%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO189+1 : 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 03:48:25 EDT 2022

% Result   : Theorem 5.36s 2.02s
% Output   : Proof 26.01s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : GEO189+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.14  % Command  : ePrincess-casc -timeout=%d %s
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Sat Jun 18 05:01:13 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.52/0.62          ____       _                          
% 0.52/0.62    ___  / __ \_____(_)___  ________  __________
% 0.52/0.62   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.52/0.62  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.52/0.62  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.52/0.62  
% 0.52/0.62  A Theorem Prover for First-Order Logic
% 0.52/0.62  (ePrincess v.1.0)
% 0.52/0.62  
% 0.52/0.62  (c) Philipp Rümmer, 2009-2015
% 0.52/0.62  (c) Peter Backeman, 2014-2015
% 0.52/0.62  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.52/0.62  Free software under GNU Lesser General Public License (LGPL).
% 0.52/0.62  Bug reports to peter@backeman.se
% 0.52/0.62  
% 0.52/0.62  For more information, visit http://user.uu.se/~petba168/breu/
% 0.52/0.62  
% 0.52/0.62  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.79/0.67  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.74/0.98  Prover 0: Preprocessing ...
% 2.12/1.16  Prover 0: Warning: ignoring some quantifiers
% 2.21/1.19  Prover 0: Constructing countermodel ...
% 3.08/1.45  Prover 0: gave up
% 3.08/1.46  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.22/1.48  Prover 1: Preprocessing ...
% 3.44/1.58  Prover 1: Constructing countermodel ...
% 3.44/1.63  Prover 1: gave up
% 3.44/1.63  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.71/1.65  Prover 2: Preprocessing ...
% 4.34/1.77  Prover 2: Warning: ignoring some quantifiers
% 4.34/1.77  Prover 2: Constructing countermodel ...
% 5.36/2.02  Prover 2: proved (394ms)
% 5.36/2.02  
% 5.36/2.02  No countermodel exists, formula is valid
% 5.36/2.02  % SZS status Theorem for theBenchmark
% 5.36/2.02  
% 5.36/2.02  Generating proof ... Warning: ignoring some quantifiers
% 24.82/7.31  found it (size 556)
% 24.82/7.31  
% 24.82/7.31  % SZS output start Proof for theBenchmark
% 24.82/7.31  Assumed formulas after preprocessing and simplification: 
% 24.82/7.31  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v4 = 0) & line_connecting(v0, v2) = v5 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v1, v5) = 0 & distinct_points(v1, v2) = 0 & distinct_points(v0, v2) = 0 & distinct_points(v0, v1) = 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) |  ~ (distinct_lines(v7, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (convergent_lines(v7, v8) = v10) |  ~ (convergent_lines(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (convergent_lines(v6, v8) = v10) |  ~ (distinct_lines(v7, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_lines(v7, v8) = v10) |  ~ (distinct_lines(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] :  ! [v10] : (v10 = 0 | v9 = 0 |  ~ (distinct_points(v7, v8) = v10) |  ~ (distinct_points(v6, v8) = v9) |  ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (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, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (apart_point_and_line(v6, v7) = 0) |  ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v7, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v8) = v9) |  ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (convergent_lines(v6, v7) = 0) |  ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v7, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_lines(v6, v8) = v9) |  ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v7, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v9 = 0 |  ~ (distinct_points(v6, v8) = v9) |  ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) &  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : (v7 = v6 |  ~ (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] : ( ~ (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] : ( ~ (intersection_point(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (intersection_point(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) &  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (line_connecting(v6, v7) = v8) |  ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) &  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) &  ! [v6] :  ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) &  ! [v6] :  ! [v7] : ( ~ (distinct_points(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) &  ! [v6] :  ! [v7] : ( ~ (distinct_points(v6, v7) = 0) |  ? [v8] :  ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) &  ! [v6] :  ~ (convergent_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_lines(v6, v6) = 0) &  ! [v6] :  ~ (distinct_points(v6, v6) = 0) &  ? [v6] :  ? [v7] :  ? [v8] : 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)
% 25.12/7.36  | 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:
% 25.12/7.36  | (1)  ~ (all_0_1_1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_0_0_0 & line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0 & distinct_points(all_0_4_4, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_3_3) = 0 & distinct_points(all_0_5_5, all_0_4_4) = 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) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_lines(v1, v2) = v4) |  ~ (distinct_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (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, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (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] : ( ~ (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] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) &  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) &  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) &  ! [v0] :  ~ (convergent_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_lines(v0, v0) = 0) &  ! [v0] :  ~ (distinct_points(v0, v0) = 0) &  ? [v0] :  ? [v1] :  ? [v2] : 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
% 25.12/7.38  |
% 25.12/7.38  | Applying alpha-rule on (1) yields:
% 25.12/7.38  | (2)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 25.12/7.38  | (3)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 25.12/7.38  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v0, v2) = v4) |  ~ (distinct_lines(v1, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 25.12/7.38  | (5)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 25.12/7.38  | (6)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 25.12/7.38  | (7)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 25.12/7.38  | (8)  ! [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)))
% 25.12/7.38  | (9)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 25.12/7.38  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 25.12/7.38  | (11)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 25.12/7.38  | (12)  ! [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))
% 25.12/7.38  | (13)  ! [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))
% 25.12/7.38  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.12/7.38  | (15)  ! [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)))
% 25.12/7.38  | (16) line_connecting(all_0_5_5, all_0_3_3) = all_0_0_0
% 25.12/7.38  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 25.12/7.38  | (18)  ! [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)
% 25.12/7.38  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 25.12/7.38  | (20) distinct_points(all_0_5_5, all_0_4_4) = 0
% 25.12/7.38  | (21) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 25.12/7.39  | (22)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 25.12/7.39  | (23)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 25.12/7.39  | (24)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (intersection_point(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 25.12/7.39  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 25.12/7.39  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 25.12/7.39  | (27)  ! [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)))
% 25.12/7.39  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 25.29/7.39  | (29)  ! [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))
% 25.29/7.39  | (30)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 25.29/7.39  | (31)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 25.29/7.39  | (32)  ~ (all_0_1_1 = 0)
% 25.29/7.39  | (33)  ! [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)
% 25.29/7.39  | (34)  ! [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)))
% 25.29/7.39  | (35) distinct_points(all_0_5_5, all_0_3_3) = 0
% 25.29/7.39  | (36)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 25.29/7.39  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 25.29/7.39  | (38)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 25.29/7.39  | (39) distinct_points(all_0_4_4, all_0_3_3) = 0
% 25.29/7.39  | (40)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (line_connecting(v0, v1) = v2) |  ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 25.29/7.39  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 25.29/7.39  | (42)  ! [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)))
% 25.29/7.39  | (43)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 25.29/7.39  | (44)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 25.29/7.39  | (45)  ! [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)))
% 25.29/7.39  | (46)  ! [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))
% 25.29/7.39  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 25.29/7.40  | (48)  ! [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)
% 25.29/7.40  | (49)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 25.29/7.40  | (50) apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1
% 25.29/7.40  | (51) apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 25.29/7.40  | (52)  ! [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)))
% 25.29/7.40  | (53)  ! [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))
% 25.29/7.40  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 25.29/7.40  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 25.29/7.40  | (56)  ! [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)
% 25.29/7.40  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (11) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 25.29/7.40  | (58)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (40) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 25.29/7.40  | (59)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (11) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 25.29/7.40  | (60)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (40) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 25.29/7.40  | (61)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (52) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 25.29/7.40  | (62) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (42) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.40  | (63) 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))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (5) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.40  | (64)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(all_0_3_3, v0) = v1)
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (43) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.40  | (65)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (42) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.40  | (66) all_0_1_1 = 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))
% 25.29/7.40  |
% 25.29/7.40  | Instantiating formula (5) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.40  | (67)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(all_0_3_3, v0) = v1)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating formula (43) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.41  | (68)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating formula (5) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 25.29/7.41  | (69)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating formula (43) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 25.29/7.41  | (70)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (70) with all_20_0_24, all_20_1_25 yields:
% 25.29/7.41  | (71)  ~ (all_20_0_24 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 25.29/7.41  |
% 25.29/7.41  | Applying alpha-rule on (71) yields:
% 25.29/7.41  | (72)  ~ (all_20_0_24 = 0)
% 25.29/7.41  | (73) line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25
% 25.29/7.41  | (74) apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (65) with all_22_0_26, all_22_1_27 yields:
% 25.29/7.41  | (75)  ~ (all_22_0_26 = 0) & line_connecting(all_0_4_4, all_0_3_3) = all_22_1_27 & apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 25.29/7.41  |
% 25.29/7.41  | Applying alpha-rule on (75) yields:
% 25.29/7.41  | (76)  ~ (all_22_0_26 = 0)
% 25.29/7.41  | (77) line_connecting(all_0_4_4, all_0_3_3) = all_22_1_27
% 25.29/7.41  | (78) apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (64) with all_24_0_28, all_24_1_29 yields:
% 25.29/7.41  | (79)  ~ (all_24_0_28 = 0) & line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29 & apart_point_and_line(all_0_3_3, all_24_1_29) = all_24_0_28
% 25.29/7.41  |
% 25.29/7.41  | Applying alpha-rule on (79) yields:
% 25.29/7.41  | (80)  ~ (all_24_0_28 = 0)
% 25.29/7.41  | (81) line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29
% 25.29/7.41  | (82) apart_point_and_line(all_0_3_3, all_24_1_29) = all_24_0_28
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (69) with all_26_0_30, all_26_1_31 yields:
% 25.29/7.41  | (83)  ~ (all_26_0_30 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_26_1_31 & apart_point_and_line(all_0_4_4, all_26_1_31) = all_26_0_30
% 25.29/7.41  |
% 25.29/7.41  | Applying alpha-rule on (83) yields:
% 25.29/7.41  | (84)  ~ (all_26_0_30 = 0)
% 25.29/7.41  | (85) line_connecting(all_0_5_5, all_0_4_4) = all_26_1_31
% 25.29/7.41  | (86) apart_point_and_line(all_0_4_4, all_26_1_31) = all_26_0_30
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (68) with all_28_0_32, all_28_1_33 yields:
% 25.29/7.41  | (87)  ~ (all_28_0_32 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_28_1_33 & apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32
% 25.29/7.41  |
% 25.29/7.41  | Applying alpha-rule on (87) yields:
% 25.29/7.41  | (88)  ~ (all_28_0_32 = 0)
% 25.29/7.41  | (89) line_connecting(all_0_5_5, all_0_3_3) = all_28_1_33
% 25.29/7.41  | (90) apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (67) with all_30_0_34, all_30_1_35 yields:
% 25.29/7.41  | (91)  ~ (all_30_0_34 = 0) & line_connecting(all_0_5_5, all_0_3_3) = all_30_1_35 & apart_point_and_line(all_0_3_3, all_30_1_35) = all_30_0_34
% 25.29/7.41  |
% 25.29/7.41  | Applying alpha-rule on (91) yields:
% 25.29/7.41  | (92)  ~ (all_30_0_34 = 0)
% 25.29/7.41  | (93) line_connecting(all_0_5_5, all_0_3_3) = all_30_1_35
% 25.29/7.41  | (94) apart_point_and_line(all_0_3_3, all_30_1_35) = all_30_0_34
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (61) with all_32_0_36 yields:
% 25.29/7.41  | (95) ( ~ (all_32_0_36 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36) | ( ~ (all_32_0_36 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (59) with all_33_0_37 yields:
% 25.29/7.41  | (96) ( ~ (all_33_0_37 = 0) & apart_point_and_line(all_0_5_5, all_0_0_0) = all_33_0_37) | ( ~ (all_33_0_37 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_33_0_37)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (58) with all_34_0_38 yields:
% 25.29/7.41  | (97) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_34_0_38)
% 25.29/7.41  |
% 25.29/7.41  | Instantiating (60) with all_35_0_39 yields:
% 25.29/7.41  | (98) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39) | ( ~ (all_35_0_39 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39)
% 25.29/7.41  |
% 25.29/7.41  +-Applying beta-rule and splitting (97), into two cases.
% 25.29/7.41  |-Branch one:
% 25.29/7.41  | (99)  ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_38
% 25.29/7.41  |
% 25.29/7.41  	| Applying alpha-rule on (99) yields:
% 25.29/7.41  	| (100)  ~ (all_34_0_38 = 0)
% 25.29/7.41  	| (101) apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_38
% 25.29/7.41  	|
% 25.29/7.41  	+-Applying beta-rule and splitting (98), into two cases.
% 25.29/7.41  	|-Branch one:
% 25.29/7.41  	| (102)  ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39
% 25.29/7.41  	|
% 25.29/7.41  		| Applying alpha-rule on (102) yields:
% 25.29/7.41  		| (103)  ~ (all_35_0_39 = 0)
% 25.29/7.41  		| (104) apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39
% 25.29/7.41  		|
% 25.29/7.41  		+-Applying beta-rule and splitting (95), into two cases.
% 25.29/7.41  		|-Branch one:
% 25.29/7.41  		| (105)  ~ (all_32_0_36 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36
% 25.29/7.41  		|
% 25.29/7.42  			| Applying alpha-rule on (105) yields:
% 25.29/7.42  			| (106)  ~ (all_32_0_36 = 0)
% 25.29/7.42  			| (107) apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36
% 25.29/7.42  			|
% 25.29/7.42  			+-Applying beta-rule and splitting (62), into two cases.
% 25.29/7.42  			|-Branch one:
% 25.29/7.42  			| (108) all_0_1_1 = 0
% 25.29/7.42  			|
% 25.29/7.42  				| Equations (108) can reduce 32 to:
% 25.29/7.42  				| (109) $false
% 25.29/7.42  				|
% 25.29/7.42  				|-The branch is then unsatisfiable
% 25.29/7.42  			|-Branch two:
% 25.29/7.42  			| (32)  ~ (all_0_1_1 = 0)
% 25.29/7.42  			| (111)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.42  			|
% 25.29/7.42  				+-Applying beta-rule and splitting (66), into two cases.
% 25.29/7.42  				|-Branch one:
% 25.29/7.42  				| (108) all_0_1_1 = 0
% 25.29/7.42  				|
% 25.29/7.42  					| Equations (108) can reduce 32 to:
% 25.29/7.42  					| (109) $false
% 25.29/7.42  					|
% 25.29/7.42  					|-The branch is then unsatisfiable
% 25.29/7.42  				|-Branch two:
% 25.29/7.42  				| (32)  ~ (all_0_1_1 = 0)
% 25.29/7.42  				| (115)  ? [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))
% 25.29/7.42  				|
% 25.29/7.42  					+-Applying beta-rule and splitting (63), into two cases.
% 25.29/7.42  					|-Branch one:
% 25.29/7.42  					| (108) all_0_1_1 = 0
% 25.29/7.42  					|
% 25.29/7.42  						| Equations (108) can reduce 32 to:
% 25.29/7.42  						| (109) $false
% 25.29/7.42  						|
% 25.29/7.42  						|-The branch is then unsatisfiable
% 25.29/7.42  					|-Branch two:
% 25.29/7.42  					| (32)  ~ (all_0_1_1 = 0)
% 25.29/7.42  					| (119)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 25.29/7.42  					|
% 25.29/7.42  						+-Applying beta-rule and splitting (96), into two cases.
