%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO188+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n003.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 03:48:24 EDT 2022

% Result   : Theorem 6.29s 2.15s
% Output   : Proof 48.07s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : GEO188+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n003.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sat Jun 18 10:51:13 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.19/0.57          ____       _                          
% 0.19/0.57    ___  / __ \_____(_)___  ________  __________
% 0.19/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.19/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.19/0.57  
% 0.19/0.57  A Theorem Prover for First-Order Logic
% 0.19/0.58  (ePrincess v.1.0)
% 0.19/0.58  
% 0.19/0.58  (c) Philipp Rümmer, 2009-2015
% 0.19/0.58  (c) Peter Backeman, 2014-2015
% 0.19/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58  Bug reports to peter@backeman.se
% 0.19/0.58  
% 0.19/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58  
% 0.19/0.58  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.63/0.92  Prover 0: Preprocessing ...
% 1.89/1.06  Prover 0: Warning: ignoring some quantifiers
% 1.89/1.07  Prover 0: Constructing countermodel ...
% 2.84/1.31  Prover 0: gave up
% 2.84/1.31  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.84/1.33  Prover 1: Preprocessing ...
% 3.08/1.42  Prover 1: Constructing countermodel ...
% 3.37/1.47  Prover 1: gave up
% 3.37/1.47  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.46/1.49  Prover 2: Preprocessing ...
% 4.03/1.61  Prover 2: Warning: ignoring some quantifiers
% 4.03/1.62  Prover 2: Constructing countermodel ...
% 6.29/2.15  Prover 2: proved (677ms)
% 6.29/2.15  
% 6.29/2.15  No countermodel exists, formula is valid
% 6.29/2.15  % SZS status Theorem for theBenchmark
% 6.29/2.15  
% 6.29/2.15  Generating proof ... Warning: ignoring some quantifiers
% 46.59/20.65  found it (size 1352)
% 46.59/20.65  
% 46.59/20.65  % SZS output start Proof for theBenchmark
% 46.59/20.65  Assumed formulas after preprocessing and simplification: 
% 46.59/20.65  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v4 = 0) & line_connecting(v2, v1) = v5 & line_connecting(v0, v1) = v3 & apart_point_and_line(v2, v3) = v4 & apart_point_and_line(v0, 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)
% 46.63/20.70  | 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:
% 46.63/20.70  | (1)  ~ (all_0_1_1 = 0) & line_connecting(all_0_3_3, all_0_4_4) = 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_5_5, 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
% 46.63/20.72  |
% 46.63/20.72  | Applying alpha-rule on (1) yields:
% 46.63/20.72  | (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)))
% 46.63/20.72  | (3)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 46.63/20.72  | (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))
% 46.63/20.72  | (5)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 46.63/20.72  | (6)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 46.63/20.72  | (7)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 46.63/20.72  | (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)))
% 46.63/20.72  | (9)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 46.63/20.72  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 46.63/20.72  | (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)))
% 46.63/20.73  | (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))
% 46.63/20.73  | (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))
% 46.63/20.73  | (14) line_connecting(all_0_3_3, all_0_4_4) = all_0_0_0
% 46.63/20.73  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 46.63/20.73  | (16)  ! [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)))
% 46.63/20.73  | (17) apart_point_and_line(all_0_5_5, all_0_0_0) = 0
% 46.63/20.73  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 46.63/20.73  | (19)  ! [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)
% 46.63/20.73  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 46.63/20.73  | (21) distinct_points(all_0_5_5, all_0_4_4) = 0
% 46.63/20.73  | (22) line_connecting(all_0_5_5, all_0_4_4) = all_0_2_2
% 46.63/20.73  | (23)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 46.63/20.73  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 46.63/20.73  | (25)  ! [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)))
% 46.63/20.73  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 46.63/20.73  | (27)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 46.63/20.73  | (28)  ! [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)))
% 46.63/20.73  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 46.63/20.73  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 46.63/20.73  | (31)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 46.63/20.73  | (32)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 46.63/20.73  | (33)  ~ (all_0_1_1 = 0)
% 46.63/20.73  | (34)  ! [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)
% 46.63/20.73  | (35)  ! [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)))
% 46.63/20.74  | (36) distinct_points(all_0_5_5, all_0_3_3) = 0
% 46.63/20.74  | (37)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 46.63/20.74  | (38)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 46.63/20.74  | (39)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 46.63/20.74  | (40) distinct_points(all_0_4_4, all_0_3_3) = 0
% 46.63/20.74  | (41)  ! [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)))
% 46.63/20.74  | (42)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 46.63/20.74  | (43)  ! [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)))
% 46.63/20.74  | (44)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 46.63/20.74  | (45)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 47.00/20.74  | (46)  ! [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)))
% 47.00/20.74  | (47)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 47.00/20.74  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 47.00/20.74  | (49)  ! [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)
% 47.00/20.74  | (50)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 47.00/20.74  | (51) apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1
% 47.00/20.74  | (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)))
% 47.00/20.74  | (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))
% 47.00/20.74  | (54)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 47.00/20.74  | (55)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 47.00/20.74  | (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)
% 47.00/20.74  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (11) with all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_4_4) = all_0_0_0, yields:
% 47.00/20.75  | (58)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (41) with all_0_0_0, all_0_4_4, all_0_3_3 and discharging atoms line_connecting(all_0_3_3, all_0_4_4) = all_0_0_0, yields:
% 47.00/20.75  | (59)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.00/20.75  |
% 47.00/20.75  | 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:
% 47.00/20.75  | (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))
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (41) 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:
% 47.00/20.75  | (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))
% 47.00/20.75  |
% 47.00/20.75  | 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:
% 47.00/20.75  | (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))
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (43) 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:
% 47.00/20.75  | (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))
% 47.00/20.75  |
% 47.00/20.75  | 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:
% 47.00/20.75  | (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)
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (44) with all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 47.00/20.75  | (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)
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (43) 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:
% 47.00/20.75  | (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))
% 47.00/20.75  |
% 47.00/20.75  | 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:
% 47.00/20.75  | (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)
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (44) with all_0_3_3, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 47.00/20.75  | (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)
% 47.00/20.75  |
% 47.00/20.75  | 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:
% 47.00/20.75  | (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)
% 47.00/20.75  |
% 47.00/20.75  | Instantiating formula (44) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 47.00/20.75  | (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)
% 47.00/20.75  |
% 47.00/20.75  | Instantiating (70) with all_20_0_24, all_20_1_25 yields:
% 47.00/20.75  | (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
% 47.00/20.75  |
% 47.00/20.75  | Applying alpha-rule on (71) yields:
% 47.00/20.75  | (72)  ~ (all_20_0_24 = 0)
% 47.00/20.75  | (73) line_connecting(all_0_5_5, all_0_4_4) = all_20_1_25
% 47.00/20.75  | (74) apart_point_and_line(all_0_5_5, all_20_1_25) = all_20_0_24
% 47.00/20.75  |
% 47.00/20.75  | Instantiating (65) with all_22_0_26, all_22_1_27 yields:
% 47.00/20.75  | (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
% 47.00/20.75  |
% 47.00/20.75  | Applying alpha-rule on (75) yields:
% 47.00/20.75  | (76)  ~ (all_22_0_26 = 0)
% 47.00/20.75  | (77) line_connecting(all_0_4_4, all_0_3_3) = all_22_1_27
% 47.00/20.75  | (78) apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26
% 47.00/20.75  |
% 47.00/20.75  | Instantiating (64) with all_24_0_28, all_24_1_29 yields:
% 47.00/20.75  | (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
% 47.00/20.76  |
% 47.00/20.76  | Applying alpha-rule on (79) yields:
% 47.00/20.76  | (80)  ~ (all_24_0_28 = 0)
% 47.00/20.76  | (81) line_connecting(all_0_4_4, all_0_3_3) = all_24_1_29
% 47.00/20.76  | (82) apart_point_and_line(all_0_3_3, all_24_1_29) = all_24_0_28
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (69) with all_26_0_30, all_26_1_31 yields:
% 47.00/20.76  | (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
% 47.00/20.76  |
% 47.00/20.76  | Applying alpha-rule on (83) yields:
% 47.00/20.76  | (84)  ~ (all_26_0_30 = 0)
% 47.00/20.76  | (85) line_connecting(all_0_5_5, all_0_4_4) = all_26_1_31
% 47.00/20.76  | (86) apart_point_and_line(all_0_4_4, all_26_1_31) = all_26_0_30
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (68) with all_28_0_32, all_28_1_33 yields:
% 47.00/20.76  | (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
% 47.00/20.76  |
% 47.00/20.76  | Applying alpha-rule on (87) yields:
% 47.00/20.76  | (88)  ~ (all_28_0_32 = 0)
% 47.00/20.76  | (89) line_connecting(all_0_5_5, all_0_3_3) = all_28_1_33
% 47.00/20.76  | (90) apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (67) with all_30_0_34, all_30_1_35 yields:
% 47.00/20.76  | (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
% 47.00/20.76  |
% 47.00/20.76  | Applying alpha-rule on (91) yields:
% 47.00/20.76  | (92)  ~ (all_30_0_34 = 0)
% 47.00/20.76  | (93) line_connecting(all_0_5_5, all_0_3_3) = all_30_1_35
% 47.00/20.76  | (94) apart_point_and_line(all_0_3_3, all_30_1_35) = all_30_0_34
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (61) with all_32_0_36 yields:
% 47.00/20.76  | (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)
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (59) with all_33_0_37 yields:
% 47.00/20.76  | (96) ( ~ (all_33_0_37 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37) | ( ~ (all_33_0_37 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_33_0_37)
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (58) with all_34_0_38 yields:
% 47.00/20.76  | (97) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_34_0_38)
% 47.00/20.76  |
% 47.00/20.76  | Instantiating (60) with all_35_0_39 yields:
% 47.00/20.76  | (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)
% 47.00/20.76  |
% 47.00/20.76  +-Applying beta-rule and splitting (98), into two cases.
% 47.00/20.76  |-Branch one:
% 47.00/20.76  | (99)  ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39
% 47.00/20.76  |
% 47.00/20.76  	| Applying alpha-rule on (99) yields:
% 47.00/20.76  	| (100)  ~ (all_35_0_39 = 0)
% 47.00/20.76  	| (101) apart_point_and_line(all_0_4_4, all_0_2_2) = all_35_0_39
% 47.00/20.76  	|
% 47.00/20.76  	+-Applying beta-rule and splitting (95), into two cases.
% 47.00/20.76  	|-Branch one:
% 47.00/20.76  	| (102)  ~ (all_32_0_36 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36
% 47.00/20.76  	|
% 47.00/20.76  		| Applying alpha-rule on (102) yields:
% 47.00/20.76  		| (103)  ~ (all_32_0_36 = 0)
% 47.00/20.76  		| (104) apart_point_and_line(all_0_5_5, all_0_2_2) = all_32_0_36
% 47.00/20.76  		|
% 47.00/20.76  		+-Applying beta-rule and splitting (62), into two cases.
% 47.00/20.76  		|-Branch one:
% 47.00/20.76  		| (105) all_0_1_1 = 0
% 47.00/20.76  		|
% 47.00/20.76  			| Equations (105) can reduce 33 to:
% 47.00/20.76  			| (106) $false
% 47.00/20.76  			|
% 47.00/20.76  			|-The branch is then unsatisfiable
% 47.00/20.76  		|-Branch two:
% 47.00/20.76  		| (33)  ~ (all_0_1_1 = 0)
% 47.00/20.76  		| (108)  ? [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))
% 47.00/20.76  		|
% 47.00/20.76  			+-Applying beta-rule and splitting (66), into two cases.
% 47.00/20.76  			|-Branch one:
% 47.00/20.76  			| (105) all_0_1_1 = 0
% 47.00/20.76  			|
% 47.00/20.76  				| Equations (105) can reduce 33 to:
% 47.00/20.76  				| (106) $false
% 47.00/20.76  				|
% 47.00/20.76  				|-The branch is then unsatisfiable
% 47.00/20.76  			|-Branch two:
% 47.00/20.76  			| (33)  ~ (all_0_1_1 = 0)
% 47.00/20.76  			| (112)  ? [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))
% 47.00/20.76  			|
% 47.00/20.76  				+-Applying beta-rule and splitting (63), into two cases.
% 47.00/20.76  				|-Branch one:
% 47.00/20.76  				| (105) all_0_1_1 = 0
% 47.00/20.76  				|
% 47.00/20.76  					| Equations (105) can reduce 33 to:
% 47.00/20.76  					| (106) $false
% 47.00/20.76  					|
% 47.00/20.76  					|-The branch is then unsatisfiable
% 47.00/20.76  				|-Branch two:
% 47.00/20.76  				| (33)  ~ (all_0_1_1 = 0)
% 47.00/20.76  				| (116)  ? [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))
% 47.00/20.76  				|
% 47.00/20.76  					| Instantiating formula (24) 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:
% 47.00/20.76  					| (117) all_24_1_29 = all_22_1_27
% 47.00/20.76  					|
% 47.00/20.76  					| Instantiating formula (24) 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:
% 47.00/20.76  					| (118) all_30_1_35 = all_28_1_33
% 47.00/20.76  					|
% 47.00/20.76  					| Instantiating formula (24) 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:
% 47.00/20.76  					| (119) all_26_1_31 = all_0_2_2
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (24) 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:
% 47.00/20.77  					| (120) all_26_1_31 = all_20_1_25
% 47.00/20.77  					|
% 47.00/20.77  					| Combining equations (119,120) yields a new equation:
% 47.00/20.77  					| (121) all_20_1_25 = all_0_2_2
% 47.00/20.77  					|
% 47.00/20.77  					| Combining equations (121,120) yields a new equation:
% 47.00/20.77  					| (119) all_26_1_31 = all_0_2_2
% 47.00/20.77  					|
% 47.00/20.77  					| From (118) and (94) follows:
% 47.00/20.77  					| (123) apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34
% 47.00/20.77  					|
% 47.00/20.77  					| From (117) and (82) follows:
% 47.00/20.77  					| (124) apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28
% 47.00/20.77  					|
% 47.00/20.77  					| From (119) and (86) follows:
% 47.00/20.77  					| (125) apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30
% 47.00/20.77  					|
% 47.00/20.77  					| From (121) and (74) follows:
% 47.00/20.77  					| (126) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (42) 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:
% 47.00/20.77  					| (127) all_35_0_39 = all_26_0_30
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (42) 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:
% 47.00/20.77  					| (128) all_32_0_36 = all_20_0_24
% 47.00/20.77  					|
% 47.00/20.77  					| Equations (127) can reduce 100 to:
% 47.00/20.77  					| (84)  ~ (all_26_0_30 = 0)
% 47.00/20.77  					|
% 47.00/20.77  					| Equations (128) can reduce 103 to:
% 47.00/20.77  					| (72)  ~ (all_20_0_24 = 0)
% 47.00/20.77  					|
% 47.00/20.77  					| From (127) and (101) follows:
% 47.00/20.77  					| (125) apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30
% 47.00/20.77  					|
% 47.00/20.77  					| From (128) and (104) follows:
% 47.00/20.77  					| (126) apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (43) with all_30_0_34, all_0_1_1, all_28_1_33, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = 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:
% 47.00/20.77  					| (133) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (43) with all_0_1_1, all_30_0_34, all_0_2_2, all_28_1_33, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = 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:
% 47.00/20.77  					| (134) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (43) with all_30_0_34, all_0_1_1, all_28_1_33, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = 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:
% 47.00/20.77  					| (135) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (43) with all_0_1_1, all_30_0_34, all_0_2_2, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = 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:
% 47.00/20.77  					| (136) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (52) with all_30_0_34, all_0_1_1, all_28_1_33, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 47.00/20.77  					| (137) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (52) with all_0_1_1, all_30_0_34, all_0_2_2, all_28_1_33, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 47.00/20.77  					| (138) all_30_0_34 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (43) with all_30_0_34, all_30_0_34, all_28_1_33, all_28_1_33, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 47.00/20.77  					| (139) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (43) with all_30_0_34, all_30_0_34, all_28_1_33, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 47.00/20.77  					| (140) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.00/20.77  					|
% 47.00/20.77  					| Instantiating formula (52) with all_30_0_34, all_30_0_34, all_28_1_33, all_28_1_33, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, yields:
% 47.00/20.77  					| (141) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) 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:
% 47.00/20.78  					| (142) 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))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) with all_0_1_1, all_24_0_28, 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_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:
% 47.00/20.78  					| (143) 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_22_1_27, all_0_2_2) = v0))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) 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:
% 47.00/20.78  					| (144) 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))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) 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:
% 47.00/20.78  					| (145) 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))
% 47.00/20.78  					|
% 47.00/20.78  					| 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:
% 47.00/20.78  					| (146) 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))
% 47.00/20.78  					|
% 47.00/20.78  					| 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:
% 47.00/20.78  					| (147) 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))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) with all_24_0_28, all_30_0_34, all_22_1_27, all_28_1_33, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, 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:
% 47.00/20.78  					| (148) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) with all_30_0_34, all_24_0_28, all_28_1_33, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, 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:
% 47.00/20.78  					| (149) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) with all_24_0_28, all_30_0_34, all_22_1_27, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, 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:
% 47.00/20.78  					| (150) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (43) with all_30_0_34, all_24_0_28, all_28_1_33, all_22_1_27, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, 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:
% 47.00/20.78  					| (151) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.00/20.78  					|
% 47.00/20.78  					| Instantiating formula (52) with all_24_0_28, all_30_0_34, all_22_1_27, all_28_1_33, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, yields:
% 47.22/20.78  					| (152) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.22/20.78  					|
% 47.22/20.78  					| Instantiating formula (52) with all_30_0_34, all_24_0_28, all_28_1_33, all_22_1_27, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_22_1_27) = all_24_0_28, yields:
% 47.22/20.78  					| (153) all_30_0_34 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.22/20.78  					|
% 47.22/20.79  					| Instantiating formula (43) 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:
% 47.22/20.79  					| (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))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (43) 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:
% 47.22/20.79  					| (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))
% 47.22/20.79  					|
% 47.22/20.79  					| 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:
% 47.22/20.79  					| (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))
% 47.22/20.79  					|
% 47.22/20.79  					| 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:
% 47.22/20.79  					| (157) 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))
% 47.22/20.79  					|
% 47.22/20.79  					| 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:
% 47.22/20.79  					| (158) 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))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (28) 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:
% 47.22/20.79  					| (159) 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))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (28) with all_0_1_1, all_22_0_26, 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_0_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 47.22/20.79  					| (160) 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_4_4, all_0_3_3) = v0))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (52) with all_22_0_26, all_30_0_34, all_22_1_27, all_28_1_33, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 47.22/20.79  					| (161) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (52) with all_30_0_34, all_22_0_26, all_28_1_33, all_22_1_27, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 47.22/20.79  					| (162) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (28) with all_22_0_26, all_30_0_34, all_28_1_33, all_22_1_27, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 47.22/20.79  					| (163) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (28) with all_30_0_34, all_22_0_26, all_22_1_27, all_28_1_33, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 47.22/20.79  					| (164) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.22/20.79  					|
% 47.22/20.79  					| 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:
% 47.22/20.79  					| (165) 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))
% 47.22/20.79  					|
% 47.22/20.79  					| Instantiating formula (52) with all_24_0_28, all_22_0_26, 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, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 47.22/20.79  					| (166) 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_4_4, all_0_3_3) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (35) with all_22_0_26, all_22_0_26, 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_4_4, all_22_1_27) = all_22_0_26, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 47.22/20.80  					| (167) all_22_0_26 = 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))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (43) 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:
% 47.22/20.80  					| (168) 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))
% 47.22/20.80  					|
% 47.22/20.80  					| 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:
% 47.22/20.80  					| (169) 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))
% 47.22/20.80  					|
% 47.22/20.80  					| 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:
% 47.22/20.80  					| (170) 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))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (52) with all_26_0_30, all_30_0_34, all_0_2_2, all_28_1_33, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.80  					| (171) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (52) with all_30_0_34, all_26_0_30, all_28_1_33, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.80  					| (172) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (28) with all_26_0_30, all_30_0_34, all_28_1_33, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.80  					| (173) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (28) with all_30_0_34, all_26_0_30, all_0_2_2, all_28_1_33, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.80  					| (174) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| 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:
% 47.22/20.80  					| (175) 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))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (52) with all_24_0_28, all_26_0_30, 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_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.80  					| (176) 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_4_4, all_0_3_3) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (28) 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:
% 47.22/20.80  					| (177) 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))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (28) with all_24_0_28, all_26_0_30, 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_22_1_27) = all_24_0_28, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.80  					| (178) 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_4_4, all_0_3_3) = v0))
% 47.22/20.80  					|
% 47.22/20.80  					| Instantiating formula (35) with all_26_0_30, 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_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_4_4, all_0_3_3) = 0, yields:
% 47.22/20.81  					| (179) all_26_0_30 = 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_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (35) with all_22_0_26, all_26_0_30, 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_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_4_4, all_0_3_3) = 0, yields:
% 47.22/20.81  					| (180) all_26_0_30 = 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_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (43) 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:
% 47.22/20.81  					| (181) 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))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (43) with all_22_0_26, all_26_0_30, 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_4_4, all_0_2_2) = all_26_0_30, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 47.22/20.81  					| (182) 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_0_2_2, all_22_1_27) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_26_0_30, all_22_0_26, all_0_2_2, 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, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 47.22/20.81  					| (183) 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_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| 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:
% 47.22/20.81  					| (184) 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))
% 47.22/20.81  					|
% 47.22/20.81  					| 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:
% 47.22/20.81  					| (185) 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))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_28_0_32, all_0_1_1, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (186) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_0_1_1, all_28_0_32, all_0_2_2, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (187) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (28) with all_28_0_32, all_0_1_1, all_0_2_2, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (188) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (28) with all_0_1_1, all_28_0_32, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (189) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_28_0_32, all_30_0_34, all_28_1_33, all_28_1_33, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (190) all_30_0_34 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_30_0_34, all_28_0_32, all_28_1_33, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (191) all_30_0_34 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_28_0_32, all_24_0_28, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (192) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (52) with all_24_0_28, all_28_0_32, all_22_1_27, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (193) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (28) with all_28_0_32, all_24_0_28, all_22_1_27, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.81  					| (194) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.81  					|
% 47.22/20.81  					| Instantiating formula (28) with all_24_0_28, all_28_0_32, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (195) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_28_0_32, all_22_0_26, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (196) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_22_0_26, all_28_0_32, all_22_1_27, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (197) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (28) with all_28_0_32, all_22_0_26, all_22_1_27, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (198) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (28) with all_22_0_26, all_28_0_32, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (199) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_28_0_32, all_26_0_30, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (200) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_26_0_30, all_28_0_32, all_0_2_2, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (201) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (28) with all_28_0_32, all_26_0_30, all_0_2_2, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (202) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (28) with all_26_0_30, all_28_0_32, all_28_1_33, 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_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (203) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (35) with all_28_0_32, all_28_0_32, all_28_1_33, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 47.22/20.82  					| (204) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (35) with all_28_0_32, all_28_0_32, all_28_1_33, all_28_1_33, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 47.22/20.82  					| (205) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_28_0_32, all_28_0_32, all_28_1_33, all_28_1_33, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, yields:
% 47.22/20.82  					| (206) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| 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:
% 47.22/20.82  					| (207) 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))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (34) with all_20_0_24, all_0_2_2, all_0_0_0, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_0_0) = 0, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.82  					| (208) all_20_0_24 = 0 | distinct_lines(all_0_0_0, all_0_2_2) = 0
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_20_0_24, all_30_0_34, all_0_2_2, all_28_1_33, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.82  					| (209) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_30_0_34, all_20_0_24, all_28_1_33, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.82  					| (210) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (28) with all_20_0_24, all_30_0_34, all_28_1_33, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.82  					| (211) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (28) with all_30_0_34, all_20_0_24, all_0_2_2, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.82  					| (212) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.82  					|
% 47.22/20.82  					| 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:
% 47.22/20.82  					| (213) 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))
% 47.22/20.82  					|
% 47.22/20.82  					| Instantiating formula (52) with all_24_0_28, all_20_0_24, 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_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.82  					| (214) 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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (28) with all_20_0_24, all_24_0_28, all_22_1_27, all_0_2_2, 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:
% 47.22/20.83  					| (215) 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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (28) with all_24_0_28, all_20_0_24, 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_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.83  					| (216) 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_5_5, all_0_3_3) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| 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:
% 47.22/20.83  					| (217) 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))
% 47.22/20.83  					|
% 47.22/20.83  					| 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:
% 47.22/20.83  					| (218) 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))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (28) 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:
% 47.22/20.83  					| (219) 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))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (28) 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:
% 47.22/20.83  					| (220) 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))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (52) with all_20_0_24, all_26_0_30, all_0_2_2, all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.83  					| (221) all_26_0_30 = 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_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (35) with all_20_0_24, all_28_0_32, all_0_2_2, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = 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:
% 47.22/20.83  					| (222) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (35) with all_28_0_32, all_20_0_24, all_28_1_33, all_0_2_2, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = 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:
% 47.22/20.83  					| (223) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (35) with all_20_0_24, all_28_0_32, all_0_2_2, all_28_1_33, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = 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:
% 47.22/20.83  					| (224) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (35) with all_28_0_32, all_20_0_24, all_28_1_33, all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = 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:
% 47.22/20.83  					| (225) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (52) with all_20_0_24, all_28_0_32, all_0_2_2, all_28_1_33, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.83  					| (226) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| Instantiating formula (52) with all_28_0_32, all_20_0_24, all_28_1_33, all_0_2_2, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 47.22/20.83  					| (227) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.22/20.83  					|
% 47.22/20.83  					| 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:
% 47.22/20.83  					| (228) 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))
% 47.22/20.83  					|
% 47.22/20.83  					+-Applying beta-rule and splitting (96), into two cases.
% 47.22/20.83  					|-Branch one:
% 47.22/20.83  					| (229)  ~ (all_33_0_37 = 0) & apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37
% 47.22/20.83  					|
% 47.22/20.83  						| Applying alpha-rule on (229) yields:
% 47.22/20.83  						| (230)  ~ (all_33_0_37 = 0)
% 47.22/20.83  						| (231) apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37
% 47.22/20.83  						|
% 47.22/20.83  						+-Applying beta-rule and splitting (167), into two cases.
% 47.22/20.83  						|-Branch one:
% 47.22/20.83  						| (232) all_22_0_26 = 0
% 47.22/20.83  						|
% 47.22/20.83  							| Equations (232) can reduce 76 to:
% 47.22/20.83  							| (106) $false
% 47.22/20.83  							|
% 47.22/20.83  							|-The branch is then unsatisfiable
% 47.22/20.83  						|-Branch two:
% 47.22/20.83  						| (76)  ~ (all_22_0_26 = 0)
% 47.22/20.83  						| (235)  ? [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))
% 47.22/20.83  						|
% 47.22/20.83  							+-Applying beta-rule and splitting (168), into two cases.
% 47.22/20.83  							|-Branch one:
% 47.22/20.83  							| (232) all_22_0_26 = 0
% 47.22/20.83  							|
% 47.22/20.83  								| Equations (232) can reduce 76 to:
% 47.22/20.83  								| (106) $false
% 47.22/20.83  								|
% 47.22/20.83  								|-The branch is then unsatisfiable
% 47.22/20.83  							|-Branch two:
% 47.22/20.83  							| (76)  ~ (all_22_0_26 = 0)
% 47.22/20.83  							| (239)  ? [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))
% 47.22/20.83  							|
% 47.22/20.83  								+-Applying beta-rule and splitting (169), into two cases.
% 47.22/20.83  								|-Branch one:
% 47.22/20.83  								| (232) all_22_0_26 = 0
% 47.22/20.83  								|
% 47.22/20.83  									| Equations (232) can reduce 76 to:
% 47.22/20.83  									| (106) $false
% 47.22/20.83  									|
% 47.22/20.83  									|-The branch is then unsatisfiable
% 47.22/20.83  								|-Branch two:
% 47.22/20.83  								| (76)  ~ (all_22_0_26 = 0)
% 47.22/20.83  								| (243)  ? [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))
% 47.22/20.83  								|
% 47.22/20.83  									+-Applying beta-rule and splitting (185), into two cases.
% 47.22/20.83  									|-Branch one:
% 47.22/20.83  									| (244) all_26_0_30 = 0
% 47.22/20.83  									|
% 47.22/20.83  										| Equations (244) can reduce 84 to:
% 47.22/20.83  										| (106) $false
% 47.22/20.83  										|
% 47.22/20.83  										|-The branch is then unsatisfiable
% 47.22/20.83  									|-Branch two:
% 47.22/20.83  									| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.83  									| (247)  ? [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))
% 47.22/20.84  									|
% 47.22/20.84  										+-Applying beta-rule and splitting (178), into two cases.
% 47.22/20.84  										|-Branch one:
% 47.22/20.84  										| (244) all_26_0_30 = 0
% 47.22/20.84  										|
% 47.22/20.84  											| Equations (244) can reduce 84 to:
% 47.22/20.84  											| (106) $false
% 47.22/20.84  											|
% 47.22/20.84  											|-The branch is then unsatisfiable
% 47.22/20.84  										|-Branch two:
% 47.22/20.84  										| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  										| (251) 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_4_4, all_0_3_3) = v0))
% 47.22/20.84  										|
% 47.22/20.84  											+-Applying beta-rule and splitting (163), into two cases.
