03/2.78  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (parallel_through_point(v3, v2) = v1) |  ~ (parallel_through_point(v3, v2) = v0))
% 9.03/2.78  | (48)  ! [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)))
% 9.03/2.78  | (49)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 9.03/2.78  | (50)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 9.03/2.78  | (51)  ! [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)))
% 9.03/2.78  | (52)  ! [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)))
% 9.03/2.78  | (53)  ! [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)))
% 9.03/2.78  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) |  ? [v4] :  ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 9.03/2.78  | (55)  ! [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)))
% 9.03/2.78  | (56)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 9.03/2.78  | (57)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 9.03/2.78  | (58)  ! [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)))
% 9.03/2.78  | (59)  ~ (all_0_1_1 = 0)
% 9.03/2.78  | (60)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 9.03/2.78  | (61)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (orthogonal_through_point(v3, v2) = v1) |  ~ (orthogonal_through_point(v3, v2) = v0))
% 9.03/2.78  | (62)  ! [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)))
% 9.03/2.78  | (63)  ! [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)))
% 9.03/2.78  | (64)  ! [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)))
% 9.03/2.78  | (65)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 9.03/2.78  | (66) orthogonal_through_point(all_0_3_3, all_0_5_5) = all_0_2_2
% 9.03/2.78  | (67)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 9.03/2.78  | (68)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 9.03/2.79  | (69)  ! [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))
% 9.03/2.79  | (70)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 9.03/2.79  | (71) apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1
% 9.03/2.79  | (72)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = 0 |  ~ (distinct_lines(v0, v1) = v2) |  ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))
% 9.03/2.79  | (73)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 9.03/2.79  | (74)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 9.03/2.79  | (75)  ! [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)
% 9.03/2.79  | (76)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0)
% 9.03/2.79  | (77)  ! [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)))
% 9.03/2.79  | (78)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 9.03/2.79  | (79)  ? [v0] :  ? [v1] :  ? [v2] : orthogonal_through_point(v1, v0) = v2
% 9.03/2.79  | (80)  ! [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)))
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (28) 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:
% 9.03/2.79  | (81)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_0_0, all_0_3_3) = v0)
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (27) 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:
% 9.03/2.79  | (82)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = v0)
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (28) 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:
% 9.03/2.79  | (83)  ? [v0] : ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (27) 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:
% 9.03/2.79  | (84)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0)
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (35) 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:
% 9.03/2.79  | (85) 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))
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (58) 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:
% 9.03/2.79  | (86) 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))
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (22) 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:
% 9.03/2.79  | (87) 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))
% 9.03/2.79  |
% 9.03/2.79  | Instantiating formula (26) 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:
% 9.03/2.79  | (88) 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))
% 9.03/2.79  |
% 9.03/2.79  | Instantiating (84) with all_26_0_33 yields:
% 9.03/2.79  | (89)  ~ (all_26_0_33 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33
% 9.03/2.79  |
% 9.03/2.79  | Applying alpha-rule on (89) yields:
% 9.03/2.79  | (90)  ~ (all_26_0_33 = 0)
% 9.03/2.79  | (91) apart_point_and_line(all_0_5_5, all_0_2_2) = all_26_0_33
% 9.03/2.79  |
% 9.03/2.79  | Instantiating (83) with all_28_0_34 yields:
% 9.03/2.79  | (92)  ~ (all_28_0_34 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34
% 9.03/2.79  |
% 9.03/2.79  | Applying alpha-rule on (92) yields:
% 9.03/2.79  | (93)  ~ (all_28_0_34 = 0)
% 9.03/2.79  | (94) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_28_0_34
% 9.03/2.79  |
% 9.03/2.79  | Instantiating (82) with all_30_0_35 yields:
% 9.03/2.79  | (95)  ~ (all_30_0_35 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35
% 9.03/2.79  |
% 9.03/2.79  | Applying alpha-rule on (95) yields:
% 9.03/2.79  | (96)  ~ (all_30_0_35 = 0)
% 9.03/2.79  | (97) apart_point_and_line(all_0_4_4, all_0_0_0) = all_30_0_35
% 9.03/2.79  |
% 9.03/2.79  | Instantiating (81) with all_32_0_36 yields:
% 9.03/2.79  | (98)  ~ (all_32_0_36 = 0) & unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36
% 9.03/2.79  |
% 9.03/2.79  | Applying alpha-rule on (98) yields:
% 9.03/2.79  | (99)  ~ (all_32_0_36 = 0)
% 9.03/2.79  | (100) unorthogonal_lines(all_0_0_0, all_0_3_3) = all_32_0_36
% 9.03/2.79  |
% 9.03/2.79  +-Applying beta-rule and splitting (88), into two cases.