% 25.29/7.42  						|-Branch one:
% 25.29/7.42  						| (120)  ~ (all_33_0_37 = 0) & apart_point_and_line(all_0_5_5, all_0_0_0) = all_33_0_37
% 25.29/7.42  						|
% 25.29/7.42  							| Applying alpha-rule on (120) yields:
% 25.29/7.42  							| (121)  ~ (all_33_0_37 = 0)
% 25.29/7.42  							| (122) apart_point_and_line(all_0_5_5, all_0_0_0) = all_33_0_37
% 25.29/7.42  							|
% 25.29/7.42  							| Instantiating formula (23) with all_0_4_4, all_0_3_3, all_22_1_27, all_24_1_29 and discharging atoms line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29, line_connecting(all_0_4_4, all_0_3_3) = all_22_1_27, yields:
% 25.29/7.42  							| (123) all_24_1_29 = all_22_1_27
% 25.29/7.42  							|
% 25.29/7.42  							| Instantiating formula (23) with all_0_5_5, all_0_3_3, all_30_1_35, all_0_0_0 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_30_1_35, line_connecting(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 25.29/7.42  							| (124) all_30_1_35 = all_0_0_0
% 25.29/7.42  							|
% 25.29/7.42  							| Instantiating formula (23) with all_0_5_5, all_0_3_3, all_28_1_33, all_30_1_35 and discharging atoms line_connecting(all_0_5_5, all_0_3_3) = all_30_1_35, line_connecting(all_0_5_5, all_0_3_3) = all_28_1_33, yields:
% 25.29/7.42  							| (125) all_30_1_35 = all_28_1_33
% 25.29/7.42  							|
% 25.29/7.42  							| Instantiating formula (23) with all_0_5_5, all_0_4_4, all_26_1_31, all_0_2_2 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_26_1_31, line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 25.29/7.42  							| (126) all_26_1_31 = all_0_2_2
% 25.29/7.42  							|
% 25.29/7.42  							| Instantiating formula (23) with all_0_5_5, all_0_4_4, all_20_1_25, all_26_1_31 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_26_1_31, line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25, yields:
% 25.29/7.42  							| (127) all_26_1_31 = all_20_1_25
% 25.29/7.42  							|
% 25.29/7.42  							| Combining equations (124,125) yields a new equation:
% 25.29/7.42  							| (128) all_28_1_33 = all_0_0_0
% 25.29/7.42  							|
% 25.29/7.42  							| Combining equations (126,127) yields a new equation:
% 25.29/7.42  							| (129) all_20_1_25 = all_0_2_2
% 25.29/7.42  							|
% 25.29/7.42  							| Combining equations (129,127) yields a new equation:
% 25.29/7.42  							| (126) all_26_1_31 = all_0_2_2
% 25.29/7.42  							|
% 25.29/7.42  							| Combining equations (128,125) yields a new equation:
% 25.29/7.42  							| (124) all_30_1_35 = all_0_0_0
% 25.29/7.42  							|
% 25.29/7.42  							| From (124) and (94) follows:
% 25.29/7.42  							| (132) apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34
% 25.29/7.42  							|
% 25.29/7.42  							| From (123) and (82) follows:
% 25.29/7.42  							| (133) apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28
% 25.29/7.42  							|
% 25.29/7.42  							| From (126) and (86) follows:
% 25.29/7.42  							| (134) apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30
% 25.29/7.42  							|
% 25.29/7.42  							| From (128) and (90) follows:
% 25.29/7.42  							| (135) apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32
% 25.29/7.42  							|
% 25.29/7.42  							| From (129) and (74) follows:
% 25.29/7.42  							| (136) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 25.29/7.42  							|
% 25.29/7.42  							| Instantiating formula (41) with all_0_3_3, all_0_0_0, all_30_0_34, all_34_0_38 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_34_0_38, apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, yields:
% 25.29/7.43  							| (137) all_34_0_38 = all_30_0_34
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (41) with all_0_4_4, all_0_2_2, all_26_0_30, all_35_0_39 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.29/7.43  							| (138) all_35_0_39 = all_26_0_30
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (41) with all_0_5_5, all_0_0_0, all_28_0_32, all_33_0_37 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_33_0_37, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.29/7.43  							| (139) all_33_0_37 = all_28_0_32
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (41) with all_0_5_5, all_0_2_2, all_20_0_24, all_32_0_36 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.29/7.43  							| (140) all_32_0_36 = all_20_0_24
% 25.29/7.43  							|
% 25.29/7.43  							| Equations (138) can reduce 103 to:
% 25.29/7.43  							| (84)  ~ (all_26_0_30 = 0)
% 25.29/7.43  							|
% 25.29/7.43  							| Equations (137) can reduce 100 to:
% 25.29/7.43  							| (92)  ~ (all_30_0_34 = 0)
% 25.29/7.43  							|
% 25.29/7.43  							| Equations (139) can reduce 121 to:
% 25.29/7.43  							| (88)  ~ (all_28_0_32 = 0)
% 25.29/7.43  							|
% 25.29/7.43  							| Equations (140) can reduce 106 to:
% 25.29/7.43  							| (72)  ~ (all_20_0_24 = 0)
% 25.29/7.43  							|
% 25.29/7.43  							| From (137) and (101) follows:
% 25.29/7.43  							| (132) apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34
% 25.29/7.43  							|
% 25.29/7.43  							| From (138) and (104) follows:
% 25.29/7.43  							| (134) apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30
% 25.29/7.43  							|
% 25.29/7.43  							| From (139) and (122) follows:
% 25.29/7.43  							| (135) apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32
% 25.29/7.43  							|
% 25.29/7.43  							| From (140) and (107) follows:
% 25.29/7.43  							| (136) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (42) with all_24_0_28, all_0_1_1, all_22_1_27, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.43  							| (149) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (42) with all_24_0_28, all_0_1_1, all_22_1_27, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.43  							| (150) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 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_22_1_27) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (42) with all_0_1_1, all_24_0_28, all_0_2_2, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.43  							| (151) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (52) with all_24_0_28, all_0_1_1, all_22_1_27, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 25.29/7.43  							| (152) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (52) with all_0_1_1, all_24_0_28, all_0_2_2, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 25.29/7.43  							| (153) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (42) with all_24_0_28, all_24_0_28, all_22_1_27, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.43  							| (154) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (42) with all_24_0_28, all_24_0_28, all_22_1_27, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.43  							| (155) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (52) with all_24_0_28, all_24_0_28, all_22_1_27, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, yields:
% 25.29/7.43  							| (156) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.43  							|
% 25.29/7.43  							| Instantiating formula (42) with all_30_0_34, all_0_1_1, all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (157) all_30_0_34 = 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_2_2, all_0_0_0) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_0_1_1, all_30_0_34, all_0_2_2, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (158) all_30_0_34 = 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))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_30_0_34, all_0_1_1, all_0_0_0, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (159) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (52) with all_30_0_34, all_0_1_1, all_0_0_0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 25.29/7.44  							| (160) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_30_0_34, all_24_0_28, all_0_0_0, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (161) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_30_0_34, all_24_0_28, all_0_0_0, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (162) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_24_0_28, all_30_0_34, all_22_1_27, all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (163) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 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_22_1_27) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (52) with all_30_0_34, all_24_0_28, all_0_0_0, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, yields:
% 25.29/7.44  							| (164) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (52) with all_24_0_28, all_30_0_34, all_22_1_27, all_0_0_0, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, yields:
% 25.29/7.44  							| (165) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_30_0_34, all_30_0_34, all_0_0_0, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (166) all_30_0_34 = 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))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (42) with all_30_0_34, all_30_0_34, all_0_0_0, all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.29/7.44  							| (167) all_30_0_34 = 0 |  ? [v0] : ((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_0_0) = v0))
% 25.29/7.44  							|
% 25.29/7.44  							| Instantiating formula (52) with all_30_0_34, all_30_0_34, all_0_0_0, all_0_0_0, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, yields:
% 25.29/7.44  							| (168) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (52) with all_22_0_26, all_0_1_1, all_22_1_27, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (169) all_22_0_26 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (52) with all_0_1_1, all_22_0_26, all_0_2_2, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (170) all_22_0_26 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (27) with all_22_0_26, all_0_1_1, all_0_2_2, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (171) all_22_0_26 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (52) with all_22_0_26, all_24_0_28, all_22_1_27, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (172) all_24_0_28 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (52) with all_22_0_26, all_30_0_34, all_22_1_27, all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (173) all_30_0_34 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 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_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (52) with all_30_0_34, all_22_0_26, all_0_0_0, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (174) all_30_0_34 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (27) with all_22_0_26, all_30_0_34, all_0_0_0, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (175) all_30_0_34 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (42) with all_22_0_26, all_22_0_26, all_22_1_27, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 25.29/7.45  							| (176) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 25.29/7.45  							|
% 25.29/7.45  							| Instantiating formula (52) with all_22_0_26, all_22_0_26, all_22_1_27, all_22_1_27, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 25.29/7.45  							| (177) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 25.29/7.45  							|
% 25.29/7.46  							| Instantiating formula (52) with all_26_0_30, all_0_1_1, all_0_2_2, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.29/7.46  							| (178) all_26_0_30 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.46  							|
% 25.29/7.46  							| Instantiating formula (33) with all_26_0_30, 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) = 0, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.29/7.46  							| (179) all_26_0_30 = 0 | distinct_lines(all_0_0_0, all_0_2_2) = 0
% 25.29/7.46  							|
% 25.29/7.46  							| Instantiating formula (52) with all_26_0_30, all_24_0_28, all_0_2_2, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.29/7.46  							| (180) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.29/7.46  							|
% 25.29/7.46  							| Instantiating formula (27) with all_26_0_30, all_24_0_28, all_22_1_27, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.29/7.46  							| (181) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (52) with all_26_0_30, all_30_0_34, all_0_2_2, all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.64/7.46  							| (182) all_30_0_34 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (52) with all_30_0_34, all_26_0_30, all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.64/7.46  							| (183) all_30_0_34 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (27) with all_26_0_30, all_30_0_34, all_0_0_0, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.64/7.46  							| (184) all_30_0_34 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (42) with all_26_0_30, all_22_0_26, all_0_2_2, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 25.64/7.46  							| (185) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (52) with all_22_0_26, all_26_0_30, all_22_1_27, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 25.64/7.46  							| (186) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (52) with all_26_0_30, all_26_0_30, 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_26_0_30, yields:
% 25.64/7.46  							| (187) all_26_0_30 = 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))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (52) with all_28_0_32, all_0_1_1, all_0_0_0, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.64/7.46  							| (188) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (52) with all_0_1_1, all_28_0_32, all_0_2_2, all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.64/7.46  							| (189) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.64/7.46  							|
% 25.64/7.46  							| Instantiating formula (27) with all_28_0_32, all_0_1_1, all_0_2_2, all_0_0_0, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.64/7.46  							| (190) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.64/7.47  							|
% 25.64/7.47  							| Instantiating formula (27) with all_0_1_1, all_28_0_32, all_0_0_0, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.64/7.47  							| (191) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.64/7.47  							|
% 25.64/7.47  							| Instantiating formula (52) with all_28_0_32, all_24_0_28, all_0_0_0, all_22_1_27, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.64/7.47  							| (192) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (27) with all_28_0_32, all_24_0_28, all_22_1_27, all_0_0_0, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (193) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (27) with all_24_0_28, all_28_0_32, all_0_0_0, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (194) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_28_0_32, all_30_0_34, all_0_0_0, all_0_0_0, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (195) all_30_0_34 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_28_0_32, all_22_0_26, all_0_0_0, all_22_1_27, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (196) all_28_0_32 = 0 | all_22_0_26 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (27) with all_22_0_26, all_28_0_32, all_0_0_0, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (197) all_28_0_32 = 0 | all_22_0_26 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_28_0_32, all_26_0_30, 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_26_0_30, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (198) all_28_0_32 = 0 | all_26_0_30 = 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_2_2) = 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))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (27) with all_26_0_30, all_28_0_32, 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_26_0_30, apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (199) all_28_0_32 = 0 | all_26_0_30 = 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_2_2) = 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))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (34) with all_28_0_32, all_28_0_32, all_0_0_0, all_0_0_0, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 25.68/7.47  							| (200) all_28_0_32 = 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))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_28_0_32, all_28_0_32, all_0_0_0, all_0_0_0, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, yields:
% 25.68/7.47  							| (201) all_28_0_32 = 0 |  ? [v0] : ((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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_20_0_24, all_0_1_1, all_0_2_2, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.47  							| (202) all_20_0_24 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_20_0_24, all_24_0_28, all_0_2_2, all_22_1_27, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.47  							| (203) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_20_0_24, all_30_0_34, all_0_2_2, all_0_0_0, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.47  							| (204) all_30_0_34 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.68/7.47  							|
% 25.68/7.47  							| Instantiating formula (52) with all_30_0_34, all_20_0_24, all_0_0_0, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.47  							| (205) all_30_0_34 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (27) with all_20_0_24, all_30_0_34, all_0_0_0, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (206) all_30_0_34 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (27) with all_30_0_34, all_20_0_24, all_0_2_2, all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (207) all_30_0_34 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (52) with all_20_0_24, all_22_0_26, all_0_2_2, all_22_1_27, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (208) all_22_0_26 = 0 | all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (52) with all_22_0_26, all_20_0_24, all_22_1_27, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (209) all_22_0_26 = 0 | all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (27) with all_20_0_24, all_22_0_26, all_22_1_27, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (210) all_22_0_26 = 0 | all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (27) with all_22_0_26, all_20_0_24, all_0_2_2, all_22_1_27, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (211) all_22_0_26 = 0 | all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (34) with all_20_0_24, all_28_0_32, all_0_2_2, all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.68/7.48  							| (212) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (34) with all_28_0_32, all_20_0_24, all_0_0_0, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 25.68/7.48  							| (213) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (34) with all_28_0_32, all_20_0_24, 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_5_5, all_0_0_0) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 25.68/7.48  							| (214) all_28_0_32 = 0 | all_20_0_24 = 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_2_2, all_0_0_0) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (52) with all_20_0_24, all_28_0_32, all_0_2_2, all_0_0_0, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (215) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (52) with all_28_0_32, all_20_0_24, 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_0_0) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 25.68/7.48  							| (216) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.68/7.48  							|
% 25.68/7.48  							| Instantiating formula (52) with all_20_0_24, all_20_0_24, 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_20_0_24, yields:
% 25.68/7.48  							| (217) all_20_0_24 = 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))
% 25.68/7.48  							|
% 25.68/7.48  							+-Applying beta-rule and splitting (154), into two cases.
% 25.68/7.48  							|-Branch one:
% 25.68/7.48  							| (218) all_24_0_28 = 0
% 25.68/7.48  							|
% 25.68/7.48  								| Equations (218) can reduce 80 to:
% 25.68/7.48  								| (109) $false
% 25.68/7.48  								|
% 25.68/7.48  								|-The branch is then unsatisfiable
% 25.68/7.48  							|-Branch two:
% 25.68/7.48  							| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.48  							| (221)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 25.68/7.48  							|
% 25.68/7.48  								+-Applying beta-rule and splitting (168), into two cases.