% 47.22/20.84  											|-Branch one:
% 47.22/20.84  											| (252) all_30_0_34 = 0
% 47.22/20.84  											|
% 47.22/20.84  												| Equations (252) can reduce 92 to:
% 47.22/20.84  												| (106) $false
% 47.22/20.84  												|
% 47.22/20.84  												|-The branch is then unsatisfiable
% 47.22/20.84  											|-Branch two:
% 47.22/20.84  											| (92)  ~ (all_30_0_34 = 0)
% 47.22/20.84  											| (255) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.22/20.84  											|
% 47.22/20.84  												+-Applying beta-rule and splitting (177), into two cases.
% 47.22/20.84  												|-Branch one:
% 47.22/20.84  												| (244) all_26_0_30 = 0
% 47.22/20.84  												|
% 47.22/20.84  													| Equations (244) can reduce 84 to:
% 47.22/20.84  													| (106) $false
% 47.22/20.84  													|
% 47.22/20.84  													|-The branch is then unsatisfiable
% 47.22/20.84  												|-Branch two:
% 47.22/20.84  												| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  												| (259) 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))
% 47.22/20.84  												|
% 47.22/20.84  													+-Applying beta-rule and splitting (179), into two cases.
% 47.22/20.84  													|-Branch one:
% 47.22/20.84  													| (244) all_26_0_30 = 0
% 47.22/20.84  													|
% 47.22/20.84  														| Equations (244) can reduce 84 to:
% 47.22/20.84  														| (106) $false
% 47.22/20.84  														|
% 47.22/20.84  														|-The branch is then unsatisfiable
% 47.22/20.84  													|-Branch two:
% 47.22/20.84  													| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  													| (263) 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_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = v0))
% 47.22/20.84  													|
% 47.22/20.84  														+-Applying beta-rule and splitting (183), into two cases.
% 47.22/20.84  														|-Branch one:
% 47.22/20.84  														| (244) all_26_0_30 = 0
% 47.22/20.84  														|
% 47.22/20.84  															| Equations (244) can reduce 84 to:
% 47.22/20.84  															| (106) $false
% 47.22/20.84  															|
% 47.22/20.84  															|-The branch is then unsatisfiable
% 47.22/20.84  														|-Branch two:
% 47.22/20.84  														| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  														| (267) 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_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 47.22/20.84  														|
% 47.22/20.84  															+-Applying beta-rule and splitting (165), into two cases.
% 47.22/20.84  															|-Branch one:
% 47.22/20.84  															| (268) all_24_0_28 = 0
% 47.22/20.84  															|
% 47.22/20.84  																| Equations (268) can reduce 80 to:
% 47.22/20.84  																| (106) $false
% 47.22/20.84  																|
% 47.22/20.84  																|-The branch is then unsatisfiable
% 47.22/20.84  															|-Branch two:
% 47.22/20.84  															| (80)  ~ (all_24_0_28 = 0)
% 47.22/20.84  															| (271) 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))
% 47.22/20.84  															|
% 47.22/20.84  																+-Applying beta-rule and splitting (166), into two cases.
% 47.22/20.84  																|-Branch one:
% 47.22/20.84  																| (268) all_24_0_28 = 0
% 47.22/20.84  																|
% 47.22/20.84  																	| Equations (268) can reduce 80 to:
% 47.22/20.84  																	| (106) $false
% 47.22/20.84  																	|
% 47.22/20.84  																	|-The branch is then unsatisfiable
% 47.22/20.84  																|-Branch two:
% 47.22/20.84  																| (80)  ~ (all_24_0_28 = 0)
% 47.22/20.84  																| (275) 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_4_4, all_0_3_3) = v0))
% 47.22/20.84  																|
% 47.22/20.84  																	+-Applying beta-rule and splitting (180), into two cases.
% 47.22/20.84  																	|-Branch one:
% 47.22/20.84  																	| (244) all_26_0_30 = 0
% 47.22/20.84  																	|
% 47.22/20.84  																		| Equations (244) can reduce 84 to:
% 47.22/20.84  																		| (106) $false
% 47.22/20.84  																		|
% 47.22/20.84  																		|-The branch is then unsatisfiable
% 47.22/20.84  																	|-Branch two:
% 47.22/20.84  																	| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  																	| (279) 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_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_22_1_27) = v0))
% 47.22/20.84  																	|
% 47.22/20.84  																		+-Applying beta-rule and splitting (181), into two cases.
% 47.22/20.84  																		|-Branch one:
% 47.22/20.84  																		| (244) all_26_0_30 = 0
% 47.22/20.84  																		|
% 47.22/20.84  																			| Equations (244) can reduce 84 to:
% 47.22/20.84  																			| (106) $false
% 47.22/20.84  																			|
% 47.22/20.84  																			|-The branch is then unsatisfiable
% 47.22/20.84  																		|-Branch two:
% 47.22/20.84  																		| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  																		| (283) 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))
% 47.22/20.84  																		|
% 47.22/20.84  																			+-Applying beta-rule and splitting (184), into two cases.
% 47.22/20.84  																			|-Branch one:
% 47.22/20.84  																			| (244) all_26_0_30 = 0
% 47.22/20.84  																			|
% 47.22/20.84  																				| Equations (244) can reduce 84 to:
% 47.22/20.84  																				| (106) $false
% 47.22/20.84  																				|
% 47.22/20.84  																				|-The branch is then unsatisfiable
% 47.22/20.84  																			|-Branch two:
% 47.22/20.84  																			| (84)  ~ (all_26_0_30 = 0)
% 47.22/20.84  																			| (287) 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))
% 47.22/20.84  																			|
% 47.22/20.84  																				+-Applying beta-rule and splitting (171), into two cases.
% 47.22/20.84  																				|-Branch one:
% 47.22/20.84  																				| (252) all_30_0_34 = 0
% 47.22/20.84  																				|
% 47.22/20.84  																					| Equations (252) can reduce 92 to:
% 47.22/20.84  																					| (106) $false
% 47.22/20.84  																					|
% 47.22/20.84  																					|-The branch is then unsatisfiable
% 47.22/20.84  																				|-Branch two:
% 47.22/20.84  																				| (92)  ~ (all_30_0_34 = 0)
% 47.22/20.84  																				| (291) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.22/20.84  																				|
% 47.22/20.84  																					+-Applying beta-rule and splitting (172), into two cases.
% 47.22/20.84  																					|-Branch one:
% 47.22/20.84  																					| (252) all_30_0_34 = 0
% 47.22/20.84  																					|
% 47.22/20.84  																						| Equations (252) can reduce 92 to:
% 47.22/20.84  																						| (106) $false
% 47.22/20.84  																						|
% 47.22/20.84  																						|-The branch is then unsatisfiable
% 47.22/20.84  																					|-Branch two:
% 47.22/20.84  																					| (92)  ~ (all_30_0_34 = 0)
% 47.22/20.84  																					| (295) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.22/20.84  																					|
% 47.22/20.84  																						+-Applying beta-rule and splitting (161), into two cases.
% 47.22/20.84  																						|-Branch one:
% 47.22/20.84  																						| (252) all_30_0_34 = 0
% 47.22/20.84  																						|
% 47.22/20.84  																							| Equations (252) can reduce 92 to:
% 47.22/20.84  																							| (106) $false
% 47.22/20.84  																							|
% 47.22/20.84  																							|-The branch is then unsatisfiable
% 47.22/20.84  																						|-Branch two:
% 47.22/20.84  																						| (92)  ~ (all_30_0_34 = 0)
% 47.22/20.84  																						| (299) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.51/20.84  																						|
% 47.51/20.84  																							+-Applying beta-rule and splitting (162), into two cases.
% 47.51/20.84  																							|-Branch one:
% 47.51/20.84  																							| (252) all_30_0_34 = 0
% 47.51/20.84  																							|
% 47.51/20.84  																								| Equations (252) can reduce 92 to:
% 47.51/20.84  																								| (106) $false
% 47.51/20.84  																								|
% 47.51/20.84  																								|-The branch is then unsatisfiable
% 47.51/20.84  																							|-Branch two:
% 47.51/20.84  																							| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.84  																							| (303) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.51/20.84  																							|
% 47.51/20.84  																								+-Applying beta-rule and splitting (182), into two cases.
% 47.51/20.84  																								|-Branch one:
% 47.51/20.84  																								| (244) all_26_0_30 = 0
% 47.51/20.84  																								|
% 47.51/20.84  																									| Equations (244) can reduce 84 to:
% 47.51/20.84  																									| (106) $false
% 47.51/20.84  																									|
% 47.51/20.84  																									|-The branch is then unsatisfiable
% 47.51/20.84  																								|-Branch two:
% 47.51/20.84  																								| (84)  ~ (all_26_0_30 = 0)
% 47.51/20.84  																								| (307) 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_0_2_2, all_22_1_27) = v0))
% 47.51/20.84  																								|
% 47.51/20.84  																									+-Applying beta-rule and splitting (187), into two cases.
% 47.51/20.84  																									|-Branch one:
% 47.51/20.84  																									| (308) all_28_0_32 = 0
% 47.51/20.84  																									|
% 47.51/20.84  																										| Equations (308) can reduce 88 to:
% 47.51/20.84  																										| (106) $false
% 47.51/20.84  																										|
% 47.51/20.84  																										|-The branch is then unsatisfiable
% 47.51/20.84  																									|-Branch two:
% 47.51/20.84  																									| (88)  ~ (all_28_0_32 = 0)
% 47.51/20.84  																									| (311) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.51/20.84  																									|
% 47.51/20.84  																										+-Applying beta-rule and splitting (164), into two cases.
% 47.51/20.84  																										|-Branch one:
% 47.51/20.84  																										| (252) all_30_0_34 = 0
% 47.51/20.84  																										|
% 47.51/20.84  																											| Equations (252) can reduce 92 to:
% 47.51/20.84  																											| (106) $false
% 47.51/20.84  																											|
% 47.51/20.84  																											|-The branch is then unsatisfiable
% 47.51/20.84  																										|-Branch two:
% 47.51/20.84  																										| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.84  																										| (315) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.51/20.84  																										|
% 47.51/20.84  																											+-Applying beta-rule and splitting (188), into two cases.
% 47.51/20.84  																											|-Branch one:
% 47.51/20.84  																											| (308) all_28_0_32 = 0
% 47.51/20.84  																											|
% 47.51/20.84  																												| Equations (308) can reduce 88 to:
% 47.51/20.84  																												| (106) $false
% 47.51/20.84  																												|
% 47.51/20.84  																												|-The branch is then unsatisfiable
% 47.51/20.84  																											|-Branch two:
% 47.51/20.84  																											| (88)  ~ (all_28_0_32 = 0)
% 47.51/20.84  																											| (319) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.51/20.84  																											|
% 47.51/20.84  																												+-Applying beta-rule and splitting (154), into two cases.
% 47.51/20.84  																												|-Branch one:
% 47.51/20.84  																												| (268) all_24_0_28 = 0
% 47.51/20.84  																												|
% 47.51/20.84  																													| Equations (268) can reduce 80 to:
% 47.51/20.84  																													| (106) $false
% 47.51/20.84  																													|
% 47.51/20.84  																													|-The branch is then unsatisfiable
% 47.51/20.84  																												|-Branch two:
% 47.51/20.84  																												| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.84  																												| (323)  ? [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))
% 47.51/20.84  																												|
% 47.51/20.84  																													+-Applying beta-rule and splitting (139), into two cases.
% 47.51/20.84  																													|-Branch one:
% 47.51/20.84  																													| (252) all_30_0_34 = 0
% 47.51/20.84  																													|
% 47.51/20.84  																														| Equations (252) can reduce 92 to:
% 47.51/20.84  																														| (106) $false
% 47.51/20.84  																														|
% 47.51/20.84  																														|-The branch is then unsatisfiable
% 47.51/20.84  																													|-Branch two:
% 47.51/20.84  																													| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.84  																													| (327)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.51/20.84  																													|
% 47.51/20.84  																														+-Applying beta-rule and splitting (140), into two cases.
% 47.51/20.84  																														|-Branch one:
% 47.51/20.84  																														| (252) all_30_0_34 = 0
% 47.51/20.84  																														|
% 47.51/20.84  																															| Equations (252) can reduce 92 to:
% 47.51/20.84  																															| (106) $false
% 47.51/20.84  																															|
% 47.51/20.84  																															|-The branch is then unsatisfiable
% 47.51/20.84  																														|-Branch two:
% 47.51/20.84  																														| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.84  																														| (331)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.51/20.85  																														|
% 47.51/20.85  																															+-Applying beta-rule and splitting (141), into two cases.
% 47.51/20.85  																															|-Branch one:
% 47.51/20.85  																															| (252) all_30_0_34 = 0
% 47.51/20.85  																															|
% 47.51/20.85  																																| Equations (252) can reduce 92 to:
% 47.51/20.85  																																| (106) $false
% 47.51/20.85  																																|
% 47.51/20.85  																																|-The branch is then unsatisfiable
% 47.51/20.85  																															|-Branch two:
% 47.51/20.85  																															| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																															| (335)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.51/20.85  																															|
% 47.51/20.85  																																+-Applying beta-rule and splitting (155), into two cases.
% 47.51/20.85  																																|-Branch one:
% 47.51/20.85  																																| (268) all_24_0_28 = 0
% 47.51/20.85  																																|
% 47.51/20.85  																																	| Equations (268) can reduce 80 to:
% 47.51/20.85  																																	| (106) $false
% 47.51/20.85  																																	|
% 47.51/20.85  																																	|-The branch is then unsatisfiable
% 47.51/20.85  																																|-Branch two:
% 47.51/20.85  																																| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.85  																																| (239)  ? [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))
% 47.51/20.85  																																|
% 47.51/20.85  																																	+-Applying beta-rule and splitting (156), into two cases.
% 47.51/20.85  																																	|-Branch one:
% 47.51/20.85  																																	| (268) all_24_0_28 = 0
% 47.51/20.85  																																	|
% 47.51/20.85  																																		| Equations (268) can reduce 80 to:
% 47.51/20.85  																																		| (106) $false
% 47.51/20.85  																																		|
% 47.51/20.85  																																		|-The branch is then unsatisfiable
% 47.51/20.85  																																	|-Branch two:
% 47.51/20.85  																																	| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.85  																																	| (343)  ? [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))
% 47.51/20.85  																																	|
% 47.51/20.85  																																		+-Applying beta-rule and splitting (157), into two cases.
% 47.51/20.85  																																		|-Branch one:
% 47.51/20.85  																																		| (232) all_22_0_26 = 0
% 47.51/20.85  																																		|
% 47.51/20.85  																																			| Equations (232) can reduce 76 to:
% 47.51/20.85  																																			| (106) $false
% 47.51/20.85  																																			|
% 47.51/20.85  																																			|-The branch is then unsatisfiable
% 47.51/20.85  																																		|-Branch two:
% 47.51/20.85  																																		| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.85  																																		| (347) 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))
% 47.51/20.85  																																		|
% 47.51/20.85  																																			+-Applying beta-rule and splitting (191), into two cases.
% 47.51/20.85  																																			|-Branch one:
% 47.51/20.85  																																			| (252) all_30_0_34 = 0
% 47.51/20.85  																																			|
% 47.51/20.85  																																				| Equations (252) can reduce 92 to:
% 47.51/20.85  																																				| (106) $false
% 47.51/20.85  																																				|
% 47.51/20.85  																																				|-The branch is then unsatisfiable
% 47.51/20.85  																																			|-Branch two:
% 47.51/20.85  																																			| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																																			| (351) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.51/20.85  																																			|
% 47.51/20.85  																																				+-Applying beta-rule and splitting (159), into two cases.
% 47.51/20.85  																																				|-Branch one:
% 47.51/20.85  																																				| (232) all_22_0_26 = 0
% 47.51/20.85  																																				|
% 47.51/20.85  																																					| Equations (232) can reduce 76 to:
% 47.51/20.85  																																					| (106) $false
% 47.51/20.85  																																					|
% 47.51/20.85  																																					|-The branch is then unsatisfiable
% 47.51/20.85  																																				|-Branch two:
% 47.51/20.85  																																				| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.85  																																				| (355) 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))
% 47.51/20.85  																																				|
% 47.51/20.85  																																					+-Applying beta-rule and splitting (143), into two cases.
% 47.51/20.85  																																					|-Branch one:
% 47.51/20.85  																																					| (268) all_24_0_28 = 0
% 47.51/20.85  																																					|
% 47.51/20.85  																																						| Equations (268) can reduce 80 to:
% 47.51/20.85  																																						| (106) $false
% 47.51/20.85  																																						|
% 47.51/20.85  																																						|-The branch is then unsatisfiable
% 47.51/20.85  																																					|-Branch two:
% 47.51/20.85  																																					| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.85  																																					| (359) 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_22_1_27, all_0_2_2) = v0))
% 47.51/20.85  																																					|
% 47.51/20.85  																																						+-Applying beta-rule and splitting (142), into two cases.
% 47.51/20.85  																																						|-Branch one:
% 47.51/20.85  																																						| (268) all_24_0_28 = 0
% 47.51/20.85  																																						|
% 47.51/20.85  																																							| Equations (268) can reduce 80 to:
% 47.51/20.85  																																							| (106) $false
% 47.51/20.85  																																							|
% 47.51/20.85  																																							|-The branch is then unsatisfiable
% 47.51/20.85  																																						|-Branch two:
% 47.51/20.85  																																						| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.85  																																						| (363) 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))
% 47.51/20.85  																																						|
% 47.51/20.85  																																							+-Applying beta-rule and splitting (137), into two cases.
% 47.51/20.85  																																							|-Branch one:
% 47.51/20.85  																																							| (252) all_30_0_34 = 0
% 47.51/20.85  																																							|
% 47.51/20.85  																																								| Equations (252) can reduce 92 to:
% 47.51/20.85  																																								| (106) $false
% 47.51/20.85  																																								|
% 47.51/20.85  																																								|-The branch is then unsatisfiable
% 47.51/20.85  																																							|-Branch two:
% 47.51/20.85  																																							| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																																							| (367) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.51/20.85  																																							|
% 47.51/20.85  																																								+-Applying beta-rule and splitting (138), into two cases.
% 47.51/20.85  																																								|-Branch one:
% 47.51/20.85  																																								| (252) all_30_0_34 = 0
% 47.51/20.85  																																								|
% 47.51/20.85  																																									| Equations (252) can reduce 92 to:
% 47.51/20.85  																																									| (106) $false
% 47.51/20.85  																																									|
% 47.51/20.85  																																									|-The branch is then unsatisfiable
% 47.51/20.85  																																								|-Branch two:
% 47.51/20.85  																																								| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																																								| (371) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.51/20.85  																																								|
% 47.51/20.85  																																									+-Applying beta-rule and splitting (158), into two cases.
% 47.51/20.85  																																									|-Branch one:
% 47.51/20.85  																																									| (232) all_22_0_26 = 0
% 47.51/20.85  																																									|
% 47.51/20.85  																																										| Equations (232) can reduce 76 to:
% 47.51/20.85  																																										| (106) $false
% 47.51/20.85  																																										|
% 47.51/20.85  																																										|-The branch is then unsatisfiable
% 47.51/20.85  																																									|-Branch two:
% 47.51/20.85  																																									| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.85  																																									| (375) 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))
% 47.51/20.85  																																									|
% 47.51/20.85  																																										+-Applying beta-rule and splitting (190), into two cases.
% 47.51/20.85  																																										|-Branch one:
% 47.51/20.85  																																										| (252) all_30_0_34 = 0
% 47.51/20.85  																																										|
% 47.51/20.85  																																											| Equations (252) can reduce 92 to:
% 47.51/20.85  																																											| (106) $false
% 47.51/20.85  																																											|
% 47.51/20.85  																																											|-The branch is then unsatisfiable
% 47.51/20.85  																																										|-Branch two:
% 47.51/20.85  																																										| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																																										| (379) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.51/20.85  																																										|
% 47.51/20.85  																																											+-Applying beta-rule and splitting (170), into two cases.
% 47.51/20.85  																																											|-Branch one:
% 47.51/20.85  																																											| (244) all_26_0_30 = 0
% 47.51/20.85  																																											|
% 47.51/20.85  																																												| Equations (244) can reduce 84 to:
% 47.51/20.85  																																												| (106) $false
% 47.51/20.85  																																												|
% 47.51/20.85  																																												|-The branch is then unsatisfiable
% 47.51/20.85  																																											|-Branch two:
% 47.51/20.85  																																											| (84)  ~ (all_26_0_30 = 0)
% 47.51/20.85  																																											| (383) 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))
% 47.51/20.85  																																											|
% 47.51/20.85  																																												+-Applying beta-rule and splitting (175), into two cases.
% 47.51/20.85  																																												|-Branch one:
% 47.51/20.85  																																												| (244) all_26_0_30 = 0
% 47.51/20.85  																																												|
% 47.51/20.85  																																													| Equations (244) can reduce 84 to:
% 47.51/20.85  																																													| (106) $false
% 47.51/20.85  																																													|
% 47.51/20.85  																																													|-The branch is then unsatisfiable
% 47.51/20.85  																																												|-Branch two:
% 47.51/20.85  																																												| (84)  ~ (all_26_0_30 = 0)
% 47.51/20.85  																																												| (387) 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))
% 47.51/20.85  																																												|
% 47.51/20.85  																																													+-Applying beta-rule and splitting (173), into two cases.
% 47.51/20.85  																																													|-Branch one:
% 47.51/20.85  																																													| (252) all_30_0_34 = 0
% 47.51/20.85  																																													|
% 47.51/20.85  																																														| Equations (252) can reduce 92 to:
% 47.51/20.85  																																														| (106) $false
% 47.51/20.85  																																														|
% 47.51/20.85  																																														|-The branch is then unsatisfiable
% 47.51/20.85  																																													|-Branch two:
% 47.51/20.85  																																													| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																																													| (391) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.51/20.85  																																													|
% 47.51/20.85  																																														+-Applying beta-rule and splitting (160), into two cases.
% 47.51/20.85  																																														|-Branch one:
% 47.51/20.85  																																														| (232) all_22_0_26 = 0
% 47.51/20.85  																																														|
% 47.51/20.85  																																															| Equations (232) can reduce 76 to:
% 47.51/20.85  																																															| (106) $false
% 47.51/20.85  																																															|
% 47.51/20.85  																																															|-The branch is then unsatisfiable
% 47.51/20.85  																																														|-Branch two:
% 47.51/20.85  																																														| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.85  																																														| (395) 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_4_4, all_0_3_3) = v0))
% 47.51/20.85  																																														|
% 47.51/20.85  																																															+-Applying beta-rule and splitting (174), into two cases.
% 47.51/20.85  																																															|-Branch one:
% 47.51/20.85  																																															| (252) all_30_0_34 = 0
% 47.51/20.85  																																															|
% 47.51/20.85  																																																| Equations (252) can reduce 92 to:
% 47.51/20.85  																																																| (106) $false
% 47.51/20.85  																																																|
% 47.51/20.85  																																																|-The branch is then unsatisfiable
% 47.51/20.85  																																															|-Branch two:
% 47.51/20.85  																																															| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.85  																																															| (399) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.51/20.85  																																															|
% 47.51/20.85  																																																+-Applying beta-rule and splitting (176), into two cases.
% 47.51/20.85  																																																|-Branch one:
% 47.51/20.85  																																																| (244) all_26_0_30 = 0
% 47.51/20.85  																																																|
% 47.51/20.85  																																																	| Equations (244) can reduce 84 to:
% 47.51/20.85  																																																	| (106) $false
% 47.51/20.85  																																																	|
% 47.51/20.85  																																																	|-The branch is then unsatisfiable
% 47.51/20.85  																																																|-Branch two:
% 47.51/20.85  																																																| (84)  ~ (all_26_0_30 = 0)
% 47.51/20.85  																																																| (403) 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_4_4, all_0_3_3) = v0))
% 47.51/20.85  																																																|
% 47.51/20.85  																																																	+-Applying beta-rule and splitting (144), into two cases.
% 47.51/20.85  																																																	|-Branch one:
% 47.51/20.85  																																																	| (268) all_24_0_28 = 0
% 47.51/20.85  																																																	|
% 47.51/20.85  																																																		| Equations (268) can reduce 80 to:
% 47.51/20.85  																																																		| (106) $false
% 47.51/20.85  																																																		|
% 47.51/20.85  																																																		|-The branch is then unsatisfiable
% 47.51/20.85  																																																	|-Branch two:
% 47.51/20.85  																																																	| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.85  																																																	| (407) 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))
% 47.51/20.85  																																																	|
% 47.51/20.85  																																																		+-Applying beta-rule and splitting (186), into two cases.
% 47.51/20.85  																																																		|-Branch one:
% 47.51/20.85  																																																		| (308) all_28_0_32 = 0
% 47.51/20.85  																																																		|
% 47.51/20.85  																																																			| Equations (308) can reduce 88 to:
% 47.51/20.85  																																																			| (106) $false
% 47.51/20.85  																																																			|
% 47.51/20.85  																																																			|-The branch is then unsatisfiable
% 47.51/20.85  																																																		|-Branch two:
% 47.51/20.85  																																																		| (88)  ~ (all_28_0_32 = 0)
% 47.51/20.85  																																																		| (411) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.51/20.85  																																																		|
% 47.51/20.85  																																																			+-Applying beta-rule and splitting (189), into two cases.
% 47.51/20.85  																																																			|-Branch one:
% 47.51/20.85  																																																			| (308) all_28_0_32 = 0
% 47.51/20.85  																																																			|
% 47.51/20.85  																																																				| Equations (308) can reduce 88 to:
% 47.51/20.85  																																																				| (106) $false
% 47.51/20.85  																																																				|
% 47.51/20.85  																																																				|-The branch is then unsatisfiable
% 47.51/20.85  																																																			|-Branch two:
% 47.51/20.85  																																																			| (88)  ~ (all_28_0_32 = 0)
% 47.51/20.85  																																																			| (415) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.51/20.85  																																																			|
% 47.51/20.85  																																																				+-Applying beta-rule and splitting (145), into two cases.
% 47.51/20.85  																																																				|-Branch one:
% 47.51/20.85  																																																				| (268) all_24_0_28 = 0
% 47.51/20.85  																																																				|
% 47.51/20.85  																																																					| Equations (268) can reduce 80 to:
% 47.51/20.85  																																																					| (106) $false
% 47.51/20.85  																																																					|
% 47.51/20.85  																																																					|-The branch is then unsatisfiable
% 47.51/20.85  																																																				|-Branch two:
% 47.51/20.85  																																																				| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.85  																																																				| (419) 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))
% 47.51/20.86  																																																				|
% 47.51/20.86  																																																					+-Applying beta-rule and splitting (146), into two cases.
% 47.51/20.86  																																																					|-Branch one:
% 47.51/20.86  																																																					| (268) all_24_0_28 = 0
% 47.51/20.86  																																																					|
% 47.51/20.86  																																																						| Equations (268) can reduce 80 to:
% 47.51/20.86  																																																						| (106) $false
% 47.51/20.86  																																																						|
% 47.51/20.86  																																																						|-The branch is then unsatisfiable
% 47.51/20.86  																																																					|-Branch two:
% 47.51/20.86  																																																					| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.86  																																																					| (423) 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))
% 47.51/20.86  																																																					|
% 47.51/20.86  																																																						+-Applying beta-rule and splitting (147), into two cases.
% 47.51/20.86  																																																						|-Branch one:
% 47.51/20.86  																																																						| (268) all_24_0_28 = 0
% 47.51/20.86  																																																						|
% 47.51/20.86  																																																							| Equations (268) can reduce 80 to:
% 47.51/20.86  																																																							| (106) $false
% 47.51/20.86  																																																							|
% 47.51/20.86  																																																							|-The branch is then unsatisfiable
% 47.51/20.86  																																																						|-Branch two:
% 47.51/20.86  																																																						| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.86  																																																						| (427) 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))
% 47.51/20.86  																																																						|
% 47.51/20.86  																																																							+-Applying beta-rule and splitting (148), into two cases.
% 47.51/20.86  																																																							|-Branch one:
% 47.51/20.86  																																																							| (252) all_30_0_34 = 0
% 47.51/20.86  																																																							|
% 47.51/20.86  																																																								| Equations (252) can reduce 92 to:
% 47.51/20.86  																																																								| (106) $false
% 47.51/20.86  																																																								|
% 47.51/20.86  																																																								|-The branch is then unsatisfiable
% 47.51/20.86  																																																							|-Branch two:
% 47.51/20.86  																																																							| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.86  																																																							| (431) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0))
% 47.51/20.86  																																																							|
% 47.51/20.86  																																																								+-Applying beta-rule and splitting (151), into two cases.
% 47.51/20.86  																																																								|-Branch one:
% 47.51/20.86  																																																								| (252) all_30_0_34 = 0
% 47.51/20.86  																																																								|
% 47.51/20.86  																																																									| Equations (252) can reduce 92 to:
% 47.51/20.86  																																																									| (106) $false
% 47.51/20.86  																																																									|
% 47.51/20.86  																																																									|-The branch is then unsatisfiable
% 47.51/20.86  																																																								|-Branch two:
% 47.51/20.86  																																																								| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.86  																																																								| (435) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.51/20.86  																																																								|
% 47.51/20.86  																																																									+-Applying beta-rule and splitting (149), into two cases.
% 47.51/20.86  																																																									|-Branch one:
% 47.51/20.86  																																																									| (252) all_30_0_34 = 0
% 47.51/20.86  																																																									|
% 47.51/20.86  																																																										| Equations (252) can reduce 92 to:
% 47.51/20.86  																																																										| (106) $false
% 47.51/20.86  																																																										|
% 47.51/20.86  																																																										|-The branch is then unsatisfiable
% 47.51/20.86  																																																									|-Branch two:
% 47.51/20.86  																																																									| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.86  																																																									| (439) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.51/20.86  																																																									|
% 47.51/20.86  																																																										+-Applying beta-rule and splitting (150), into two cases.