% 9.03/2.79  |-Branch one:
% 9.03/2.79  | (101) all_0_1_1 = 0
% 9.03/2.79  |
% 9.03/2.79  	| Equations (101) can reduce 59 to:
% 9.03/2.79  	| (102) $false
% 9.03/2.79  	|
% 9.03/2.79  	|-The branch is then unsatisfiable
% 9.03/2.79  |-Branch two:
% 9.03/2.79  | (59)  ~ (all_0_1_1 = 0)
% 9.03/2.79  | (104)  ? [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))
% 9.03/2.79  |
% 9.03/2.79  	+-Applying beta-rule and splitting (86), into two cases.
% 9.03/2.79  	|-Branch one:
% 9.03/2.79  	| (101) all_0_1_1 = 0
% 9.03/2.79  	|
% 9.03/2.79  		| Equations (101) can reduce 59 to:
% 9.03/2.79  		| (102) $false
% 9.03/2.79  		|
% 9.03/2.79  		|-The branch is then unsatisfiable
% 9.03/2.79  	|-Branch two:
% 9.03/2.79  	| (59)  ~ (all_0_1_1 = 0)
% 9.03/2.79  	| (108)  ? [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))
% 9.03/2.79  	|
% 9.03/2.79  		+-Applying beta-rule and splitting (87), into two cases.
% 9.03/2.79  		|-Branch one:
% 9.03/2.79  		| (101) all_0_1_1 = 0
% 9.03/2.79  		|
% 9.03/2.79  			| Equations (101) can reduce 59 to:
% 9.03/2.79  			| (102) $false
% 9.03/2.79  			|
% 9.03/2.79  			|-The branch is then unsatisfiable
% 9.03/2.79  		|-Branch two:
% 9.03/2.79  		| (59)  ~ (all_0_1_1 = 0)
% 9.03/2.79  		| (112)  ? [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))
% 9.03/2.79  		|
% 9.03/2.79  			+-Applying beta-rule and splitting (85), into two cases.
% 9.03/2.79  			|-Branch one:
% 9.03/2.79  			| (101) all_0_1_1 = 0
% 9.03/2.79  			|
% 9.03/2.79  				| Equations (101) can reduce 59 to:
% 9.03/2.79  				| (102) $false
% 9.03/2.79  				|
% 9.03/2.79  				|-The branch is then unsatisfiable
% 9.03/2.79  			|-Branch two:
% 9.03/2.79  			| (59)  ~ (all_0_1_1 = 0)
% 9.03/2.79  			| (116)  ? [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))
% 9.03/2.79  			|
% 9.03/2.79  				| Instantiating formula (62) 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:
% 9.03/2.79  				| (117) 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))
% 9.03/2.79  				|
% 9.03/2.79  				| Instantiating formula (34) 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:
% 9.03/2.79  				| (118) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (16) with all_28_0_34, 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_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, distinct_lines(all_0_2_2, all_0_0_0) = 0, yields:
% 9.03/2.80  				| (119) all_28_0_34 = 0 | all_0_1_1 = 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_0_0) = 0))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (64) 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:
% 9.03/2.80  				| (120) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (62) with all_32_0_36, all_30_0_35, all_0_3_3, all_0_0_0, 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_0_0) = all_30_0_35, yields:
% 9.03/2.80  				| (121) all_32_0_36 = 0 | all_30_0_35 = 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_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (62) 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:
% 9.03/2.80  				| (122) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (35) 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:
% 9.03/2.80  				| (123) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (124) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (35) 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:
% 9.03/2.80  				| (125) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (126) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (62) 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:
% 9.03/2.80  				| (127) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (34) 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:
% 9.03/2.80  				| (128) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (22) 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:
% 9.03/2.80  				| (129) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (22) 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:
% 9.03/2.80  				| (130) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (131) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (132) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (133) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (134) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (32) 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:
% 9.03/2.80  				| (135) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (32) 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:
% 9.03/2.80  				| (136) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (35) 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:
% 9.03/2.80  				| (137) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (22) 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:
% 9.03/2.80  				| (138) 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))
% 9.03/2.80  				|
% 9.03/2.80  				| Instantiating formula (58) 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:
% 9.03/2.80  				| (139) 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))
% 9.03/2.80  				|
% 9.03/2.80  				+-Applying beta-rule and splitting (117), into two cases.