% 25.68/7.48  								|-Branch one:
% 25.68/7.48  								| (222) all_30_0_34 = 0
% 25.68/7.48  								|
% 25.68/7.48  									| Equations (222) can reduce 92 to:
% 25.68/7.48  									| (109) $false
% 25.68/7.48  									|
% 25.68/7.48  									|-The branch is then unsatisfiable
% 25.68/7.48  								|-Branch two:
% 25.68/7.48  								| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.48  								| (225)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.48  								|
% 25.68/7.48  									+-Applying beta-rule and splitting (217), into two cases.
% 25.68/7.48  									|-Branch one:
% 25.68/7.48  									| (226) all_20_0_24 = 0
% 25.68/7.48  									|
% 25.68/7.48  										| Equations (226) can reduce 72 to:
% 25.68/7.48  										| (109) $false
% 25.68/7.48  										|
% 25.68/7.48  										|-The branch is then unsatisfiable
% 25.68/7.48  									|-Branch two:
% 25.68/7.48  									| (72)  ~ (all_20_0_24 = 0)
% 25.68/7.48  									| (229)  ? [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))
% 25.68/7.48  									|
% 25.68/7.48  										+-Applying beta-rule and splitting (153), into two cases.
% 25.68/7.48  										|-Branch one:
% 25.68/7.48  										| (218) all_24_0_28 = 0
% 25.68/7.48  										|
% 25.68/7.48  											| Equations (218) can reduce 80 to:
% 25.68/7.48  											| (109) $false
% 25.68/7.48  											|
% 25.68/7.48  											|-The branch is then unsatisfiable
% 25.68/7.48  										|-Branch two:
% 25.68/7.48  										| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.48  										| (233) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.48  										|
% 25.68/7.48  											+-Applying beta-rule and splitting (149), into two cases.
% 25.68/7.48  											|-Branch one:
% 25.68/7.48  											| (218) all_24_0_28 = 0
% 25.68/7.48  											|
% 25.68/7.48  												| Equations (218) can reduce 80 to:
% 25.68/7.48  												| (109) $false
% 25.68/7.48  												|
% 25.68/7.48  												|-The branch is then unsatisfiable
% 25.68/7.48  											|-Branch two:
% 25.68/7.48  											| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.48  											| (237) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 25.68/7.49  											|
% 25.68/7.49  												+-Applying beta-rule and splitting (167), into two cases.
% 25.68/7.49  												|-Branch one:
% 25.68/7.49  												| (222) all_30_0_34 = 0
% 25.68/7.49  												|
% 25.68/7.49  													| Equations (222) can reduce 92 to:
% 25.68/7.49  													| (109) $false
% 25.68/7.49  													|
% 25.68/7.49  													|-The branch is then unsatisfiable
% 25.68/7.49  												|-Branch two:
% 25.68/7.49  												| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  												| (241)  ? [v0] : ((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_0_0) = v0))
% 25.68/7.49  												|
% 25.68/7.49  													+-Applying beta-rule and splitting (170), into two cases.
% 25.68/7.49  													|-Branch one:
% 25.68/7.49  													| (242) all_22_0_26 = 0
% 25.68/7.49  													|
% 25.68/7.49  														| Equations (242) can reduce 76 to:
% 25.68/7.49  														| (109) $false
% 25.68/7.49  														|
% 25.68/7.49  														|-The branch is then unsatisfiable
% 25.68/7.49  													|-Branch two:
% 25.68/7.49  													| (76)  ~ (all_22_0_26 = 0)
% 25.68/7.49  													| (245) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.68/7.49  													|
% 25.68/7.49  														+-Applying beta-rule and splitting (165), into two cases.
% 25.68/7.49  														|-Branch one:
% 25.68/7.49  														| (222) all_30_0_34 = 0
% 25.68/7.49  														|
% 25.68/7.49  															| Equations (222) can reduce 92 to:
% 25.68/7.49  															| (109) $false
% 25.68/7.49  															|
% 25.68/7.49  															|-The branch is then unsatisfiable
% 25.68/7.49  														|-Branch two:
% 25.68/7.49  														| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  														| (249) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.49  														|
% 25.68/7.49  															+-Applying beta-rule and splitting (164), into two cases.
% 25.68/7.49  															|-Branch one:
% 25.68/7.49  															| (222) all_30_0_34 = 0
% 25.68/7.49  															|
% 25.68/7.49  																| Equations (222) can reduce 92 to:
% 25.68/7.49  																| (109) $false
% 25.68/7.49  																|
% 25.68/7.49  																|-The branch is then unsatisfiable
% 25.68/7.49  															|-Branch two:
% 25.68/7.49  															| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  															| (253) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.49  															|
% 25.68/7.49  																+-Applying beta-rule and splitting (171), into two cases.
% 25.68/7.49  																|-Branch one:
% 25.68/7.49  																| (242) all_22_0_26 = 0
% 25.68/7.49  																|
% 25.68/7.49  																	| Equations (242) can reduce 76 to:
% 25.68/7.49  																	| (109) $false
% 25.68/7.49  																	|
% 25.68/7.49  																	|-The branch is then unsatisfiable
% 25.68/7.49  																|-Branch two:
% 25.68/7.49  																| (76)  ~ (all_22_0_26 = 0)
% 25.68/7.49  																| (257) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.49  																|
% 25.68/7.49  																	+-Applying beta-rule and splitting (166), into two cases.
% 25.68/7.49  																	|-Branch one:
% 25.68/7.49  																	| (222) all_30_0_34 = 0
% 25.68/7.49  																	|
% 25.68/7.49  																		| Equations (222) can reduce 92 to:
% 25.68/7.49  																		| (109) $false
% 25.68/7.49  																		|
% 25.68/7.49  																		|-The branch is then unsatisfiable
% 25.68/7.49  																	|-Branch two:
% 25.68/7.49  																	| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  																	| (261)  ? [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))
% 25.68/7.49  																	|
% 25.68/7.49  																		+-Applying beta-rule and splitting (215), into two cases.
% 25.68/7.49  																		|-Branch one:
% 25.68/7.49  																		| (262) all_28_0_32 = 0
% 25.68/7.49  																		|
% 25.68/7.49  																			| Equations (262) can reduce 88 to:
% 25.68/7.49  																			| (109) $false
% 25.68/7.49  																			|
% 25.68/7.49  																			|-The branch is then unsatisfiable
% 25.68/7.49  																		|-Branch two:
% 25.68/7.49  																		| (88)  ~ (all_28_0_32 = 0)
% 25.68/7.49  																		| (265) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.68/7.49  																		|
% 25.68/7.49  																			+-Applying beta-rule and splitting (216), into two cases.
% 25.68/7.49  																			|-Branch one:
% 25.68/7.49  																			| (262) all_28_0_32 = 0
% 25.68/7.49  																			|
% 25.68/7.49  																				| Equations (262) can reduce 88 to:
% 25.68/7.49  																				| (109) $false
% 25.68/7.49  																				|
% 25.68/7.49  																				|-The branch is then unsatisfiable
% 25.68/7.49  																			|-Branch two:
% 25.68/7.49  																			| (88)  ~ (all_28_0_32 = 0)
% 25.68/7.49  																			| (269) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.68/7.49  																			|
% 25.68/7.49  																				+-Applying beta-rule and splitting (237), into two cases.
% 25.68/7.49  																				|-Branch one:
% 25.68/7.49  																				| (108) all_0_1_1 = 0
% 25.68/7.49  																				|
% 25.68/7.49  																					| Equations (108) can reduce 32 to:
% 25.68/7.49  																					| (109) $false
% 25.68/7.49  																					|
% 25.68/7.49  																					|-The branch is then unsatisfiable
% 25.68/7.49  																				|-Branch two:
% 25.68/7.49  																				| (32)  ~ (all_0_1_1 = 0)
% 25.68/7.49  																				| (273)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 25.68/7.49  																				|
% 25.68/7.49  																					+-Applying beta-rule and splitting (163), into two cases.
% 25.68/7.49  																					|-Branch one:
% 25.68/7.49  																					| (222) all_30_0_34 = 0
% 25.68/7.49  																					|
% 25.68/7.49  																						| Equations (222) can reduce 92 to:
% 25.68/7.49  																						| (109) $false
% 25.68/7.49  																						|
% 25.68/7.49  																						|-The branch is then unsatisfiable
% 25.68/7.49  																					|-Branch two:
% 25.68/7.49  																					| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  																					| (277) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 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_22_1_27) = v0))
% 25.68/7.49  																					|
% 25.68/7.49  																						+-Applying beta-rule and splitting (161), into two cases.
% 25.68/7.49  																						|-Branch one:
% 25.68/7.49  																						| (222) all_30_0_34 = 0
% 25.68/7.49  																						|
% 25.68/7.49  																							| Equations (222) can reduce 92 to:
% 25.68/7.49  																							| (109) $false
% 25.68/7.49  																							|
% 25.68/7.49  																							|-The branch is then unsatisfiable
% 25.68/7.49  																						|-Branch two:
% 25.68/7.49  																						| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  																						| (281) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0))
% 25.68/7.49  																						|
% 25.68/7.49  																							+-Applying beta-rule and splitting (162), into two cases.
% 25.68/7.49  																							|-Branch one:
% 25.68/7.49  																							| (222) all_30_0_34 = 0
% 25.68/7.49  																							|
% 25.68/7.49  																								| Equations (222) can reduce 92 to:
% 25.68/7.49  																								| (109) $false
% 25.68/7.49  																								|
% 25.68/7.49  																								|-The branch is then unsatisfiable
% 25.68/7.49  																							|-Branch two:
% 25.68/7.49  																							| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.49  																							| (285) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0))
% 25.68/7.49  																							|
% 25.68/7.49  																								+-Applying beta-rule and splitting (245), into two cases.
% 25.68/7.49  																								|-Branch one:
% 25.68/7.49  																								| (108) all_0_1_1 = 0
% 25.68/7.49  																								|
% 25.68/7.49  																									| Equations (108) can reduce 32 to:
% 25.68/7.49  																									| (109) $false
% 25.68/7.49  																									|
% 25.68/7.49  																									|-The branch is then unsatisfiable
% 25.68/7.49  																								|-Branch two:
% 25.68/7.49  																								| (32)  ~ (all_0_1_1 = 0)
% 25.68/7.49  																								| (289)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.68/7.49  																								|
% 25.68/7.49  																									+-Applying beta-rule and splitting (253), into two cases.
% 25.68/7.49  																									|-Branch one:
% 25.68/7.49  																									| (218) all_24_0_28 = 0
% 25.68/7.49  																									|
% 25.68/7.49  																										| Equations (218) can reduce 80 to:
% 25.68/7.49  																										| (109) $false
% 25.68/7.49  																										|
% 25.68/7.49  																										|-The branch is then unsatisfiable
% 25.68/7.49  																									|-Branch two:
% 25.68/7.49  																									| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.49  																									| (293)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.49  																									|
% 25.68/7.49  																										+-Applying beta-rule and splitting (257), into two cases.
% 25.68/7.49  																										|-Branch one:
% 25.68/7.49  																										| (108) all_0_1_1 = 0
% 25.68/7.49  																										|
% 25.68/7.49  																											| Equations (108) can reduce 32 to:
% 25.68/7.49  																											| (109) $false
% 25.68/7.49  																											|
% 25.68/7.49  																											|-The branch is then unsatisfiable
% 25.68/7.49  																										|-Branch two:
% 25.68/7.49  																										| (32)  ~ (all_0_1_1 = 0)
% 25.68/7.49  																										| (297)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.49  																										|
% 25.68/7.49  																											+-Applying beta-rule and splitting (277), into two cases.
% 25.68/7.49  																											|-Branch one:
% 25.68/7.49  																											| (218) all_24_0_28 = 0
% 25.68/7.49  																											|
% 25.68/7.49  																												| Equations (218) can reduce 80 to:
% 25.68/7.49  																												| (109) $false
% 25.68/7.49  																												|
% 25.68/7.49  																												|-The branch is then unsatisfiable
% 25.68/7.49  																											|-Branch two:
% 25.68/7.49  																											| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.49  																											| (301)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 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_22_1_27) = v0))
% 25.68/7.49  																											|
% 25.68/7.49  																												+-Applying beta-rule and splitting (156), into two cases.
% 25.68/7.49  																												|-Branch one:
% 25.68/7.49  																												| (218) all_24_0_28 = 0
% 25.68/7.49  																												|
% 25.68/7.49  																													| Equations (218) can reduce 80 to:
% 25.68/7.49  																													| (109) $false
% 25.68/7.49  																													|
% 25.68/7.49  																													|-The branch is then unsatisfiable
% 25.68/7.49  																												|-Branch two:
% 25.68/7.49  																												| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.49  																												| (305)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.49  																												|
% 25.68/7.49  																													+-Applying beta-rule and splitting (187), into two cases.
% 25.68/7.49  																													|-Branch one:
% 25.68/7.49  																													| (306) all_26_0_30 = 0
% 25.68/7.49  																													|
% 25.68/7.49  																														| Equations (306) can reduce 84 to:
% 25.68/7.49  																														| (109) $false
% 25.68/7.49  																														|
% 25.68/7.49  																														|-The branch is then unsatisfiable
% 25.68/7.49  																													|-Branch two:
% 25.68/7.49  																													| (84)  ~ (all_26_0_30 = 0)
% 25.68/7.49  																													| (309)  ? [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))
% 25.68/7.49  																													|
% 25.68/7.49  																														+-Applying beta-rule and splitting (201), into two cases.
% 25.68/7.49  																														|-Branch one:
% 25.68/7.49  																														| (262) all_28_0_32 = 0
% 25.68/7.49  																														|
% 25.68/7.49  																															| Equations (262) can reduce 88 to:
% 25.68/7.49  																															| (109) $false
% 25.68/7.49  																															|
% 25.68/7.49  																															|-The branch is then unsatisfiable
% 25.68/7.49  																														|-Branch two:
% 25.68/7.49  																														| (88)  ~ (all_28_0_32 = 0)
% 25.68/7.49  																														| (313)  ? [v0] : ((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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.68/7.49  																														|
% 25.68/7.49  																															+-Applying beta-rule and splitting (150), into two cases.
% 25.68/7.49  																															|-Branch one:
% 25.68/7.49  																															| (218) all_24_0_28 = 0
% 25.68/7.49  																															|
% 25.68/7.49  																																| Equations (218) can reduce 80 to:
% 25.68/7.49  																																| (109) $false
% 25.68/7.49  																																|
% 25.68/7.49  																																|-The branch is then unsatisfiable
% 25.68/7.49  																															|-Branch two:
% 25.68/7.49  																															| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.49  																															| (317) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 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_22_1_27) = v0))
% 25.68/7.50  																															|
% 25.68/7.50  																																+-Applying beta-rule and splitting (157), into two cases.