% 47.51/20.86  																																																										|-Branch one:
% 47.51/20.86  																																																										| (252) all_30_0_34 = 0
% 47.51/20.86  																																																										|
% 47.51/20.86  																																																											| Equations (252) can reduce 92 to:
% 47.51/20.86  																																																											| (106) $false
% 47.51/20.86  																																																											|
% 47.51/20.86  																																																											|-The branch is then unsatisfiable
% 47.51/20.86  																																																										|-Branch two:
% 47.51/20.86  																																																										| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.86  																																																										| (443) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0))
% 47.51/20.86  																																																										|
% 47.51/20.86  																																																											+-Applying beta-rule and splitting (152), into two cases.
% 47.51/20.86  																																																											|-Branch one:
% 47.51/20.86  																																																											| (252) all_30_0_34 = 0
% 47.51/20.86  																																																											|
% 47.51/20.86  																																																												| Equations (252) can reduce 92 to:
% 47.51/20.86  																																																												| (106) $false
% 47.51/20.86  																																																												|
% 47.51/20.86  																																																												|-The branch is then unsatisfiable
% 47.51/20.86  																																																											|-Branch two:
% 47.51/20.86  																																																											| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.86  																																																											| (447) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.51/20.86  																																																											|
% 47.51/20.86  																																																												+-Applying beta-rule and splitting (251), into two cases.
% 47.51/20.86  																																																												|-Branch one:
% 47.51/20.86  																																																												| (268) all_24_0_28 = 0
% 47.51/20.86  																																																												|
% 47.51/20.86  																																																													| Equations (268) can reduce 80 to:
% 47.51/20.86  																																																													| (106) $false
% 47.51/20.86  																																																													|
% 47.51/20.86  																																																													|-The branch is then unsatisfiable
% 47.51/20.86  																																																												|-Branch two:
% 47.51/20.86  																																																												| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.86  																																																												| (451)  ? [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_4_4, all_0_3_3) = v0))
% 47.51/20.86  																																																												|
% 47.51/20.86  																																																													| Instantiating (451) with all_262_0_473 yields:
% 47.51/20.86  																																																													| (452) (all_262_0_473 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_262_0_473 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (all_262_0_473 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473) | ( ~ (all_262_0_473 = 0) & distinct_points(all_0_4_4, all_0_3_3) = all_262_0_473)
% 47.51/20.86  																																																													|
% 47.51/20.86  																																																													+-Applying beta-rule and splitting (259), into two cases.
% 47.51/20.86  																																																													|-Branch one:
% 47.51/20.86  																																																													| (268) all_24_0_28 = 0
% 47.51/20.86  																																																													|
% 47.51/20.86  																																																														| Equations (268) can reduce 80 to:
% 47.51/20.86  																																																														| (106) $false
% 47.51/20.86  																																																														|
% 47.51/20.86  																																																														|-The branch is then unsatisfiable
% 47.51/20.86  																																																													|-Branch two:
% 47.51/20.86  																																																													| (80)  ~ (all_24_0_28 = 0)
% 47.51/20.86  																																																													| (456)  ? [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))
% 47.51/20.86  																																																													|
% 47.51/20.86  																																																														+-Applying beta-rule and splitting (263), into two cases.
% 47.51/20.86  																																																														|-Branch one:
% 47.51/20.86  																																																														| (232) all_22_0_26 = 0
% 47.51/20.86  																																																														|
% 47.51/20.86  																																																															| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																															| (106) $false
% 47.51/20.86  																																																															|
% 47.51/20.86  																																																															|-The branch is then unsatisfiable
% 47.51/20.86  																																																														|-Branch two:
% 47.51/20.86  																																																														| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																														| (460)  ? [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))
% 47.51/20.86  																																																														|
% 47.51/20.86  																																																															| Instantiating (460) with all_270_0_475 yields:
% 47.51/20.86  																																																															| (461) (all_270_0_475 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (all_270_0_475 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_270_0_475 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = all_270_0_475)
% 47.51/20.86  																																																															|
% 47.51/20.86  																																																															+-Applying beta-rule and splitting (267), into two cases.
% 47.51/20.86  																																																															|-Branch one:
% 47.51/20.86  																																																															| (232) all_22_0_26 = 0
% 47.51/20.86  																																																															|
% 47.51/20.86  																																																																| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																| (106) $false
% 47.51/20.86  																																																																|
% 47.51/20.86  																																																																|-The branch is then unsatisfiable
% 47.51/20.86  																																																															|-Branch two:
% 47.51/20.86  																																																															| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																															| (465)  ? [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_22_1_27, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 47.51/20.86  																																																															|
% 47.51/20.86  																																																																+-Applying beta-rule and splitting (271), into two cases.
% 47.51/20.86  																																																																|-Branch one:
% 47.51/20.86  																																																																| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																|
% 47.51/20.86  																																																																	| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																	| (106) $false
% 47.51/20.86  																																																																	|
% 47.51/20.86  																																																																	|-The branch is then unsatisfiable
% 47.51/20.86  																																																																|-Branch two:
% 47.51/20.86  																																																																| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																| (469)  ? [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))
% 47.51/20.86  																																																																|
% 47.51/20.86  																																																																	+-Applying beta-rule and splitting (275), into two cases.
% 47.51/20.86  																																																																	|-Branch one:
% 47.51/20.86  																																																																	| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																	|
% 47.51/20.86  																																																																		| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																		| (106) $false
% 47.51/20.86  																																																																		|
% 47.51/20.86  																																																																		|-The branch is then unsatisfiable
% 47.51/20.86  																																																																	|-Branch two:
% 47.51/20.86  																																																																	| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																	| (473)  ? [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_4_4, all_0_3_3) = v0))
% 47.51/20.86  																																																																	|
% 47.51/20.86  																																																																		+-Applying beta-rule and splitting (279), into two cases.
% 47.51/20.86  																																																																		|-Branch one:
% 47.51/20.86  																																																																		| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																		|
% 47.51/20.86  																																																																			| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																			| (106) $false
% 47.51/20.86  																																																																			|
% 47.51/20.86  																																																																			|-The branch is then unsatisfiable
% 47.51/20.86  																																																																		|-Branch two:
% 47.51/20.86  																																																																		| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																		| (477)  ? [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))
% 47.51/20.86  																																																																		|
% 47.51/20.86  																																																																			+-Applying beta-rule and splitting (283), into two cases.
% 47.51/20.86  																																																																			|-Branch one:
% 47.51/20.86  																																																																			| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																			|
% 47.51/20.86  																																																																				| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																				| (106) $false
% 47.51/20.86  																																																																				|
% 47.51/20.86  																																																																				|-The branch is then unsatisfiable
% 47.51/20.86  																																																																			|-Branch two:
% 47.51/20.86  																																																																			| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																			| (481)  ? [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))
% 47.51/20.86  																																																																			|
% 47.51/20.86  																																																																				+-Applying beta-rule and splitting (295), into two cases.
% 47.51/20.86  																																																																				|-Branch one:
% 47.51/20.86  																																																																				| (244) all_26_0_30 = 0
% 47.51/20.86  																																																																				|
% 47.51/20.86  																																																																					| Equations (244) can reduce 84 to:
% 47.51/20.86  																																																																					| (106) $false
% 47.51/20.86  																																																																					|
% 47.51/20.86  																																																																					|-The branch is then unsatisfiable
% 47.51/20.86  																																																																				|-Branch two:
% 47.51/20.86  																																																																				| (84)  ~ (all_26_0_30 = 0)
% 47.51/20.86  																																																																				| (485)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.51/20.86  																																																																				|
% 47.51/20.86  																																																																					+-Applying beta-rule and splitting (299), into two cases.
% 47.51/20.86  																																																																					|-Branch one:
% 47.51/20.86  																																																																					| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																					|
% 47.51/20.86  																																																																						| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																						| (106) $false
% 47.51/20.86  																																																																						|
% 47.51/20.86  																																																																						|-The branch is then unsatisfiable
% 47.51/20.86  																																																																					|-Branch two:
% 47.51/20.86  																																																																					| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																					| (489)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.51/20.86  																																																																					|
% 47.51/20.86  																																																																						+-Applying beta-rule and splitting (303), into two cases.
% 47.51/20.86  																																																																						|-Branch one:
% 47.51/20.86  																																																																						| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																						|
% 47.51/20.86  																																																																							| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																							| (106) $false
% 47.51/20.86  																																																																							|
% 47.51/20.86  																																																																							|-The branch is then unsatisfiable
% 47.51/20.86  																																																																						|-Branch two:
% 47.51/20.86  																																																																						| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																						| (493)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.51/20.86  																																																																						|
% 47.51/20.86  																																																																							+-Applying beta-rule and splitting (307), into two cases.
% 47.51/20.86  																																																																							|-Branch one:
% 47.51/20.86  																																																																							| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																							|
% 47.51/20.86  																																																																								| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																								| (106) $false
% 47.51/20.86  																																																																								|
% 47.51/20.86  																																																																								|-The branch is then unsatisfiable
% 47.51/20.86  																																																																							|-Branch two:
% 47.51/20.86  																																																																							| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																							| (497)  ? [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))
% 47.51/20.86  																																																																							|
% 47.51/20.86  																																																																								+-Applying beta-rule and splitting (315), into two cases.
% 47.51/20.86  																																																																								|-Branch one:
% 47.51/20.86  																																																																								| (232) all_22_0_26 = 0
% 47.51/20.86  																																																																								|
% 47.51/20.86  																																																																									| Equations (232) can reduce 76 to:
% 47.51/20.86  																																																																									| (106) $false
% 47.51/20.86  																																																																									|
% 47.51/20.86  																																																																									|-The branch is then unsatisfiable
% 47.51/20.86  																																																																								|-Branch two:
% 47.51/20.86  																																																																								| (76)  ~ (all_22_0_26 = 0)
% 47.51/20.86  																																																																								| (501)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.51/20.87  																																																																								|
% 47.51/20.87  																																																																									+-Applying beta-rule and splitting (319), into two cases.
% 47.51/20.87  																																																																									|-Branch one:
% 47.51/20.87  																																																																									| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																									|
% 47.51/20.87  																																																																										| Equations (105) can reduce 33 to:
% 47.51/20.87  																																																																										| (106) $false
% 47.51/20.87  																																																																										|
% 47.51/20.87  																																																																										|-The branch is then unsatisfiable
% 47.51/20.87  																																																																									|-Branch two:
% 47.51/20.87  																																																																									| (33)  ~ (all_0_1_1 = 0)
% 47.51/20.87  																																																																									| (505)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.51/20.87  																																																																									|
% 47.51/20.87  																																																																										+-Applying beta-rule and splitting (452), into two cases.
% 47.51/20.87  																																																																										|-Branch one:
% 47.51/20.87  																																																																										| (506) (all_262_0_473 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_262_0_473 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (all_262_0_473 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473)
% 47.51/20.87  																																																																										|
% 47.51/20.87  																																																																											+-Applying beta-rule and splitting (506), into two cases.
% 47.51/20.87  																																																																											|-Branch one:
% 47.51/20.87  																																																																											| (507) (all_262_0_473 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_262_0_473 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0)
% 47.51/20.87  																																																																											|
% 47.51/20.87  																																																																												+-Applying beta-rule and splitting (507), into two cases.
% 47.51/20.87  																																																																												|-Branch one:
% 47.51/20.87  																																																																												| (508) all_262_0_473 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 47.51/20.87  																																																																												|
% 47.51/20.87  																																																																													| Applying alpha-rule on (508) yields:
% 47.51/20.87  																																																																													| (509) all_262_0_473 = 0
% 47.51/20.87  																																																																													| (510) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 47.51/20.87  																																																																													|
% 47.51/20.87  																																																																													+-Applying beta-rule and splitting (407), into two cases.
% 47.51/20.87  																																																																													|-Branch one:
% 47.51/20.87  																																																																													| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																													|
% 47.51/20.87  																																																																														| Equations (105) can reduce 33 to:
% 47.51/20.87  																																																																														| (106) $false
% 47.51/20.87  																																																																														|
% 47.51/20.87  																																																																														|-The branch is then unsatisfiable
% 47.51/20.87  																																																																													|-Branch two:
% 47.51/20.87  																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.51/20.87  																																																																													| (497)  ? [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))
% 47.51/20.87  																																																																													|
% 47.51/20.87  																																																																														+-Applying beta-rule and splitting (419), into two cases.
% 47.51/20.87  																																																																														|-Branch one:
% 47.51/20.87  																																																																														| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																														|
% 47.51/20.87  																																																																															| Equations (105) can reduce 33 to:
% 47.51/20.87  																																																																															| (106) $false
% 47.51/20.87  																																																																															|
% 47.51/20.87  																																																																															|-The branch is then unsatisfiable
% 47.51/20.87  																																																																														|-Branch two:
% 47.51/20.87  																																																																														| (33)  ~ (all_0_1_1 = 0)
% 47.51/20.87  																																																																														| (481)  ? [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))
% 47.51/20.87  																																																																														|
% 47.51/20.87  																																																																															+-Applying beta-rule and splitting (427), into two cases.
% 47.51/20.87  																																																																															|-Branch one:
% 47.51/20.87  																																																																															| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																															|
% 47.51/20.87  																																																																																| Equations (105) can reduce 33 to:
% 47.51/20.87  																																																																																| (106) $false
% 47.51/20.87  																																																																																|
% 47.51/20.87  																																																																																|-The branch is then unsatisfiable
% 47.51/20.87  																																																																															|-Branch two:
% 47.51/20.87  																																																																															| (33)  ~ (all_0_1_1 = 0)
% 47.51/20.87  																																																																															| (522)  ? [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))
% 47.51/20.87  																																																																															|
% 47.51/20.87  																																																																																+-Applying beta-rule and splitting (228), into two cases.
% 47.51/20.87  																																																																																|-Branch one:
% 47.51/20.87  																																																																																| (523) all_20_0_24 = 0
% 47.51/20.87  																																																																																|
% 47.51/20.87  																																																																																	| Equations (523) can reduce 72 to:
% 47.51/20.87  																																																																																	| (106) $false
% 47.51/20.87  																																																																																	|
% 47.51/20.87  																																																																																	|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																|-Branch two:
% 47.51/20.87  																																																																																| (72)  ~ (all_20_0_24 = 0)
% 47.51/20.87  																																																																																| (526)  ? [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))
% 47.51/20.87  																																																																																|
% 47.51/20.87  																																																																																	+-Applying beta-rule and splitting (133), into two cases.
% 47.51/20.87  																																																																																	|-Branch one:
% 47.51/20.87  																																																																																	| (252) all_30_0_34 = 0
% 47.51/20.87  																																																																																	|
% 47.51/20.87  																																																																																		| Equations (252) can reduce 92 to:
% 47.51/20.87  																																																																																		| (106) $false
% 47.51/20.87  																																																																																		|
% 47.51/20.87  																																																																																		|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																	|-Branch two:
% 47.51/20.87  																																																																																	| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.87  																																																																																	| (530) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.51/20.87  																																																																																	|
% 47.51/20.87  																																																																																		+-Applying beta-rule and splitting (134), into two cases.
% 47.51/20.87  																																																																																		|-Branch one:
% 47.51/20.87  																																																																																		| (252) all_30_0_34 = 0
% 47.51/20.87  																																																																																		|
% 47.51/20.87  																																																																																			| Equations (252) can reduce 92 to:
% 47.51/20.87  																																																																																			| (106) $false
% 47.51/20.87  																																																																																			|
% 47.51/20.87  																																																																																			|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																		|-Branch two:
% 47.51/20.87  																																																																																		| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.87  																																																																																		| (534) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.51/20.87  																																																																																		|
% 47.51/20.87  																																																																																			+-Applying beta-rule and splitting (135), into two cases.
% 47.51/20.87  																																																																																			|-Branch one:
% 47.51/20.87  																																																																																			| (252) all_30_0_34 = 0
% 47.51/20.87  																																																																																			|
% 47.51/20.87  																																																																																				| Equations (252) can reduce 92 to:
% 47.51/20.87  																																																																																				| (106) $false
% 47.51/20.87  																																																																																				|
% 47.51/20.87  																																																																																				|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																			|-Branch two:
% 47.51/20.87  																																																																																			| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.87  																																																																																			| (538) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.51/20.87  																																																																																			|
% 47.51/20.87  																																																																																				+-Applying beta-rule and splitting (136), into two cases.
% 47.51/20.87  																																																																																				|-Branch one:
% 47.51/20.87  																																																																																				| (252) all_30_0_34 = 0
% 47.51/20.87  																																																																																				|
% 47.51/20.87  																																																																																					| Equations (252) can reduce 92 to:
% 47.51/20.87  																																																																																					| (106) $false
% 47.51/20.87  																																																																																					|
% 47.51/20.87  																																																																																					|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																				|-Branch two:
% 47.51/20.87  																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 47.51/20.87  																																																																																				| (542) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.51/20.87  																																																																																				|
% 47.51/20.87  																																																																																					+-Applying beta-rule and splitting (311), into two cases.
% 47.51/20.87  																																																																																					|-Branch one:
% 47.51/20.87  																																																																																					| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																																					|
% 47.51/20.87  																																																																																						| Equations (105) can reduce 33 to:
% 47.51/20.87  																																																																																						| (106) $false
% 47.51/20.87  																																																																																						|
% 47.51/20.87  																																																																																						|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																					|-Branch two:
% 47.51/20.87  																																																																																					| (33)  ~ (all_0_1_1 = 0)
% 47.51/20.87  																																																																																					| (546)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.51/20.87  																																																																																					|
% 47.51/20.87  																																																																																						+-Applying beta-rule and splitting (367), into two cases.
% 47.51/20.87  																																																																																						|-Branch one:
% 47.51/20.87  																																																																																						| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																																						|
% 47.51/20.87  																																																																																							| Equations (105) can reduce 33 to:
% 47.51/20.87  																																																																																							| (106) $false
% 47.51/20.87  																																																																																							|
% 47.51/20.87  																																																																																							|-The branch is then unsatisfiable
% 47.51/20.87  																																																																																						|-Branch two:
% 47.51/20.87  																																																																																						| (33)  ~ (all_0_1_1 = 0)
% 47.51/20.87  																																																																																						| (550)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.51/20.87  																																																																																						|
% 47.51/20.87  																																																																																							+-Applying beta-rule and splitting (375), into two cases.
% 47.51/20.87  																																																																																							|-Branch one:
% 47.51/20.87  																																																																																							| (105) all_0_1_1 = 0
% 47.51/20.87  																																																																																							|
% 47.51/20.87  																																																																																								| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																								| (106) $false
% 47.64/20.87  																																																																																								|
% 47.64/20.87  																																																																																								|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																							|-Branch two:
% 47.64/20.87  																																																																																							| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.87  																																																																																							| (554)  ? [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))
% 47.64/20.87  																																																																																							|
% 47.64/20.87  																																																																																								+-Applying beta-rule and splitting (207), into two cases.
% 47.64/20.87  																																																																																								|-Branch one:
% 47.64/20.87  																																																																																								| (523) all_20_0_24 = 0
% 47.64/20.87  																																																																																								|
% 47.64/20.87  																																																																																									| Equations (523) can reduce 72 to:
% 47.64/20.87  																																																																																									| (106) $false
% 47.64/20.87  																																																																																									|
% 47.64/20.87  																																																																																									|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																								|-Branch two:
% 47.64/20.87  																																																																																								| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.87  																																																																																								| (558) 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))
% 47.64/20.87  																																																																																								|
% 47.64/20.87  																																																																																									+-Applying beta-rule and splitting (530), into two cases.
% 47.64/20.87  																																																																																									|-Branch one:
% 47.64/20.87  																																																																																									| (105) all_0_1_1 = 0
% 47.64/20.87  																																																																																									|
% 47.64/20.87  																																																																																										| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																										| (106) $false
% 47.64/20.87  																																																																																										|
% 47.64/20.87  																																																																																										|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																									|-Branch two:
% 47.64/20.87  																																																																																									| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.87  																																																																																									| (562)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.87  																																																																																									|
% 47.64/20.87  																																																																																										+-Applying beta-rule and splitting (534), into two cases.
% 47.64/20.87  																																																																																										|-Branch one:
% 47.64/20.87  																																																																																										| (105) all_0_1_1 = 0
% 47.64/20.87  																																																																																										|
% 47.64/20.87  																																																																																											| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																											| (106) $false
% 47.64/20.87  																																																																																											|
% 47.64/20.87  																																																																																											|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																										|-Branch two:
% 47.64/20.87  																																																																																										| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.87  																																																																																										| (566)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.87  																																																																																										|
% 47.64/20.87  																																																																																											+-Applying beta-rule and splitting (347), into two cases.
% 47.64/20.87  																																																																																											|-Branch one:
% 47.64/20.87  																																																																																											| (105) all_0_1_1 = 0
% 47.64/20.87  																																																																																											|
% 47.64/20.87  																																																																																												| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																												| (106) $false
% 47.64/20.87  																																																																																												|
% 47.64/20.87  																																																																																												|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																											|-Branch two:
% 47.64/20.87  																																																																																											| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.87  																																																																																											| (570)  ? [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))
% 47.64/20.87  																																																																																											|
% 47.64/20.87  																																																																																												+-Applying beta-rule and splitting (355), into two cases.
% 47.64/20.87  																																																																																												|-Branch one:
% 47.64/20.87  																																																																																												| (105) all_0_1_1 = 0
% 47.64/20.87  																																																																																												|
% 47.64/20.87  																																																																																													| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																													| (106) $false
% 47.64/20.87  																																																																																													|
% 47.64/20.87  																																																																																													|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																												|-Branch two:
% 47.64/20.87  																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.87  																																																																																												| (574)  ? [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))
% 47.64/20.87  																																																																																												|
% 47.64/20.87  																																																																																													+-Applying beta-rule and splitting (359), into two cases.
% 47.64/20.87  																																																																																													|-Branch one:
% 47.64/20.87  																																																																																													| (105) all_0_1_1 = 0
% 47.64/20.87  																																																																																													|
% 47.64/20.87  																																																																																														| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																														| (106) $false
% 47.64/20.87  																																																																																														|
% 47.64/20.87  																																																																																														|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																													|-Branch two:
% 47.64/20.87  																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.87  																																																																																													| (578)  ? [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_22_1_27, all_0_2_2) = v0))
% 47.64/20.87  																																																																																													|
% 47.64/20.87  																																																																																														+-Applying beta-rule and splitting (363), into two cases.
% 47.64/20.87  																																																																																														|-Branch one:
% 47.64/20.87  																																																																																														| (105) all_0_1_1 = 0
% 47.64/20.87  																																																																																														|
% 47.64/20.87  																																																																																															| Equations (105) can reduce 33 to:
% 47.64/20.87  																																																																																															| (106) $false
% 47.64/20.87  																																																																																															|
% 47.64/20.87  																																																																																															|-The branch is then unsatisfiable
% 47.64/20.87  																																																																																														|-Branch two:
% 47.64/20.87  																																																																																														| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																														| (582)  ? [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))
% 47.64/20.88  																																																																																														|
% 47.64/20.88  																																																																																															+-Applying beta-rule and splitting (371), into two cases.
% 47.64/20.88  																																																																																															|-Branch one:
% 47.64/20.88  																																																																																															| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																															|
% 47.64/20.88  																																																																																																| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																| (106) $false
% 47.64/20.88  																																																																																																|
% 47.64/20.88  																																																																																																|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																															|-Branch two:
% 47.64/20.88  																																																																																															| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																															| (586)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.64/20.88  																																																																																															|
% 47.64/20.88  																																																																																																+-Applying beta-rule and splitting (383), into two cases.
% 47.64/20.88  																																																																																																|-Branch one:
% 47.64/20.88  																																																																																																| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																|
% 47.64/20.88  																																																																																																	| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																	| (106) $false
% 47.64/20.88  																																																																																																	|
% 47.64/20.88  																																																																																																	|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																|-Branch two:
% 47.64/20.88  																																																																																																| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																| (590)  ? [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))
% 47.64/20.88  																																																																																																|
% 47.64/20.88  																																																																																																	+-Applying beta-rule and splitting (395), into two cases.
% 47.64/20.88  																																																																																																	|-Branch one:
% 47.64/20.88  																																																																																																	| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																	|
% 47.64/20.88  																																																																																																		| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																		| (106) $false
% 47.64/20.88  																																																																																																		|
% 47.64/20.88  																																																																																																		|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																	|-Branch two:
% 47.64/20.88  																																																																																																	| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																	| (594)  ? [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_4_4, all_0_3_3) = v0))
% 47.64/20.88  																																																																																																	|
% 47.64/20.88  																																																																																																		+-Applying beta-rule and splitting (411), into two cases.
% 47.64/20.88  																																																																																																		|-Branch one:
% 47.64/20.88  																																																																																																		| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																		|
% 47.64/20.88  																																																																																																			| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																			| (106) $false
% 47.64/20.88  																																																																																																			|
% 47.64/20.88  																																																																																																			|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																		|-Branch two:
% 47.64/20.88  																																																																																																		| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																		| (598)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.88  																																																																																																		|
% 47.64/20.88  																																																																																																			+-Applying beta-rule and splitting (415), into two cases.
% 47.64/20.88  																																																																																																			|-Branch one:
% 47.64/20.88  																																																																																																			| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																			|
% 47.64/20.88  																																																																																																				| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																				| (106) $false
% 47.64/20.88  																																																																																																				|
% 47.64/20.88  																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																			|-Branch two:
% 47.64/20.88  																																																																																																			| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																			| (602)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.88  																																																																																																			|
% 47.64/20.88  																																																																																																				+-Applying beta-rule and splitting (423), into two cases.
% 47.64/20.88  																																																																																																				|-Branch one:
% 47.64/20.88  																																																																																																				| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																				|
% 47.64/20.88  																																																																																																					| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																					| (106) $false
% 47.64/20.88  																																																																																																					|
% 47.64/20.88  																																																																																																					|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																				|-Branch two:
% 47.64/20.88  																																																																																																				| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																				| (606)  ? [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))
% 47.64/20.88  																																																																																																				|
% 47.64/20.88  																																																																																																					+-Applying beta-rule and splitting (538), into two cases.
% 47.64/20.88  																																																																																																					|-Branch one:
% 47.64/20.88  																																																																																																					| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																					|
% 47.64/20.88  																																																																																																						| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																						| (106) $false
% 47.64/20.88  																																																																																																						|
% 47.64/20.88  																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																					|-Branch two:
% 47.64/20.88  																																																																																																					| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																					| (610)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.88  																																																																																																					|
% 47.64/20.88  																																																																																																						+-Applying beta-rule and splitting (542), into two cases.
% 47.64/20.88  																																																																																																						|-Branch one:
% 47.64/20.88  																																																																																																						| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																						|
% 47.64/20.88  																																																																																																							| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																							| (106) $false
% 47.64/20.88  																																																																																																							|
% 47.64/20.88  																																																																																																							|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																						|-Branch two:
% 47.64/20.88  																																																																																																						| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																						| (614)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.88  																																																																																																						|
% 47.64/20.88  																																																																																																							+-Applying beta-rule and splitting (558), into two cases.
% 47.64/20.88  																																																																																																							|-Branch one:
% 47.64/20.88  																																																																																																							| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																							|
% 47.64/20.88  																																																																																																								| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																								| (106) $false
% 47.64/20.88  																																																																																																								|
% 47.64/20.88  																																																																																																								|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																																							|-Branch two:
% 47.64/20.88  																																																																																																							| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.88  																																																																																																							| (618)  ? [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))
% 47.64/20.88  																																																																																																							|
% 47.64/20.88  																																																																																																								| Instantiating formula (42) 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:
% 47.64/20.88  																																																																																																								| (105) all_0_1_1 = 0
% 47.64/20.88  																																																																																																								|
% 47.64/20.88  																																																																																																								| Equations (105) can reduce 33 to:
% 47.64/20.88  																																																																																																								| (106) $false
% 47.64/20.88  																																																																																																								|
% 47.64/20.88  																																																																																																								|-The branch is then unsatisfiable
% 47.64/20.88  																																																																												|-Branch two:
% 47.64/20.88  																																																																												| (621) all_262_0_473 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0
% 47.64/20.88  																																																																												|
% 47.64/20.88  																																																																													| Applying alpha-rule on (621) yields:
% 47.64/20.88  																																																																													| (509) all_262_0_473 = 0
% 47.64/20.88  																																																																													| (623) apart_point_and_line(all_0_4_4, all_22_1_27) = 0
% 47.64/20.88  																																																																													|
% 47.64/20.88  																																																																													+-Applying beta-rule and splitting (224), into two cases.
% 47.64/20.88  																																																																													|-Branch one:
% 47.64/20.88  																																																																													| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																													|
% 47.64/20.88  																																																																														| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																														| (106) $false
% 47.64/20.88  																																																																														|
% 47.64/20.88  																																																																														|-The branch is then unsatisfiable
% 47.64/20.88  																																																																													|-Branch two:
% 47.64/20.88  																																																																													| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																													| (627) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.88  																																																																													|
% 47.64/20.88  																																																																														+-Applying beta-rule and splitting (225), into two cases.
% 47.64/20.88  																																																																														|-Branch one:
% 47.64/20.88  																																																																														| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																														|
% 47.64/20.88  																																																																															| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																															| (106) $false
% 47.64/20.88  																																																																															|
% 47.64/20.88  																																																																															|-The branch is then unsatisfiable
% 47.64/20.88  																																																																														|-Branch two:
% 47.64/20.88  																																																																														| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																														| (631) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.88  																																																																														|
% 47.64/20.88  																																																																															+-Applying beta-rule and splitting (227), into two cases.