% 9.03/2.80  				|-Branch one:
% 9.03/2.80  				| (140) all_32_0_36 = 0
% 9.03/2.80  				|
% 9.03/2.80  					| Equations (140) can reduce 99 to:
% 9.03/2.80  					| (102) $false
% 9.03/2.80  					|
% 9.03/2.80  					|-The branch is then unsatisfiable
% 9.03/2.80  				|-Branch two:
% 9.03/2.80  				| (99)  ~ (all_32_0_36 = 0)
% 9.03/2.80  				| (143) 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))
% 9.03/2.80  				|
% 9.03/2.80  					+-Applying beta-rule and splitting (139), into two cases.
% 9.03/2.80  					|-Branch one:
% 9.03/2.80  					| (144) all_26_0_33 = 0
% 9.03/2.80  					|
% 9.03/2.80  						| Equations (144) can reduce 90 to:
% 9.03/2.80  						| (102) $false
% 9.03/2.80  						|
% 9.03/2.80  						|-The branch is then unsatisfiable
% 9.03/2.80  					|-Branch two:
% 9.03/2.80  					| (90)  ~ (all_26_0_33 = 0)
% 9.03/2.80  					| (147)  ? [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))
% 9.03/2.80  					|
% 9.03/2.80  						+-Applying beta-rule and splitting (118), into two cases.
% 9.03/2.80  						|-Branch one:
% 9.03/2.80  						| (140) all_32_0_36 = 0
% 9.03/2.80  						|
% 9.03/2.80  							| Equations (140) can reduce 99 to:
% 9.03/2.80  							| (102) $false
% 9.03/2.80  							|
% 9.03/2.80  							|-The branch is then unsatisfiable
% 9.03/2.80  						|-Branch two:
% 9.03/2.80  						| (99)  ~ (all_32_0_36 = 0)
% 9.03/2.80  						| (151) 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))
% 9.03/2.80  						|
% 9.03/2.80  							+-Applying beta-rule and splitting (119), into two cases.
% 9.03/2.80  							|-Branch one:
% 9.03/2.80  							| (152) all_28_0_34 = 0
% 9.03/2.80  							|
% 9.03/2.80  								| Equations (152) can reduce 93 to:
% 9.03/2.80  								| (102) $false
% 9.03/2.80  								|
% 9.03/2.80  								|-The branch is then unsatisfiable
% 9.03/2.80  							|-Branch two:
% 9.03/2.80  							| (93)  ~ (all_28_0_34 = 0)
% 9.03/2.80  							| (155) all_0_1_1 = 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_0_0) = 0))
% 9.03/2.81  							|
% 9.03/2.81  								+-Applying beta-rule and splitting (151), into two cases.
% 9.03/2.81  								|-Branch one:
% 9.03/2.81  								| (101) all_0_1_1 = 0
% 9.03/2.81  								|
% 9.03/2.81  									| Equations (101) can reduce 59 to:
% 9.03/2.81  									| (102) $false
% 9.03/2.81  									|
% 9.03/2.81  									|-The branch is then unsatisfiable
% 9.03/2.81  								|-Branch two:
% 9.03/2.81  								| (59)  ~ (all_0_1_1 = 0)
% 9.03/2.81  								| (159)  ? [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))
% 9.03/2.81  								|
% 9.03/2.81  									+-Applying beta-rule and splitting (155), into two cases.