% 25.68/7.50  																																|-Branch one:
% 25.68/7.50  																																| (222) all_30_0_34 = 0
% 25.68/7.50  																																|
% 25.68/7.50  																																	| Equations (222) can reduce 92 to:
% 25.68/7.50  																																	| (109) $false
% 25.68/7.50  																																	|
% 25.68/7.50  																																	|-The branch is then unsatisfiable
% 25.68/7.50  																																|-Branch two:
% 25.68/7.50  																																| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																| (321) 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_2_2, all_0_0_0) = v0))
% 25.68/7.50  																																|
% 25.68/7.50  																																	+-Applying beta-rule and splitting (158), into two cases.
% 25.68/7.50  																																	|-Branch one:
% 25.68/7.50  																																	| (222) all_30_0_34 = 0
% 25.68/7.50  																																	|
% 25.68/7.50  																																		| Equations (222) can reduce 92 to:
% 25.68/7.50  																																		| (109) $false
% 25.68/7.50  																																		|
% 25.68/7.50  																																		|-The branch is then unsatisfiable
% 25.68/7.50  																																	|-Branch two:
% 25.68/7.50  																																	| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																	| (325) 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))
% 25.68/7.50  																																	|
% 25.68/7.50  																																		+-Applying beta-rule and splitting (249), into two cases.
% 25.68/7.50  																																		|-Branch one:
% 25.68/7.50  																																		| (218) all_24_0_28 = 0
% 25.68/7.50  																																		|
% 25.68/7.50  																																			| Equations (218) can reduce 80 to:
% 25.68/7.50  																																			| (109) $false
% 25.68/7.50  																																			|
% 25.68/7.50  																																			|-The branch is then unsatisfiable
% 25.68/7.50  																																		|-Branch two:
% 25.68/7.50  																																		| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.50  																																		| (329)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.68/7.50  																																		|
% 25.68/7.50  																																			+-Applying beta-rule and splitting (179), into two cases.
% 25.68/7.50  																																			|-Branch one:
% 25.68/7.50  																																			| (330) distinct_lines(all_0_0_0, all_0_2_2) = 0
% 25.68/7.50  																																			|
% 25.68/7.50  																																				+-Applying beta-rule and splitting (176), into two cases.
% 25.68/7.50  																																				|-Branch one:
% 25.68/7.50  																																				| (242) all_22_0_26 = 0
% 25.68/7.50  																																				|
% 25.68/7.50  																																					| Equations (242) can reduce 76 to:
% 25.68/7.50  																																					| (109) $false
% 25.68/7.50  																																					|
% 25.68/7.50  																																					|-The branch is then unsatisfiable
% 25.68/7.50  																																				|-Branch two:
% 25.68/7.50  																																				| (76)  ~ (all_22_0_26 = 0)
% 25.68/7.50  																																				| (334)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 25.68/7.50  																																				|
% 25.68/7.50  																																					+-Applying beta-rule and splitting (177), into two cases.
% 25.68/7.50  																																					|-Branch one:
% 25.68/7.50  																																					| (242) all_22_0_26 = 0
% 25.68/7.50  																																					|
% 25.68/7.50  																																						| Equations (242) can reduce 76 to:
% 25.68/7.50  																																						| (109) $false
% 25.68/7.50  																																						|
% 25.68/7.50  																																						|-The branch is then unsatisfiable
% 25.68/7.50  																																					|-Branch two:
% 25.68/7.50  																																					| (76)  ~ (all_22_0_26 = 0)
% 25.68/7.50  																																					| (338)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 25.68/7.50  																																					|
% 25.68/7.50  																																						+-Applying beta-rule and splitting (185), into two cases.
% 25.68/7.50  																																						|-Branch one:
% 25.68/7.50  																																						| (306) all_26_0_30 = 0
% 25.68/7.50  																																						|
% 25.68/7.50  																																							| Equations (306) can reduce 84 to:
% 25.68/7.50  																																							| (109) $false
% 25.68/7.50  																																							|
% 25.68/7.50  																																							|-The branch is then unsatisfiable
% 25.68/7.50  																																						|-Branch two:
% 25.68/7.50  																																						| (84)  ~ (all_26_0_30 = 0)
% 25.68/7.50  																																						| (342) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 25.68/7.50  																																						|
% 25.68/7.50  																																							+-Applying beta-rule and splitting (186), into two cases.
% 25.68/7.50  																																							|-Branch one:
% 25.68/7.50  																																							| (306) all_26_0_30 = 0
% 25.68/7.50  																																							|
% 25.68/7.50  																																								| Equations (306) can reduce 84 to:
% 25.68/7.50  																																								| (109) $false
% 25.68/7.50  																																								|
% 25.68/7.50  																																								|-The branch is then unsatisfiable
% 25.68/7.50  																																							|-Branch two:
% 25.68/7.50  																																							| (84)  ~ (all_26_0_30 = 0)
% 25.68/7.50  																																							| (346) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 25.68/7.50  																																							|
% 25.68/7.50  																																								+-Applying beta-rule and splitting (317), into two cases.
% 25.68/7.50  																																								|-Branch one:
% 25.68/7.50  																																								| (108) all_0_1_1 = 0
% 25.68/7.50  																																								|
% 25.68/7.50  																																									| Equations (108) can reduce 32 to:
% 25.68/7.50  																																									| (109) $false
% 25.68/7.50  																																									|
% 25.68/7.50  																																									|-The branch is then unsatisfiable
% 25.68/7.50  																																								|-Branch two:
% 25.68/7.50  																																								| (32)  ~ (all_0_1_1 = 0)
% 25.68/7.50  																																								| (350)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 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_22_1_27) = v0))
% 25.68/7.50  																																								|
% 25.68/7.50  																																									+-Applying beta-rule and splitting (155), into two cases.
% 25.68/7.50  																																									|-Branch one:
% 25.68/7.50  																																									| (218) all_24_0_28 = 0
% 25.68/7.50  																																									|
% 25.68/7.50  																																										| Equations (218) can reduce 80 to:
% 25.68/7.50  																																										| (109) $false
% 25.68/7.50  																																										|
% 25.68/7.50  																																										|-The branch is then unsatisfiable
% 25.68/7.50  																																									|-Branch two:
% 25.68/7.50  																																									| (80)  ~ (all_24_0_28 = 0)
% 25.68/7.50  																																									| (334)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0))
% 25.68/7.50  																																									|
% 25.68/7.50  																																										+-Applying beta-rule and splitting (180), into two cases.
% 25.68/7.50  																																										|-Branch one:
% 25.68/7.50  																																										| (306) all_26_0_30 = 0
% 25.68/7.50  																																										|
% 25.68/7.50  																																											| Equations (306) can reduce 84 to:
% 25.68/7.50  																																											| (109) $false
% 25.68/7.50  																																											|
% 25.68/7.50  																																											|-The branch is then unsatisfiable
% 25.68/7.50  																																										|-Branch two:
% 25.68/7.50  																																										| (84)  ~ (all_26_0_30 = 0)
% 25.68/7.50  																																										| (358) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																										|
% 25.68/7.50  																																											+-Applying beta-rule and splitting (183), into two cases.
% 25.68/7.50  																																											|-Branch one:
% 25.68/7.50  																																											| (222) all_30_0_34 = 0
% 25.68/7.50  																																											|
% 25.68/7.50  																																												| Equations (222) can reduce 92 to:
% 25.68/7.50  																																												| (109) $false
% 25.68/7.50  																																												|
% 25.68/7.50  																																												|-The branch is then unsatisfiable
% 25.68/7.50  																																											|-Branch two:
% 25.68/7.50  																																											| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																											| (362) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.68/7.50  																																											|
% 25.68/7.50  																																												+-Applying beta-rule and splitting (182), into two cases.
% 25.68/7.50  																																												|-Branch one:
% 25.68/7.50  																																												| (222) all_30_0_34 = 0
% 25.68/7.50  																																												|
% 25.68/7.50  																																													| Equations (222) can reduce 92 to:
% 25.68/7.50  																																													| (109) $false
% 25.68/7.50  																																													|
% 25.68/7.50  																																													|-The branch is then unsatisfiable
% 25.68/7.50  																																												|-Branch two:
% 25.68/7.50  																																												| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																												| (366) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																												|
% 25.68/7.50  																																													+-Applying beta-rule and splitting (184), into two cases.
% 25.68/7.50  																																													|-Branch one:
% 25.68/7.50  																																													| (222) all_30_0_34 = 0
% 25.68/7.50  																																													|
% 25.68/7.50  																																														| Equations (222) can reduce 92 to:
% 25.68/7.50  																																														| (109) $false
% 25.68/7.50  																																														|
% 25.68/7.50  																																														|-The branch is then unsatisfiable
% 25.68/7.50  																																													|-Branch two:
% 25.68/7.50  																																													| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																													| (370) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 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) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																													|
% 25.68/7.50  																																														+-Applying beta-rule and splitting (181), into two cases.
% 25.68/7.50  																																														|-Branch one:
% 25.68/7.50  																																														| (306) all_26_0_30 = 0
% 25.68/7.50  																																														|
% 25.68/7.50  																																															| Equations (306) can reduce 84 to:
% 25.68/7.50  																																															| (109) $false
% 25.68/7.50  																																															|
% 25.68/7.50  																																															|-The branch is then unsatisfiable
% 25.68/7.50  																																														|-Branch two:
% 25.68/7.50  																																														| (84)  ~ (all_26_0_30 = 0)
% 25.68/7.50  																																														| (374) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																														|
% 25.68/7.50  																																															+-Applying beta-rule and splitting (175), into two cases.
% 25.68/7.50  																																															|-Branch one:
% 25.68/7.50  																																															| (222) all_30_0_34 = 0
% 25.68/7.50  																																															|
% 25.68/7.50  																																																| Equations (222) can reduce 92 to:
% 25.68/7.50  																																																| (109) $false
% 25.68/7.50  																																																|
% 25.68/7.50  																																																|-The branch is then unsatisfiable
% 25.68/7.50  																																															|-Branch two:
% 25.68/7.50  																																															| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																															| (378) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																															|
% 25.68/7.50  																																																+-Applying beta-rule and splitting (173), into two cases.
% 25.68/7.50  																																																|-Branch one:
% 25.68/7.50  																																																| (222) all_30_0_34 = 0
% 25.68/7.50  																																																|
% 25.68/7.50  																																																	| Equations (222) can reduce 92 to:
% 25.68/7.50  																																																	| (109) $false
% 25.68/7.50  																																																	|
% 25.68/7.50  																																																	|-The branch is then unsatisfiable
% 25.68/7.50  																																																|-Branch two:
% 25.68/7.50  																																																| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																																| (382) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 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_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																																|
% 25.68/7.50  																																																	+-Applying beta-rule and splitting (174), into two cases.
% 25.68/7.50  																																																	|-Branch one:
% 25.68/7.50  																																																	| (222) all_30_0_34 = 0
% 25.68/7.50  																																																	|
% 25.68/7.50  																																																		| Equations (222) can reduce 92 to:
% 25.68/7.50  																																																		| (109) $false
% 25.68/7.50  																																																		|
% 25.68/7.50  																																																		|-The branch is then unsatisfiable
% 25.68/7.50  																																																	|-Branch two:
% 25.68/7.50  																																																	| (92)  ~ (all_30_0_34 = 0)
% 25.68/7.50  																																																	| (386) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 25.68/7.50  																																																	|
% 25.68/7.50  																																																		+-Applying beta-rule and splitting (178), into two cases.
% 25.68/7.50  																																																		|-Branch one:
% 25.68/7.50  																																																		| (306) all_26_0_30 = 0
% 25.68/7.50  																																																		|
% 25.68/7.50  																																																			| Equations (306) can reduce 84 to:
% 25.68/7.50  																																																			| (109) $false
% 25.68/7.50  																																																			|
% 25.68/7.50  																																																			|-The branch is then unsatisfiable
% 25.68/7.50  																																																		|-Branch two:
% 25.68/7.50  																																																		| (84)  ~ (all_26_0_30 = 0)
% 25.68/7.50  																																																		| (390) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.68/7.50  																																																		|
% 25.68/7.50  																																																			+-Applying beta-rule and splitting (342), into two cases.
% 25.68/7.50  																																																			|-Branch one:
% 25.68/7.50  																																																			| (242) all_22_0_26 = 0
% 25.68/7.50  																																																			|
% 25.68/7.50  																																																				| Equations (242) can reduce 76 to:
% 25.68/7.50  																																																				| (109) $false
% 25.68/7.50  																																																				|
% 25.68/7.50  																																																				|-The branch is then unsatisfiable
% 25.68/7.50  																																																			|-Branch two:
% 25.68/7.50  																																																			| (76)  ~ (all_22_0_26 = 0)
% 25.68/7.50  																																																			| (394)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 25.68/7.50  																																																			|
% 25.68/7.50  																																																				+-Applying beta-rule and splitting (346), into two cases.
% 25.68/7.50  																																																				|-Branch one:
% 25.68/7.50  																																																				| (242) all_22_0_26 = 0
% 25.68/7.50  																																																				|
% 25.68/7.50  																																																					| Equations (242) can reduce 76 to:
% 25.68/7.50  																																																					| (109) $false
% 25.68/7.50  																																																					|
% 25.68/7.50  																																																					|-The branch is then unsatisfiable
% 25.68/7.50  																																																				|-Branch two:
% 25.68/7.50  																																																				| (76)  ~ (all_22_0_26 = 0)
% 25.68/7.50  																																																				| (398)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 25.68/7.50  																																																				|
% 25.68/7.50  																																																					+-Applying beta-rule and splitting (200), into two cases.
% 25.68/7.50  																																																					|-Branch one:
% 25.68/7.50  																																																					| (262) all_28_0_32 = 0
% 25.68/7.50  																																																					|
% 25.68/7.50  																																																						| Equations (262) can reduce 88 to:
% 25.68/7.50  																																																						| (109) $false
% 25.68/7.50  																																																						|
% 25.68/7.50  																																																						|-The branch is then unsatisfiable
% 25.68/7.50  																																																					|-Branch two:
% 25.68/7.50  																																																					| (88)  ~ (all_28_0_32 = 0)
% 25.68/7.51  																																																					| (261)  ? [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))
% 25.68/7.51  																																																					|
% 25.68/7.51  																																																						+-Applying beta-rule and splitting (193), into two cases.
% 25.68/7.51  																																																						|-Branch one:
% 25.68/7.51  																																																						| (262) all_28_0_32 = 0
% 25.68/7.51  																																																						|
% 25.68/7.51  																																																							| Equations (262) can reduce 88 to:
% 25.68/7.51  																																																							| (109) $false
% 25.68/7.51  																																																							|
% 25.68/7.51  																																																							|-The branch is then unsatisfiable
% 25.68/7.51  																																																						|-Branch two:
% 25.68/7.51  																																																						| (88)  ~ (all_28_0_32 = 0)
% 25.68/7.51  																																																						| (406) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.68/7.51  																																																						|
% 25.68/7.51  																																																							+-Applying beta-rule and splitting (265), into two cases.