% 47.64/20.88  																																																																															|-Branch one:
% 47.64/20.88  																																																																															| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																															|
% 47.64/20.88  																																																																																| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																																| (106) $false
% 47.64/20.88  																																																																																|
% 47.64/20.88  																																																																																|-The branch is then unsatisfiable
% 47.64/20.88  																																																																															|-Branch two:
% 47.64/20.88  																																																																															| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																															| (635) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.88  																																																																															|
% 47.64/20.88  																																																																																+-Applying beta-rule and splitting (226), into two cases.
% 47.64/20.88  																																																																																|-Branch one:
% 47.64/20.88  																																																																																| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																																|
% 47.64/20.88  																																																																																	| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																																	| (106) $false
% 47.64/20.88  																																																																																	|
% 47.64/20.88  																																																																																	|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																|-Branch two:
% 47.64/20.88  																																																																																| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																																| (639) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.88  																																																																																|
% 47.64/20.88  																																																																																	+-Applying beta-rule and splitting (287), into two cases.
% 47.64/20.88  																																																																																	|-Branch one:
% 47.64/20.88  																																																																																	| (232) all_22_0_26 = 0
% 47.64/20.88  																																																																																	|
% 47.64/20.88  																																																																																		| Equations (232) can reduce 76 to:
% 47.64/20.88  																																																																																		| (106) $false
% 47.64/20.88  																																																																																		|
% 47.64/20.88  																																																																																		|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																	|-Branch two:
% 47.64/20.88  																																																																																	| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.88  																																																																																	| (643)  ? [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))
% 47.64/20.88  																																																																																	|
% 47.64/20.88  																																																																																		+-Applying beta-rule and splitting (204), into two cases.
% 47.64/20.88  																																																																																		|-Branch one:
% 47.64/20.88  																																																																																		| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																																		|
% 47.64/20.88  																																																																																			| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																																			| (106) $false
% 47.64/20.88  																																																																																			|
% 47.64/20.88  																																																																																			|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																		|-Branch two:
% 47.64/20.88  																																																																																		| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																																		| (647)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.64/20.88  																																																																																		|
% 47.64/20.88  																																																																																			+-Applying beta-rule and splitting (205), into two cases.
% 47.64/20.88  																																																																																			|-Branch one:
% 47.64/20.88  																																																																																			| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																																			|
% 47.64/20.88  																																																																																				| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																																				| (106) $false
% 47.64/20.88  																																																																																				|
% 47.64/20.88  																																																																																				|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																			|-Branch two:
% 47.64/20.88  																																																																																			| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																																			| (327)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.64/20.88  																																																																																			|
% 47.64/20.88  																																																																																				+-Applying beta-rule and splitting (206), into two cases.
% 47.64/20.88  																																																																																				|-Branch one:
% 47.64/20.88  																																																																																				| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																																				|
% 47.64/20.88  																																																																																					| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																																					| (106) $false
% 47.64/20.88  																																																																																					|
% 47.64/20.88  																																																																																					|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																				|-Branch two:
% 47.64/20.88  																																																																																				| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																																				| (655)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.88  																																																																																				|
% 47.64/20.88  																																																																																					+-Applying beta-rule and splitting (192), into two cases.
% 47.64/20.88  																																																																																					|-Branch one:
% 47.64/20.88  																																																																																					| (308) all_28_0_32 = 0
% 47.64/20.88  																																																																																					|
% 47.64/20.88  																																																																																						| Equations (308) can reduce 88 to:
% 47.64/20.88  																																																																																						| (106) $false
% 47.64/20.88  																																																																																						|
% 47.64/20.88  																																																																																						|-The branch is then unsatisfiable
% 47.64/20.88  																																																																																					|-Branch two:
% 47.64/20.88  																																																																																					| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.88  																																																																																					| (659) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.89  																																																																																					|
% 47.64/20.89  																																																																																						+-Applying beta-rule and splitting (193), into two cases.
% 47.64/20.89  																																																																																						|-Branch one:
% 47.64/20.89  																																																																																						| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																						|
% 47.64/20.89  																																																																																							| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																							| (106) $false
% 47.64/20.89  																																																																																							|
% 47.64/20.89  																																																																																							|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																						|-Branch two:
% 47.64/20.89  																																																																																						| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																						| (663) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.89  																																																																																						|
% 47.64/20.89  																																																																																							+-Applying beta-rule and splitting (194), into two cases.
% 47.64/20.89  																																																																																							|-Branch one:
% 47.64/20.89  																																																																																							| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																							|
% 47.64/20.89  																																																																																								| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																								| (106) $false
% 47.64/20.89  																																																																																								|
% 47.64/20.89  																																																																																								|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																							|-Branch two:
% 47.64/20.89  																																																																																							| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																							| (667) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.89  																																																																																							|
% 47.64/20.89  																																																																																								+-Applying beta-rule and splitting (197), into two cases.
% 47.64/20.89  																																																																																								|-Branch one:
% 47.64/20.89  																																																																																								| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																								|
% 47.64/20.89  																																																																																									| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																									| (106) $false
% 47.64/20.89  																																																																																									|
% 47.64/20.89  																																																																																									|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																								|-Branch two:
% 47.64/20.89  																																																																																								| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																								| (671) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.64/20.89  																																																																																								|
% 47.64/20.89  																																																																																									+-Applying beta-rule and splitting (195), into two cases.
% 47.64/20.89  																																																																																									|-Branch one:
% 47.64/20.89  																																																																																									| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																									|
% 47.64/20.89  																																																																																										| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																										| (106) $false
% 47.64/20.89  																																																																																										|
% 47.64/20.89  																																																																																										|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																									|-Branch two:
% 47.64/20.89  																																																																																									| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																									| (675) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.89  																																																																																									|
% 47.64/20.89  																																																																																										+-Applying beta-rule and splitting (198), into two cases.
% 47.64/20.89  																																																																																										|-Branch one:
% 47.64/20.89  																																																																																										| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																										|
% 47.64/20.89  																																																																																											| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																											| (106) $false
% 47.64/20.89  																																																																																											|
% 47.64/20.89  																																																																																											|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																										|-Branch two:
% 47.64/20.89  																																																																																										| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																										| (679) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.64/20.89  																																																																																										|
% 47.64/20.89  																																																																																											+-Applying beta-rule and splitting (196), into two cases.
% 47.64/20.89  																																																																																											|-Branch one:
% 47.64/20.89  																																																																																											| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																											|
% 47.64/20.89  																																																																																												| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																												| (106) $false
% 47.64/20.89  																																																																																												|
% 47.64/20.89  																																																																																												|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																											|-Branch two:
% 47.64/20.89  																																																																																											| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																											| (683) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.64/20.89  																																																																																											|
% 47.64/20.89  																																																																																												+-Applying beta-rule and splitting (199), into two cases.
% 47.64/20.89  																																																																																												|-Branch one:
% 47.64/20.89  																																																																																												| (308) all_28_0_32 = 0
% 47.64/20.89  																																																																																												|
% 47.64/20.89  																																																																																													| Equations (308) can reduce 88 to:
% 47.64/20.89  																																																																																													| (106) $false
% 47.64/20.89  																																																																																													|
% 47.64/20.89  																																																																																													|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																												|-Branch two:
% 47.64/20.89  																																																																																												| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.89  																																																																																												| (687) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.64/20.89  																																																																																												|
% 47.64/20.89  																																																																																													+-Applying beta-rule and splitting (255), into two cases.
% 47.64/20.89  																																																																																													|-Branch one:
% 47.64/20.89  																																																																																													| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																													|
% 47.64/20.89  																																																																																														| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																														| (106) $false
% 47.64/20.89  																																																																																														|
% 47.64/20.89  																																																																																														|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																													|-Branch two:
% 47.64/20.89  																																																																																													| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																													| (691)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.64/20.89  																																																																																													|
% 47.64/20.89  																																																																																														+-Applying beta-rule and splitting (217), into two cases.
% 47.64/20.89  																																																																																														|-Branch one:
% 47.64/20.89  																																																																																														| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																														|
% 47.64/20.89  																																																																																															| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																															| (106) $false
% 47.64/20.89  																																																																																															|
% 47.64/20.89  																																																																																															|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																														|-Branch two:
% 47.64/20.89  																																																																																														| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																														| (695) 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))
% 47.64/20.89  																																																																																														|
% 47.64/20.89  																																																																																															+-Applying beta-rule and splitting (218), into two cases.
% 47.64/20.89  																																																																																															|-Branch one:
% 47.64/20.89  																																																																																															| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																															|
% 47.64/20.89  																																																																																																| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																| (106) $false
% 47.64/20.89  																																																																																																|
% 47.64/20.89  																																																																																																|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																															|-Branch two:
% 47.64/20.89  																																																																																															| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																															| (699) 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))
% 47.64/20.89  																																																																																															|
% 47.64/20.89  																																																																																																+-Applying beta-rule and splitting (219), into two cases.
% 47.64/20.89  																																																																																																|-Branch one:
% 47.64/20.89  																																																																																																| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																|
% 47.64/20.89  																																																																																																	| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																	| (106) $false
% 47.64/20.89  																																																																																																	|
% 47.64/20.89  																																																																																																	|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																																|-Branch two:
% 47.64/20.89  																																																																																																| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																																| (703) 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))
% 47.64/20.89  																																																																																																|
% 47.64/20.89  																																																																																																	+-Applying beta-rule and splitting (220), into two cases.
% 47.64/20.89  																																																																																																	|-Branch one:
% 47.64/20.89  																																																																																																	| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																	|
% 47.64/20.89  																																																																																																		| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																		| (106) $false
% 47.64/20.89  																																																																																																		|
% 47.64/20.89  																																																																																																		|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																																	|-Branch two:
% 47.64/20.89  																																																																																																	| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																																	| (707) 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))
% 47.64/20.89  																																																																																																	|
% 47.64/20.89  																																																																																																		+-Applying beta-rule and splitting (671), into two cases.
% 47.64/20.89  																																																																																																		|-Branch one:
% 47.64/20.89  																																																																																																		| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																		|
% 47.64/20.89  																																																																																																			| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																			| (106) $false
% 47.64/20.89  																																																																																																			|
% 47.64/20.89  																																																																																																			|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																																		|-Branch two:
% 47.64/20.89  																																																																																																		| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																																		| (711)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.64/20.89  																																																																																																		|
% 47.64/20.89  																																																																																																			+-Applying beta-rule and splitting (679), into two cases.
% 47.64/20.89  																																																																																																			|-Branch one:
% 47.64/20.89  																																																																																																			| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																			|
% 47.64/20.89  																																																																																																				| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																				| (106) $false
% 47.64/20.89  																																																																																																				|
% 47.64/20.89  																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																																			|-Branch two:
% 47.64/20.89  																																																																																																			| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																																			| (715)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.64/20.89  																																																																																																			|
% 47.64/20.89  																																																																																																				+-Applying beta-rule and splitting (687), into two cases.
% 47.64/20.89  																																																																																																				|-Branch one:
% 47.64/20.89  																																																																																																				| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																				|
% 47.64/20.89  																																																																																																					| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																					| (106) $false
% 47.64/20.89  																																																																																																					|
% 47.64/20.89  																																																																																																					|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																																				|-Branch two:
% 47.64/20.89  																																																																																																				| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																																				| (719)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.64/20.89  																																																																																																				|
% 47.64/20.89  																																																																																																					+-Applying beta-rule and splitting (683), into two cases.
% 47.64/20.89  																																																																																																					|-Branch one:
% 47.64/20.89  																																																																																																					| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																					|
% 47.64/20.89  																																																																																																						| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																						| (106) $false
% 47.64/20.89  																																																																																																						|
% 47.64/20.89  																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																																					|-Branch two:
% 47.64/20.89  																																																																																																					| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.89  																																																																																																					| (723)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.64/20.89  																																																																																																					|
% 47.64/20.89  																																																																																																						| Instantiating formula (42) with all_0_4_4, all_22_1_27, 0, all_22_0_26 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_22_1_27) = 0, yields:
% 47.64/20.89  																																																																																																						| (232) all_22_0_26 = 0
% 47.64/20.89  																																																																																																						|
% 47.64/20.89  																																																																																																						| Equations (232) can reduce 76 to:
% 47.64/20.89  																																																																																																						| (106) $false
% 47.64/20.89  																																																																																																						|
% 47.64/20.89  																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.89  																																																																											|-Branch two:
% 47.64/20.89  																																																																											| (726)  ~ (all_262_0_473 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473
% 47.64/20.89  																																																																											|
% 47.64/20.89  																																																																												| Applying alpha-rule on (726) yields:
% 47.64/20.89  																																																																												| (727)  ~ (all_262_0_473 = 0)
% 47.64/20.89  																																																																												| (728) distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473
% 47.64/20.89  																																																																												|
% 47.64/20.89  																																																																												+-Applying beta-rule and splitting (407), into two cases.
% 47.64/20.89  																																																																												|-Branch one:
% 47.64/20.89  																																																																												| (105) all_0_1_1 = 0
% 47.64/20.89  																																																																												|
% 47.64/20.89  																																																																													| Equations (105) can reduce 33 to:
% 47.64/20.89  																																																																													| (106) $false
% 47.64/20.89  																																																																													|
% 47.64/20.89  																																																																													|-The branch is then unsatisfiable
% 47.64/20.89  																																																																												|-Branch two:
% 47.64/20.89  																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.89  																																																																												| (497)  ? [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))
% 47.64/20.89  																																																																												|
% 47.64/20.89  																																																																													+-Applying beta-rule and splitting (419), into two cases.
% 47.64/20.89  																																																																													|-Branch one:
% 47.64/20.89  																																																																													| (105) all_0_1_1 = 0
% 47.64/20.89  																																																																													|
% 47.64/20.89  																																																																														| Equations (105) can reduce 33 to:
% 47.64/20.89  																																																																														| (106) $false
% 47.64/20.89  																																																																														|
% 47.64/20.89  																																																																														|-The branch is then unsatisfiable
% 47.64/20.89  																																																																													|-Branch two:
% 47.64/20.89  																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.89  																																																																													| (481)  ? [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))
% 47.64/20.89  																																																																													|
% 47.64/20.89  																																																																														+-Applying beta-rule and splitting (427), into two cases.
% 47.64/20.89  																																																																														|-Branch one:
% 47.64/20.89  																																																																														| (105) all_0_1_1 = 0
% 47.64/20.89  																																																																														|
% 47.64/20.89  																																																																															| Equations (105) can reduce 33 to:
% 47.64/20.89  																																																																															| (106) $false
% 47.64/20.89  																																																																															|
% 47.64/20.89  																																																																															|-The branch is then unsatisfiable
% 47.64/20.89  																																																																														|-Branch two:
% 47.64/20.89  																																																																														| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.89  																																																																														| (522)  ? [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))
% 47.64/20.89  																																																																														|
% 47.64/20.89  																																																																															+-Applying beta-rule and splitting (447), into two cases.
% 47.64/20.89  																																																																															|-Branch one:
% 47.64/20.89  																																																																															| (268) all_24_0_28 = 0
% 47.64/20.89  																																																																															|
% 47.64/20.89  																																																																																| Equations (268) can reduce 80 to:
% 47.64/20.89  																																																																																| (106) $false
% 47.64/20.89  																																																																																|
% 47.64/20.89  																																																																																|-The branch is then unsatisfiable
% 47.64/20.89  																																																																															|-Branch two:
% 47.64/20.89  																																																																															| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.89  																																																																															| (744)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.64/20.89  																																																																															|
% 47.64/20.89  																																																																																+-Applying beta-rule and splitting (461), into two cases.
% 47.64/20.89  																																																																																|-Branch one:
% 47.64/20.89  																																																																																| (745) (all_270_0_475 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | (all_270_0_475 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0)
% 47.64/20.89  																																																																																|
% 47.64/20.89  																																																																																	+-Applying beta-rule and splitting (745), into two cases.
% 47.64/20.89  																																																																																	|-Branch one:
% 47.64/20.89  																																																																																	| (746) all_270_0_475 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0
% 47.64/20.89  																																																																																	|
% 47.64/20.89  																																																																																		| Applying alpha-rule on (746) yields:
% 47.64/20.89  																																																																																		| (747) all_270_0_475 = 0
% 47.64/20.89  																																																																																		| (748) apart_point_and_line(all_0_3_3, all_22_1_27) = 0
% 47.64/20.89  																																																																																		|
% 47.64/20.89  																																																																																		+-Applying beta-rule and splitting (133), into two cases.
% 47.64/20.89  																																																																																		|-Branch one:
% 47.64/20.89  																																																																																		| (252) all_30_0_34 = 0
% 47.64/20.89  																																																																																		|
% 47.64/20.89  																																																																																			| Equations (252) can reduce 92 to:
% 47.64/20.89  																																																																																			| (106) $false
% 47.64/20.89  																																																																																			|
% 47.64/20.89  																																																																																			|-The branch is then unsatisfiable
% 47.64/20.89  																																																																																		|-Branch two:
% 47.64/20.89  																																																																																		| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.89  																																																																																		| (530) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.89  																																																																																		|
% 47.64/20.89  																																																																																			+-Applying beta-rule and splitting (134), into two cases.
% 47.64/20.89  																																																																																			|-Branch one:
% 47.64/20.89  																																																																																			| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																			|
% 47.64/20.90  																																																																																				| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																				| (106) $false
% 47.64/20.90  																																																																																				|
% 47.64/20.90  																																																																																				|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																			|-Branch two:
% 47.64/20.90  																																																																																			| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																			| (534) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.90  																																																																																			|
% 47.64/20.90  																																																																																				+-Applying beta-rule and splitting (135), into two cases.
% 47.64/20.90  																																																																																				|-Branch one:
% 47.64/20.90  																																																																																				| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																				|
% 47.64/20.90  																																																																																					| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																					| (106) $false
% 47.64/20.90  																																																																																					|
% 47.64/20.90  																																																																																					|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																				|-Branch two:
% 47.64/20.90  																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																				| (538) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.90  																																																																																				|
% 47.64/20.90  																																																																																					+-Applying beta-rule and splitting (224), into two cases.
% 47.64/20.90  																																																																																					|-Branch one:
% 47.64/20.90  																																																																																					| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																					|
% 47.64/20.90  																																																																																						| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																						| (106) $false
% 47.64/20.90  																																																																																						|
% 47.64/20.90  																																																																																						|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																					|-Branch two:
% 47.64/20.90  																																																																																					| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																					| (627) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.90  																																																																																					|
% 47.64/20.90  																																																																																						+-Applying beta-rule and splitting (225), into two cases.
% 47.64/20.90  																																																																																						|-Branch one:
% 47.64/20.90  																																																																																						| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																						|
% 47.64/20.90  																																																																																							| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																							| (106) $false
% 47.64/20.90  																																																																																							|
% 47.64/20.90  																																																																																							|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																						|-Branch two:
% 47.64/20.90  																																																																																						| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																						| (631) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.90  																																																																																						|
% 47.64/20.90  																																																																																							+-Applying beta-rule and splitting (227), into two cases.
% 47.64/20.90  																																																																																							|-Branch one:
% 47.64/20.90  																																																																																							| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																							|
% 47.64/20.90  																																																																																								| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																								| (106) $false
% 47.64/20.90  																																																																																								|
% 47.64/20.90  																																																																																								|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																							|-Branch two:
% 47.64/20.90  																																																																																							| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																							| (635) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.90  																																																																																							|
% 47.64/20.90  																																																																																								+-Applying beta-rule and splitting (136), into two cases.
% 47.64/20.90  																																																																																								|-Branch one:
% 47.64/20.90  																																																																																								| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																								|
% 47.64/20.90  																																																																																									| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																									| (106) $false
% 47.64/20.90  																																																																																									|
% 47.64/20.90  																																																																																									|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																								|-Branch two:
% 47.64/20.90  																																																																																								| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																								| (542) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.90  																																																																																								|
% 47.64/20.90  																																																																																									+-Applying beta-rule and splitting (226), into two cases.
% 47.64/20.90  																																																																																									|-Branch one:
% 47.64/20.90  																																																																																									| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																									|
% 47.64/20.90  																																																																																										| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																										| (106) $false
% 47.64/20.90  																																																																																										|
% 47.64/20.90  																																																																																										|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																									|-Branch two:
% 47.64/20.90  																																																																																									| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																									| (639) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.90  																																																																																									|
% 47.64/20.90  																																																																																										+-Applying beta-rule and splitting (206), into two cases.
% 47.64/20.90  																																																																																										|-Branch one:
% 47.64/20.90  																																																																																										| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																										|
% 47.64/20.90  																																																																																											| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																											| (106) $false
% 47.64/20.90  																																																																																											|
% 47.64/20.90  																																																																																											|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																										|-Branch two:
% 47.64/20.90  																																																																																										| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																										| (655)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.90  																																																																																										|
% 47.64/20.90  																																																																																											+-Applying beta-rule and splitting (210), into two cases.
% 47.64/20.90  																																																																																											|-Branch one:
% 47.64/20.90  																																																																																											| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																											|
% 47.64/20.90  																																																																																												| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																												| (106) $false
% 47.64/20.90  																																																																																												|
% 47.64/20.90  																																																																																												|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																											|-Branch two:
% 47.64/20.90  																																																																																											| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																											| (788) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.90  																																																																																											|
% 47.64/20.90  																																																																																												+-Applying beta-rule and splitting (211), into two cases.
% 47.64/20.90  																																																																																												|-Branch one:
% 47.64/20.90  																																																																																												| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																												|
% 47.64/20.90  																																																																																													| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																													| (106) $false
% 47.64/20.90  																																																																																													|
% 47.64/20.90  																																																																																													|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																												|-Branch two:
% 47.64/20.90  																																																																																												| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																												| (792) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.90  																																																																																												|
% 47.64/20.90  																																																																																													+-Applying beta-rule and splitting (216), into two cases.
% 47.64/20.90  																																																																																													|-Branch one:
% 47.64/20.90  																																																																																													| (268) all_24_0_28 = 0
% 47.64/20.90  																																																																																													|
% 47.64/20.90  																																																																																														| Equations (268) can reduce 80 to:
% 47.64/20.90  																																																																																														| (106) $false
% 47.64/20.90  																																																																																														|
% 47.64/20.90  																																																																																														|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																													|-Branch two:
% 47.64/20.90  																																																																																													| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.90  																																																																																													| (796) 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_5_5, all_0_3_3) = v0))
% 47.64/20.90  																																																																																													|
% 47.64/20.90  																																																																																														+-Applying beta-rule and splitting (222), into two cases.
% 47.64/20.90  																																																																																														|-Branch one:
% 47.64/20.90  																																																																																														| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																														|
% 47.64/20.90  																																																																																															| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																															| (106) $false
% 47.64/20.90  																																																																																															|
% 47.64/20.90  																																																																																															|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																														|-Branch two:
% 47.64/20.90  																																																																																														| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																														| (800) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.90  																																																																																														|
% 47.64/20.90  																																																																																															+-Applying beta-rule and splitting (223), into two cases.
% 47.64/20.90  																																																																																															|-Branch one:
% 47.64/20.90  																																																																																															| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																															|
% 47.64/20.90  																																																																																																| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																| (106) $false
% 47.64/20.90  																																																																																																|
% 47.64/20.90  																																																																																																|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																															|-Branch two:
% 47.64/20.90  																																																																																															| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																															| (804) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.90  																																																																																															|
% 47.64/20.90  																																																																																																+-Applying beta-rule and splitting (204), into two cases.
% 47.64/20.90  																																																																																																|-Branch one:
% 47.64/20.90  																																																																																																| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																																|
% 47.64/20.90  																																																																																																	| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																	| (106) $false
% 47.64/20.90  																																																																																																	|
% 47.64/20.90  																																																																																																	|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																|-Branch two:
% 47.64/20.90  																																																																																																| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																																| (647)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.64/20.90  																																																																																																|
% 47.64/20.90  																																																																																																	+-Applying beta-rule and splitting (205), into two cases.
% 47.64/20.90  																																																																																																	|-Branch one:
% 47.64/20.90  																																																																																																	| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																																	|
% 47.64/20.90  																																																																																																		| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																		| (106) $false
% 47.64/20.90  																																																																																																		|
% 47.64/20.90  																																																																																																		|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																	|-Branch two:
% 47.64/20.90  																																																																																																	| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																																	| (327)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.64/20.90  																																																																																																	|
% 47.64/20.90  																																																																																																		+-Applying beta-rule and splitting (192), into two cases.
% 47.64/20.90  																																																																																																		|-Branch one:
% 47.64/20.90  																																																																																																		| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																																		|
% 47.64/20.90  																																																																																																			| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																			| (106) $false
% 47.64/20.90  																																																																																																			|
% 47.64/20.90  																																																																																																			|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																		|-Branch two:
% 47.64/20.90  																																																																																																		| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																																		| (659) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.90  																																																																																																		|
% 47.64/20.90  																																																																																																			+-Applying beta-rule and splitting (193), into two cases.
% 47.64/20.90  																																																																																																			|-Branch one:
% 47.64/20.90  																																																																																																			| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																																			|
% 47.64/20.90  																																																																																																				| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																				| (106) $false
% 47.64/20.90  																																																																																																				|
% 47.64/20.90  																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																			|-Branch two:
% 47.64/20.90  																																																																																																			| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																																			| (663) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.90  																																																																																																			|
% 47.64/20.90  																																																																																																				+-Applying beta-rule and splitting (194), into two cases.
% 47.64/20.90  																																																																																																				|-Branch one:
% 47.64/20.90  																																																																																																				| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																																				|
% 47.64/20.90  																																																																																																					| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																					| (106) $false
% 47.64/20.90  																																																																																																					|
% 47.64/20.90  																																																																																																					|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																				|-Branch two:
% 47.64/20.90  																																																																																																				| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																																				| (667) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.90  																																																																																																				|
% 47.64/20.90  																																																																																																					+-Applying beta-rule and splitting (195), into two cases.
% 47.64/20.90  																																																																																																					|-Branch one:
% 47.64/20.90  																																																																																																					| (308) all_28_0_32 = 0
% 47.64/20.90  																																																																																																					|
% 47.64/20.90  																																																																																																						| Equations (308) can reduce 88 to:
% 47.64/20.90  																																																																																																						| (106) $false
% 47.64/20.90  																																																																																																						|
% 47.64/20.90  																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																					|-Branch two:
% 47.64/20.90  																																																																																																					| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.90  																																																																																																					| (675) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.90  																																																																																																					|
% 47.64/20.90  																																																																																																						+-Applying beta-rule and splitting (212), into two cases.
% 47.64/20.90  																																																																																																						|-Branch one:
% 47.64/20.90  																																																																																																						| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																																						|
% 47.64/20.90  																																																																																																							| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																																							| (106) $false
% 47.64/20.90  																																																																																																							|
% 47.64/20.90  																																																																																																							|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																						|-Branch two:
% 47.64/20.90  																																																																																																						| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																																						| (832) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.90  																																																																																																						|
% 47.64/20.90  																																																																																																							+-Applying beta-rule and splitting (213), into two cases.
% 47.64/20.90  																																																																																																							|-Branch one:
% 47.64/20.90  																																																																																																							| (268) all_24_0_28 = 0
% 47.64/20.90  																																																																																																							|
% 47.64/20.90  																																																																																																								| Equations (268) can reduce 80 to:
% 47.64/20.90  																																																																																																								| (106) $false
% 47.64/20.90  																																																																																																								|
% 47.64/20.90  																																																																																																								|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																							|-Branch two:
% 47.64/20.90  																																																																																																							| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.90  																																																																																																							| (836) 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))
% 47.64/20.90  																																																																																																							|
% 47.64/20.90  																																																																																																								+-Applying beta-rule and splitting (153), into two cases.
% 47.64/20.90  																																																																																																								|-Branch one:
% 47.64/20.90  																																																																																																								| (252) all_30_0_34 = 0
% 47.64/20.90  																																																																																																								|
% 47.64/20.90  																																																																																																									| Equations (252) can reduce 92 to:
% 47.64/20.90  																																																																																																									| (106) $false
% 47.64/20.90  																																																																																																									|
% 47.64/20.90  																																																																																																									|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																								|-Branch two:
% 47.64/20.90  																																																																																																								| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.90  																																																																																																								| (840) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.64/20.90  																																																																																																								|
% 47.64/20.90  																																																																																																									+-Applying beta-rule and splitting (214), into two cases.
% 47.64/20.90  																																																																																																									|-Branch one:
% 47.64/20.90  																																																																																																									| (268) all_24_0_28 = 0
% 47.64/20.90  																																																																																																									|
% 47.64/20.90  																																																																																																										| Equations (268) can reduce 80 to:
% 47.64/20.90  																																																																																																										| (106) $false
% 47.64/20.90  																																																																																																										|
% 47.64/20.90  																																																																																																										|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																									|-Branch two:
% 47.64/20.90  																																																																																																									| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.90  																																																																																																									| (844) 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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.90  																																																																																																									|
% 47.64/20.90  																																																																																																										+-Applying beta-rule and splitting (215), into two cases.
% 47.64/20.90  																																																																																																										|-Branch one:
% 47.64/20.90  																																																																																																										| (268) all_24_0_28 = 0
% 47.64/20.90  																																																																																																										|
% 47.64/20.90  																																																																																																											| Equations (268) can reduce 80 to:
% 47.64/20.90  																																																																																																											| (106) $false
% 47.64/20.90  																																																																																																											|
% 47.64/20.90  																																																																																																											|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																										|-Branch two:
% 47.64/20.90  																																																																																																										| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.90  																																																																																																										| (848) 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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.90  																																																																																																										|
% 47.64/20.90  																																																																																																											+-Applying beta-rule and splitting (387), into two cases.