% 9.03/2.81  									|-Branch one:
% 9.03/2.81  									| (101) all_0_1_1 = 0
% 9.03/2.81  									|
% 9.03/2.81  										| Equations (101) can reduce 59 to:
% 9.03/2.81  										| (102) $false
% 9.03/2.81  										|
% 9.03/2.81  										|-The branch is then unsatisfiable
% 9.03/2.81  									|-Branch two:
% 9.03/2.81  									| (59)  ~ (all_0_1_1 = 0)
% 9.03/2.81  									| (163)  ? [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_0_0) = 0))
% 9.03/2.81  									|
% 9.03/2.81  										+-Applying beta-rule and splitting (138), into two cases.
% 9.03/2.81  										|-Branch one:
% 9.03/2.81  										| (144) all_26_0_33 = 0
% 9.03/2.81  										|
% 9.03/2.81  											| Equations (144) can reduce 90 to:
% 9.03/2.81  											| (102) $false
% 9.03/2.81  											|
% 9.03/2.81  											|-The branch is then unsatisfiable
% 9.03/2.81  										|-Branch two:
% 9.03/2.81  										| (90)  ~ (all_26_0_33 = 0)
% 9.03/2.81  										| (167)  ? [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))
% 9.03/2.81  										|
% 9.03/2.81  											+-Applying beta-rule and splitting (137), into two cases.
% 9.03/2.81  											|-Branch one:
% 9.03/2.81  											| (144) all_26_0_33 = 0
% 9.03/2.81  											|
% 9.03/2.81  												| Equations (144) can reduce 90 to:
% 9.03/2.81  												| (102) $false
% 9.03/2.81  												|
% 9.03/2.81  												|-The branch is then unsatisfiable
% 9.03/2.81  											|-Branch two:
% 9.03/2.81  											| (90)  ~ (all_26_0_33 = 0)
% 9.03/2.81  											| (116)  ? [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))
% 9.03/2.81  											|
% 9.03/2.81  												+-Applying beta-rule and splitting (126), into two cases.
% 9.03/2.81  												|-Branch one:
% 9.03/2.81  												| (172) all_30_0_35 = 0
% 9.03/2.81  												|
% 9.03/2.81  													| Equations (172) can reduce 96 to:
% 9.03/2.81  													| (102) $false
% 9.03/2.81  													|
% 9.03/2.81  													|-The branch is then unsatisfiable
% 9.50/2.81  												|-Branch two:
% 9.50/2.81  												| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  												| (175)  ? [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))
% 9.50/2.81  												|
% 9.50/2.81  													+-Applying beta-rule and splitting (125), into two cases.
% 9.50/2.81  													|-Branch one:
% 9.50/2.81  													| (172) all_30_0_35 = 0
% 9.50/2.81  													|
% 9.50/2.81  														| Equations (172) can reduce 96 to:
% 9.50/2.81  														| (102) $false
% 9.50/2.81  														|
% 9.50/2.81  														|-The branch is then unsatisfiable
% 9.50/2.81  													|-Branch two:
% 9.50/2.81  													| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  													| (179)  ? [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))
% 9.50/2.81  													|
% 9.50/2.81  														+-Applying beta-rule and splitting (124), into two cases.
% 9.50/2.81  														|-Branch one:
% 9.50/2.81  														| (172) all_30_0_35 = 0
% 9.50/2.81  														|
% 9.50/2.81  															| Equations (172) can reduce 96 to:
% 9.50/2.81  															| (102) $false
% 9.50/2.81  															|
% 9.50/2.81  															|-The branch is then unsatisfiable
% 9.50/2.81  														|-Branch two:
% 9.50/2.81  														| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  														| (183) 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))
% 9.50/2.81  														|
% 9.50/2.81  															+-Applying beta-rule and splitting (133), into two cases.
% 9.50/2.81  															|-Branch one:
% 9.50/2.81  															| (172) all_30_0_35 = 0
% 9.50/2.81  															|
% 9.50/2.81  																| Equations (172) can reduce 96 to:
% 9.50/2.81  																| (102) $false
% 9.50/2.81  																|
% 9.50/2.81  																|-The branch is then unsatisfiable
% 9.50/2.81  															|-Branch two:
% 9.50/2.81  															| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  															| (187) 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))
% 9.50/2.81  															|
% 9.50/2.81  																+-Applying beta-rule and splitting (134), into two cases.