% 25.68/7.51  																																																							|-Branch one:
% 25.68/7.51  																																																							| (226) all_20_0_24 = 0
% 25.68/7.51  																																																							|
% 25.68/7.51  																																																								| Equations (226) can reduce 72 to:
% 25.68/7.51  																																																								| (109) $false
% 25.68/7.51  																																																								|
% 25.68/7.51  																																																								|-The branch is then unsatisfiable
% 25.68/7.51  																																																							|-Branch two:
% 25.68/7.51  																																																							| (72)  ~ (all_20_0_24 = 0)
% 25.68/7.51  																																																							| (410)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.88/7.51  																																																							|
% 25.88/7.51  																																																								+-Applying beta-rule and splitting (269), into two cases.
% 25.88/7.51  																																																								|-Branch one:
% 25.88/7.51  																																																								| (226) all_20_0_24 = 0
% 25.88/7.51  																																																								|
% 25.88/7.51  																																																									| Equations (226) can reduce 72 to:
% 25.88/7.51  																																																									| (109) $false
% 25.88/7.51  																																																									|
% 25.88/7.51  																																																									|-The branch is then unsatisfiable
% 25.88/7.51  																																																								|-Branch two:
% 25.88/7.51  																																																								| (72)  ~ (all_20_0_24 = 0)
% 25.88/7.51  																																																								| (414)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 25.88/7.51  																																																								|
% 25.88/7.51  																																																									+-Applying beta-rule and splitting (374), into two cases.
% 25.88/7.51  																																																									|-Branch one:
% 25.88/7.51  																																																									| (218) all_24_0_28 = 0
% 25.88/7.51  																																																									|
% 25.88/7.51  																																																										| Equations (218) can reduce 80 to:
% 25.88/7.51  																																																										| (109) $false
% 25.88/7.51  																																																										|
% 25.88/7.51  																																																										|-The branch is then unsatisfiable
% 25.88/7.51  																																																									|-Branch two:
% 25.88/7.51  																																																									| (80)  ~ (all_24_0_28 = 0)
% 25.88/7.51  																																																									| (418)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.88/7.51  																																																									|
% 25.88/7.51  																																																										+-Applying beta-rule and splitting (382), into two cases.
% 25.88/7.51  																																																										|-Branch one:
% 25.88/7.51  																																																										| (242) all_22_0_26 = 0
% 25.88/7.51  																																																										|
% 25.88/7.51  																																																											| Equations (242) can reduce 76 to:
% 25.88/7.51  																																																											| (109) $false
% 25.88/7.51  																																																											|
% 25.88/7.51  																																																											|-The branch is then unsatisfiable
% 25.88/7.51  																																																										|-Branch two:
% 25.88/7.51  																																																										| (76)  ~ (all_22_0_26 = 0)
% 25.88/7.51  																																																										| (422)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 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_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.88/7.51  																																																										|
% 25.88/7.51  																																																											+-Applying beta-rule and splitting (212), into two cases.
% 25.88/7.51  																																																											|-Branch one:
% 25.88/7.51  																																																											| (262) all_28_0_32 = 0
% 25.88/7.51  																																																											|
% 25.88/7.51  																																																												| Equations (262) can reduce 88 to:
% 25.88/7.51  																																																												| (109) $false
% 25.88/7.51  																																																												|
% 25.88/7.51  																																																												|-The branch is then unsatisfiable
% 25.88/7.51  																																																											|-Branch two:
% 25.88/7.51  																																																											| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.51  																																																											| (426) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 25.88/7.51  																																																											|
% 25.88/7.51  																																																												+-Applying beta-rule and splitting (213), into two cases.
% 25.88/7.51  																																																												|-Branch one:
% 25.88/7.51  																																																												| (262) all_28_0_32 = 0
% 25.88/7.51  																																																												|
% 25.88/7.51  																																																													| Equations (262) can reduce 88 to:
% 25.88/7.51  																																																													| (109) $false
% 25.88/7.51  																																																													|
% 25.88/7.51  																																																													|-The branch is then unsatisfiable
% 25.88/7.51  																																																												|-Branch two:
% 25.88/7.51  																																																												| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.51  																																																												| (430) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0))
% 25.88/7.51  																																																												|
% 25.88/7.51  																																																													+-Applying beta-rule and splitting (214), into two cases.
% 25.88/7.51  																																																													|-Branch one:
% 25.88/7.51  																																																													| (262) all_28_0_32 = 0
% 25.88/7.51  																																																													|
% 25.88/7.51  																																																														| Equations (262) can reduce 88 to:
% 25.88/7.51  																																																														| (109) $false
% 25.88/7.51  																																																														|
% 25.88/7.51  																																																														|-The branch is then unsatisfiable
% 25.88/7.51  																																																													|-Branch two:
% 25.88/7.51  																																																													| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.51  																																																													| (434) all_20_0_24 = 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_2_2, all_0_0_0) = v0))
% 25.88/7.51  																																																													|
% 25.88/7.51  																																																														+-Applying beta-rule and splitting (160), into two cases.
% 25.88/7.51  																																																														|-Branch one:
% 25.88/7.51  																																																														| (222) all_30_0_34 = 0
% 25.88/7.51  																																																														|
% 25.88/7.51  																																																															| Equations (222) can reduce 92 to:
% 25.88/7.51  																																																															| (109) $false
% 25.88/7.51  																																																															|
% 25.88/7.51  																																																															|-The branch is then unsatisfiable
% 25.88/7.51  																																																														|-Branch two:
% 25.88/7.51  																																																														| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.51  																																																														| (438) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.88/7.51  																																																														|
% 25.88/7.51  																																																															+-Applying beta-rule and splitting (202), into two cases.
% 25.88/7.51  																																																															|-Branch one:
% 25.88/7.51  																																																															| (226) all_20_0_24 = 0
% 25.88/7.51  																																																															|
% 25.88/7.51  																																																																| Equations (226) can reduce 72 to:
% 25.88/7.51  																																																																| (109) $false
% 25.88/7.51  																																																																|
% 25.88/7.51  																																																																|-The branch is then unsatisfiable
% 25.88/7.51  																																																															|-Branch two:
% 25.88/7.51  																																																															| (72)  ~ (all_20_0_24 = 0)
% 25.88/7.51  																																																															| (442) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.88/7.51  																																																															|
% 25.88/7.51  																																																																+-Applying beta-rule and splitting (203), into two cases.
% 25.88/7.51  																																																																|-Branch one:
% 25.88/7.51  																																																																| (218) all_24_0_28 = 0
% 25.88/7.51  																																																																|
% 25.88/7.51  																																																																	| Equations (218) can reduce 80 to:
% 25.88/7.51  																																																																	| (109) $false
% 25.88/7.51  																																																																	|
% 25.88/7.51  																																																																	|-The branch is then unsatisfiable
% 25.88/7.51  																																																																|-Branch two:
% 25.88/7.51  																																																																| (80)  ~ (all_24_0_28 = 0)
% 25.88/7.51  																																																																| (446) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.51  																																																																|
% 25.88/7.51  																																																																	+-Applying beta-rule and splitting (192), into two cases.
% 25.88/7.51  																																																																	|-Branch one:
% 25.88/7.51  																																																																	| (262) all_28_0_32 = 0
% 25.88/7.51  																																																																	|
% 25.88/7.51  																																																																		| Equations (262) can reduce 88 to:
% 25.88/7.51  																																																																		| (109) $false
% 25.88/7.51  																																																																		|
% 25.88/7.51  																																																																		|-The branch is then unsatisfiable
% 25.88/7.51  																																																																	|-Branch two:
% 25.88/7.51  																																																																	| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.51  																																																																	| (450) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.51  																																																																	|
% 25.88/7.51  																																																																		+-Applying beta-rule and splitting (321), into two cases.
% 25.88/7.51  																																																																		|-Branch one:
% 25.88/7.51  																																																																		| (108) all_0_1_1 = 0
% 25.88/7.51  																																																																		|
% 25.88/7.51  																																																																			| Equations (108) can reduce 32 to:
% 25.88/7.51  																																																																			| (109) $false
% 25.88/7.51  																																																																			|
% 25.88/7.51  																																																																			|-The branch is then unsatisfiable
% 25.88/7.51  																																																																		|-Branch two:
% 25.88/7.51  																																																																		| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.51  																																																																		| (454)  ? [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_2_2, all_0_0_0) = v0))
% 25.88/7.51  																																																																		|
% 25.88/7.51  																																																																			+-Applying beta-rule and splitting (207), into two cases.
% 25.88/7.51  																																																																			|-Branch one:
% 25.88/7.51  																																																																			| (222) all_30_0_34 = 0
% 25.88/7.51  																																																																			|
% 25.88/7.51  																																																																				| Equations (222) can reduce 92 to:
% 25.88/7.51  																																																																				| (109) $false
% 25.88/7.51  																																																																				|
% 25.88/7.51  																																																																				|-The branch is then unsatisfiable
% 25.88/7.51  																																																																			|-Branch two:
% 25.88/7.51  																																																																			| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.51  																																																																			| (458) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3) = v0))
% 25.88/7.51  																																																																			|
% 25.88/7.51  																																																																				+-Applying beta-rule and splitting (208), into two cases.
% 25.88/7.51  																																																																				|-Branch one:
% 25.88/7.51  																																																																				| (242) all_22_0_26 = 0
% 25.88/7.51  																																																																				|
% 25.88/7.51  																																																																					| Equations (242) can reduce 76 to:
% 25.88/7.51  																																																																					| (109) $false
% 25.88/7.51  																																																																					|
% 25.88/7.51  																																																																					|-The branch is then unsatisfiable
% 25.88/7.51  																																																																				|-Branch two:
% 25.88/7.51  																																																																				| (76)  ~ (all_22_0_26 = 0)
% 25.88/7.51  																																																																				| (462) all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 25.88/7.51  																																																																				|
% 25.88/7.51  																																																																					+-Applying beta-rule and splitting (211), into two cases.
% 25.88/7.51  																																																																					|-Branch one:
% 25.88/7.51  																																																																					| (242) all_22_0_26 = 0
% 25.88/7.51  																																																																					|
% 25.88/7.51  																																																																						| Equations (242) can reduce 76 to:
% 25.88/7.51  																																																																						| (109) $false
% 25.88/7.51  																																																																						|
% 25.88/7.51  																																																																						|-The branch is then unsatisfiable
% 25.88/7.51  																																																																					|-Branch two:
% 25.88/7.51  																																																																					| (76)  ~ (all_22_0_26 = 0)
% 25.88/7.51  																																																																					| (466) all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.88/7.51  																																																																					|
% 25.88/7.51  																																																																						+-Applying beta-rule and splitting (209), into two cases.
% 25.88/7.51  																																																																						|-Branch one:
% 25.88/7.51  																																																																						| (242) all_22_0_26 = 0
% 25.88/7.51  																																																																						|
% 25.88/7.51  																																																																							| Equations (242) can reduce 76 to:
% 25.88/7.51  																																																																							| (109) $false
% 25.88/7.51  																																																																							|
% 25.88/7.51  																																																																							|-The branch is then unsatisfiable
% 25.88/7.51  																																																																						|-Branch two:
% 25.88/7.51  																																																																						| (76)  ~ (all_22_0_26 = 0)
% 25.88/7.51  																																																																						| (470) all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.88/7.51  																																																																						|
% 25.88/7.51  																																																																							+-Applying beta-rule and splitting (210), into two cases.
% 25.88/7.51  																																																																							|-Branch one:
% 25.88/7.51  																																																																							| (242) all_22_0_26 = 0
% 25.88/7.51  																																																																							|
% 25.88/7.51  																																																																								| Equations (242) can reduce 76 to:
% 25.88/7.51  																																																																								| (109) $false
% 25.88/7.51  																																																																								|
% 25.88/7.51  																																																																								|-The branch is then unsatisfiable
% 25.88/7.51  																																																																							|-Branch two:
% 25.88/7.51  																																																																							| (76)  ~ (all_22_0_26 = 0)
% 25.88/7.51  																																																																							| (474) all_20_0_24 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 25.88/7.51  																																																																							|
% 25.88/7.51  																																																																								+-Applying beta-rule and splitting (194), into two cases.
% 25.88/7.51  																																																																								|-Branch one:
% 25.88/7.51  																																																																								| (262) all_28_0_32 = 0
% 25.88/7.51  																																																																								|
% 25.88/7.51  																																																																									| Equations (262) can reduce 88 to:
% 25.88/7.51  																																																																									| (109) $false
% 25.88/7.51  																																																																									|
% 25.88/7.51  																																																																									|-The branch is then unsatisfiable
% 25.88/7.51  																																																																								|-Branch two:
% 25.88/7.51  																																																																								| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.51  																																																																								| (478) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.88/7.52  																																																																								|
% 25.88/7.52  																																																																									+-Applying beta-rule and splitting (195), into two cases.
% 25.88/7.52  																																																																									|-Branch one:
% 25.88/7.52  																																																																									| (222) all_30_0_34 = 0
% 25.88/7.52  																																																																									|
% 25.88/7.52  																																																																										| Equations (222) can reduce 92 to:
% 25.88/7.52  																																																																										| (109) $false
% 25.88/7.52  																																																																										|
% 25.88/7.52  																																																																										|-The branch is then unsatisfiable
% 25.88/7.52  																																																																									|-Branch two:
% 25.88/7.52  																																																																									| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.52  																																																																									| (482) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.52  																																																																									|
% 25.88/7.52  																																																																										+-Applying beta-rule and splitting (196), into two cases.
% 25.88/7.52  																																																																										|-Branch one:
% 25.88/7.52  																																																																										| (262) all_28_0_32 = 0
% 25.88/7.52  																																																																										|
% 25.88/7.52  																																																																											| Equations (262) can reduce 88 to:
% 25.88/7.52  																																																																											| (109) $false
% 25.88/7.52  																																																																											|
% 25.88/7.52  																																																																											|-The branch is then unsatisfiable
% 25.88/7.52  																																																																										|-Branch two:
% 25.88/7.52  																																																																										| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.52  																																																																										| (486) all_22_0_26 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 25.88/7.52  																																																																										|
% 25.88/7.52  																																																																											+-Applying beta-rule and splitting (197), into two cases.
% 25.88/7.52  																																																																											|-Branch one:
% 25.88/7.52  																																																																											| (262) all_28_0_32 = 0
% 25.88/7.52  																																																																											|
% 25.88/7.52  																																																																												| Equations (262) can reduce 88 to:
% 25.88/7.52  																																																																												| (109) $false
% 25.88/7.52  																																																																												|
% 25.88/7.52  																																																																												|-The branch is then unsatisfiable
% 25.88/7.52  																																																																											|-Branch two:
% 25.88/7.52  																																																																											| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.52  																																																																											| (490) all_22_0_26 = 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_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 25.88/7.52  																																																																											|
% 25.88/7.52  																																																																												+-Applying beta-rule and splitting (172), into two cases.
% 25.88/7.52  																																																																												|-Branch one:
% 25.88/7.52  																																																																												| (218) all_24_0_28 = 0
% 25.88/7.52  																																																																												|
% 25.88/7.52  																																																																													| Equations (218) can reduce 80 to:
% 25.88/7.52  																																																																													| (109) $false
% 25.88/7.52  																																																																													|
% 25.88/7.52  																																																																													|-The branch is then unsatisfiable
% 25.88/7.52  																																																																												|-Branch two:
% 25.88/7.52  																																																																												| (80)  ~ (all_24_0_28 = 0)
% 25.88/7.52  																																																																												| (494) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.88/7.52  																																																																												|
% 25.88/7.52  																																																																													+-Applying beta-rule and splitting (151), into two cases.