% 47.64/20.90  																																																																																																											|-Branch one:
% 47.64/20.90  																																																																																																											| (268) all_24_0_28 = 0
% 47.64/20.90  																																																																																																											|
% 47.64/20.90  																																																																																																												| Equations (268) can reduce 80 to:
% 47.64/20.90  																																																																																																												| (106) $false
% 47.64/20.90  																																																																																																												|
% 47.64/20.90  																																																																																																												|-The branch is then unsatisfiable
% 47.64/20.90  																																																																																																											|-Branch two:
% 47.64/20.90  																																																																																																											| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.90  																																																																																																											| (852)  ? [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))
% 47.64/20.91  																																																																																																											|
% 47.64/20.91  																																																																																																												+-Applying beta-rule and splitting (403), into two cases.
% 47.64/20.91  																																																																																																												|-Branch one:
% 47.64/20.91  																																																																																																												| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																												|
% 47.64/20.91  																																																																																																													| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																													| (106) $false
% 47.64/20.91  																																																																																																													|
% 47.64/20.91  																																																																																																													|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																												|-Branch two:
% 47.64/20.91  																																																																																																												| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																												| (856)  ? [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_4_4, all_0_3_3) = v0))
% 47.64/20.91  																																																																																																												|
% 47.64/20.91  																																																																																																													+-Applying beta-rule and splitting (431), into two cases.
% 47.64/20.91  																																																																																																													|-Branch one:
% 47.64/20.91  																																																																																																													| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																													|
% 47.64/20.91  																																																																																																														| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																														| (106) $false
% 47.64/20.91  																																																																																																														|
% 47.64/20.91  																																																																																																														|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																													|-Branch two:
% 47.64/20.91  																																																																																																													| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																													| (860)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0))
% 47.64/20.91  																																																																																																													|
% 47.64/20.91  																																																																																																														+-Applying beta-rule and splitting (435), into two cases.
% 47.64/20.91  																																																																																																														|-Branch one:
% 47.64/20.91  																																																																																																														| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																														|
% 47.64/20.91  																																																																																																															| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																															| (106) $false
% 47.64/20.91  																																																																																																															|
% 47.64/20.91  																																																																																																															|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																														|-Branch two:
% 47.64/20.91  																																																																																																														| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																														| (864)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.91  																																																																																																														|
% 47.64/20.91  																																																																																																															+-Applying beta-rule and splitting (439), into two cases.
% 47.64/20.91  																																																																																																															|-Branch one:
% 47.64/20.91  																																																																																																															| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																															|
% 47.64/20.91  																																																																																																																| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																| (106) $false
% 47.64/20.91  																																																																																																																|
% 47.64/20.91  																																																																																																																|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																															|-Branch two:
% 47.64/20.91  																																																																																																															| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																															| (868)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.91  																																																																																																															|
% 47.64/20.91  																																																																																																																+-Applying beta-rule and splitting (443), into two cases.
% 47.64/20.91  																																																																																																																|-Branch one:
% 47.64/20.91  																																																																																																																| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																|
% 47.64/20.91  																																																																																																																	| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																	| (106) $false
% 47.64/20.91  																																																																																																																	|
% 47.64/20.91  																																																																																																																	|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																																|-Branch two:
% 47.64/20.91  																																																																																																																| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																																| (872)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0))
% 47.64/20.91  																																																																																																																|
% 47.64/20.91  																																																																																																																	+-Applying beta-rule and splitting (659), into two cases.
% 47.64/20.91  																																																																																																																	|-Branch one:
% 47.64/20.91  																																																																																																																	| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																	|
% 47.64/20.91  																																																																																																																		| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																		| (106) $false
% 47.64/20.91  																																																																																																																		|
% 47.64/20.91  																																																																																																																		|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																																	|-Branch two:
% 47.64/20.91  																																																																																																																	| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																																	| (876)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.91  																																																																																																																	|
% 47.64/20.91  																																																																																																																		+-Applying beta-rule and splitting (840), into two cases.
% 47.64/20.91  																																																																																																																		|-Branch one:
% 47.64/20.91  																																																																																																																		| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																		|
% 47.64/20.91  																																																																																																																			| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																			| (106) $false
% 47.64/20.91  																																																																																																																			|
% 47.64/20.91  																																																																																																																			|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																																		|-Branch two:
% 47.64/20.91  																																																																																																																		| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																																		| (880)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.64/20.91  																																																																																																																		|
% 47.64/20.91  																																																																																																																			+-Applying beta-rule and splitting (663), into two cases.
% 47.64/20.91  																																																																																																																			|-Branch one:
% 47.64/20.91  																																																																																																																			| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																			|
% 47.64/20.91  																																																																																																																				| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																				| (106) $false
% 47.64/20.91  																																																																																																																				|
% 47.64/20.91  																																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																																			|-Branch two:
% 47.64/20.91  																																																																																																																			| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																																			| (884)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.91  																																																																																																																			|
% 47.64/20.91  																																																																																																																				+-Applying beta-rule and splitting (667), into two cases.
% 47.64/20.91  																																																																																																																				|-Branch one:
% 47.64/20.91  																																																																																																																				| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																				|
% 47.64/20.91  																																																																																																																					| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																					| (106) $false
% 47.64/20.91  																																																																																																																					|
% 47.64/20.91  																																																																																																																					|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																																				|-Branch two:
% 47.64/20.91  																																																																																																																				| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																																				| (888)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.91  																																																																																																																				|
% 47.64/20.91  																																																																																																																					+-Applying beta-rule and splitting (675), into two cases.
% 47.64/20.91  																																																																																																																					|-Branch one:
% 47.64/20.91  																																																																																																																					| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																					|
% 47.64/20.91  																																																																																																																						| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																						| (106) $false
% 47.64/20.91  																																																																																																																						|
% 47.64/20.91  																																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																																																					|-Branch two:
% 47.64/20.91  																																																																																																																					| (80)  ~ (all_24_0_28 = 0)
% 47.64/20.91  																																																																																																																					| (892)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.91  																																																																																																																					|
% 47.64/20.91  																																																																																																																						| Instantiating formula (42) with all_0_3_3, all_22_1_27, 0, all_24_0_28 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_22_1_27) = 0, yields:
% 47.64/20.91  																																																																																																																						| (268) all_24_0_28 = 0
% 47.64/20.91  																																																																																																																						|
% 47.64/20.91  																																																																																																																						| Equations (268) can reduce 80 to:
% 47.64/20.91  																																																																																																																						| (106) $false
% 47.64/20.91  																																																																																																																						|
% 47.64/20.91  																																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																	|-Branch two:
% 47.64/20.91  																																																																																	| (895) all_270_0_475 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 47.64/20.91  																																																																																	|
% 47.64/20.91  																																																																																		| Applying alpha-rule on (895) yields:
% 47.64/20.91  																																																																																		| (747) all_270_0_475 = 0
% 47.64/20.91  																																																																																		| (510) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 47.64/20.91  																																																																																		|
% 47.64/20.91  																																																																																		+-Applying beta-rule and splitting (228), into two cases.
% 47.64/20.91  																																																																																		|-Branch one:
% 47.64/20.91  																																																																																		| (523) all_20_0_24 = 0
% 47.64/20.91  																																																																																		|
% 47.64/20.91  																																																																																			| Equations (523) can reduce 72 to:
% 47.64/20.91  																																																																																			| (106) $false
% 47.64/20.91  																																																																																			|
% 47.64/20.91  																																																																																			|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																		|-Branch two:
% 47.64/20.91  																																																																																		| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.91  																																																																																		| (526)  ? [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))
% 47.64/20.91  																																																																																		|
% 47.64/20.91  																																																																																			+-Applying beta-rule and splitting (133), into two cases.
% 47.64/20.91  																																																																																			|-Branch one:
% 47.64/20.91  																																																																																			| (252) all_30_0_34 = 0
% 47.64/20.91  																																																																																			|
% 47.64/20.91  																																																																																				| Equations (252) can reduce 92 to:
% 47.64/20.91  																																																																																				| (106) $false
% 47.64/20.91  																																																																																				|
% 47.64/20.91  																																																																																				|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																			|-Branch two:
% 47.64/20.91  																																																																																			| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.91  																																																																																			| (530) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.91  																																																																																			|
% 47.64/20.91  																																																																																				+-Applying beta-rule and splitting (134), into two cases.
% 47.64/20.91  																																																																																				|-Branch one:
% 47.64/20.91  																																																																																				| (252) all_30_0_34 = 0
% 47.64/20.91  																																																																																				|
% 47.64/20.91  																																																																																					| Equations (252) can reduce 92 to:
% 47.64/20.91  																																																																																					| (106) $false
% 47.64/20.91  																																																																																					|
% 47.64/20.91  																																																																																					|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																				|-Branch two:
% 47.64/20.91  																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.91  																																																																																				| (534) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.91  																																																																																				|
% 47.64/20.91  																																																																																					+-Applying beta-rule and splitting (135), into two cases.
% 47.64/20.91  																																																																																					|-Branch one:
% 47.64/20.91  																																																																																					| (252) all_30_0_34 = 0
% 47.64/20.91  																																																																																					|
% 47.64/20.91  																																																																																						| Equations (252) can reduce 92 to:
% 47.64/20.91  																																																																																						| (106) $false
% 47.64/20.91  																																																																																						|
% 47.64/20.91  																																																																																						|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																					|-Branch two:
% 47.64/20.91  																																																																																					| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.91  																																																																																					| (538) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.91  																																																																																					|
% 47.64/20.91  																																																																																						+-Applying beta-rule and splitting (224), into two cases.
% 47.64/20.91  																																																																																						|-Branch one:
% 47.64/20.91  																																																																																						| (308) all_28_0_32 = 0
% 47.64/20.91  																																																																																						|
% 47.64/20.91  																																																																																							| Equations (308) can reduce 88 to:
% 47.64/20.91  																																																																																							| (106) $false
% 47.64/20.91  																																																																																							|
% 47.64/20.91  																																																																																							|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																						|-Branch two:
% 47.64/20.91  																																																																																						| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.91  																																																																																						| (627) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.91  																																																																																						|
% 47.64/20.91  																																																																																							+-Applying beta-rule and splitting (225), into two cases.
% 47.64/20.91  																																																																																							|-Branch one:
% 47.64/20.91  																																																																																							| (308) all_28_0_32 = 0
% 47.64/20.91  																																																																																							|
% 47.64/20.91  																																																																																								| Equations (308) can reduce 88 to:
% 47.64/20.91  																																																																																								| (106) $false
% 47.64/20.91  																																																																																								|
% 47.64/20.91  																																																																																								|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																							|-Branch two:
% 47.64/20.91  																																																																																							| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.91  																																																																																							| (631) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.91  																																																																																							|
% 47.64/20.91  																																																																																								+-Applying beta-rule and splitting (227), into two cases.
% 47.64/20.91  																																																																																								|-Branch one:
% 47.64/20.91  																																																																																								| (308) all_28_0_32 = 0
% 47.64/20.91  																																																																																								|
% 47.64/20.91  																																																																																									| Equations (308) can reduce 88 to:
% 47.64/20.91  																																																																																									| (106) $false
% 47.64/20.91  																																																																																									|
% 47.64/20.91  																																																																																									|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																								|-Branch two:
% 47.64/20.91  																																																																																								| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.91  																																																																																								| (635) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.91  																																																																																								|
% 47.64/20.91  																																																																																									+-Applying beta-rule and splitting (136), into two cases.
% 47.64/20.91  																																																																																									|-Branch one:
% 47.64/20.91  																																																																																									| (252) all_30_0_34 = 0
% 47.64/20.91  																																																																																									|
% 47.64/20.91  																																																																																										| Equations (252) can reduce 92 to:
% 47.64/20.91  																																																																																										| (106) $false
% 47.64/20.91  																																																																																										|
% 47.64/20.91  																																																																																										|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																									|-Branch two:
% 47.64/20.91  																																																																																									| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.91  																																																																																									| (542) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.91  																																																																																									|
% 47.64/20.91  																																																																																										+-Applying beta-rule and splitting (226), into two cases.
% 47.64/20.91  																																																																																										|-Branch one:
% 47.64/20.91  																																																																																										| (308) all_28_0_32 = 0
% 47.64/20.91  																																																																																										|
% 47.64/20.91  																																																																																											| Equations (308) can reduce 88 to:
% 47.64/20.91  																																																																																											| (106) $false
% 47.64/20.91  																																																																																											|
% 47.64/20.91  																																																																																											|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																										|-Branch two:
% 47.64/20.91  																																																																																										| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.91  																																																																																										| (639) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.91  																																																																																										|
% 47.64/20.91  																																																																																											+-Applying beta-rule and splitting (287), into two cases.
% 47.64/20.91  																																																																																											|-Branch one:
% 47.64/20.91  																																																																																											| (232) all_22_0_26 = 0
% 47.64/20.91  																																																																																											|
% 47.64/20.91  																																																																																												| Equations (232) can reduce 76 to:
% 47.64/20.91  																																																																																												| (106) $false
% 47.64/20.91  																																																																																												|
% 47.64/20.91  																																																																																												|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																											|-Branch two:
% 47.64/20.91  																																																																																											| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.91  																																																																																											| (643)  ? [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))
% 47.64/20.91  																																																																																											|
% 47.64/20.91  																																																																																												+-Applying beta-rule and splitting (311), into two cases.
% 47.64/20.91  																																																																																												|-Branch one:
% 47.64/20.91  																																																																																												| (105) all_0_1_1 = 0
% 47.64/20.91  																																																																																												|
% 47.64/20.91  																																																																																													| Equations (105) can reduce 33 to:
% 47.64/20.91  																																																																																													| (106) $false
% 47.64/20.91  																																																																																													|
% 47.64/20.91  																																																																																													|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																												|-Branch two:
% 47.64/20.91  																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.91  																																																																																												| (546)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.91  																																																																																												|
% 47.64/20.91  																																																																																													+-Applying beta-rule and splitting (367), into two cases.
% 47.64/20.91  																																																																																													|-Branch one:
% 47.64/20.91  																																																																																													| (105) all_0_1_1 = 0
% 47.64/20.91  																																																																																													|
% 47.64/20.91  																																																																																														| Equations (105) can reduce 33 to:
% 47.64/20.91  																																																																																														| (106) $false
% 47.64/20.91  																																																																																														|
% 47.64/20.91  																																																																																														|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																													|-Branch two:
% 47.64/20.91  																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.91  																																																																																													| (550)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.64/20.91  																																																																																													|
% 47.64/20.91  																																																																																														+-Applying beta-rule and splitting (206), into two cases.
% 47.64/20.91  																																																																																														|-Branch one:
% 47.64/20.91  																																																																																														| (308) all_28_0_32 = 0
% 47.64/20.91  																																																																																														|
% 47.64/20.91  																																																																																															| Equations (308) can reduce 88 to:
% 47.64/20.91  																																																																																															| (106) $false
% 47.64/20.91  																																																																																															|
% 47.64/20.91  																																																																																															|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																														|-Branch two:
% 47.64/20.91  																																																																																														| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.91  																																																																																														| (655)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.91  																																																																																														|
% 47.64/20.91  																																																																																															+-Applying beta-rule and splitting (220), into two cases.
% 47.64/20.91  																																																																																															|-Branch one:
% 47.64/20.91  																																																																																															| (232) all_22_0_26 = 0
% 47.64/20.91  																																																																																															|
% 47.64/20.91  																																																																																																| Equations (232) can reduce 76 to:
% 47.64/20.91  																																																																																																| (106) $false
% 47.64/20.91  																																																																																																|
% 47.64/20.91  																																																																																																|-The branch is then unsatisfiable
% 47.64/20.91  																																																																																															|-Branch two:
% 47.64/20.91  																																																																																															| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.91  																																																																																															| (707) 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))
% 47.64/20.91  																																																																																															|
% 47.64/20.92  																																																																																																+-Applying beta-rule and splitting (222), into two cases.
% 47.64/20.92  																																																																																																|-Branch one:
% 47.64/20.92  																																																																																																| (308) all_28_0_32 = 0
% 47.64/20.92  																																																																																																|
% 47.64/20.92  																																																																																																	| Equations (308) can reduce 88 to:
% 47.64/20.92  																																																																																																	| (106) $false
% 47.64/20.92  																																																																																																	|
% 47.64/20.92  																																																																																																	|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																|-Branch two:
% 47.64/20.92  																																																																																																| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.92  																																																																																																| (800) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.92  																																																																																																|
% 47.64/20.92  																																																																																																	+-Applying beta-rule and splitting (538), into two cases.
% 47.64/20.92  																																																																																																	|-Branch one:
% 47.64/20.92  																																																																																																	| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																	|
% 47.64/20.92  																																																																																																		| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																		| (106) $false
% 47.64/20.92  																																																																																																		|
% 47.64/20.92  																																																																																																		|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																	|-Branch two:
% 47.64/20.92  																																																																																																	| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																	| (610)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.92  																																																																																																	|
% 47.64/20.92  																																																																																																		+-Applying beta-rule and splitting (542), into two cases.
% 47.64/20.92  																																																																																																		|-Branch one:
% 47.64/20.92  																																																																																																		| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																		|
% 47.64/20.92  																																																																																																			| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																			| (106) $false
% 47.64/20.92  																																																																																																			|
% 47.64/20.92  																																																																																																			|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																		|-Branch two:
% 47.64/20.92  																																																																																																		| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																		| (614)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.92  																																																																																																		|
% 47.64/20.92  																																																																																																			+-Applying beta-rule and splitting (639), into two cases.
% 47.64/20.92  																																																																																																			|-Branch one:
% 47.64/20.92  																																																																																																			| (523) all_20_0_24 = 0
% 47.64/20.92  																																																																																																			|
% 47.64/20.92  																																																																																																				| Equations (523) can reduce 72 to:
% 47.64/20.92  																																																																																																				| (106) $false
% 47.64/20.92  																																																																																																				|
% 47.64/20.92  																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																			|-Branch two:
% 47.64/20.92  																																																																																																			| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.92  																																																																																																			| (969)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.92  																																																																																																			|
% 47.64/20.92  																																																																																																				+-Applying beta-rule and splitting (347), into two cases.
% 47.64/20.92  																																																																																																				|-Branch one:
% 47.64/20.92  																																																																																																				| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																				|
% 47.64/20.92  																																																																																																					| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																					| (106) $false
% 47.64/20.92  																																																																																																					|
% 47.64/20.92  																																																																																																					|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																				|-Branch two:
% 47.64/20.92  																																																																																																				| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																				| (570)  ? [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))
% 47.64/20.92  																																																																																																				|
% 47.64/20.92  																																																																																																					+-Applying beta-rule and splitting (371), into two cases.
% 47.64/20.92  																																																																																																					|-Branch one:
% 47.64/20.92  																																																																																																					| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																					|
% 47.64/20.92  																																																																																																						| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																						| (106) $false
% 47.64/20.92  																																																																																																						|
% 47.64/20.92  																																																																																																						|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																					|-Branch two:
% 47.64/20.92  																																																																																																					| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																					| (586)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.64/20.92  																																																																																																					|
% 47.64/20.92  																																																																																																						+-Applying beta-rule and splitting (395), into two cases.
% 47.64/20.92  																																																																																																						|-Branch one:
% 47.64/20.92  																																																																																																						| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																						|
% 47.64/20.92  																																																																																																							| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																							| (106) $false
% 47.64/20.92  																																																																																																							|
% 47.64/20.92  																																																																																																							|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																						|-Branch two:
% 47.64/20.92  																																																																																																						| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																						| (594)  ? [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_4_4, all_0_3_3) = v0))
% 47.64/20.92  																																																																																																						|
% 47.64/20.92  																																																																																																							+-Applying beta-rule and splitting (411), into two cases.
% 47.64/20.92  																																																																																																							|-Branch one:
% 47.64/20.92  																																																																																																							| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																							|
% 47.64/20.92  																																																																																																								| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																								| (106) $false
% 47.64/20.92  																																																																																																								|
% 47.64/20.92  																																																																																																								|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																							|-Branch two:
% 47.64/20.92  																																																																																																							| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																							| (598)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.64/20.92  																																																																																																							|
% 47.64/20.92  																																																																																																								+-Applying beta-rule and splitting (707), into two cases.
% 47.64/20.92  																																																																																																								|-Branch one:
% 47.64/20.92  																																																																																																								| (523) all_20_0_24 = 0
% 47.64/20.92  																																																																																																								|
% 47.64/20.92  																																																																																																									| Equations (523) can reduce 72 to:
% 47.64/20.92  																																																																																																									| (106) $false
% 47.64/20.92  																																																																																																									|
% 47.64/20.92  																																																																																																									|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																								|-Branch two:
% 47.64/20.92  																																																																																																								| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.92  																																																																																																								| (989)  ? [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))
% 47.64/20.92  																																																																																																								|
% 47.64/20.92  																																																																																																									+-Applying beta-rule and splitting (800), into two cases.
% 47.64/20.92  																																																																																																									|-Branch one:
% 47.64/20.92  																																																																																																									| (523) all_20_0_24 = 0
% 47.64/20.92  																																																																																																									|
% 47.64/20.92  																																																																																																										| Equations (523) can reduce 72 to:
% 47.64/20.92  																																																																																																										| (106) $false
% 47.64/20.92  																																																																																																										|
% 47.64/20.92  																																																																																																										|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																									|-Branch two:
% 47.64/20.92  																																																																																																									| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.92  																																																																																																									| (993)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.92  																																																																																																									|
% 47.64/20.92  																																																																																																										+-Applying beta-rule and splitting (207), into two cases.
% 47.64/20.92  																																																																																																										|-Branch one:
% 47.64/20.92  																																																																																																										| (523) all_20_0_24 = 0
% 47.64/20.92  																																																																																																										|
% 47.64/20.92  																																																																																																											| Equations (523) can reduce 72 to:
% 47.64/20.92  																																																																																																											| (106) $false
% 47.64/20.92  																																																																																																											|
% 47.64/20.92  																																																																																																											|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																										|-Branch two:
% 47.64/20.92  																																																																																																										| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.92  																																																																																																										| (558) 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))
% 47.64/20.92  																																																																																																										|
% 47.64/20.92  																																																																																																											+-Applying beta-rule and splitting (359), into two cases.
% 47.64/20.92  																																																																																																											|-Branch one:
% 47.64/20.92  																																																																																																											| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																											|
% 47.64/20.92  																																																																																																												| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																												| (106) $false
% 47.64/20.92  																																																																																																												|
% 47.64/20.92  																																																																																																												|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																											|-Branch two:
% 47.64/20.92  																																																																																																											| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																											| (578)  ? [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_22_1_27, all_0_2_2) = v0))
% 47.64/20.92  																																																																																																											|
% 47.64/20.92  																																																																																																												+-Applying beta-rule and splitting (363), into two cases.
% 47.64/20.92  																																																																																																												|-Branch one:
% 47.64/20.92  																																																																																																												| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																												|
% 47.64/20.92  																																																																																																													| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																													| (106) $false
% 47.64/20.92  																																																																																																													|
% 47.64/20.92  																																																																																																													|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																												|-Branch two:
% 47.64/20.92  																																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																												| (582)  ? [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))
% 47.64/20.92  																																																																																																												|
% 47.64/20.92  																																																																																																													+-Applying beta-rule and splitting (415), into two cases.
% 47.64/20.92  																																																																																																													|-Branch one:
% 47.64/20.92  																																																																																																													| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																													|
% 47.64/20.92  																																																																																																														| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																														| (106) $false
% 47.64/20.92  																																																																																																														|
% 47.64/20.92  																																																																																																														|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																													|-Branch two:
% 47.64/20.92  																																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																													| (602)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.64/20.92  																																																																																																													|
% 47.64/20.92  																																																																																																														+-Applying beta-rule and splitting (423), into two cases.
% 47.64/20.92  																																																																																																														|-Branch one:
% 47.64/20.92  																																																																																																														| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																														|
% 47.64/20.92  																																																																																																															| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																															| (106) $false
% 47.64/20.92  																																																																																																															|
% 47.64/20.92  																																																																																																															|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																														|-Branch two:
% 47.64/20.92  																																																																																																														| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																														| (606)  ? [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))
% 47.64/20.92  																																																																																																														|
% 47.64/20.92  																																																																																																															+-Applying beta-rule and splitting (355), into two cases.
% 47.64/20.92  																																																																																																															|-Branch one:
% 47.64/20.92  																																																																																																															| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																															|
% 47.64/20.92  																																																																																																																| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																																| (106) $false
% 47.64/20.92  																																																																																																																|
% 47.64/20.92  																																																																																																																|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																															|-Branch two:
% 47.64/20.92  																																																																																																															| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																															| (574)  ? [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))
% 47.64/20.92  																																																																																																															|
% 47.64/20.92  																																																																																																																+-Applying beta-rule and splitting (383), into two cases.
% 47.64/20.92  																																																																																																																|-Branch one:
% 47.64/20.92  																																																																																																																| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																																|
% 47.64/20.92  																																																																																																																	| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																																	| (106) $false
% 47.64/20.92  																																																																																																																	|
% 47.64/20.92  																																																																																																																	|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																																|-Branch two:
% 47.64/20.92  																																																																																																																| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																																| (590)  ? [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))
% 47.64/20.92  																																																																																																																|
% 47.64/20.92  																																																																																																																	+-Applying beta-rule and splitting (530), into two cases.
% 47.64/20.92  																																																																																																																	|-Branch one:
% 47.64/20.92  																																																																																																																	| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																																	|
% 47.64/20.92  																																																																																																																		| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																																		| (106) $false
% 47.64/20.92  																																																																																																																		|
% 47.64/20.92  																																																																																																																		|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																																	|-Branch two:
% 47.64/20.92  																																																																																																																	| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																																	| (562)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.92  																																																																																																																	|
% 47.64/20.92  																																																																																																																		+-Applying beta-rule and splitting (534), into two cases.
% 47.64/20.92  																																																																																																																		|-Branch one:
% 47.64/20.92  																																																																																																																		| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																																		|
% 47.64/20.92  																																																																																																																			| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																																			| (106) $false
% 47.64/20.92  																																																																																																																			|
% 47.64/20.92  																																																																																																																			|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																																		|-Branch two:
% 47.64/20.92  																																																																																																																		| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																																		| (566)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.92  																																																																																																																		|
% 47.64/20.92  																																																																																																																			+-Applying beta-rule and splitting (558), into two cases.
% 47.64/20.92  																																																																																																																			|-Branch one:
% 47.64/20.92  																																																																																																																			| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																																			|
% 47.64/20.92  																																																																																																																				| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																																				| (106) $false
% 47.64/20.92  																																																																																																																				|
% 47.64/20.92  																																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																																																			|-Branch two:
% 47.64/20.92  																																																																																																																			| (33)  ~ (all_0_1_1 = 0)
% 47.64/20.92  																																																																																																																			| (618)  ? [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))
% 47.64/20.92  																																																																																																																			|
% 47.64/20.92  																																																																																																																				| Instantiating formula (42) 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:
% 47.64/20.92  																																																																																																																				| (105) all_0_1_1 = 0
% 47.64/20.92  																																																																																																																				|
% 47.64/20.92  																																																																																																																				| Equations (105) can reduce 33 to:
% 47.64/20.92  																																																																																																																				| (106) $false
% 47.64/20.92  																																																																																																																				|
% 47.64/20.92  																																																																																																																				|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																|-Branch two:
% 47.64/20.92  																																																																																| (1036)  ~ (all_270_0_475 = 0) & distinct_lines(all_22_1_27, all_0_2_2) = all_270_0_475
% 47.64/20.92  																																																																																|
% 47.64/20.92  																																																																																	| Applying alpha-rule on (1036) yields:
% 47.64/20.92  																																																																																	| (1037)  ~ (all_270_0_475 = 0)
% 47.64/20.92  																																																																																	| (1038) distinct_lines(all_22_1_27, all_0_2_2) = all_270_0_475
% 47.64/20.92  																																																																																	|
% 47.64/20.92  																																																																																	+-Applying beta-rule and splitting (228), into two cases.
% 47.64/20.92  																																																																																	|-Branch one:
% 47.64/20.92  																																																																																	| (523) all_20_0_24 = 0
% 47.64/20.92  																																																																																	|
% 47.64/20.92  																																																																																		| Equations (523) can reduce 72 to:
% 47.64/20.92  																																																																																		| (106) $false
% 47.64/20.92  																																																																																		|
% 47.64/20.92  																																																																																		|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																	|-Branch two:
% 47.64/20.92  																																																																																	| (72)  ~ (all_20_0_24 = 0)
% 47.64/20.92  																																																																																	| (526)  ? [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))
% 47.64/20.92  																																																																																	|
% 47.64/20.92  																																																																																		+-Applying beta-rule and splitting (133), into two cases.
% 47.64/20.92  																																																																																		|-Branch one:
% 47.64/20.92  																																																																																		| (252) all_30_0_34 = 0
% 47.64/20.92  																																																																																		|
% 47.64/20.92  																																																																																			| Equations (252) can reduce 92 to:
% 47.64/20.92  																																																																																			| (106) $false
% 47.64/20.92  																																																																																			|
% 47.64/20.92  																																																																																			|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																		|-Branch two:
% 47.64/20.92  																																																																																		| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.92  																																																																																		| (530) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.92  																																																																																		|
% 47.64/20.92  																																																																																			+-Applying beta-rule and splitting (134), into two cases.