% 9.50/2.81  																|-Branch one:
% 9.50/2.81  																| (172) all_30_0_35 = 0
% 9.50/2.81  																|
% 9.50/2.81  																	| Equations (172) can reduce 96 to:
% 9.50/2.81  																	| (102) $false
% 9.50/2.81  																	|
% 9.50/2.81  																	|-The branch is then unsatisfiable
% 9.50/2.81  																|-Branch two:
% 9.50/2.81  																| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  																| (191) 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))
% 9.50/2.81  																|
% 9.50/2.81  																	+-Applying beta-rule and splitting (129), into two cases.
% 9.50/2.81  																	|-Branch one:
% 9.50/2.81  																	| (144) all_26_0_33 = 0
% 9.50/2.81  																	|
% 9.50/2.81  																		| Equations (144) can reduce 90 to:
% 9.50/2.81  																		| (102) $false
% 9.50/2.81  																		|
% 9.50/2.81  																		|-The branch is then unsatisfiable
% 9.50/2.81  																	|-Branch two:
% 9.50/2.81  																	| (90)  ~ (all_26_0_33 = 0)
% 9.50/2.81  																	| (195) 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))
% 9.50/2.81  																	|
% 9.50/2.81  																		+-Applying beta-rule and splitting (130), into two cases.
% 9.50/2.81  																		|-Branch one:
% 9.50/2.81  																		| (144) all_26_0_33 = 0
% 9.50/2.81  																		|
% 9.50/2.81  																			| Equations (144) can reduce 90 to:
% 9.50/2.81  																			| (102) $false
% 9.50/2.81  																			|
% 9.50/2.81  																			|-The branch is then unsatisfiable
% 9.50/2.81  																		|-Branch two:
% 9.50/2.81  																		| (90)  ~ (all_26_0_33 = 0)
% 9.50/2.81  																		| (199) 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))
% 9.50/2.81  																		|
% 9.50/2.81  																			+-Applying beta-rule and splitting (131), into two cases.
% 9.50/2.81  																			|-Branch one:
% 9.50/2.81  																			| (144) all_26_0_33 = 0
% 9.50/2.81  																			|
% 9.50/2.81  																				| Equations (144) can reduce 90 to:
% 9.50/2.81  																				| (102) $false
% 9.50/2.81  																				|
% 9.50/2.81  																				|-The branch is then unsatisfiable
% 9.50/2.81  																			|-Branch two:
% 9.50/2.81  																			| (90)  ~ (all_26_0_33 = 0)
% 9.50/2.81  																			| (203) 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))
% 9.50/2.81  																			|
% 9.50/2.81  																				+-Applying beta-rule and splitting (132), into two cases.
% 9.50/2.81  																				|-Branch one:
% 9.50/2.81  																				| (144) all_26_0_33 = 0
% 9.50/2.81  																				|
% 9.50/2.81  																					| Equations (144) can reduce 90 to:
% 9.50/2.81  																					| (102) $false
% 9.50/2.81  																					|
% 9.50/2.81  																					|-The branch is then unsatisfiable
% 9.50/2.81  																				|-Branch two:
% 9.50/2.81  																				| (90)  ~ (all_26_0_33 = 0)
% 9.50/2.81  																				| (207) 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))
% 9.50/2.81  																				|
% 9.50/2.81  																					+-Applying beta-rule and splitting (135), into two cases.
% 9.50/2.81  																					|-Branch one:
% 9.50/2.81  																					| (172) all_30_0_35 = 0
% 9.50/2.81  																					|
% 9.50/2.81  																						| Equations (172) can reduce 96 to:
% 9.50/2.81  																						| (102) $false
% 9.50/2.81  																						|
% 9.50/2.81  																						|-The branch is then unsatisfiable
% 9.50/2.81  																					|-Branch two:
% 9.50/2.81  																					| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  																					| (211) 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))
% 9.50/2.81  																					|
% 9.50/2.81  																						+-Applying beta-rule and splitting (136), into two cases.
% 9.50/2.81  																						|-Branch one:
% 9.50/2.81  																						| (172) all_30_0_35 = 0
% 9.50/2.81  																						|
% 9.50/2.81  																							| Equations (172) can reduce 96 to:
% 9.50/2.81  																							| (102) $false
% 9.50/2.81  																							|
% 9.50/2.81  																							|-The branch is then unsatisfiable
% 9.50/2.81  																						|-Branch two:
% 9.50/2.81  																						| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  																						| (215) 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))
% 9.50/2.81  																						|
% 9.50/2.81  																							+-Applying beta-rule and splitting (123), into two cases.