% 25.88/7.52  																																																																													|-Branch one:
% 25.88/7.52  																																																																													| (218) all_24_0_28 = 0
% 25.88/7.52  																																																																													|
% 25.88/7.52  																																																																														| Equations (218) can reduce 80 to:
% 25.88/7.52  																																																																														| (109) $false
% 25.88/7.52  																																																																														|
% 25.88/7.52  																																																																														|-The branch is then unsatisfiable
% 25.88/7.52  																																																																													|-Branch two:
% 25.88/7.52  																																																																													| (80)  ~ (all_24_0_28 = 0)
% 25.88/7.52  																																																																													| (498) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 25.88/7.52  																																																																													|
% 25.88/7.52  																																																																														+-Applying beta-rule and splitting (152), into two cases.
% 25.88/7.52  																																																																														|-Branch one:
% 25.88/7.52  																																																																														| (218) all_24_0_28 = 0
% 25.88/7.52  																																																																														|
% 25.88/7.52  																																																																															| Equations (218) can reduce 80 to:
% 25.88/7.52  																																																																															| (109) $false
% 25.88/7.52  																																																																															|
% 25.88/7.52  																																																																															|-The branch is then unsatisfiable
% 25.88/7.52  																																																																														|-Branch two:
% 25.88/7.52  																																																																														| (80)  ~ (all_24_0_28 = 0)
% 25.88/7.52  																																																																														| (502) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.88/7.52  																																																																														|
% 25.88/7.52  																																																																															+-Applying beta-rule and splitting (199), into two cases.
% 25.88/7.52  																																																																															|-Branch one:
% 25.88/7.52  																																																																															| (262) all_28_0_32 = 0
% 25.88/7.52  																																																																															|
% 25.88/7.52  																																																																																| Equations (262) can reduce 88 to:
% 25.88/7.52  																																																																																| (109) $false
% 25.88/7.52  																																																																																|
% 25.88/7.52  																																																																																|-The branch is then unsatisfiable
% 25.88/7.52  																																																																															|-Branch two:
% 25.88/7.52  																																																																															| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.52  																																																																															| (506) all_26_0_30 = 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_2_2) = 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))
% 25.88/7.52  																																																																															|
% 25.88/7.52  																																																																																+-Applying beta-rule and splitting (169), into two cases.
% 25.88/7.52  																																																																																|-Branch one:
% 25.88/7.52  																																																																																| (242) all_22_0_26 = 0
% 25.88/7.52  																																																																																|
% 25.88/7.52  																																																																																	| Equations (242) can reduce 76 to:
% 25.88/7.52  																																																																																	| (109) $false
% 25.88/7.52  																																																																																	|
% 25.88/7.52  																																																																																	|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																|-Branch two:
% 25.88/7.52  																																																																																| (76)  ~ (all_22_0_26 = 0)
% 25.88/7.52  																																																																																| (510) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.88/7.52  																																																																																|
% 25.88/7.52  																																																																																	+-Applying beta-rule and splitting (198), into two cases.
% 25.88/7.52  																																																																																	|-Branch one:
% 25.88/7.52  																																																																																	| (262) all_28_0_32 = 0
% 25.88/7.52  																																																																																	|
% 25.88/7.52  																																																																																		| Equations (262) can reduce 88 to:
% 25.88/7.52  																																																																																		| (109) $false
% 25.88/7.52  																																																																																		|
% 25.88/7.52  																																																																																		|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																	|-Branch two:
% 25.88/7.52  																																																																																	| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.52  																																																																																	| (514) all_26_0_30 = 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_2_2) = 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))
% 25.88/7.52  																																																																																	|
% 25.88/7.52  																																																																																		+-Applying beta-rule and splitting (233), into two cases.
% 25.88/7.52  																																																																																		|-Branch one:
% 25.88/7.52  																																																																																		| (108) all_0_1_1 = 0
% 25.88/7.52  																																																																																		|
% 25.88/7.52  																																																																																			| Equations (108) can reduce 32 to:
% 25.88/7.52  																																																																																			| (109) $false
% 25.88/7.52  																																																																																			|
% 25.88/7.52  																																																																																			|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																		|-Branch two:
% 25.88/7.52  																																																																																		| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.52  																																																																																		| (518)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.88/7.52  																																																																																		|
% 25.88/7.52  																																																																																			+-Applying beta-rule and splitting (446), into two cases.
% 25.88/7.52  																																																																																			|-Branch one:
% 25.88/7.52  																																																																																			| (226) all_20_0_24 = 0
% 25.88/7.52  																																																																																			|
% 25.88/7.52  																																																																																				| Equations (226) can reduce 72 to:
% 25.88/7.52  																																																																																				| (109) $false
% 25.88/7.52  																																																																																				|
% 25.88/7.52  																																																																																				|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																			|-Branch two:
% 25.88/7.52  																																																																																			| (72)  ~ (all_20_0_24 = 0)
% 25.88/7.52  																																																																																			| (522)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.52  																																																																																			|
% 25.88/7.52  																																																																																				+-Applying beta-rule and splitting (458), into two cases.
% 25.88/7.52  																																																																																				|-Branch one:
% 25.88/7.52  																																																																																				| (226) all_20_0_24 = 0
% 25.88/7.52  																																																																																				|
% 25.88/7.52  																																																																																					| Equations (226) can reduce 72 to:
% 25.88/7.52  																																																																																					| (109) $false
% 25.88/7.52  																																																																																					|
% 25.88/7.52  																																																																																					|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																				|-Branch two:
% 25.88/7.52  																																																																																				| (72)  ~ (all_20_0_24 = 0)
% 25.88/7.52  																																																																																				| (526)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3) = v0))
% 25.88/7.52  																																																																																				|
% 25.88/7.52  																																																																																					| Instantiating (526) with all_417_0_2413 yields:
% 25.88/7.52  																																																																																					| (527) (all_417_0_2413 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_417_0_2413 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (all_417_0_2413 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_417_0_2413) | ( ~ (all_417_0_2413 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_417_0_2413)
% 25.88/7.52  																																																																																					|
% 25.88/7.52  																																																																																					+-Applying beta-rule and splitting (204), into two cases.
% 25.88/7.52  																																																																																					|-Branch one:
% 25.88/7.52  																																																																																					| (222) all_30_0_34 = 0
% 25.88/7.52  																																																																																					|
% 25.88/7.52  																																																																																						| Equations (222) can reduce 92 to:
% 25.88/7.52  																																																																																						| (109) $false
% 25.88/7.52  																																																																																						|
% 25.88/7.52  																																																																																						|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																					|-Branch two:
% 25.88/7.52  																																																																																					| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.52  																																																																																					| (531) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.88/7.52  																																																																																					|
% 25.88/7.52  																																																																																						+-Applying beta-rule and splitting (426), into two cases.
% 25.88/7.52  																																																																																						|-Branch one:
% 25.88/7.52  																																																																																						| (226) all_20_0_24 = 0
% 25.88/7.52  																																																																																						|
% 25.88/7.52  																																																																																							| Equations (226) can reduce 72 to:
% 25.88/7.52  																																																																																							| (109) $false
% 25.88/7.52  																																																																																							|
% 25.88/7.52  																																																																																							|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																						|-Branch two:
% 25.88/7.52  																																																																																						| (72)  ~ (all_20_0_24 = 0)
% 25.88/7.52  																																																																																						| (535)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0))
% 25.88/7.52  																																																																																						|
% 25.88/7.52  																																																																																							| Instantiating (535) with all_428_0_2414 yields:
% 25.88/7.52  																																																																																							| (536) (all_428_0_2414 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (all_428_0_2414 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_428_0_2414 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_428_0_2414)
% 25.88/7.52  																																																																																							|
% 25.88/7.52  																																																																																							+-Applying beta-rule and splitting (536), into two cases.
% 25.88/7.52  																																																																																							|-Branch one:
% 25.88/7.52  																																																																																							| (537) (all_428_0_2414 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (all_428_0_2414 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0)
% 25.88/7.52  																																																																																							|
% 25.88/7.52  																																																																																								+-Applying beta-rule and splitting (537), into two cases.
% 25.88/7.52  																																																																																								|-Branch one:
% 25.88/7.52  																																																																																								| (538) all_428_0_2414 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 25.88/7.52  																																																																																								|
% 25.88/7.52  																																																																																									| Applying alpha-rule on (538) yields:
% 25.88/7.52  																																																																																									| (539) all_428_0_2414 = 0
% 25.88/7.52  																																																																																									| (540) apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 25.88/7.52  																																																																																									|
% 25.88/7.52  																																																																																									+-Applying beta-rule and splitting (206), into two cases.
% 25.88/7.52  																																																																																									|-Branch one:
% 25.88/7.52  																																																																																									| (222) all_30_0_34 = 0
% 25.88/7.52  																																																																																									|
% 25.88/7.52  																																																																																										| Equations (222) can reduce 92 to:
% 25.88/7.52  																																																																																										| (109) $false
% 25.88/7.52  																																																																																										|
% 25.88/7.52  																																																																																										|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																									|-Branch two:
% 25.88/7.52  																																																																																									| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.52  																																																																																									| (544) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.88/7.52  																																																																																									|
% 25.88/7.52  																																																																																										+-Applying beta-rule and splitting (159), into two cases.
% 25.88/7.52  																																																																																										|-Branch one:
% 25.88/7.52  																																																																																										| (222) all_30_0_34 = 0
% 25.88/7.52  																																																																																										|
% 25.88/7.52  																																																																																											| Equations (222) can reduce 92 to:
% 25.88/7.52  																																																																																											| (109) $false
% 25.88/7.52  																																																																																											|
% 25.88/7.52  																																																																																											|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																										|-Branch two:
% 25.88/7.52  																																																																																										| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.52  																																																																																										| (548) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0))
% 25.88/7.52  																																																																																										|
% 25.88/7.52  																																																																																											+-Applying beta-rule and splitting (205), into two cases.
% 25.88/7.52  																																																																																											|-Branch one:
% 25.88/7.52  																																																																																											| (222) all_30_0_34 = 0
% 25.88/7.52  																																																																																											|
% 25.88/7.52  																																																																																												| Equations (222) can reduce 92 to:
% 25.88/7.52  																																																																																												| (109) $false
% 25.88/7.52  																																																																																												|
% 25.88/7.52  																																																																																												|-The branch is then unsatisfiable
% 25.88/7.52  																																																																																											|-Branch two:
% 25.88/7.52  																																																																																											| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.52  																																																																																											| (552) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3) = v0))
% 25.88/7.52  																																																																																											|
% 25.88/7.52  																																																																																												| Instantiating formula (41) with all_0_3_3, all_0_0_0, 0, all_30_0_34 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = 0, yields:
% 25.88/7.53  																																																																																												| (222) all_30_0_34 = 0
% 25.88/7.53  																																																																																												|
% 25.88/7.53  																																																																																												| Equations (222) can reduce 92 to:
% 25.88/7.53  																																																																																												| (109) $false
% 25.88/7.53  																																																																																												|
% 25.88/7.53  																																																																																												|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																								|-Branch two:
% 25.88/7.53  																																																																																								| (555) all_428_0_2414 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 25.88/7.53  																																																																																								|
% 25.88/7.53  																																																																																									| Applying alpha-rule on (555) yields:
% 25.88/7.53  																																																																																									| (539) all_428_0_2414 = 0
% 25.88/7.53  																																																																																									| (557) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 25.88/7.53  																																																																																									|
% 25.88/7.53  																																																																																									+-Applying beta-rule and splitting (482), into two cases.
% 25.88/7.53  																																																																																									|-Branch one:
% 25.88/7.53  																																																																																									| (262) all_28_0_32 = 0
% 25.88/7.53  																																																																																									|
% 25.88/7.53  																																																																																										| Equations (262) can reduce 88 to:
% 25.88/7.53  																																																																																										| (109) $false
% 25.88/7.53  																																																																																										|
% 25.88/7.53  																																																																																										|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																									|-Branch two:
% 25.88/7.53  																																																																																									| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.53  																																																																																									| (561)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																									|
% 25.88/7.53  																																																																																										+-Applying beta-rule and splitting (498), into two cases.
% 25.88/7.53  																																																																																										|-Branch one:
% 25.88/7.53  																																																																																										| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																										|
% 25.88/7.53  																																																																																											| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																											| (109) $false
% 25.88/7.53  																																																																																											|
% 25.88/7.53  																																																																																											|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																										|-Branch two:
% 25.88/7.53  																																																																																										| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																										| (394)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 25.88/7.53  																																																																																										|
% 25.88/7.53  																																																																																											+-Applying beta-rule and splitting (502), into two cases.
% 25.88/7.53  																																																																																											|-Branch one:
% 25.88/7.53  																																																																																											| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																											|
% 25.88/7.53  																																																																																												| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																												| (109) $false
% 25.88/7.53  																																																																																												|
% 25.88/7.53  																																																																																												|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																											|-Branch two:
% 25.88/7.53  																																																																																											| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																											| (569)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.88/7.53  																																																																																											|
% 25.88/7.53  																																																																																												+-Applying beta-rule and splitting (510), into two cases.
% 25.88/7.53  																																																																																												|-Branch one:
% 25.88/7.53  																																																																																												| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																												|
% 25.88/7.53  																																																																																													| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																													| (109) $false
% 25.88/7.53  																																																																																													|
% 25.88/7.53  																																																																																													|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																												|-Branch two:
% 25.88/7.53  																																																																																												| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																												| (573)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.88/7.53  																																																																																												|
% 25.88/7.53  																																																																																													+-Applying beta-rule and splitting (189), into two cases.
% 25.88/7.53  																																																																																													|-Branch one:
% 25.88/7.53  																																																																																													| (262) all_28_0_32 = 0
% 25.88/7.53  																																																																																													|
% 25.88/7.53  																																																																																														| Equations (262) can reduce 88 to:
% 25.88/7.53  																																																																																														| (109) $false
% 25.88/7.53  																																																																																														|
% 25.88/7.53  																																																																																														|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																													|-Branch two:
% 25.88/7.53  																																																																																													| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.53  																																																																																													| (577) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.88/7.53  																																																																																													|
% 25.88/7.53  																																																																																														+-Applying beta-rule and splitting (191), into two cases.
% 25.88/7.53  																																																																																														|-Branch one:
% 25.88/7.53  																																																																																														| (262) all_28_0_32 = 0
% 25.88/7.53  																																																																																														|
% 25.88/7.53  																																																																																															| Equations (262) can reduce 88 to:
% 25.88/7.53  																																																																																															| (109) $false
% 25.88/7.53  																																																																																															|
% 25.88/7.53  																																																																																															|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																														|-Branch two:
% 25.88/7.53  																																																																																														| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.53  																																																																																														| (581) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.88/7.53  																																																																																														|
% 25.88/7.53  																																																																																															+-Applying beta-rule and splitting (206), into two cases.