% 47.64/20.92  																																																																																			|-Branch one:
% 47.64/20.92  																																																																																			| (252) all_30_0_34 = 0
% 47.64/20.92  																																																																																			|
% 47.64/20.92  																																																																																				| Equations (252) can reduce 92 to:
% 47.64/20.92  																																																																																				| (106) $false
% 47.64/20.92  																																																																																				|
% 47.64/20.92  																																																																																				|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																			|-Branch two:
% 47.64/20.92  																																																																																			| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.92  																																																																																			| (534) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.92  																																																																																			|
% 47.64/20.92  																																																																																				+-Applying beta-rule and splitting (135), into two cases.
% 47.64/20.92  																																																																																				|-Branch one:
% 47.64/20.92  																																																																																				| (252) all_30_0_34 = 0
% 47.64/20.92  																																																																																				|
% 47.64/20.92  																																																																																					| Equations (252) can reduce 92 to:
% 47.64/20.92  																																																																																					| (106) $false
% 47.64/20.92  																																																																																					|
% 47.64/20.92  																																																																																					|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																				|-Branch two:
% 47.64/20.92  																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.92  																																																																																				| (538) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.92  																																																																																				|
% 47.64/20.92  																																																																																					+-Applying beta-rule and splitting (224), into two cases.
% 47.64/20.92  																																																																																					|-Branch one:
% 47.64/20.92  																																																																																					| (308) all_28_0_32 = 0
% 47.64/20.92  																																																																																					|
% 47.64/20.92  																																																																																						| Equations (308) can reduce 88 to:
% 47.64/20.92  																																																																																						| (106) $false
% 47.64/20.92  																																																																																						|
% 47.64/20.92  																																																																																						|-The branch is then unsatisfiable
% 47.64/20.92  																																																																																					|-Branch two:
% 47.64/20.92  																																																																																					| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.92  																																																																																					| (627) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.93  																																																																																					|
% 47.64/20.93  																																																																																						+-Applying beta-rule and splitting (225), into two cases.
% 47.64/20.93  																																																																																						|-Branch one:
% 47.64/20.93  																																																																																						| (308) all_28_0_32 = 0
% 47.64/20.93  																																																																																						|
% 47.64/20.93  																																																																																							| Equations (308) can reduce 88 to:
% 47.64/20.93  																																																																																							| (106) $false
% 47.64/20.93  																																																																																							|
% 47.64/20.93  																																																																																							|-The branch is then unsatisfiable
% 47.64/20.93  																																																																																						|-Branch two:
% 47.64/20.93  																																																																																						| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.93  																																																																																						| (631) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.64/20.93  																																																																																						|
% 47.64/20.93  																																																																																							+-Applying beta-rule and splitting (227), into two cases.
% 47.64/20.93  																																																																																							|-Branch one:
% 47.64/20.93  																																																																																							| (308) all_28_0_32 = 0
% 47.64/20.93  																																																																																							|
% 47.64/20.93  																																																																																								| Equations (308) can reduce 88 to:
% 47.64/20.93  																																																																																								| (106) $false
% 47.64/20.93  																																																																																								|
% 47.64/20.93  																																																																																								|-The branch is then unsatisfiable
% 47.64/20.93  																																																																																							|-Branch two:
% 47.64/20.93  																																																																																							| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.93  																																																																																							| (635) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.93  																																																																																							|
% 47.64/20.93  																																																																																								+-Applying beta-rule and splitting (136), into two cases.
% 47.64/20.93  																																																																																								|-Branch one:
% 47.64/20.93  																																																																																								| (252) all_30_0_34 = 0
% 47.64/20.93  																																																																																								|
% 47.64/20.93  																																																																																									| Equations (252) can reduce 92 to:
% 47.64/20.93  																																																																																									| (106) $false
% 47.64/20.93  																																																																																									|
% 47.64/20.93  																																																																																									|-The branch is then unsatisfiable
% 47.64/20.93  																																																																																								|-Branch two:
% 47.64/20.93  																																																																																								| (92)  ~ (all_30_0_34 = 0)
% 47.64/20.93  																																																																																								| (542) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.64/20.93  																																																																																								|
% 47.64/20.93  																																																																																									+-Applying beta-rule and splitting (226), into two cases.
% 47.64/20.93  																																																																																									|-Branch one:
% 47.64/20.93  																																																																																									| (308) all_28_0_32 = 0
% 47.64/20.93  																																																																																									|
% 47.64/20.93  																																																																																										| Equations (308) can reduce 88 to:
% 47.64/20.93  																																																																																										| (106) $false
% 47.64/20.93  																																																																																										|
% 47.64/20.93  																																																																																										|-The branch is then unsatisfiable
% 47.64/20.93  																																																																																									|-Branch two:
% 47.64/20.93  																																																																																									| (88)  ~ (all_28_0_32 = 0)
% 47.64/20.93  																																																																																									| (639) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.64/20.93  																																																																																									|
% 47.64/20.93  																																																																																										+-Applying beta-rule and splitting (287), into two cases.
% 47.64/20.93  																																																																																										|-Branch one:
% 47.64/20.93  																																																																																										| (232) all_22_0_26 = 0
% 47.64/20.93  																																																																																										|
% 47.64/20.93  																																																																																											| Equations (232) can reduce 76 to:
% 47.64/20.93  																																																																																											| (106) $false
% 47.64/20.93  																																																																																											|
% 47.64/20.93  																																																																																											|-The branch is then unsatisfiable
% 47.64/20.93  																																																																																										|-Branch two:
% 47.64/20.93  																																																																																										| (76)  ~ (all_22_0_26 = 0)
% 47.64/20.93  																																																																																										| (643)  ? [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))
% 47.64/20.93  																																																																																										|
% 47.64/20.93  																																																																																											+-Applying beta-rule and splitting (291), into two cases.
% 47.64/20.93  																																																																																											|-Branch one:
% 47.64/20.93  																																																																																											| (244) all_26_0_30 = 0
% 47.64/20.93  																																																																																											|
% 47.64/20.93  																																																																																												| Equations (244) can reduce 84 to:
% 47.64/20.93  																																																																																												| (106) $false
% 47.64/20.93  																																																																																												|
% 47.64/20.93  																																																																																												|-The branch is then unsatisfiable
% 47.64/20.93  																																																																																											|-Branch two:
% 47.64/20.93  																																																																																											| (84)  ~ (all_26_0_30 = 0)
% 47.64/20.93  																																																																																											| (1082)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.87/20.93  																																																																																											|
% 47.87/20.93  																																																																																												+-Applying beta-rule and splitting (311), into two cases.
% 47.87/20.93  																																																																																												|-Branch one:
% 47.87/20.93  																																																																																												| (105) all_0_1_1 = 0
% 47.87/20.93  																																																																																												|
% 47.87/20.93  																																																																																													| Equations (105) can reduce 33 to:
% 47.87/20.93  																																																																																													| (106) $false
% 47.87/20.93  																																																																																													|
% 47.87/20.93  																																																																																													|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																												|-Branch two:
% 47.87/20.93  																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.93  																																																																																												| (546)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.93  																																																																																												|
% 47.87/20.93  																																																																																													| Instantiating (546) with all_382_0_1266 yields:
% 47.87/20.93  																																																																																													| (1087) (all_382_0_1266 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (all_382_0_1266 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_382_0_1266 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266) | ( ~ (all_382_0_1266 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_382_0_1266)
% 47.87/20.93  																																																																																													|
% 47.87/20.93  																																																																																													+-Applying beta-rule and splitting (367), into two cases.
% 47.87/20.93  																																																																																													|-Branch one:
% 47.87/20.93  																																																																																													| (105) all_0_1_1 = 0
% 47.87/20.93  																																																																																													|
% 47.87/20.93  																																																																																														| Equations (105) can reduce 33 to:
% 47.87/20.93  																																																																																														| (106) $false
% 47.87/20.93  																																																																																														|
% 47.87/20.93  																																																																																														|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																													|-Branch two:
% 47.87/20.93  																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.93  																																																																																													| (550)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.87/20.93  																																																																																													|
% 47.87/20.93  																																																																																														+-Applying beta-rule and splitting (208), into two cases.
% 47.87/20.93  																																																																																														|-Branch one:
% 47.87/20.93  																																																																																														| (1092) distinct_lines(all_0_0_0, all_0_2_2) = 0
% 47.87/20.93  																																																																																														|
% 47.87/20.93  																																																																																															+-Applying beta-rule and splitting (206), into two cases.
% 47.87/20.93  																																																																																															|-Branch one:
% 47.87/20.93  																																																																																															| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																															|
% 47.87/20.93  																																																																																																| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																| (106) $false
% 47.87/20.93  																																																																																																|
% 47.87/20.93  																																																																																																|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																															|-Branch two:
% 47.87/20.93  																																																																																															| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																															| (655)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.87/20.93  																																																																																															|
% 47.87/20.93  																																																																																																+-Applying beta-rule and splitting (222), into two cases.
% 47.87/20.93  																																																																																																|-Branch one:
% 47.87/20.93  																																																																																																| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																|
% 47.87/20.93  																																																																																																	| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																	| (106) $false
% 47.87/20.93  																																																																																																	|
% 47.87/20.93  																																																																																																	|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																|-Branch two:
% 47.87/20.93  																																																																																																| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																| (800) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.87/20.93  																																																																																																|
% 47.87/20.93  																																																																																																	+-Applying beta-rule and splitting (223), into two cases.
% 47.87/20.93  																																																																																																	|-Branch one:
% 47.87/20.93  																																																																																																	| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																	|
% 47.87/20.93  																																																																																																		| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																		| (106) $false
% 47.87/20.93  																																																																																																		|
% 47.87/20.93  																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																	|-Branch two:
% 47.87/20.93  																																																																																																	| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																	| (804) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.93  																																																																																																	|
% 47.87/20.93  																																																																																																		+-Applying beta-rule and splitting (204), into two cases.
% 47.87/20.93  																																																																																																		|-Branch one:
% 47.87/20.93  																																																																																																		| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																		|
% 47.87/20.93  																																																																																																			| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																			| (106) $false
% 47.87/20.93  																																																																																																			|
% 47.87/20.93  																																																																																																			|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																		|-Branch two:
% 47.87/20.93  																																																																																																		| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																		| (647)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.87/20.93  																																																																																																		|
% 47.87/20.93  																																																																																																			+-Applying beta-rule and splitting (205), into two cases.
% 47.87/20.93  																																																																																																			|-Branch one:
% 47.87/20.93  																																																																																																			| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																			|
% 47.87/20.93  																																																																																																				| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																				| (106) $false
% 47.87/20.93  																																																																																																				|
% 47.87/20.93  																																																																																																				|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																			|-Branch two:
% 47.87/20.93  																																																																																																			| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																			| (327)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_28_1_33) = v0))
% 47.87/20.93  																																																																																																			|
% 47.87/20.93  																																																																																																				+-Applying beta-rule and splitting (210), into two cases.
% 47.87/20.93  																																																																																																				|-Branch one:
% 47.87/20.93  																																																																																																				| (252) all_30_0_34 = 0
% 47.87/20.93  																																																																																																				|
% 47.87/20.93  																																																																																																					| Equations (252) can reduce 92 to:
% 47.87/20.93  																																																																																																					| (106) $false
% 47.87/20.93  																																																																																																					|
% 47.87/20.93  																																																																																																					|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																				|-Branch two:
% 47.87/20.93  																																																																																																				| (92)  ~ (all_30_0_34 = 0)
% 47.87/20.93  																																																																																																				| (788) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.93  																																																																																																				|
% 47.87/20.93  																																																																																																					+-Applying beta-rule and splitting (211), into two cases.
% 47.87/20.93  																																																																																																					|-Branch one:
% 47.87/20.93  																																																																																																					| (252) all_30_0_34 = 0
% 47.87/20.93  																																																																																																					|
% 47.87/20.93  																																																																																																						| Equations (252) can reduce 92 to:
% 47.87/20.93  																																																																																																						| (106) $false
% 47.87/20.93  																																																																																																						|
% 47.87/20.93  																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																					|-Branch two:
% 47.87/20.93  																																																																																																					| (92)  ~ (all_30_0_34 = 0)
% 47.87/20.93  																																																																																																					| (792) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.93  																																																																																																					|
% 47.87/20.93  																																																																																																						+-Applying beta-rule and splitting (220), into two cases.
% 47.87/20.93  																																																																																																						|-Branch one:
% 47.87/20.93  																																																																																																						| (232) all_22_0_26 = 0
% 47.87/20.93  																																																																																																						|
% 47.87/20.93  																																																																																																							| Equations (232) can reduce 76 to:
% 47.87/20.93  																																																																																																							| (106) $false
% 47.87/20.93  																																																																																																							|
% 47.87/20.93  																																																																																																							|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																						|-Branch two:
% 47.87/20.93  																																																																																																						| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.93  																																																																																																						| (707) 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))
% 47.87/20.93  																																																																																																						|
% 47.87/20.93  																																																																																																							+-Applying beta-rule and splitting (197), into two cases.
% 47.87/20.93  																																																																																																							|-Branch one:
% 47.87/20.93  																																																																																																							| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																							|
% 47.87/20.93  																																																																																																								| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																								| (106) $false
% 47.87/20.93  																																																																																																								|
% 47.87/20.93  																																																																																																								|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																							|-Branch two:
% 47.87/20.93  																																																																																																							| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																							| (671) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.93  																																																																																																							|
% 47.87/20.93  																																																																																																								+-Applying beta-rule and splitting (192), into two cases.
% 47.87/20.93  																																																																																																								|-Branch one:
% 47.87/20.93  																																																																																																								| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																								|
% 47.87/20.93  																																																																																																									| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																									| (106) $false
% 47.87/20.93  																																																																																																									|
% 47.87/20.93  																																																																																																									|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																								|-Branch two:
% 47.87/20.93  																																																																																																								| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																								| (659) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.93  																																																																																																								|
% 47.87/20.93  																																																																																																									+-Applying beta-rule and splitting (193), into two cases.
% 47.87/20.93  																																																																																																									|-Branch one:
% 47.87/20.93  																																																																																																									| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																									|
% 47.87/20.93  																																																																																																										| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																										| (106) $false
% 47.87/20.93  																																																																																																										|
% 47.87/20.93  																																																																																																										|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																									|-Branch two:
% 47.87/20.93  																																																																																																									| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																									| (663) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.93  																																																																																																									|
% 47.87/20.93  																																																																																																										+-Applying beta-rule and splitting (196), into two cases.
% 47.87/20.93  																																																																																																										|-Branch one:
% 47.87/20.93  																																																																																																										| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																										|
% 47.87/20.93  																																																																																																											| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																											| (106) $false
% 47.87/20.93  																																																																																																											|
% 47.87/20.93  																																																																																																											|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																										|-Branch two:
% 47.87/20.93  																																																																																																										| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																										| (683) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.93  																																																																																																										|
% 47.87/20.93  																																																																																																											+-Applying beta-rule and splitting (194), into two cases.
% 47.87/20.93  																																																																																																											|-Branch one:
% 47.87/20.93  																																																																																																											| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																											|
% 47.87/20.93  																																																																																																												| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																												| (106) $false
% 47.87/20.93  																																																																																																												|
% 47.87/20.93  																																																																																																												|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																											|-Branch two:
% 47.87/20.93  																																																																																																											| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																											| (667) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.93  																																																																																																											|
% 47.87/20.93  																																																																																																												+-Applying beta-rule and splitting (195), into two cases.
% 47.87/20.93  																																																																																																												|-Branch one:
% 47.87/20.93  																																																																																																												| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																												|
% 47.87/20.93  																																																																																																													| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																													| (106) $false
% 47.87/20.93  																																																																																																													|
% 47.87/20.93  																																																																																																													|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																												|-Branch two:
% 47.87/20.93  																																																																																																												| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																												| (675) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.93  																																																																																																												|
% 47.87/20.93  																																																																																																													+-Applying beta-rule and splitting (198), into two cases.
% 47.87/20.93  																																																																																																													|-Branch one:
% 47.87/20.93  																																																																																																													| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																													|
% 47.87/20.93  																																																																																																														| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																														| (106) $false
% 47.87/20.93  																																																																																																														|
% 47.87/20.93  																																																																																																														|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																													|-Branch two:
% 47.87/20.93  																																																																																																													| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																													| (679) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.93  																																																																																																													|
% 47.87/20.93  																																																																																																														+-Applying beta-rule and splitting (199), into two cases.
% 47.87/20.93  																																																																																																														|-Branch one:
% 47.87/20.93  																																																																																																														| (308) all_28_0_32 = 0
% 47.87/20.93  																																																																																																														|
% 47.87/20.93  																																																																																																															| Equations (308) can reduce 88 to:
% 47.87/20.93  																																																																																																															| (106) $false
% 47.87/20.93  																																																																																																															|
% 47.87/20.93  																																																																																																															|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																														|-Branch two:
% 47.87/20.93  																																																																																																														| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.93  																																																																																																														| (687) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.93  																																																																																																														|
% 47.87/20.93  																																																																																																															+-Applying beta-rule and splitting (221), into two cases.
% 47.87/20.93  																																																																																																															|-Branch one:
% 47.87/20.93  																																																																																																															| (244) all_26_0_30 = 0
% 47.87/20.93  																																																																																																															|
% 47.87/20.93  																																																																																																																| Equations (244) can reduce 84 to:
% 47.87/20.93  																																																																																																																| (106) $false
% 47.87/20.93  																																																																																																																|
% 47.87/20.93  																																																																																																																|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																															|-Branch two:
% 47.87/20.93  																																																																																																															| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.93  																																																																																																															| (1160) 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_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.93  																																																																																																															|
% 47.87/20.93  																																																																																																																+-Applying beta-rule and splitting (800), into two cases.
% 47.87/20.93  																																																																																																																|-Branch one:
% 47.87/20.93  																																																																																																																| (523) all_20_0_24 = 0
% 47.87/20.93  																																																																																																																|
% 47.87/20.93  																																																																																																																	| Equations (523) can reduce 72 to:
% 47.87/20.93  																																																																																																																	| (106) $false
% 47.87/20.93  																																																																																																																	|
% 47.87/20.93  																																																																																																																	|-The branch is then unsatisfiable
% 47.87/20.93  																																																																																																																|-Branch two:
% 47.87/20.93  																																																																																																																| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.93  																																																																																																																| (993)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.87/20.94  																																																																																																																|
% 47.87/20.94  																																																																																																																	| Instantiating (993) with all_456_0_1547 yields:
% 47.87/20.94  																																																																																																																	| (1165) (all_456_0_1547 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (all_456_0_1547 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_456_0_1547 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = all_456_0_1547)
% 47.87/20.94  																																																																																																																	|
% 47.87/20.94  																																																																																																																	+-Applying beta-rule and splitting (804), into two cases.
% 47.87/20.94  																																																																																																																	|-Branch one:
% 47.87/20.94  																																																																																																																	| (523) all_20_0_24 = 0
% 47.87/20.94  																																																																																																																	|
% 47.87/20.94  																																																																																																																		| Equations (523) can reduce 72 to:
% 47.87/20.94  																																																																																																																		| (106) $false
% 47.87/20.94  																																																																																																																		|
% 47.87/20.94  																																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																	|-Branch two:
% 47.87/20.94  																																																																																																																	| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.94  																																																																																																																	| (1169)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.94  																																																																																																																	|
% 47.87/20.94  																																																																																																																		+-Applying beta-rule and splitting (200), into two cases.
% 47.87/20.94  																																																																																																																		|-Branch one:
% 47.87/20.94  																																																																																																																		| (308) all_28_0_32 = 0
% 47.87/20.94  																																																																																																																		|
% 47.87/20.94  																																																																																																																			| Equations (308) can reduce 88 to:
% 47.87/20.94  																																																																																																																			| (106) $false
% 47.87/20.94  																																																																																																																			|
% 47.87/20.94  																																																																																																																			|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																		|-Branch two:
% 47.87/20.94  																																																																																																																		| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.94  																																																																																																																		| (1173) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.94  																																																																																																																		|
% 47.87/20.94  																																																																																																																			+-Applying beta-rule and splitting (201), into two cases.
% 47.87/20.94  																																																																																																																			|-Branch one:
% 47.87/20.94  																																																																																																																			| (308) all_28_0_32 = 0
% 47.87/20.94  																																																																																																																			|
% 47.87/20.94  																																																																																																																				| Equations (308) can reduce 88 to:
% 47.87/20.94  																																																																																																																				| (106) $false
% 47.87/20.94  																																																																																																																				|
% 47.87/20.94  																																																																																																																				|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																			|-Branch two:
% 47.87/20.94  																																																																																																																			| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.94  																																																																																																																			| (1177) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.94  																																																																																																																			|
% 47.87/20.94  																																																																																																																				+-Applying beta-rule and splitting (202), into two cases.
% 47.87/20.94  																																																																																																																				|-Branch one:
% 47.87/20.94  																																																																																																																				| (308) all_28_0_32 = 0
% 47.87/20.94  																																																																																																																				|
% 47.87/20.94  																																																																																																																					| Equations (308) can reduce 88 to:
% 47.87/20.94  																																																																																																																					| (106) $false
% 47.87/20.94  																																																																																																																					|
% 47.87/20.94  																																																																																																																					|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																				|-Branch two:
% 47.87/20.94  																																																																																																																				| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.94  																																																																																																																				| (1181) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.94  																																																																																																																				|
% 47.87/20.94  																																																																																																																					+-Applying beta-rule and splitting (203), into two cases.
% 47.87/20.94  																																																																																																																					|-Branch one:
% 47.87/20.94  																																																																																																																					| (308) all_28_0_32 = 0
% 47.87/20.94  																																																																																																																					|
% 47.87/20.94  																																																																																																																						| Equations (308) can reduce 88 to:
% 47.87/20.94  																																																																																																																						| (106) $false
% 47.87/20.94  																																																																																																																						|
% 47.87/20.94  																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																					|-Branch two:
% 47.87/20.94  																																																																																																																					| (88)  ~ (all_28_0_32 = 0)
% 47.87/20.94  																																																																																																																					| (1185) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.94  																																																																																																																					|
% 47.87/20.94  																																																																																																																						+-Applying beta-rule and splitting (207), into two cases.
% 47.87/20.94  																																																																																																																						|-Branch one:
% 47.87/20.94  																																																																																																																						| (523) all_20_0_24 = 0
% 47.87/20.94  																																																																																																																						|
% 47.87/20.94  																																																																																																																							| Equations (523) can reduce 72 to:
% 47.87/20.94  																																																																																																																							| (106) $false
% 47.87/20.94  																																																																																																																							|
% 47.87/20.94  																																																																																																																							|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																						|-Branch two:
% 47.87/20.94  																																																																																																																						| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.94  																																																																																																																						| (558) 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))
% 47.87/20.94  																																																																																																																						|
% 47.87/20.94  																																																																																																																							+-Applying beta-rule and splitting (212), into two cases.
% 47.87/20.94  																																																																																																																							|-Branch one:
% 47.87/20.94  																																																																																																																							| (252) all_30_0_34 = 0
% 47.87/20.94  																																																																																																																							|
% 47.87/20.94  																																																																																																																								| Equations (252) can reduce 92 to:
% 47.87/20.94  																																																																																																																								| (106) $false
% 47.87/20.94  																																																																																																																								|
% 47.87/20.94  																																																																																																																								|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																							|-Branch two:
% 47.87/20.94  																																																																																																																							| (92)  ~ (all_30_0_34 = 0)
% 47.87/20.94  																																																																																																																							| (832) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.94  																																																																																																																							|
% 47.87/20.94  																																																																																																																								+-Applying beta-rule and splitting (213), into two cases.
% 47.87/20.94  																																																																																																																								|-Branch one:
% 47.87/20.94  																																																																																																																								| (268) all_24_0_28 = 0
% 47.87/20.94  																																																																																																																								|
% 47.87/20.94  																																																																																																																									| Equations (268) can reduce 80 to:
% 47.87/20.94  																																																																																																																									| (106) $false
% 47.87/20.94  																																																																																																																									|
% 47.87/20.94  																																																																																																																									|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																								|-Branch two:
% 47.87/20.94  																																																																																																																								| (80)  ~ (all_24_0_28 = 0)
% 47.87/20.94  																																																																																																																								| (836) 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))
% 47.87/20.94  																																																																																																																								|
% 47.87/20.94  																																																																																																																									+-Applying beta-rule and splitting (209), into two cases.
% 47.87/20.94  																																																																																																																									|-Branch one:
% 47.87/20.94  																																																																																																																									| (252) all_30_0_34 = 0
% 47.87/20.94  																																																																																																																									|
% 47.87/20.94  																																																																																																																										| Equations (252) can reduce 92 to:
% 47.87/20.94  																																																																																																																										| (106) $false
% 47.87/20.94  																																																																																																																										|
% 47.87/20.94  																																																																																																																										|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																									|-Branch two:
% 47.87/20.94  																																																																																																																									| (92)  ~ (all_30_0_34 = 0)
% 47.87/20.94  																																																																																																																									| (1201) 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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.94  																																																																																																																									|
% 47.87/20.94  																																																																																																																										+-Applying beta-rule and splitting (153), into two cases.
% 47.87/20.94  																																																																																																																										|-Branch one:
% 47.87/20.94  																																																																																																																										| (252) all_30_0_34 = 0
% 47.87/20.94  																																																																																																																										|
% 47.87/20.94  																																																																																																																											| Equations (252) can reduce 92 to:
% 47.87/20.94  																																																																																																																											| (106) $false
% 47.87/20.94  																																																																																																																											|
% 47.87/20.94  																																																																																																																											|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																										|-Branch two:
% 47.87/20.94  																																																																																																																										| (92)  ~ (all_30_0_34 = 0)
% 47.87/20.94  																																																																																																																										| (840) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.87/20.94  																																																																																																																										|
% 47.87/20.94  																																																																																																																											+-Applying beta-rule and splitting (214), into two cases.
% 47.87/20.94  																																																																																																																											|-Branch one:
% 47.87/20.94  																																																																																																																											| (268) all_24_0_28 = 0
% 47.87/20.94  																																																																																																																											|
% 47.87/20.94  																																																																																																																												| Equations (268) can reduce 80 to:
% 47.87/20.94  																																																																																																																												| (106) $false
% 47.87/20.94  																																																																																																																												|
% 47.87/20.94  																																																																																																																												|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																											|-Branch two:
% 47.87/20.94  																																																																																																																											| (80)  ~ (all_24_0_28 = 0)
% 47.87/20.94  																																																																																																																											| (844) 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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.94  																																																																																																																											|
% 47.87/20.94  																																																																																																																												+-Applying beta-rule and splitting (215), into two cases.
% 47.87/20.94  																																																																																																																												|-Branch one:
% 47.87/20.94  																																																																																																																												| (268) all_24_0_28 = 0
% 47.87/20.94  																																																																																																																												|
% 47.87/20.94  																																																																																																																													| Equations (268) can reduce 80 to:
% 47.87/20.94  																																																																																																																													| (106) $false
% 47.87/20.94  																																																																																																																													|
% 47.87/20.94  																																																																																																																													|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																												|-Branch two:
% 47.87/20.94  																																																																																																																												| (80)  ~ (all_24_0_28 = 0)
% 47.87/20.94  																																																																																																																												| (848) 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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.94  																																																																																																																												|
% 47.87/20.94  																																																																																																																													+-Applying beta-rule and splitting (255), into two cases.
% 47.87/20.94  																																																																																																																													|-Branch one:
% 47.87/20.94  																																																																																																																													| (232) all_22_0_26 = 0
% 47.87/20.94  																																																																																																																													|
% 47.87/20.94  																																																																																																																														| Equations (232) can reduce 76 to:
% 47.87/20.94  																																																																																																																														| (106) $false
% 47.87/20.94  																																																																																																																														|
% 47.87/20.94  																																																																																																																														|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																													|-Branch two:
% 47.87/20.94  																																																																																																																													| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.94  																																																																																																																													| (691)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.87/20.94  																																																																																																																													|
% 47.87/20.94  																																																																																																																														+-Applying beta-rule and splitting (671), into two cases.
% 47.87/20.94  																																																																																																																														|-Branch one:
% 47.87/20.94  																																																																																																																														| (232) all_22_0_26 = 0
% 47.87/20.94  																																																																																																																														|
% 47.87/20.94  																																																																																																																															| Equations (232) can reduce 76 to:
% 47.87/20.94  																																																																																																																															| (106) $false
% 47.87/20.94  																																																																																																																															|
% 47.87/20.94  																																																																																																																															|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																														|-Branch two:
% 47.87/20.94  																																																																																																																														| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.94  																																																																																																																														| (711)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.94  																																																																																																																														|
% 47.87/20.94  																																																																																																																															+-Applying beta-rule and splitting (663), into two cases.
% 47.87/20.94  																																																																																																																															|-Branch one:
% 47.87/20.94  																																																																																																																															| (268) all_24_0_28 = 0
% 47.87/20.94  																																																																																																																															|
% 47.87/20.94  																																																																																																																																| Equations (268) can reduce 80 to:
% 47.87/20.94  																																																																																																																																| (106) $false
% 47.87/20.94  																																																																																																																																|
% 47.87/20.94  																																																																																																																																|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																															|-Branch two:
% 47.87/20.94  																																																																																																																															| (80)  ~ (all_24_0_28 = 0)
% 47.87/20.94  																																																																																																																															| (884)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.94  																																																																																																																															|
% 47.87/20.94  																																																																																																																																+-Applying beta-rule and splitting (667), into two cases.