% 9.50/2.81  																							|-Branch one:
% 9.50/2.81  																							| (172) all_30_0_35 = 0
% 9.50/2.81  																							|
% 9.50/2.81  																								| Equations (172) can reduce 96 to:
% 9.50/2.81  																								| (102) $false
% 9.50/2.81  																								|
% 9.50/2.81  																								|-The branch is then unsatisfiable
% 9.50/2.81  																							|-Branch two:
% 9.50/2.81  																							| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  																							| (219) 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))
% 9.50/2.81  																							|
% 9.50/2.81  																								+-Applying beta-rule and splitting (127), into two cases.
% 9.50/2.81  																								|-Branch one:
% 9.50/2.81  																								| (140) all_32_0_36 = 0
% 9.50/2.81  																								|
% 9.50/2.81  																									| Equations (140) can reduce 99 to:
% 9.50/2.81  																									| (102) $false
% 9.50/2.81  																									|
% 9.50/2.81  																									|-The branch is then unsatisfiable
% 9.50/2.81  																								|-Branch two:
% 9.50/2.81  																								| (99)  ~ (all_32_0_36 = 0)
% 9.50/2.81  																								| (223) 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))
% 9.50/2.81  																								|
% 9.50/2.81  																									+-Applying beta-rule and splitting (128), into two cases.
% 9.50/2.81  																									|-Branch one:
% 9.50/2.81  																									| (140) all_32_0_36 = 0
% 9.50/2.81  																									|
% 9.50/2.81  																										| Equations (140) can reduce 99 to:
% 9.50/2.81  																										| (102) $false
% 9.50/2.81  																										|
% 9.50/2.81  																										|-The branch is then unsatisfiable
% 9.50/2.81  																									|-Branch two:
% 9.50/2.81  																									| (99)  ~ (all_32_0_36 = 0)
% 9.50/2.81  																									| (227) 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))
% 9.50/2.81  																									|
% 9.50/2.81  																										+-Applying beta-rule and splitting (122), into two cases.
% 9.50/2.81  																										|-Branch one:
% 9.50/2.81  																										| (172) all_30_0_35 = 0
% 9.50/2.81  																										|
% 9.50/2.81  																											| Equations (172) can reduce 96 to:
% 9.50/2.81  																											| (102) $false
% 9.50/2.81  																											|
% 9.50/2.81  																											|-The branch is then unsatisfiable
% 9.50/2.81  																										|-Branch two:
% 9.50/2.81  																										| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.81  																										| (231) 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))
% 9.50/2.81  																										|
% 9.50/2.81  																											+-Applying beta-rule and splitting (183), into two cases.
% 9.50/2.81  																											|-Branch one:
% 9.50/2.81  																											| (101) all_0_1_1 = 0
% 9.50/2.81  																											|
% 9.50/2.81  																												| Equations (101) can reduce 59 to:
% 9.50/2.81  																												| (102) $false
% 9.50/2.81  																												|
% 9.50/2.81  																												|-The branch is then unsatisfiable
% 9.50/2.81  																											|-Branch two:
% 9.50/2.81  																											| (59)  ~ (all_0_1_1 = 0)
% 9.50/2.81  																											| (235)  ? [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))
% 9.50/2.81  																											|
% 9.50/2.81  																												+-Applying beta-rule and splitting (195), into two cases.
% 9.50/2.81  																												|-Branch one:
% 9.50/2.81  																												| (101) all_0_1_1 = 0
% 9.50/2.81  																												|
% 9.50/2.81  																													| Equations (101) can reduce 59 to:
% 9.50/2.81  																													| (102) $false
% 9.50/2.81  																													|
% 9.50/2.81  																													|-The branch is then unsatisfiable
% 9.50/2.81  																												|-Branch two:
% 9.50/2.81  																												| (59)  ~ (all_0_1_1 = 0)
% 9.50/2.81  																												| (239)  ? [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))
% 9.50/2.81  																												|
% 9.50/2.81  																													+-Applying beta-rule and splitting (121), into two cases.