% 25.88/7.53  																																																																																															|-Branch one:
% 25.88/7.53  																																																																																															| (222) all_30_0_34 = 0
% 25.88/7.53  																																																																																															|
% 25.88/7.53  																																																																																																| Equations (222) can reduce 92 to:
% 25.88/7.53  																																																																																																| (109) $false
% 25.88/7.53  																																																																																																|
% 25.88/7.53  																																																																																																|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																															|-Branch two:
% 25.88/7.53  																																																																																															| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.53  																																																																																															| (544) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																															|
% 25.88/7.53  																																																																																																+-Applying beta-rule and splitting (190), into two cases.
% 25.88/7.53  																																																																																																|-Branch one:
% 25.88/7.53  																																																																																																| (262) all_28_0_32 = 0
% 25.88/7.53  																																																																																																|
% 25.88/7.53  																																																																																																	| Equations (262) can reduce 88 to:
% 25.88/7.53  																																																																																																	| (109) $false
% 25.88/7.53  																																																																																																	|
% 25.88/7.53  																																																																																																	|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																|-Branch two:
% 25.88/7.53  																																																																																																| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.53  																																																																																																| (589) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																																|
% 25.88/7.53  																																																																																																	+-Applying beta-rule and splitting (188), into two cases.
% 25.88/7.53  																																																																																																	|-Branch one:
% 25.88/7.53  																																																																																																	| (262) all_28_0_32 = 0
% 25.88/7.53  																																																																																																	|
% 25.88/7.53  																																																																																																		| Equations (262) can reduce 88 to:
% 25.88/7.53  																																																																																																		| (109) $false
% 25.88/7.53  																																																																																																		|
% 25.88/7.53  																																																																																																		|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																	|-Branch two:
% 25.88/7.53  																																																																																																	| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.53  																																																																																																	| (593) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																																	|
% 25.88/7.53  																																																																																																		+-Applying beta-rule and splitting (577), into two cases.
% 25.88/7.53  																																																																																																		|-Branch one:
% 25.88/7.53  																																																																																																		| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																		|
% 25.88/7.53  																																																																																																			| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																			| (109) $false
% 25.88/7.53  																																																																																																			|
% 25.88/7.53  																																																																																																			|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																		|-Branch two:
% 25.88/7.53  																																																																																																		| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																		| (597)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.88/7.53  																																																																																																		|
% 25.88/7.53  																																																																																																			+-Applying beta-rule and splitting (205), into two cases.
% 25.88/7.53  																																																																																																			|-Branch one:
% 25.88/7.53  																																																																																																			| (222) all_30_0_34 = 0
% 25.88/7.53  																																																																																																			|
% 25.88/7.53  																																																																																																				| Equations (222) can reduce 92 to:
% 25.88/7.53  																																																																																																				| (109) $false
% 25.88/7.53  																																																																																																				|
% 25.88/7.53  																																																																																																				|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																			|-Branch two:
% 25.88/7.53  																																																																																																			| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.53  																																																																																																			| (552) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3) = v0))
% 25.88/7.53  																																																																																																			|
% 25.88/7.53  																																																																																																				+-Applying beta-rule and splitting (159), into two cases.
% 25.88/7.53  																																																																																																				|-Branch one:
% 25.88/7.53  																																																																																																				| (222) all_30_0_34 = 0
% 25.88/7.53  																																																																																																				|
% 25.88/7.53  																																																																																																					| Equations (222) can reduce 92 to:
% 25.88/7.53  																																																																																																					| (109) $false
% 25.88/7.53  																																																																																																					|
% 25.88/7.53  																																																																																																					|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																				|-Branch two:
% 25.88/7.53  																																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 25.88/7.53  																																																																																																				| (548) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0))
% 25.88/7.53  																																																																																																				|
% 25.88/7.53  																																																																																																					+-Applying beta-rule and splitting (390), into two cases.
% 25.88/7.53  																																																																																																					|-Branch one:
% 25.88/7.53  																																																																																																					| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																					|
% 25.88/7.53  																																																																																																						| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																						| (109) $false
% 25.88/7.53  																																																																																																						|
% 25.88/7.53  																																																																																																						|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																					|-Branch two:
% 25.88/7.53  																																																																																																					| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																					| (609)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 25.88/7.53  																																																																																																					|
% 25.88/7.53  																																																																																																						+-Applying beta-rule and splitting (438), into two cases.
% 25.88/7.53  																																																																																																						|-Branch one:
% 25.88/7.53  																																																																																																						| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																						|
% 25.88/7.53  																																																																																																							| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																							| (109) $false
% 25.88/7.53  																																																																																																							|
% 25.88/7.53  																																																																																																							|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																						|-Branch two:
% 25.88/7.53  																																																																																																						| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																						| (613)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 25.88/7.53  																																																																																																						|
% 25.88/7.53  																																																																																																							+-Applying beta-rule and splitting (442), into two cases.
% 25.88/7.53  																																																																																																							|-Branch one:
% 25.88/7.53  																																																																																																							| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																							|
% 25.88/7.53  																																																																																																								| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																								| (109) $false
% 25.88/7.53  																																																																																																								|
% 25.88/7.53  																																																																																																								|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																							|-Branch two:
% 25.88/7.53  																																																																																																							| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																							| (617)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																																							|
% 25.88/7.53  																																																																																																								+-Applying beta-rule and splitting (581), into two cases.
% 25.88/7.53  																																																																																																								|-Branch one:
% 25.88/7.53  																																																																																																								| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																								|
% 25.88/7.53  																																																																																																									| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																									| (109) $false
% 25.88/7.53  																																																																																																									|
% 25.88/7.53  																																																																																																									|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																								|-Branch two:
% 25.88/7.53  																																																																																																								| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																								| (621)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 25.88/7.53  																																																																																																								|
% 25.88/7.53  																																																																																																									+-Applying beta-rule and splitting (589), into two cases.
% 25.88/7.53  																																																																																																									|-Branch one:
% 25.88/7.53  																																																																																																									| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																									|
% 25.88/7.53  																																																																																																										| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																										| (109) $false
% 25.88/7.53  																																																																																																										|
% 25.88/7.53  																																																																																																										|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																									|-Branch two:
% 25.88/7.53  																																																																																																									| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																									| (625)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																																									|
% 25.88/7.53  																																																																																																										+-Applying beta-rule and splitting (593), into two cases.
% 25.88/7.53  																																																																																																										|-Branch one:
% 25.88/7.53  																																																																																																										| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																										|
% 25.88/7.53  																																																																																																											| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																											| (109) $false
% 25.88/7.53  																																																																																																											|
% 25.88/7.53  																																																																																																											|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																										|-Branch two:
% 25.88/7.53  																																																																																																										| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																										| (629)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.53  																																																																																																										|
% 25.88/7.53  																																																																																																											+-Applying beta-rule and splitting (548), into two cases.
% 25.88/7.53  																																																																																																											|-Branch one:
% 25.88/7.53  																																																																																																											| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																											|
% 25.88/7.53  																																																																																																												| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																												| (109) $false
% 25.88/7.53  																																																																																																												|
% 25.88/7.53  																																																																																																												|-The branch is then unsatisfiable
% 25.88/7.53  																																																																																																											|-Branch two:
% 25.88/7.53  																																																																																																											| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.53  																																																																																																											| (633)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0))
% 25.88/7.53  																																																																																																											|
% 25.88/7.53  																																																																																																												| Instantiating formula (41) with all_0_3_3, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_3_3, all_0_2_2) = 0, yields:
% 25.88/7.53  																																																																																																												| (108) all_0_1_1 = 0
% 25.88/7.53  																																																																																																												|
% 25.88/7.53  																																																																																																												| Equations (108) can reduce 32 to:
% 25.88/7.53  																																																																																																												| (109) $false
% 25.88/7.53  																																																																																																												|
% 25.88/7.53  																																																																																																												|-The branch is then unsatisfiable
% 25.88/7.54  																																																																																							|-Branch two:
% 25.88/7.54  																																																																																							| (636)  ~ (all_428_0_2414 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_428_0_2414
% 25.88/7.54  																																																																																							|
% 25.88/7.54  																																																																																								| Applying alpha-rule on (636) yields:
% 25.88/7.54  																																																																																								| (637)  ~ (all_428_0_2414 = 0)
% 25.88/7.54  																																																																																								| (638) distinct_lines(all_0_0_0, all_0_2_2) = all_428_0_2414
% 25.88/7.54  																																																																																								|
% 25.88/7.54  																																																																																								+-Applying beta-rule and splitting (482), into two cases.
% 25.88/7.54  																																																																																								|-Branch one:
% 25.88/7.54  																																																																																								| (262) all_28_0_32 = 0
% 25.88/7.54  																																																																																								|
% 25.88/7.54  																																																																																									| Equations (262) can reduce 88 to:
% 25.88/7.54  																																																																																									| (109) $false
% 25.88/7.54  																																																																																									|
% 25.88/7.54  																																																																																									|-The branch is then unsatisfiable
% 25.88/7.54  																																																																																								|-Branch two:
% 25.88/7.54  																																																																																								| (88)  ~ (all_28_0_32 = 0)
% 25.88/7.54  																																																																																								| (561)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 25.88/7.54  																																																																																								|
% 25.88/7.54  																																																																																									+-Applying beta-rule and splitting (498), into two cases.
% 25.88/7.54  																																																																																									|-Branch one:
% 25.88/7.54  																																																																																									| (108) all_0_1_1 = 0
% 25.88/7.54  																																																																																									|
% 25.88/7.54  																																																																																										| Equations (108) can reduce 32 to:
% 25.88/7.54  																																																																																										| (109) $false
% 25.88/7.54  																																																																																										|
% 25.88/7.54  																																																																																										|-The branch is then unsatisfiable
% 25.88/7.54  																																																																																									|-Branch two:
% 25.88/7.54  																																																																																									| (32)  ~ (all_0_1_1 = 0)
% 25.88/7.54  																																																																																									| (394)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 26.01/7.54  																																																																																									|
% 26.01/7.54  																																																																																										+-Applying beta-rule and splitting (502), into two cases.
% 26.01/7.54  																																																																																										|-Branch one:
% 26.01/7.54  																																																																																										| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																										|
% 26.01/7.54  																																																																																											| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																											| (109) $false
% 26.01/7.54  																																																																																											|
% 26.01/7.54  																																																																																											|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																										|-Branch two:
% 26.01/7.54  																																																																																										| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																										| (569)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 26.01/7.54  																																																																																										|
% 26.01/7.54  																																																																																											+-Applying beta-rule and splitting (510), into two cases.
% 26.01/7.54  																																																																																											|-Branch one:
% 26.01/7.54  																																																																																											| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																											|
% 26.01/7.54  																																																																																												| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																												| (109) $false
% 26.01/7.54  																																																																																												|
% 26.01/7.54  																																																																																												|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																											|-Branch two:
% 26.01/7.54  																																																																																											| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																											| (573)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 26.01/7.54  																																																																																											|
% 26.01/7.54  																																																																																												+-Applying beta-rule and splitting (527), into two cases.
% 26.01/7.54  																																																																																												|-Branch one:
% 26.01/7.54  																																																																																												| (655) (all_417_0_2413 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_417_0_2413 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (all_417_0_2413 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_417_0_2413)
% 26.01/7.54  																																																																																												|
% 26.01/7.54  																																																																																													+-Applying beta-rule and splitting (655), into two cases.
% 26.01/7.54  																																																																																													|-Branch one:
% 26.01/7.54  																																																																																													| (656) (all_417_0_2413 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_417_0_2413 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0)
% 26.01/7.54  																																																																																													|
% 26.01/7.54  																																																																																														+-Applying beta-rule and splitting (656), into two cases.
% 26.01/7.54  																																																																																														|-Branch one:
% 26.01/7.54  																																																																																														| (657) all_417_0_2413 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 26.01/7.54  																																																																																														|
% 26.01/7.54  																																																																																															| Applying alpha-rule on (657) yields:
% 26.01/7.54  																																																																																															| (658) all_417_0_2413 = 0
% 26.01/7.54  																																																																																															| (557) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 26.01/7.54  																																																																																															|
% 26.01/7.54  																																																																																															+-Applying beta-rule and splitting (190), into two cases.
% 26.01/7.54  																																																																																															|-Branch one:
% 26.01/7.54  																																																																																															| (262) all_28_0_32 = 0
% 26.01/7.54  																																																																																															|
% 26.01/7.54  																																																																																																| Equations (262) can reduce 88 to:
% 26.01/7.54  																																																																																																| (109) $false
% 26.01/7.54  																																																																																																|
% 26.01/7.54  																																																																																																|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																															|-Branch two:
% 26.01/7.54  																																																																																															| (88)  ~ (all_28_0_32 = 0)
% 26.01/7.54  																																																																																															| (589) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																															|
% 26.01/7.54  																																																																																																+-Applying beta-rule and splitting (188), into two cases.
% 26.01/7.54  																																																																																																|-Branch one:
% 26.01/7.54  																																																																																																| (262) all_28_0_32 = 0
% 26.01/7.54  																																																																																																|
% 26.01/7.54  																																																																																																	| Equations (262) can reduce 88 to:
% 26.01/7.54  																																																																																																	| (109) $false
% 26.01/7.54  																																																																																																	|
% 26.01/7.54  																																																																																																	|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																|-Branch two:
% 26.01/7.54  																																																																																																| (88)  ~ (all_28_0_32 = 0)
% 26.01/7.54  																																																																																																| (593) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																																|
% 26.01/7.54  																																																																																																	+-Applying beta-rule and splitting (191), into two cases.
% 26.01/7.54  																																																																																																	|-Branch one:
% 26.01/7.54  																																																																																																	| (262) all_28_0_32 = 0
% 26.01/7.54  																																																																																																	|
% 26.01/7.54  																																																																																																		| Equations (262) can reduce 88 to:
% 26.01/7.54  																																																																																																		| (109) $false
% 26.01/7.54  																																																																																																		|
% 26.01/7.54  																																																																																																		|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																	|-Branch two:
% 26.01/7.54  																																																																																																	| (88)  ~ (all_28_0_32 = 0)
% 26.01/7.54  																																																																																																	| (581) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 26.01/7.54  																																																																																																	|
% 26.01/7.54  																																																																																																		+-Applying beta-rule and splitting (206), into two cases.
% 26.01/7.54  																																																																																																		|-Branch one:
% 26.01/7.54  																																																																																																		| (222) all_30_0_34 = 0
% 26.01/7.54  																																																																																																		|
% 26.01/7.54  																																																																																																			| Equations (222) can reduce 92 to:
% 26.01/7.54  																																																																																																			| (109) $false
% 26.01/7.54  																																																																																																			|
% 26.01/7.54  																																																																																																			|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																		|-Branch two:
% 26.01/7.54  																																																																																																		| (92)  ~ (all_30_0_34 = 0)
% 26.01/7.54  																																																																																																		| (544) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																																		|
% 26.01/7.54  																																																																																																			+-Applying beta-rule and splitting (390), into two cases.