% 47.87/20.94  																																																																																																																																|-Branch one:
% 47.87/20.94  																																																																																																																																| (268) all_24_0_28 = 0
% 47.87/20.94  																																																																																																																																|
% 47.87/20.94  																																																																																																																																	| Equations (268) can reduce 80 to:
% 47.87/20.94  																																																																																																																																	| (106) $false
% 47.87/20.94  																																																																																																																																	|
% 47.87/20.94  																																																																																																																																	|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																|-Branch two:
% 47.87/20.94  																																																																																																																																| (80)  ~ (all_24_0_28 = 0)
% 47.87/20.94  																																																																																																																																| (888)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.94  																																																																																																																																|
% 47.87/20.94  																																																																																																																																	+-Applying beta-rule and splitting (679), into two cases.
% 47.87/20.94  																																																																																																																																	|-Branch one:
% 47.87/20.94  																																																																																																																																	| (232) all_22_0_26 = 0
% 47.87/20.94  																																																																																																																																	|
% 47.87/20.94  																																																																																																																																		| Equations (232) can reduce 76 to:
% 47.87/20.94  																																																																																																																																		| (106) $false
% 47.87/20.94  																																																																																																																																		|
% 47.87/20.94  																																																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																	|-Branch two:
% 47.87/20.94  																																																																																																																																	| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.94  																																																																																																																																	| (715)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_22_1_27) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.94  																																																																																																																																	|
% 47.87/20.94  																																																																																																																																		+-Applying beta-rule and splitting (1165), into two cases.
% 47.87/20.94  																																																																																																																																		|-Branch one:
% 47.87/20.94  																																																																																																																																		| (1234) (all_456_0_1547 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (all_456_0_1547 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0)
% 47.87/20.94  																																																																																																																																		|
% 47.87/20.94  																																																																																																																																			+-Applying beta-rule and splitting (1234), into two cases.
% 47.87/20.94  																																																																																																																																			|-Branch one:
% 47.87/20.94  																																																																																																																																			| (1235) all_456_0_1547 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0
% 47.87/20.94  																																																																																																																																			|
% 47.87/20.94  																																																																																																																																				| Applying alpha-rule on (1235) yields:
% 47.87/20.94  																																																																																																																																				| (1236) all_456_0_1547 = 0
% 47.87/20.94  																																																																																																																																				| (1237) apart_point_and_line(all_0_3_3, all_28_1_33) = 0
% 47.87/20.94  																																																																																																																																				|
% 47.87/20.94  																																																																																																																																				| Instantiating formula (42) with all_0_3_3, all_28_1_33, 0, all_30_0_34 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_28_1_33) = 0, yields:
% 47.87/20.94  																																																																																																																																				| (252) all_30_0_34 = 0
% 47.87/20.94  																																																																																																																																				|
% 47.87/20.94  																																																																																																																																				| Equations (252) can reduce 92 to:
% 47.87/20.94  																																																																																																																																				| (106) $false
% 47.87/20.94  																																																																																																																																				|
% 47.87/20.94  																																																																																																																																				|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																			|-Branch two:
% 47.87/20.94  																																																																																																																																			| (1240) all_456_0_1547 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 47.87/20.94  																																																																																																																																			|
% 47.87/20.94  																																																																																																																																				| Applying alpha-rule on (1240) yields:
% 47.87/20.94  																																																																																																																																				| (1236) all_456_0_1547 = 0
% 47.87/20.94  																																																																																																																																				| (510) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 47.87/20.94  																																																																																																																																				|
% 47.87/20.94  																																																																																																																																				+-Applying beta-rule and splitting (355), into two cases.
% 47.87/20.94  																																																																																																																																				|-Branch one:
% 47.87/20.94  																																																																																																																																				| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																				|
% 47.87/20.94  																																																																																																																																					| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																					| (106) $false
% 47.87/20.94  																																																																																																																																					|
% 47.87/20.94  																																																																																																																																					|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																				|-Branch two:
% 47.87/20.94  																																																																																																																																				| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																				| (574)  ? [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))
% 47.87/20.94  																																																																																																																																				|
% 47.87/20.94  																																																																																																																																					+-Applying beta-rule and splitting (383), into two cases.
% 47.87/20.94  																																																																																																																																					|-Branch one:
% 47.87/20.94  																																																																																																																																					| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																					|
% 47.87/20.94  																																																																																																																																						| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																						| (106) $false
% 47.87/20.94  																																																																																																																																						|
% 47.87/20.94  																																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																					|-Branch two:
% 47.87/20.94  																																																																																																																																					| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																					| (590)  ? [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))
% 47.87/20.94  																																																																																																																																					|
% 47.87/20.94  																																																																																																																																						+-Applying beta-rule and splitting (538), into two cases.
% 47.87/20.94  																																																																																																																																						|-Branch one:
% 47.87/20.94  																																																																																																																																						| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																						|
% 47.87/20.94  																																																																																																																																							| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																							| (106) $false
% 47.87/20.94  																																																																																																																																							|
% 47.87/20.94  																																																																																																																																							|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																						|-Branch two:
% 47.87/20.94  																																																																																																																																						| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																						| (610)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.94  																																																																																																																																						|
% 47.87/20.94  																																																																																																																																							+-Applying beta-rule and splitting (542), into two cases.
% 47.87/20.94  																																																																																																																																							|-Branch one:
% 47.87/20.94  																																																																																																																																							| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																							|
% 47.87/20.94  																																																																																																																																								| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																								| (106) $false
% 47.87/20.94  																																																																																																																																								|
% 47.87/20.94  																																																																																																																																								|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																							|-Branch two:
% 47.87/20.94  																																																																																																																																							| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																							| (614)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.87/20.94  																																																																																																																																							|
% 47.87/20.94  																																																																																																																																								+-Applying beta-rule and splitting (347), into two cases.
% 47.87/20.94  																																																																																																																																								|-Branch one:
% 47.87/20.94  																																																																																																																																								| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																								|
% 47.87/20.94  																																																																																																																																									| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																									| (106) $false
% 47.87/20.94  																																																																																																																																									|
% 47.87/20.94  																																																																																																																																									|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																								|-Branch two:
% 47.87/20.94  																																																																																																																																								| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																								| (570)  ? [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))
% 47.87/20.94  																																																																																																																																								|
% 47.87/20.94  																																																																																																																																									+-Applying beta-rule and splitting (359), into two cases.
% 47.87/20.94  																																																																																																																																									|-Branch one:
% 47.87/20.94  																																																																																																																																									| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																									|
% 47.87/20.94  																																																																																																																																										| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																										| (106) $false
% 47.87/20.94  																																																																																																																																										|
% 47.87/20.94  																																																																																																																																										|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																									|-Branch two:
% 47.87/20.94  																																																																																																																																									| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																									| (578)  ? [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_22_1_27, all_0_2_2) = v0))
% 47.87/20.94  																																																																																																																																									|
% 47.87/20.94  																																																																																																																																										+-Applying beta-rule and splitting (371), into two cases.
% 47.87/20.94  																																																																																																																																										|-Branch one:
% 47.87/20.94  																																																																																																																																										| (105) all_0_1_1 = 0
% 47.87/20.94  																																																																																																																																										|
% 47.87/20.94  																																																																																																																																											| Equations (105) can reduce 33 to:
% 47.87/20.94  																																																																																																																																											| (106) $false
% 47.87/20.94  																																																																																																																																											|
% 47.87/20.94  																																																																																																																																											|-The branch is then unsatisfiable
% 47.87/20.94  																																																																																																																																										|-Branch two:
% 47.87/20.94  																																																																																																																																										| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.94  																																																																																																																																										| (586)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.87/20.95  																																																																																																																																										|
% 47.87/20.95  																																																																																																																																											+-Applying beta-rule and splitting (411), into two cases.
% 47.87/20.95  																																																																																																																																											|-Branch one:
% 47.87/20.95  																																																																																																																																											| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																											|
% 47.87/20.95  																																																																																																																																												| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																												| (106) $false
% 47.87/20.95  																																																																																																																																												|
% 47.87/20.95  																																																																																																																																												|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																											|-Branch two:
% 47.87/20.95  																																																																																																																																											| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																											| (598)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.95  																																																																																																																																											|
% 47.87/20.95  																																																																																																																																												+-Applying beta-rule and splitting (558), into two cases.
% 47.87/20.95  																																																																																																																																												|-Branch one:
% 47.87/20.95  																																																																																																																																												| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																												|
% 47.87/20.95  																																																																																																																																													| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																													| (106) $false
% 47.87/20.95  																																																																																																																																													|
% 47.87/20.95  																																																																																																																																													|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																												|-Branch two:
% 47.87/20.95  																																																																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																												| (618)  ? [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))
% 47.87/20.95  																																																																																																																																												|
% 47.87/20.95  																																																																																																																																													+-Applying beta-rule and splitting (363), into two cases.
% 47.87/20.95  																																																																																																																																													|-Branch one:
% 47.87/20.95  																																																																																																																																													| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																													|
% 47.87/20.95  																																																																																																																																														| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																														| (106) $false
% 47.87/20.95  																																																																																																																																														|
% 47.87/20.95  																																																																																																																																														|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																													|-Branch two:
% 47.87/20.95  																																																																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																													| (582)  ? [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))
% 47.87/20.95  																																																																																																																																													|
% 47.87/20.95  																																																																																																																																														+-Applying beta-rule and splitting (415), into two cases.
% 47.87/20.95  																																																																																																																																														|-Branch one:
% 47.87/20.95  																																																																																																																																														| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																														|
% 47.87/20.95  																																																																																																																																															| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																															| (106) $false
% 47.87/20.95  																																																																																																																																															|
% 47.87/20.95  																																																																																																																																															|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																														|-Branch two:
% 47.87/20.95  																																																																																																																																														| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																														| (602)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.95  																																																																																																																																														|
% 47.87/20.95  																																																																																																																																															+-Applying beta-rule and splitting (423), into two cases.
% 47.87/20.95  																																																																																																																																															|-Branch one:
% 47.87/20.95  																																																																																																																																															| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																															|
% 47.87/20.95  																																																																																																																																																| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																																| (106) $false
% 47.87/20.95  																																																																																																																																																|
% 47.87/20.95  																																																																																																																																																|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																															|-Branch two:
% 47.87/20.95  																																																																																																																																															| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																															| (606)  ? [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))
% 47.87/20.95  																																																																																																																																															|
% 47.87/20.95  																																																																																																																																																+-Applying beta-rule and splitting (530), into two cases.
% 47.87/20.95  																																																																																																																																																|-Branch one:
% 47.87/20.95  																																																																																																																																																| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																																|
% 47.87/20.95  																																																																																																																																																	| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																																	| (106) $false
% 47.87/20.95  																																																																																																																																																	|
% 47.87/20.95  																																																																																																																																																	|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																|-Branch two:
% 47.87/20.95  																																																																																																																																																| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																																| (562)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.95  																																																																																																																																																|
% 47.87/20.95  																																																																																																																																																	+-Applying beta-rule and splitting (534), into two cases.
% 47.87/20.95  																																																																																																																																																	|-Branch one:
% 47.87/20.95  																																																																																																																																																	| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																																	|
% 47.87/20.95  																																																																																																																																																		| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																																		| (106) $false
% 47.87/20.95  																																																																																																																																																		|
% 47.87/20.95  																																																																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																	|-Branch two:
% 47.87/20.95  																																																																																																																																																	| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																																	| (566)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.87/20.95  																																																																																																																																																	|
% 47.87/20.95  																																																																																																																																																		| Instantiating formula (42) 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:
% 47.87/20.95  																																																																																																																																																		| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																																		|
% 47.87/20.95  																																																																																																																																																		| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																																		| (106) $false
% 47.87/20.95  																																																																																																																																																		|
% 47.87/20.95  																																																																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																		|-Branch two:
% 47.87/20.95  																																																																																																																																		| (1301)  ~ (all_456_0_1547 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = all_456_0_1547
% 47.87/20.95  																																																																																																																																		|
% 47.87/20.95  																																																																																																																																			| Applying alpha-rule on (1301) yields:
% 47.87/20.95  																																																																																																																																			| (1302)  ~ (all_456_0_1547 = 0)
% 47.87/20.95  																																																																																																																																			| (1303) distinct_lines(all_28_1_33, all_0_2_2) = all_456_0_1547
% 47.87/20.95  																																																																																																																																			|
% 47.87/20.95  																																																																																																																																			+-Applying beta-rule and splitting (216), into two cases.
% 47.87/20.95  																																																																																																																																			|-Branch one:
% 47.87/20.95  																																																																																																																																			| (268) all_24_0_28 = 0
% 47.87/20.95  																																																																																																																																			|
% 47.87/20.95  																																																																																																																																				| Equations (268) can reduce 80 to:
% 47.87/20.95  																																																																																																																																				| (106) $false
% 47.87/20.95  																																																																																																																																				|
% 47.87/20.95  																																																																																																																																				|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																			|-Branch two:
% 47.87/20.95  																																																																																																																																			| (80)  ~ (all_24_0_28 = 0)
% 47.87/20.95  																																																																																																																																			| (796) 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_5_5, all_0_3_3) = v0))
% 47.87/20.95  																																																																																																																																			|
% 47.87/20.95  																																																																																																																																				+-Applying beta-rule and splitting (217), into two cases.
% 47.87/20.95  																																																																																																																																				|-Branch one:
% 47.87/20.95  																																																																																																																																				| (232) all_22_0_26 = 0
% 47.87/20.95  																																																																																																																																				|
% 47.87/20.95  																																																																																																																																					| Equations (232) can reduce 76 to:
% 47.87/20.95  																																																																																																																																					| (106) $false
% 47.87/20.95  																																																																																																																																					|
% 47.87/20.95  																																																																																																																																					|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																				|-Branch two:
% 47.87/20.95  																																																																																																																																				| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.95  																																																																																																																																				| (695) 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))
% 47.87/20.95  																																																																																																																																				|
% 47.87/20.95  																																																																																																																																					+-Applying beta-rule and splitting (218), into two cases.
% 47.87/20.95  																																																																																																																																					|-Branch one:
% 47.87/20.95  																																																																																																																																					| (232) all_22_0_26 = 0
% 47.87/20.95  																																																																																																																																					|
% 47.87/20.95  																																																																																																																																						| Equations (232) can reduce 76 to:
% 47.87/20.95  																																																																																																																																						| (106) $false
% 47.87/20.95  																																																																																																																																						|
% 47.87/20.95  																																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																					|-Branch two:
% 47.87/20.95  																																																																																																																																					| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.95  																																																																																																																																					| (699) 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))
% 47.87/20.95  																																																																																																																																					|
% 47.87/20.95  																																																																																																																																						+-Applying beta-rule and splitting (219), into two cases.
% 47.87/20.95  																																																																																																																																						|-Branch one:
% 47.87/20.95  																																																																																																																																						| (232) all_22_0_26 = 0
% 47.87/20.95  																																																																																																																																						|
% 47.87/20.95  																																																																																																																																							| Equations (232) can reduce 76 to:
% 47.87/20.95  																																																																																																																																							| (106) $false
% 47.87/20.95  																																																																																																																																							|
% 47.87/20.95  																																																																																																																																							|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																						|-Branch two:
% 47.87/20.95  																																																																																																																																						| (76)  ~ (all_22_0_26 = 0)
% 47.87/20.95  																																																																																																																																						| (703) 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))
% 47.87/20.95  																																																																																																																																						|
% 47.87/20.95  																																																																																																																																							+-Applying beta-rule and splitting (355), into two cases.
% 47.87/20.95  																																																																																																																																							|-Branch one:
% 47.87/20.95  																																																																																																																																							| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																							|
% 47.87/20.95  																																																																																																																																								| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																								| (106) $false
% 47.87/20.95  																																																																																																																																								|
% 47.87/20.95  																																																																																																																																								|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																							|-Branch two:
% 47.87/20.95  																																																																																																																																							| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																							| (574)  ? [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))
% 47.87/20.95  																																																																																																																																							|
% 47.87/20.95  																																																																																																																																								+-Applying beta-rule and splitting (383), into two cases.
% 47.87/20.95  																																																																																																																																								|-Branch one:
% 47.87/20.95  																																																																																																																																								| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																								|
% 47.87/20.95  																																																																																																																																									| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																									| (106) $false
% 47.87/20.95  																																																																																																																																									|
% 47.87/20.95  																																																																																																																																									|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																								|-Branch two:
% 47.87/20.95  																																																																																																																																								| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																								| (590)  ? [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))
% 47.87/20.95  																																																																																																																																								|
% 47.87/20.95  																																																																																																																																									+-Applying beta-rule and splitting (788), into two cases.
% 47.87/20.95  																																																																																																																																									|-Branch one:
% 47.87/20.95  																																																																																																																																									| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																									|
% 47.87/20.95  																																																																																																																																										| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																										| (106) $false
% 47.87/20.95  																																																																																																																																										|
% 47.87/20.95  																																																																																																																																										|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																									|-Branch two:
% 47.87/20.95  																																																																																																																																									| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																									| (1331)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.95  																																																																																																																																									|
% 47.87/20.95  																																																																																																																																										+-Applying beta-rule and splitting (792), into two cases.
% 47.87/20.95  																																																																																																																																										|-Branch one:
% 47.87/20.95  																																																																																																																																										| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																										|
% 47.87/20.95  																																																																																																																																											| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																											| (106) $false
% 47.87/20.95  																																																																																																																																											|
% 47.87/20.95  																																																																																																																																											|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																										|-Branch two:
% 47.87/20.95  																																																																																																																																										| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																										| (1335)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.95  																																																																																																																																										|
% 47.87/20.95  																																																																																																																																											+-Applying beta-rule and splitting (707), into two cases.
% 47.87/20.95  																																																																																																																																											|-Branch one:
% 47.87/20.95  																																																																																																																																											| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																											|
% 47.87/20.95  																																																																																																																																												| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																												| (106) $false
% 47.87/20.95  																																																																																																																																												|
% 47.87/20.95  																																																																																																																																												|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																											|-Branch two:
% 47.87/20.95  																																																																																																																																											| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																											| (989)  ? [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))
% 47.87/20.95  																																																																																																																																											|
% 47.87/20.95  																																																																																																																																												+-Applying beta-rule and splitting (1160), into two cases.
% 47.87/20.95  																																																																																																																																												|-Branch one:
% 47.87/20.95  																																																																																																																																												| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																												|
% 47.87/20.95  																																																																																																																																													| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																													| (106) $false
% 47.87/20.95  																																																																																																																																													|
% 47.87/20.95  																																																																																																																																													|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																												|-Branch two:
% 47.87/20.95  																																																																																																																																												| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																												| (1343)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.95  																																																																																																																																												|
% 47.87/20.95  																																																																																																																																													+-Applying beta-rule and splitting (1177), into two cases.
% 47.87/20.95  																																																																																																																																													|-Branch one:
% 47.87/20.95  																																																																																																																																													| (244) all_26_0_30 = 0
% 47.87/20.95  																																																																																																																																													|
% 47.87/20.95  																																																																																																																																														| Equations (244) can reduce 84 to:
% 47.87/20.95  																																																																																																																																														| (106) $false
% 47.87/20.95  																																																																																																																																														|
% 47.87/20.95  																																																																																																																																														|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																													|-Branch two:
% 47.87/20.95  																																																																																																																																													| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.95  																																																																																																																																													| (1347)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.95  																																																																																																																																													|
% 47.87/20.95  																																																																																																																																														+-Applying beta-rule and splitting (844), into two cases.
% 47.87/20.95  																																																																																																																																														|-Branch one:
% 47.87/20.95  																																																																																																																																														| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																														|
% 47.87/20.95  																																																																																																																																															| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																															| (106) $false
% 47.87/20.95  																																																																																																																																															|
% 47.87/20.95  																																																																																																																																															|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																														|-Branch two:
% 47.87/20.95  																																																																																																																																														| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																														| (1351)  ? [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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 47.87/20.95  																																																																																																																																														|
% 47.87/20.95  																																																																																																																																															+-Applying beta-rule and splitting (538), into two cases.
% 47.87/20.95  																																																																																																																																															|-Branch one:
% 47.87/20.95  																																																																																																																																															| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																															|
% 47.87/20.95  																																																																																																																																																| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																																| (106) $false
% 47.87/20.95  																																																																																																																																																|
% 47.87/20.95  																																																																																																																																																|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																															|-Branch two:
% 47.87/20.95  																																																																																																																																															| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																															| (610)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.95  																																																																																																																																															|
% 47.87/20.95  																																																																																																																																																+-Applying beta-rule and splitting (639), into two cases.
% 47.87/20.95  																																																																																																																																																|-Branch one:
% 47.87/20.95  																																																																																																																																																| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																																|
% 47.87/20.95  																																																																																																																																																	| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																																	| (106) $false
% 47.87/20.95  																																																																																																																																																	|
% 47.87/20.95  																																																																																																																																																	|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																|-Branch two:
% 47.87/20.95  																																																																																																																																																| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																																| (969)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.87/20.95  																																																																																																																																																|
% 47.87/20.95  																																																																																																																																																	+-Applying beta-rule and splitting (836), into two cases.
% 47.87/20.95  																																																																																																																																																	|-Branch one:
% 47.87/20.95  																																																																																																																																																	| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																																	|
% 47.87/20.95  																																																																																																																																																		| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																																		| (106) $false
% 47.87/20.95  																																																																																																																																																		|
% 47.87/20.95  																																																																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																	|-Branch two:
% 47.87/20.95  																																																																																																																																																	| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																																	| (1363)  ? [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))
% 47.87/20.95  																																																																																																																																																	|
% 47.87/20.95  																																																																																																																																																		+-Applying beta-rule and splitting (627), into two cases.
% 47.87/20.95  																																																																																																																																																		|-Branch one:
% 47.87/20.95  																																																																																																																																																		| (523) all_20_0_24 = 0
% 47.87/20.95  																																																																																																																																																		|
% 47.87/20.95  																																																																																																																																																			| Equations (523) can reduce 72 to:
% 47.87/20.95  																																																																																																																																																			| (106) $false
% 47.87/20.95  																																																																																																																																																			|
% 47.87/20.95  																																																																																																																																																			|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																		|-Branch two:
% 47.87/20.95  																																																																																																																																																		| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.95  																																																																																																																																																		| (566)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.87/20.95  																																																																																																																																																		|
% 47.87/20.95  																																																																																																																																																			+-Applying beta-rule and splitting (1173), into two cases.
% 47.87/20.95  																																																																																																																																																			|-Branch one:
% 47.87/20.95  																																																																																																																																																			| (244) all_26_0_30 = 0
% 47.87/20.95  																																																																																																																																																			|
% 47.87/20.95  																																																																																																																																																				| Equations (244) can reduce 84 to:
% 47.87/20.95  																																																																																																																																																				| (106) $false
% 47.87/20.95  																																																																																																																																																				|
% 47.87/20.95  																																																																																																																																																				|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																			|-Branch two:
% 47.87/20.95  																																																																																																																																																			| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.95  																																																																																																																																																			| (1371)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.95  																																																																																																																																																			|
% 47.87/20.95  																																																																																																																																																				+-Applying beta-rule and splitting (558), into two cases.
% 47.87/20.95  																																																																																																																																																				|-Branch one:
% 47.87/20.95  																																																																																																																																																				| (105) all_0_1_1 = 0
% 47.87/20.95  																																																																																																																																																				|
% 47.87/20.95  																																																																																																																																																					| Equations (105) can reduce 33 to:
% 47.87/20.95  																																																																																																																																																					| (106) $false
% 47.87/20.95  																																																																																																																																																					|
% 47.87/20.95  																																																																																																																																																					|-The branch is then unsatisfiable
% 47.87/20.95  																																																																																																																																																				|-Branch two:
% 47.87/20.95  																																																																																																																																																				| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.95  																																																																																																																																																				| (618)  ? [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))
% 47.87/20.96  																																																																																																																																																				|
% 47.87/20.96  																																																																																																																																																					+-Applying beta-rule and splitting (1201), into two cases.
% 47.87/20.96  																																																																																																																																																					|-Branch one:
% 47.87/20.96  																																																																																																																																																					| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																						| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																						| (106) $false
% 47.87/20.96  																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																					|-Branch two:
% 47.87/20.96  																																																																																																																																																					| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																					| (1379)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.96  																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																						+-Applying beta-rule and splitting (848), into two cases.
% 47.87/20.96  																																																																																																																																																						|-Branch one:
% 47.87/20.96  																																																																																																																																																						| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																							| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																							| (106) $false
% 47.87/20.96  																																																																																																																																																							|
% 47.87/20.96  																																																																																																																																																							|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																						|-Branch two:
% 47.87/20.96  																																																																																																																																																						| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																						| (1383)  ? [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_0_2_2, all_22_1_27) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.96  																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																							+-Applying beta-rule and splitting (796), into two cases.
% 47.87/20.96  																																																																																																																																																							|-Branch one:
% 47.87/20.96  																																																																																																																																																							| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																							|
% 47.87/20.96  																																																																																																																																																								| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																								| (106) $false
% 47.87/20.96  																																																																																																																																																								|
% 47.87/20.96  																																																																																																																																																								|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																							|-Branch two:
% 47.87/20.96  																																																																																																																																																							| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																							| (1387)  ? [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_5_5, all_0_3_3) = v0))
% 47.87/20.96  																																																																																																																																																							|
% 47.87/20.96  																																																																																																																																																								+-Applying beta-rule and splitting (695), into two cases.
% 47.87/20.96  																																																																																																																																																								|-Branch one:
% 47.87/20.96  																																																																																																																																																								| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																								|
% 47.87/20.96  																																																																																																																																																									| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																									| (106) $false
% 47.87/20.96  																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																									|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																								|-Branch two:
% 47.87/20.96  																																																																																																																																																								| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																								| (1391)  ? [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))
% 47.87/20.96  																																																																																																																																																								|
% 47.87/20.96  																																																																																																																																																									+-Applying beta-rule and splitting (699), into two cases.
% 47.87/20.96  																																																																																																																																																									|-Branch one:
% 47.87/20.96  																																																																																																																																																									| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																										| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																										| (106) $false
% 47.87/20.96  																																																																																																																																																										|
% 47.87/20.96  																																																																																																																																																										|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																									|-Branch two:
% 47.87/20.96  																																																																																																																																																									| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																									| (1395)  ? [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))
% 47.87/20.96  																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																										+-Applying beta-rule and splitting (703), into two cases.
% 47.87/20.96  																																																																																																																																																										|-Branch one:
% 47.87/20.96  																																																																																																																																																										| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																										|
% 47.87/20.96  																																																																																																																																																											| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																											| (106) $false
% 47.87/20.96  																																																																																																																																																											|
% 47.87/20.96  																																																																																																																																																											|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																										|-Branch two:
% 47.87/20.96  																																																																																																																																																										| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																										| (1399)  ? [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))
% 47.87/20.96  																																																																																																																																																										|
% 47.87/20.96  																																																																																																																																																											+-Applying beta-rule and splitting (399), into two cases.
% 47.87/20.96  																																																																																																																																																											|-Branch one:
% 47.87/20.96  																																																																																																																																																											| (244) all_26_0_30 = 0
% 47.87/20.96  																																																																																																																																																											|
% 47.87/20.96  																																																																																																																																																												| Equations (244) can reduce 84 to:
% 47.87/20.96  																																																																																																																																																												| (106) $false
% 47.87/20.96  																																																																																																																																																												|
% 47.87/20.96  																																																																																																																																																												|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																											|-Branch two:
% 47.87/20.96  																																																																																																																																																											| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.96  																																																																																																																																																											| (1403)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 47.87/20.96  																																																																																																																																																											|
% 47.87/20.96  																																																																																																																																																												+-Applying beta-rule and splitting (423), into two cases.
% 47.87/20.96  																																																																																																																																																												|-Branch one:
% 47.87/20.96  																																																																																																																																																												| (105) all_0_1_1 = 0
% 47.87/20.96  																																																																																																																																																												|
% 47.87/20.96  																																																																																																																																																													| Equations (105) can reduce 33 to:
% 47.87/20.96  																																																																																																																																																													| (106) $false
% 47.87/20.96  																																																																																																																																																													|
% 47.87/20.96  																																																																																																																																																													|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																												|-Branch two:
% 47.87/20.96  																																																																																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.96  																																																																																																																																																												| (606)  ? [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))
% 47.87/20.96  																																																																																																																																																												|
% 47.87/20.96  																																																																																																																																																													+-Applying beta-rule and splitting (530), into two cases.
% 47.87/20.96  																																																																																																																																																													|-Branch one:
% 47.87/20.96  																																																																																																																																																													| (105) all_0_1_1 = 0
% 47.87/20.96  																																																																																																																																																													|
% 47.87/20.96  																																																																																																																																																														| Equations (105) can reduce 33 to:
% 47.87/20.96  																																																																																																																																																														| (106) $false
% 47.87/20.96  																																																																																																																																																														|
% 47.87/20.96  																																																																																																																																																														|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																													|-Branch two:
% 47.87/20.96  																																																																																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.96  																																																																																																																																																													| (562)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.96  																																																																																																																																																													|
% 47.87/20.96  																																																																																																																																																														+-Applying beta-rule and splitting (534), into two cases.
% 47.87/20.96  																																																																																																																																																														|-Branch one:
% 47.87/20.96  																																																																																																																																																														| (105) all_0_1_1 = 0
% 47.87/20.96  																																																																																																																																																														|
% 47.87/20.96  																																																																																																																																																															| Equations (105) can reduce 33 to:
% 47.87/20.96  																																																																																																																																																															| (106) $false
% 47.87/20.96  																																																																																																																																																															|
% 47.87/20.96  																																																																																																																																																															|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																														|-Branch two:
% 47.87/20.96  																																																																																																																																																														| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.96  																																																																																																																																																														| (566)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0))
% 47.87/20.96  																																																																																																																																																														|
% 47.87/20.96  																																																																																																																																																															+-Applying beta-rule and splitting (631), into two cases.