% 9.50/2.81  																													|-Branch one:
% 9.50/2.81  																													| (140) all_32_0_36 = 0
% 9.50/2.81  																													|
% 9.50/2.81  																														| Equations (140) can reduce 99 to:
% 9.50/2.81  																														| (102) $false
% 9.50/2.81  																														|
% 9.50/2.81  																														|-The branch is then unsatisfiable
% 9.50/2.81  																													|-Branch two:
% 9.50/2.81  																													| (99)  ~ (all_32_0_36 = 0)
% 9.50/2.81  																													| (243) all_30_0_35 = 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_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 9.50/2.81  																													|
% 9.50/2.81  																														+-Applying beta-rule and splitting (120), into two cases.
% 9.50/2.81  																														|-Branch one:
% 9.50/2.81  																														| (140) all_32_0_36 = 0
% 9.50/2.81  																														|
% 9.50/2.81  																															| Equations (140) can reduce 99 to:
% 9.50/2.81  																															| (102) $false
% 9.50/2.81  																															|
% 9.50/2.81  																															|-The branch is then unsatisfiable
% 9.50/2.81  																														|-Branch two:
% 9.50/2.81  																														| (99)  ~ (all_32_0_36 = 0)
% 9.50/2.81  																														| (247) 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))
% 9.50/2.81  																														|
% 9.50/2.81  																															+-Applying beta-rule and splitting (243), into two cases.
% 9.50/2.81  																															|-Branch one:
% 9.50/2.81  																															| (172) all_30_0_35 = 0
% 9.50/2.81  																															|
% 9.50/2.81  																																| Equations (172) can reduce 96 to:
% 9.50/2.81  																																| (102) $false
% 9.50/2.81  																																|
% 9.50/2.81  																																|-The branch is then unsatisfiable
% 9.50/2.82  																															|-Branch two:
% 9.50/2.82  																															| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.82  																															| (251)  ? [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_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0))
% 9.50/2.82  																															|
% 9.50/2.82  																																+-Applying beta-rule and splitting (247), into two cases.
% 9.50/2.82  																																|-Branch one:
% 9.50/2.82  																																| (172) all_30_0_35 = 0
% 9.50/2.82  																																|
% 9.50/2.82  																																	| Equations (172) can reduce 96 to:
% 9.50/2.82  																																	| (102) $false
% 9.50/2.82  																																	|
% 9.50/2.82  																																	|-The branch is then unsatisfiable
% 9.50/2.82  																																|-Branch two:
% 9.50/2.82  																																| (96)  ~ (all_30_0_35 = 0)
% 9.50/2.82  																																| (255)  ? [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))
% 9.50/2.82  																																|
% 9.50/2.82  																																	| Instantiating (255) with all_213_0_117 yields:
% 9.50/2.82  																																	| (256) (all_213_0_117 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_213_0_117 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 9.50/2.82  																																	|
% 9.50/2.82  																																	+-Applying beta-rule and splitting (199), into two cases.
% 9.50/2.82  																																	|-Branch one:
% 9.50/2.82  																																	| (101) all_0_1_1 = 0
% 9.50/2.82  																																	|
% 9.50/2.82  																																		| Equations (101) can reduce 59 to:
% 9.50/2.82  																																		| (102) $false
% 9.50/2.82  																																		|
% 9.50/2.82  																																		|-The branch is then unsatisfiable
% 9.50/2.82  																																	|-Branch two:
% 9.50/2.82  																																	| (59)  ~ (all_0_1_1 = 0)
% 9.50/2.82  																																	| (260)  ? [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))
% 9.50/2.82  																																	|
% 9.50/2.82  																																		+-Applying beta-rule and splitting (203), into two cases.
% 9.50/2.82  																																		|-Branch one:
% 9.50/2.82  																																		| (101) all_0_1_1 = 0
% 9.50/2.82  																																		|
% 9.50/2.82  																																			| Equations (101) can reduce 59 to:
% 9.50/2.82  																																			| (102) $false
% 9.50/2.82  																																			|
% 9.50/2.82  																																			|-The branch is then unsatisfiable
% 9.50/2.82  																																		|-Branch two:
% 9.50/2.82  																																		| (59)  ~ (all_0_1_1 = 0)
% 9.50/2.82  																																		| (264)  ? [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))
% 9.50/2.82  																																		|
% 9.50/2.82  																																			+-Applying beta-rule and splitting (207), into two cases.