% 26.01/7.54  																																																																																																			|-Branch one:
% 26.01/7.54  																																																																																																			| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																			|
% 26.01/7.54  																																																																																																				| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																				| (109) $false
% 26.01/7.54  																																																																																																				|
% 26.01/7.54  																																																																																																				|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																			|-Branch two:
% 26.01/7.54  																																																																																																			| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																			| (609)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 26.01/7.54  																																																																																																			|
% 26.01/7.54  																																																																																																				+-Applying beta-rule and splitting (159), into two cases.
% 26.01/7.54  																																																																																																				|-Branch one:
% 26.01/7.54  																																																																																																				| (222) all_30_0_34 = 0
% 26.01/7.54  																																																																																																				|
% 26.01/7.54  																																																																																																					| Equations (222) can reduce 92 to:
% 26.01/7.54  																																																																																																					| (109) $false
% 26.01/7.54  																																																																																																					|
% 26.01/7.54  																																																																																																					|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																				|-Branch two:
% 26.01/7.54  																																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 26.01/7.54  																																																																																																				| (548) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0))
% 26.01/7.54  																																																																																																				|
% 26.01/7.54  																																																																																																					+-Applying beta-rule and splitting (438), into two cases.
% 26.01/7.54  																																																																																																					|-Branch one:
% 26.01/7.54  																																																																																																					| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																					|
% 26.01/7.54  																																																																																																						| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																						| (109) $false
% 26.01/7.54  																																																																																																						|
% 26.01/7.54  																																																																																																						|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																					|-Branch two:
% 26.01/7.54  																																																																																																					| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																					| (613)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 26.01/7.54  																																																																																																					|
% 26.01/7.54  																																																																																																						+-Applying beta-rule and splitting (442), into two cases.
% 26.01/7.54  																																																																																																						|-Branch one:
% 26.01/7.54  																																																																																																						| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																						|
% 26.01/7.54  																																																																																																							| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																							| (109) $false
% 26.01/7.54  																																																																																																							|
% 26.01/7.54  																																																																																																							|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																						|-Branch two:
% 26.01/7.54  																																																																																																						| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																						| (617)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, 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_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																																						|
% 26.01/7.54  																																																																																																							+-Applying beta-rule and splitting (589), into two cases.
% 26.01/7.54  																																																																																																							|-Branch one:
% 26.01/7.54  																																																																																																							| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																							|
% 26.01/7.54  																																																																																																								| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																								| (109) $false
% 26.01/7.54  																																																																																																								|
% 26.01/7.54  																																																																																																								|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																							|-Branch two:
% 26.01/7.54  																																																																																																							| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																							| (625)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																																							|
% 26.01/7.54  																																																																																																								+-Applying beta-rule and splitting (593), into two cases.
% 26.01/7.54  																																																																																																								|-Branch one:
% 26.01/7.54  																																																																																																								| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																								|
% 26.01/7.54  																																																																																																									| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																									| (109) $false
% 26.01/7.54  																																																																																																									|
% 26.01/7.54  																																																																																																									|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																								|-Branch two:
% 26.01/7.54  																																																																																																								| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																								| (629)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																																								|
% 26.01/7.54  																																																																																																									+-Applying beta-rule and splitting (581), into two cases.
% 26.01/7.54  																																																																																																									|-Branch one:
% 26.01/7.54  																																																																																																									| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																									|
% 26.01/7.54  																																																																																																										| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																										| (109) $false
% 26.01/7.54  																																																																																																										|
% 26.01/7.54  																																																																																																										|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																									|-Branch two:
% 26.01/7.54  																																																																																																									| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																									| (621)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 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_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 26.01/7.54  																																																																																																									|
% 26.01/7.54  																																																																																																										+-Applying beta-rule and splitting (548), into two cases.
% 26.01/7.54  																																																																																																										|-Branch one:
% 26.01/7.54  																																																																																																										| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																										|
% 26.01/7.54  																																																																																																											| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																											| (109) $false
% 26.01/7.54  																																																																																																											|
% 26.01/7.54  																																																																																																											|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																										|-Branch two:
% 26.01/7.54  																																																																																																										| (32)  ~ (all_0_1_1 = 0)
% 26.01/7.54  																																																																																																										| (633)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 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_0_0) = v0))
% 26.01/7.54  																																																																																																										|
% 26.01/7.54  																																																																																																											| Instantiating formula (41) with all_0_3_3, all_0_2_2, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, apart_point_and_line(all_0_3_3, all_0_2_2) = 0, yields:
% 26.01/7.54  																																																																																																											| (108) all_0_1_1 = 0
% 26.01/7.54  																																																																																																											|
% 26.01/7.54  																																																																																																											| Equations (108) can reduce 32 to:
% 26.01/7.54  																																																																																																											| (109) $false
% 26.01/7.54  																																																																																																											|
% 26.01/7.54  																																																																																																											|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																														|-Branch two:
% 26.01/7.54  																																																																																														| (710) all_417_0_2413 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 26.01/7.54  																																																																																														|
% 26.01/7.54  																																																																																															| Applying alpha-rule on (710) yields:
% 26.01/7.54  																																																																																															| (658) all_417_0_2413 = 0
% 26.01/7.54  																																																																																															| (712) apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 26.01/7.54  																																																																																															|
% 26.01/7.54  																																																																																															+-Applying beta-rule and splitting (190), into two cases.
% 26.01/7.54  																																																																																															|-Branch one:
% 26.01/7.54  																																																																																															| (262) all_28_0_32 = 0
% 26.01/7.54  																																																																																															|
% 26.01/7.54  																																																																																																| Equations (262) can reduce 88 to:
% 26.01/7.54  																																																																																																| (109) $false
% 26.01/7.54  																																																																																																|
% 26.01/7.54  																																																																																																|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																															|-Branch two:
% 26.01/7.54  																																																																																															| (88)  ~ (all_28_0_32 = 0)
% 26.01/7.54  																																																																																															| (589) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 26.01/7.54  																																																																																															|
% 26.01/7.54  																																																																																																+-Applying beta-rule and splitting (188), into two cases.
% 26.01/7.54  																																																																																																|-Branch one:
% 26.01/7.54  																																																																																																| (262) all_28_0_32 = 0
% 26.01/7.54  																																																																																																|
% 26.01/7.54  																																																																																																	| Equations (262) can reduce 88 to:
% 26.01/7.54  																																																																																																	| (109) $false
% 26.01/7.54  																																																																																																	|
% 26.01/7.54  																																																																																																	|-The branch is then unsatisfiable
% 26.01/7.54  																																																																																																|-Branch two:
% 26.01/7.54  																																																																																																| (88)  ~ (all_28_0_32 = 0)
% 26.01/7.54  																																																																																																| (593) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 26.01/7.55  																																																																																																|
% 26.01/7.55  																																																																																																	+-Applying beta-rule and splitting (191), into two cases.
% 26.01/7.55  																																																																																																	|-Branch one:
% 26.01/7.55  																																																																																																	| (262) all_28_0_32 = 0
% 26.01/7.55  																																																																																																	|
% 26.01/7.55  																																																																																																		| Equations (262) can reduce 88 to:
% 26.01/7.55  																																																																																																		| (109) $false
% 26.01/7.55  																																																																																																		|
% 26.01/7.55  																																																																																																		|-The branch is then unsatisfiable
% 26.01/7.55  																																																																																																	|-Branch two:
% 26.01/7.55  																																																																																																	| (88)  ~ (all_28_0_32 = 0)
% 26.01/7.55  																																																																																																	| (581) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 26.01/7.55  																																																																																																	|
% 26.01/7.55  																																																																																																		| Instantiating formula (41) with all_0_5_5, all_0_0_0, 0, all_28_0_32 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_0_0) = 0, yields:
% 26.01/7.55  																																																																																																		| (262) all_28_0_32 = 0
% 26.01/7.55  																																																																																																		|
% 26.01/7.55  																																																																																																		| Equations (262) can reduce 88 to:
% 26.01/7.55  																																																																																																		| (109) $false
% 26.01/7.55  																																																																																																		|
% 26.01/7.55  																																																																																																		|-The branch is then unsatisfiable
% 26.01/7.55  																																																																																													|-Branch two:
% 26.01/7.55  																																																																																													| (727)  ~ (all_417_0_2413 = 0) & distinct_lines(all_0_0_0, all_0_2_2) = all_417_0_2413
% 26.01/7.55  																																																																																													|
% 26.01/7.55  																																																																																														| Applying alpha-rule on (727) yields:
% 26.01/7.55  																																																																																														| (728)  ~ (all_417_0_2413 = 0)
% 26.01/7.55  																																																																																														| (729) distinct_lines(all_0_0_0, all_0_2_2) = all_417_0_2413
% 26.01/7.55  																																																																																														|
% 26.01/7.55  																																																																																														| Instantiating formula (47) with all_0_0_0, all_0_2_2, all_417_0_2413, all_428_0_2414 and discharging atoms distinct_lines(all_0_0_0, all_0_2_2) = all_428_0_2414, distinct_lines(all_0_0_0, all_0_2_2) = all_417_0_2413, yields:
% 26.01/7.55  																																																																																														| (730) all_428_0_2414 = all_417_0_2413
% 26.01/7.55  																																																																																														|
% 26.01/7.55  																																																																																														| Instantiating formula (47) with all_0_0_0, all_0_2_2, 0, all_428_0_2414 and discharging atoms distinct_lines(all_0_0_0, all_0_2_2) = all_428_0_2414, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 26.01/7.55  																																																																																														| (539) all_428_0_2414 = 0
% 26.01/7.55  																																																																																														|
% 26.01/7.55  																																																																																														| Combining equations (539,730) yields a new equation:
% 26.01/7.55  																																																																																														| (658) all_417_0_2413 = 0
% 26.01/7.55  																																																																																														|
% 26.01/7.55  																																																																																														| Equations (658) can reduce 728 to:
% 26.01/7.55  																																																																																														| (109) $false
% 26.01/7.55  																																																																																														|
% 26.01/7.55  																																																																																														|-The branch is then unsatisfiable
% 26.01/7.55  																																																																																												|-Branch two:
% 26.01/7.55  																																																																																												| (734)  ~ (all_417_0_2413 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_417_0_2413
% 26.01/7.55  																																																																																												|
% 26.01/7.55  																																																																																													| Applying alpha-rule on (734) yields:
% 26.01/7.55  																																																																																													| (728)  ~ (all_417_0_2413 = 0)
% 26.01/7.55  																																																																																													| (736) distinct_points(all_0_5_5, all_0_3_3) = all_417_0_2413
% 26.01/7.55  																																																																																													|
% 26.01/7.55  																																																																																													| Instantiating formula (25) with all_0_5_5, all_0_3_3, all_417_0_2413, 0 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = all_417_0_2413, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 26.01/7.55  																																																																																													| (658) all_417_0_2413 = 0
% 26.01/7.55  																																																																																													|
% 26.01/7.55  																																																																																													| Equations (658) can reduce 728 to:
% 26.01/7.55  																																																																																													| (109) $false
% 26.01/7.55  																																																																																													|
% 26.01/7.55  																																																																																													|-The branch is then unsatisfiable
% 26.01/7.55  																																			|-Branch two:
% 26.01/7.55  																																			| (739)  ~ (distinct_lines(all_0_0_0, all_0_2_2) = 0)
% 26.01/7.55  																																			| (306) all_26_0_30 = 0
% 26.01/7.55  																																			|
% 26.01/7.55  																																				| Equations (306) can reduce 84 to:
% 26.01/7.55  																																				| (109) $false
% 26.01/7.55  																																				|
% 26.01/7.55  																																				|-The branch is then unsatisfiable
% 26.01/7.55  						|-Branch two:
% 26.01/7.55  						| (742)  ~ (all_33_0_37 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_33_0_37
% 26.01/7.55  						|
% 26.01/7.55  							| Applying alpha-rule on (742) yields:
% 26.01/7.55  							| (121)  ~ (all_33_0_37 = 0)
% 26.01/7.55  							| (744) distinct_points(all_0_5_5, all_0_3_3) = all_33_0_37
% 26.01/7.55  							|
% 26.01/7.55  							| Instantiating formula (25) with all_0_5_5, all_0_3_3, all_33_0_37, 0 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = all_33_0_37, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 26.01/7.55  							| (745) all_33_0_37 = 0
% 26.01/7.55  							|
% 26.01/7.55  							| Equations (745) can reduce 121 to:
% 26.01/7.55  							| (109) $false
% 26.01/7.55  							|
% 26.01/7.55  							|-The branch is then unsatisfiable
% 26.01/7.55  		|-Branch two:
% 26.01/7.55  		| (747)  ~ (all_32_0_36 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36
% 26.01/7.55  		|
% 26.01/7.55  			| Applying alpha-rule on (747) yields:
% 26.01/7.55  			| (106)  ~ (all_32_0_36 = 0)
% 26.01/7.55  			| (749) distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36
% 26.01/7.55  			|
% 26.01/7.55  			| Instantiating formula (25) with all_0_5_5, all_0_4_4, all_32_0_36, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 26.01/7.55  			| (750) all_32_0_36 = 0
% 26.01/7.55  			|
% 26.01/7.55  			| Equations (750) can reduce 106 to:
% 26.01/7.55  			| (109) $false
% 26.01/7.55  			|
% 26.01/7.55  			|-The branch is then unsatisfiable
% 26.01/7.55  	|-Branch two:
% 26.01/7.55  	| (752)  ~ (all_35_0_39 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39
% 26.01/7.55  	|
% 26.01/7.55  		| Applying alpha-rule on (752) yields:
% 26.01/7.55  		| (103)  ~ (all_35_0_39 = 0)
% 26.01/7.55  		| (754) distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39
% 26.01/7.55  		|
% 26.01/7.55  		| Instantiating formula (25) with all_0_5_5, all_0_4_4, all_35_0_39, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 26.01/7.55  		| (755) all_35_0_39 = 0
% 26.01/7.55  		|
% 26.01/7.55  		| Equations (755) can reduce 103 to:
% 26.01/7.55  		| (109) $false
% 26.01/7.55  		|
% 26.01/7.55  		|-The branch is then unsatisfiable
% 26.01/7.55  |-Branch two:
% 26.01/7.55  | (757)  ~ (all_34_0_38 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_34_0_38
% 26.01/7.55  |
% 26.01/7.55  	| Applying alpha-rule on (757) yields:
% 26.01/7.55  	| (100)  ~ (all_34_0_38 = 0)
% 26.01/7.55  	| (759) distinct_points(all_0_5_5, all_0_3_3) = all_34_0_38
% 26.01/7.55  	|
% 26.01/7.55  	| Instantiating formula (25) with all_0_5_5, all_0_3_3, all_34_0_38, 0 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = all_34_0_38, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 26.01/7.55  	| (760) all_34_0_38 = 0
% 26.01/7.55  	|
% 26.01/7.55  	| Equations (760) can reduce 100 to:
% 26.01/7.55  	| (109) $false
% 26.01/7.55  	|
% 26.01/7.55  	|-The branch is then unsatisfiable
% 26.01/7.55  % SZS output end Proof for theBenchmark
% 26.01/7.55  
% 26.01/7.55  6923ms
%------------------------------------------------------------------------------