% 9.50/2.82  																																			|-Branch one:
% 9.50/2.82  																																			| (101) all_0_1_1 = 0
% 9.50/2.82  																																			|
% 9.50/2.82  																																				| Equations (101) can reduce 59 to:
% 9.50/2.82  																																				| (102) $false
% 9.50/2.82  																																				|
% 9.50/2.82  																																				|-The branch is then unsatisfiable
% 9.50/2.82  																																			|-Branch two:
% 9.50/2.82  																																			| (59)  ~ (all_0_1_1 = 0)
% 9.50/2.82  																																			| (268)  ? [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))
% 9.50/2.82  																																			|
% 9.50/2.82  																																				+-Applying beta-rule and splitting (256), into two cases.
% 9.50/2.82  																																				|-Branch one:
% 9.50/2.82  																																				| (269) all_213_0_117 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0
% 9.50/2.82  																																				|
% 9.50/2.82  																																					| Applying alpha-rule on (269) yields:
% 9.50/2.82  																																					| (270) all_213_0_117 = 0
% 9.50/2.82  																																					| (271) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0
% 9.50/2.82  																																					|
% 9.50/2.82  																																					+-Applying beta-rule and splitting (231), into two cases.
% 9.50/2.82  																																					|-Branch one:
% 9.50/2.82  																																					| (152) all_28_0_34 = 0
% 9.50/2.82  																																					|
% 9.50/2.82  																																						| Equations (152) can reduce 93 to:
% 9.50/2.82  																																						| (102) $false
% 9.50/2.82  																																						|
% 9.50/2.82  																																						|-The branch is then unsatisfiable
% 9.50/2.82  																																					|-Branch two:
% 9.50/2.82  																																					| (93)  ~ (all_28_0_34 = 0)
% 9.50/2.82  																																					| (275)  ? [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))
% 9.50/2.82  																																					|
% 9.50/2.82  																																						| Instantiating formula (29) 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:
% 9.50/2.82  																																						| (152) all_28_0_34 = 0
% 9.50/2.82  																																						|
% 9.50/2.82  																																						| Equations (152) can reduce 93 to:
% 9.50/2.82  																																						| (102) $false
% 9.50/2.82  																																						|
% 9.50/2.82  																																						|-The branch is then unsatisfiable
% 9.50/2.82  																																				|-Branch two:
% 9.50/2.82  																																				| (278) all_213_0_117 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 9.50/2.82  																																				|
% 9.50/2.82  																																					| Applying alpha-rule on (278) yields:
% 9.50/2.82  																																					| (270) all_213_0_117 = 0
% 9.50/2.82  																																					| (280) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 9.50/2.82  																																					|
% 9.50/2.82  																																					+-Applying beta-rule and splitting (219), into two cases.
% 9.50/2.82  																																					|-Branch one:
% 9.50/2.82  																																					| (101) all_0_1_1 = 0
% 9.50/2.82  																																					|
% 9.50/2.82  																																						| Equations (101) can reduce 59 to:
% 9.50/2.82  																																						| (102) $false
% 9.50/2.82  																																						|
% 9.50/2.82  																																						|-The branch is then unsatisfiable
% 9.50/2.82  																																					|-Branch two:
% 9.50/2.82  																																					| (59)  ~ (all_0_1_1 = 0)
% 9.50/2.82  																																					| (284)  ? [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))
% 9.50/2.82  																																					|
% 9.50/2.82  																																						| Instantiating formula (65) 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:
% 9.50/2.82  																																						| (101) all_0_1_1 = 0
% 9.50/2.82  																																						|
% 9.50/2.82  																																						| Equations (101) can reduce 59 to:
% 9.50/2.82  																																						| (102) $false
% 9.50/2.82  																																						|
% 9.50/2.82  																																						|-The branch is then unsatisfiable
% 9.50/2.82  % SZS output end Proof for theBenchmark
% 9.50/2.82  
% 9.50/2.82  2189ms
%------------------------------------------------------------------------------