% 47.87/20.96  																																																																																																																																																															|-Branch one:
% 47.87/20.96  																																																																																																																																																															| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																															|
% 47.87/20.96  																																																																																																																																																																| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																																| (106) $false
% 47.87/20.96  																																																																																																																																																																|
% 47.87/20.96  																																																																																																																																																																|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																															|-Branch two:
% 47.87/20.96  																																																																																																																																																															| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																															| (562)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0))
% 47.87/20.96  																																																																																																																																																															|
% 47.87/20.96  																																																																																																																																																																+-Applying beta-rule and splitting (635), into two cases.
% 47.87/20.96  																																																																																																																																																																|-Branch one:
% 47.87/20.96  																																																																																																																																																																| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																																|
% 47.87/20.96  																																																																																																																																																																	| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																																	| (106) $false
% 47.87/20.96  																																																																																																																																																																	|
% 47.87/20.96  																																																																																																																																																																	|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																|-Branch two:
% 47.87/20.96  																																																																																																																																																																| (72)  ~ (all_20_0_24 = 0)
% 47.87/20.96  																																																																																																																																																																| (1423)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 47.87/20.96  																																																																																																																																																																|
% 47.87/20.96  																																																																																																																																																																	+-Applying beta-rule and splitting (1181), into two cases.
% 47.87/20.96  																																																																																																																																																																	|-Branch one:
% 47.87/20.96  																																																																																																																																																																	| (244) all_26_0_30 = 0
% 47.87/20.96  																																																																																																																																																																	|
% 47.87/20.96  																																																																																																																																																																		| Equations (244) can reduce 84 to:
% 47.87/20.96  																																																																																																																																																																		| (106) $false
% 47.87/20.96  																																																																																																																																																																		|
% 47.87/20.96  																																																																																																																																																																		|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																	|-Branch two:
% 47.87/20.96  																																																																																																																																																																	| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.96  																																																																																																																																																																	| (1427)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 47.87/20.96  																																																																																																																																																																	|
% 47.87/20.96  																																																																																																																																																																		+-Applying beta-rule and splitting (1185), into two cases.
% 47.87/20.96  																																																																																																																																																																		|-Branch one:
% 47.87/20.96  																																																																																																																																																																		| (244) all_26_0_30 = 0
% 47.87/20.96  																																																																																																																																																																		|
% 47.87/20.96  																																																																																																																																																																			| Equations (244) can reduce 84 to:
% 47.87/20.96  																																																																																																																																																																			| (106) $false
% 47.87/20.96  																																																																																																																																																																			|
% 47.87/20.96  																																																																																																																																																																			|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																		|-Branch two:
% 47.87/20.96  																																																																																																																																																																		| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.96  																																																																																																																																																																		| (1431)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 47.87/20.96  																																																																																																																																																																		|
% 47.87/20.96  																																																																																																																																																																			+-Applying beta-rule and splitting (1087), into two cases.
% 47.87/20.96  																																																																																																																																																																			|-Branch one:
% 47.87/20.96  																																																																																																																																																																			| (1432) (all_382_0_1266 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (all_382_0_1266 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | ( ~ (all_382_0_1266 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266)
% 47.87/20.96  																																																																																																																																																																			|
% 47.87/20.96  																																																																																																																																																																				+-Applying beta-rule and splitting (1432), into two cases.
% 47.87/20.96  																																																																																																																																																																				|-Branch one:
% 47.87/20.96  																																																																																																																																																																				| (1433) (all_382_0_1266 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (all_382_0_1266 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 47.87/20.96  																																																																																																																																																																				|
% 47.87/20.96  																																																																																																																																																																					+-Applying beta-rule and splitting (1433), into two cases.
% 47.87/20.96  																																																																																																																																																																					|-Branch one:
% 47.87/20.96  																																																																																																																																																																					| (1434) all_382_0_1266 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0
% 47.87/20.96  																																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																																						| Applying alpha-rule on (1434) yields:
% 47.87/20.96  																																																																																																																																																																						| (1435) all_382_0_1266 = 0
% 47.87/20.96  																																																																																																																																																																						| (1237) apart_point_and_line(all_0_3_3, all_28_1_33) = 0
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						| Instantiating formula (42) with all_0_3_3, all_28_1_33, 0, all_30_0_34 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_28_1_33) = 0, yields:
% 47.87/20.96  																																																																																																																																																																						| (252) all_30_0_34 = 0
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						| Equations (252) can reduce 92 to:
% 47.87/20.96  																																																																																																																																																																						| (106) $false
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																					|-Branch two:
% 47.87/20.96  																																																																																																																																																																					| (1439) all_382_0_1266 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 47.87/20.96  																																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																																						| Applying alpha-rule on (1439) yields:
% 47.87/20.96  																																																																																																																																																																						| (1435) all_382_0_1266 = 0
% 47.87/20.96  																																																																																																																																																																						| (1441) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						| Instantiating formula (42) with all_0_5_5, all_0_2_2, 0, all_20_0_24 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 47.87/20.96  																																																																																																																																																																						| (523) all_20_0_24 = 0
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						| Equations (523) can reduce 72 to:
% 47.87/20.96  																																																																																																																																																																						| (106) $false
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																				|-Branch two:
% 47.87/20.96  																																																																																																																																																																				| (1444)  ~ (all_382_0_1266 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266
% 47.87/20.96  																																																																																																																																																																				|
% 47.87/20.96  																																																																																																																																																																					| Applying alpha-rule on (1444) yields:
% 47.87/20.96  																																																																																																																																																																					| (1445)  ~ (all_382_0_1266 = 0)
% 47.87/20.96  																																																																																																																																																																					| (1446) distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266
% 47.87/20.96  																																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																																					+-Applying beta-rule and splitting (347), into two cases.
% 47.87/20.96  																																																																																																																																																																					|-Branch one:
% 47.87/20.96  																																																																																																																																																																					| (105) all_0_1_1 = 0
% 47.87/20.96  																																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																																						| Equations (105) can reduce 33 to:
% 47.87/20.96  																																																																																																																																																																						| (106) $false
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																						|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																					|-Branch two:
% 47.87/20.96  																																																																																																																																																																					| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.96  																																																																																																																																																																					| (570)  ? [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))
% 47.87/20.96  																																																																																																																																																																					|
% 47.87/20.96  																																																																																																																																																																						+-Applying beta-rule and splitting (371), into two cases.
% 47.87/20.96  																																																																																																																																																																						|-Branch one:
% 47.87/20.96  																																																																																																																																																																						| (105) all_0_1_1 = 0
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																							| Equations (105) can reduce 33 to:
% 47.87/20.96  																																																																																																																																																																							| (106) $false
% 47.87/20.96  																																																																																																																																																																							|
% 47.87/20.96  																																																																																																																																																																							|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																						|-Branch two:
% 47.87/20.96  																																																																																																																																																																						| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.96  																																																																																																																																																																						| (586)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.87/20.96  																																																																																																																																																																						|
% 47.87/20.96  																																																																																																																																																																							+-Applying beta-rule and splitting (391), into two cases.
% 47.87/20.96  																																																																																																																																																																							|-Branch one:
% 47.87/20.96  																																																																																																																																																																							| (244) all_26_0_30 = 0
% 47.87/20.96  																																																																																																																																																																							|
% 47.87/20.96  																																																																																																																																																																								| Equations (244) can reduce 84 to:
% 47.87/20.96  																																																																																																																																																																								| (106) $false
% 47.87/20.96  																																																																																																																																																																								|
% 47.87/20.96  																																																																																																																																																																								|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																							|-Branch two:
% 47.87/20.96  																																																																																																																																																																							| (84)  ~ (all_26_0_30 = 0)
% 47.87/20.96  																																																																																																																																																																							| (1458)  ? [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_28_1_33) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 47.87/20.96  																																																																																																																																																																							|
% 47.87/20.96  																																																																																																																																																																								+-Applying beta-rule and splitting (411), into two cases.
% 47.87/20.96  																																																																																																																																																																								|-Branch one:
% 47.87/20.96  																																																																																																																																																																								| (105) all_0_1_1 = 0
% 47.87/20.96  																																																																																																																																																																								|
% 47.87/20.96  																																																																																																																																																																									| Equations (105) can reduce 33 to:
% 47.87/20.96  																																																																																																																																																																									| (106) $false
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									|-The branch is then unsatisfiable
% 47.87/20.96  																																																																																																																																																																								|-Branch two:
% 47.87/20.96  																																																																																																																																																																								| (33)  ~ (all_0_1_1 = 0)
% 47.87/20.96  																																																																																																																																																																								| (598)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 47.87/20.96  																																																																																																																																																																								|
% 47.87/20.96  																																																																																																																																																																									| Instantiating formula (48) with all_28_1_33, all_0_2_2, all_382_0_1266, all_456_0_1547 and discharging atoms distinct_lines(all_28_1_33, all_0_2_2) = all_456_0_1547, distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266, yields:
% 47.87/20.96  																																																																																																																																																																									| (1463) all_456_0_1547 = all_382_0_1266
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									| Instantiating formula (48) with all_22_1_27, all_0_2_2, all_262_0_473, all_270_0_475 and discharging atoms distinct_lines(all_22_1_27, all_0_2_2) = all_270_0_475, distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473, yields:
% 47.87/20.96  																																																																																																																																																																									| (1464) all_270_0_475 = all_262_0_473
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									| Equations (1463) can reduce 1302 to:
% 47.87/20.96  																																																																																																																																																																									| (1445)  ~ (all_382_0_1266 = 0)
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									| From (1463) and (1303) follows:
% 47.87/20.96  																																																																																																																																																																									| (1446) distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									| From (1464) and (1038) follows:
% 47.87/20.96  																																																																																																																																																																									| (728) distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, all_30_0_34, all_0_0_0, all_28_1_33, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 47.87/20.96  																																																																																																																																																																									| (1468) all_33_0_37 = 0 | all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0))
% 47.87/20.96  																																																																																																																																																																									|
% 47.87/20.96  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, all_30_0_34, all_0_0_0, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 47.87/20.96  																																																																																																																																																																									| (1469) all_33_0_37 = 0 | all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, all_30_0_34, all_0_0_0, all_28_1_33, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, yields:
% 47.87/20.97  																																																																																																																																																																									| (1470) all_33_0_37 = 0 | all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_30_0_34, all_33_0_37, all_28_1_33, all_0_0_0, all_0_3_3, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_28_1_33) = all_30_0_34, apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, yields:
% 47.87/20.97  																																																																																																																																																																									| (1471) all_33_0_37 = 0 | all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, 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_33_0_37, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 47.87/20.97  																																																																																																																																																																									| (1472) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_24_0_28, all_33_0_37, all_22_1_27, all_0_0_0, 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_33_0_37, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 47.87/20.97  																																																																																																																																																																									| (1473) all_33_0_37 = 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_0_0_0, all_22_1_27) = v0))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, 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_33_0_37, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 47.87/20.97  																																																																																																																																																																									| (1474) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_24_0_28, all_33_0_37, 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_33_0_37, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 47.87/20.97  																																																																																																																																																																									| (1475) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, 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_33_0_37, yields:
% 47.87/20.97  																																																																																																																																																																									| (1476) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_24_0_28, all_33_0_37, 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_33_0_37, yields:
% 47.87/20.97  																																																																																																																																																																									| (1477) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, 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_33_0_37, 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:
% 47.87/20.97  																																																																																																																																																																									| (1478) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_0_1_1, all_33_0_37, 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_33_0_37, 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:
% 47.87/20.97  																																																																																																																																																																									| (1479) all_33_0_37 = 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))
% 47.87/20.97  																																																																																																																																																																									|
% 47.87/20.97  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, 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_33_0_37, 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:
% 48.07/20.97  																																																																																																																																																																									| (1480) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 48.07/20.97  																																																																																																																																																																									| (1481) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_0_1_1, all_33_0_37, all_0_2_2, 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_33_0_37, apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_1_1, yields:
% 48.07/20.97  																																																																																																																																																																									| (1482) all_33_0_37 = 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_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 48.07/20.97  																																																																																																																																																																									| (1483) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_22_0_26, all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 48.07/20.97  																																																																																																																																																																									| (1484) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (28) with all_33_0_37, all_22_0_26, all_22_1_27, 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_33_0_37, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 48.07/20.97  																																																																																																																																																																									| (1485) all_33_0_37 = 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_4_4, all_0_3_3) = v0))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (28) with all_22_0_26, all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_4_4, all_22_1_27) = all_22_0_26, yields:
% 48.07/20.97  																																																																																																																																																																									| (1486) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 48.07/20.97  																																																																																																																																																																									| (1487) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_26_0_30, all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 48.07/20.97  																																																																																																																																																																									| (1488) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (28) with all_33_0_37, all_26_0_30, 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_33_0_37, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 48.07/20.97  																																																																																																																																																																									| (1489) all_33_0_37 = 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_4_4, all_0_3_3) = v0))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (28) with all_26_0_30, all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, yields:
% 48.07/20.97  																																																																																																																																																																									| (1490) all_33_0_37 = 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))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, all_28_0_32, all_0_0_0, all_28_1_33, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, yields:
% 48.07/20.97  																																																																																																																																																																									| (1491) all_33_0_37 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_28_0_32, all_33_0_37, all_28_1_33, 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_33_0_37, apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, yields:
% 48.07/20.97  																																																																																																																																																																									| (1492) all_33_0_37 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (28) with all_28_0_32, all_33_0_37, all_0_0_0, all_28_1_33, all_0_5_5, all_0_3_3 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, apart_point_and_line(all_0_5_5, all_28_1_33) = all_28_0_32, yields:
% 48.07/20.97  																																																																																																																																																																									| (1493) all_33_0_37 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/20.97  																																																																																																																																																																									|
% 48.07/20.97  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 48.07/20.97  																																																																																																																																																																									| (1494) all_33_0_37 = 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (52) with all_20_0_24, all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 48.07/20.98  																																																																																																																																																																									| (1495) all_33_0_37 = 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (28) with all_20_0_24, all_33_0_37, 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_33_0_37, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, yields:
% 48.07/20.98  																																																																																																																																																																									| (1496) all_33_0_37 = 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, all_33_0_37, 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_33_0_37, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1497) all_33_0_37 = 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (43) with all_33_0_37, all_33_0_37, 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_33_0_37, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1498) all_33_0_37 = 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (52) with all_33_0_37, all_33_0_37, 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_33_0_37, yields:
% 48.07/20.98  																																																																																																																																																																									| (1499) all_33_0_37 = 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (13) with all_26_0_30, all_382_0_1266, all_0_2_2, all_28_1_33, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266, yields:
% 48.07/20.98  																																																																																																																																																																									| (1500) all_382_0_1266 = 0 | all_26_0_30 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_28_1_33) = v0)
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (53) with all_382_0_1266, all_262_0_473, all_0_2_2, all_28_1_33, all_22_1_27 and discharging atoms distinct_lines(all_28_1_33, all_0_2_2) = all_382_0_1266, distinct_lines(all_22_1_27, all_0_2_2) = all_262_0_473, yields:
% 48.07/20.98  																																																																																																																																																																									| (1501) all_382_0_1266 = 0 | all_262_0_473 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0)
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_0_1_1, all_0_1_1, all_0_2_2, 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_2_2) = all_0_1_1, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1502) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_0_1_1, all_26_0_30, 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_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1503) all_26_0_30 = 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_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_26_0_30, all_0_1_1, 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_2_2) = all_0_1_1, apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1504) all_26_0_30 = 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_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_26_0_30, all_26_0_30, all_0_2_2, all_0_0_0, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1505) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_20_0_24, 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_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1506) all_20_0_24 = 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_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_20_0_24, all_26_0_30, all_0_2_2, all_0_0_0, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_26_0_30, apart_point_and_line(all_0_5_5, all_0_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1507) all_26_0_30 = 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_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (46) with all_20_0_24, all_20_0_24, 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_2_2) = all_20_0_24, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1508) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (16) with all_33_0_37, all_33_0_37, all_0_2_2, 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_33_0_37, distinct_lines(all_0_0_0, all_0_2_2) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1509) all_33_0_37 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating formula (8) with all_0_2_2, all_0_0_0, all_0_3_3, all_0_4_4 and discharging atoms distinct_lines(all_0_0_0, all_0_2_2) = 0, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 48.07/20.98  																																																																																																																																																																									| (1510)  ? [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 & 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))
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									| Instantiating (1510) with all_735_0_2478 yields:
% 48.07/20.98  																																																																																																																																																																									| (1511) (all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_735_0_2478 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | (all_735_0_2478 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																									+-Applying beta-rule and splitting (97), into two cases.
% 48.07/20.98  																																																																																																																																																																									|-Branch one:
% 48.07/20.98  																																																																																																																																																																									| (1512)  ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_4_4, all_0_0_0) = all_34_0_38
% 48.07/20.98  																																																																																																																																																																									|
% 48.07/20.98  																																																																																																																																																																										| Applying alpha-rule on (1512) yields:
% 48.07/20.98  																																																																																																																																																																										| (1513)  ~ (all_34_0_38 = 0)
% 48.07/20.98  																																																																																																																																																																										| (1514) apart_point_and_line(all_0_4_4, all_0_0_0) = all_34_0_38
% 48.07/20.98  																																																																																																																																																																										|
% 48.07/20.98  																																																																																																																																																																										+-Applying beta-rule and splitting (1489), into two cases.
% 48.07/20.98  																																																																																																																																																																										|-Branch one:
% 48.07/20.98  																																																																																																																																																																										| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																										|
% 48.07/20.98  																																																																																																																																																																											| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																											| (106) $false
% 48.07/20.98  																																																																																																																																																																											|
% 48.07/20.98  																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																										|-Branch two:
% 48.07/20.98  																																																																																																																																																																										| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																										| (1518) 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_4_4, all_0_3_3) = v0))
% 48.07/20.98  																																																																																																																																																																										|
% 48.07/20.98  																																																																																																																																																																											+-Applying beta-rule and splitting (1498), into two cases.
% 48.07/20.98  																																																																																																																																																																											|-Branch one:
% 48.07/20.98  																																																																																																																																																																											| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																											|
% 48.07/20.98  																																																																																																																																																																												| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																												| (106) $false
% 48.07/20.98  																																																																																																																																																																												|
% 48.07/20.98  																																																																																																																																																																												|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																											|-Branch two:
% 48.07/20.98  																																																																																																																																																																											| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																											| (1522)  ? [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))
% 48.07/20.98  																																																																																																																																																																											|
% 48.07/20.98  																																																																																																																																																																												+-Applying beta-rule and splitting (1508), into two cases.
% 48.07/20.98  																																																																																																																																																																												|-Branch one:
% 48.07/20.98  																																																																																																																																																																												| (523) all_20_0_24 = 0
% 48.07/20.98  																																																																																																																																																																												|
% 48.07/20.98  																																																																																																																																																																													| Equations (523) can reduce 72 to:
% 48.07/20.98  																																																																																																																																																																													| (106) $false
% 48.07/20.98  																																																																																																																																																																													|
% 48.07/20.98  																																																																																																																																																																													|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																												|-Branch two:
% 48.07/20.98  																																																																																																																																																																												| (72)  ~ (all_20_0_24 = 0)
% 48.07/20.98  																																																																																																																																																																												| (1526)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 48.07/20.98  																																																																																																																																																																												|
% 48.07/20.98  																																																																																																																																																																													+-Applying beta-rule and splitting (1509), into two cases.
% 48.07/20.98  																																																																																																																																																																													|-Branch one:
% 48.07/20.98  																																																																																																																																																																													| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																													|
% 48.07/20.98  																																																																																																																																																																														| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																														| (106) $false
% 48.07/20.98  																																																																																																																																																																														|
% 48.07/20.98  																																																																																																																																																																														|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																													|-Branch two:
% 48.07/20.98  																																																																																																																																																																													| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																													| (1530)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.98  																																																																																																																																																																													|
% 48.07/20.98  																																																																																																																																																																														+-Applying beta-rule and splitting (1487), into two cases.
% 48.07/20.98  																																																																																																																																																																														|-Branch one:
% 48.07/20.98  																																																																																																																																																																														| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																														|
% 48.07/20.98  																																																																																																																																																																															| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																															| (106) $false
% 48.07/20.98  																																																																																																																																																																															|
% 48.07/20.98  																																																																																																																																																																															|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																														|-Branch two:
% 48.07/20.98  																																																																																																																																																																														| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																														| (1534) 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))
% 48.07/20.98  																																																																																																																																																																														|
% 48.07/20.98  																																																																																																																																																																															+-Applying beta-rule and splitting (1488), into two cases.
% 48.07/20.98  																																																																																																																																																																															|-Branch one:
% 48.07/20.98  																																																																																																																																																																															| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																															|
% 48.07/20.98  																																																																																																																																																																																| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																																| (106) $false
% 48.07/20.98  																																																																																																																																																																																|
% 48.07/20.98  																																																																																																																																																																																|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																															|-Branch two:
% 48.07/20.98  																																																																																																																																																																															| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																															| (1538) 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))
% 48.07/20.98  																																																																																																																																																																															|
% 48.07/20.98  																																																																																																																																																																																+-Applying beta-rule and splitting (1490), into two cases.
% 48.07/20.98  																																																																																																																																																																																|-Branch one:
% 48.07/20.98  																																																																																																																																																																																| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																																|
% 48.07/20.98  																																																																																																																																																																																	| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																																	| (106) $false
% 48.07/20.98  																																																																																																																																																																																	|
% 48.07/20.98  																																																																																																																																																																																	|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																																|-Branch two:
% 48.07/20.98  																																																																																																																																																																																| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																																| (1542) 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))
% 48.07/20.98  																																																																																																																																																																																|
% 48.07/20.98  																																																																																																																																																																																	+-Applying beta-rule and splitting (1495), into two cases.
% 48.07/20.98  																																																																																																																																																																																	|-Branch one:
% 48.07/20.98  																																																																																																																																																																																	| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																																	|
% 48.07/20.98  																																																																																																																																																																																		| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																																		| (106) $false
% 48.07/20.98  																																																																																																																																																																																		|
% 48.07/20.98  																																																																																																																																																																																		|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																																	|-Branch two:
% 48.07/20.98  																																																																																																																																																																																	| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																																	| (1546) 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))
% 48.07/20.98  																																																																																																																																																																																	|
% 48.07/20.98  																																																																																																																																																																																		+-Applying beta-rule and splitting (1496), into two cases.
% 48.07/20.98  																																																																																																																																																																																		|-Branch one:
% 48.07/20.98  																																																																																																																																																																																		| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																																		|
% 48.07/20.98  																																																																																																																																																																																			| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																																			| (106) $false
% 48.07/20.98  																																																																																																																																																																																			|
% 48.07/20.98  																																																																																																																																																																																			|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																																		|-Branch two:
% 48.07/20.98  																																																																																																																																																																																		| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.98  																																																																																																																																																																																		| (1550) 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))
% 48.07/20.98  																																																																																																																																																																																		|
% 48.07/20.98  																																																																																																																																																																																			+-Applying beta-rule and splitting (1479), into two cases.
% 48.07/20.98  																																																																																																																																																																																			|-Branch one:
% 48.07/20.98  																																																																																																																																																																																			| (1515) all_33_0_37 = 0
% 48.07/20.98  																																																																																																																																																																																			|
% 48.07/20.98  																																																																																																																																																																																				| Equations (1515) can reduce 230 to:
% 48.07/20.98  																																																																																																																																																																																				| (106) $false
% 48.07/20.98  																																																																																																																																																																																				|
% 48.07/20.98  																																																																																																																																																																																				|-The branch is then unsatisfiable
% 48.07/20.98  																																																																																																																																																																																			|-Branch two:
% 48.07/20.98  																																																																																																																																																																																			| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																			| (1554) 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))
% 48.07/20.99  																																																																																																																																																																																			|
% 48.07/20.99  																																																																																																																																																																																				+-Applying beta-rule and splitting (1497), into two cases.
% 48.07/20.99  																																																																																																																																																																																				|-Branch one:
% 48.07/20.99  																																																																																																																																																																																				| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																				|
% 48.07/20.99  																																																																																																																																																																																					| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																					| (106) $false
% 48.07/20.99  																																																																																																																																																																																					|
% 48.07/20.99  																																																																																																																																																																																					|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																				|-Branch two:
% 48.07/20.99  																																																																																																																																																																																				| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																				| (1558)  ? [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))
% 48.07/20.99  																																																																																																																																																																																				|
% 48.07/20.99  																																																																																																																																																																																					+-Applying beta-rule and splitting (1480), into two cases.
% 48.07/20.99  																																																																																																																																																																																					|-Branch one:
% 48.07/20.99  																																																																																																																																																																																					| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																					|
% 48.07/20.99  																																																																																																																																																																																						| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																						| (106) $false
% 48.07/20.99  																																																																																																																																																																																						|
% 48.07/20.99  																																																																																																																																																																																						|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																					|-Branch two:
% 48.07/20.99  																																																																																																																																																																																					| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																					| (1562) 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))
% 48.07/20.99  																																																																																																																																																																																					|
% 48.07/20.99  																																																																																																																																																																																						+-Applying beta-rule and splitting (1475), into two cases.
% 48.07/20.99  																																																																																																																																																																																						|-Branch one:
% 48.07/20.99  																																																																																																																																																																																						| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																						|
% 48.07/20.99  																																																																																																																																																																																							| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																							| (106) $false
% 48.07/20.99  																																																																																																																																																																																							|
% 48.07/20.99  																																																																																																																																																																																							|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																						|-Branch two:
% 48.07/20.99  																																																																																																																																																																																						| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																						| (1566) 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))
% 48.07/20.99  																																																																																																																																																																																						|
% 48.07/20.99  																																																																																																																																																																																							+-Applying beta-rule and splitting (1476), into two cases.
% 48.07/20.99  																																																																																																																																																																																							|-Branch one:
% 48.07/20.99  																																																																																																																																																																																							| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																							|
% 48.07/20.99  																																																																																																																																																																																								| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																								| (106) $false
% 48.07/20.99  																																																																																																																																																																																								|
% 48.07/20.99  																																																																																																																																																																																								|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																							|-Branch two:
% 48.07/20.99  																																																																																																																																																																																							| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																							| (1570) 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))
% 48.07/20.99  																																																																																																																																																																																							|
% 48.07/20.99  																																																																																																																																																																																								+-Applying beta-rule and splitting (1477), into two cases.
% 48.07/20.99  																																																																																																																																																																																								|-Branch one:
% 48.07/20.99  																																																																																																																																																																																								| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																								|
% 48.07/20.99  																																																																																																																																																																																									| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																									| (106) $false
% 48.07/20.99  																																																																																																																																																																																									|
% 48.07/20.99  																																																																																																																																																																																									|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																								|-Branch two:
% 48.07/20.99  																																																																																																																																																																																								| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																								| (1574) 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))
% 48.07/20.99  																																																																																																																																																																																								|
% 48.07/20.99  																																																																																																																																																																																									+-Applying beta-rule and splitting (1478), into two cases.
% 48.07/20.99  																																																																																																																																																																																									|-Branch one:
% 48.07/20.99  																																																																																																																																																																																									| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																									|
% 48.07/20.99  																																																																																																																																																																																										| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																										| (106) $false
% 48.07/20.99  																																																																																																																																																																																										|
% 48.07/20.99  																																																																																																																																																																																										|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																									|-Branch two:
% 48.07/20.99  																																																																																																																																																																																									| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																									| (1578) 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))
% 48.07/20.99  																																																																																																																																																																																									|
% 48.07/20.99  																																																																																																																																																																																										+-Applying beta-rule and splitting (1481), into two cases.
% 48.07/20.99  																																																																																																																																																																																										|-Branch one:
% 48.07/20.99  																																																																																																																																																																																										| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																										|
% 48.07/20.99  																																																																																																																																																																																											| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																											| (106) $false
% 48.07/20.99  																																																																																																																																																																																											|
% 48.07/20.99  																																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																										|-Branch two:
% 48.07/20.99  																																																																																																																																																																																										| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																										| (1582) 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))
% 48.07/20.99  																																																																																																																																																																																										|
% 48.07/20.99  																																																																																																																																																																																											+-Applying beta-rule and splitting (1482), into two cases.
% 48.07/20.99  																																																																																																																																																																																											|-Branch one:
% 48.07/20.99  																																																																																																																																																																																											| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																											|
% 48.07/20.99  																																																																																																																																																																																												| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																												| (106) $false
% 48.07/20.99  																																																																																																																																																																																												|
% 48.07/20.99  																																																																																																																																																																																												|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																											|-Branch two:
% 48.07/20.99  																																																																																																																																																																																											| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																											| (1586) 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_0_0, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.99  																																																																																																																																																																																											|
% 48.07/20.99  																																																																																																																																																																																												+-Applying beta-rule and splitting (1491), into two cases.
% 48.07/20.99  																																																																																																																																																																																												|-Branch one:
% 48.07/20.99  																																																																																																																																																																																												| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																												|
% 48.07/20.99  																																																																																																																																																																																													| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																													| (106) $false
% 48.07/20.99  																																																																																																																																																																																													|
% 48.07/20.99  																																																																																																																																																																																													|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																												|-Branch two:
% 48.07/20.99  																																																																																																																																																																																												| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																												| (1590) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_3_3) = v0))
% 48.07/20.99  																																																																																																																																																																																												|
% 48.07/20.99  																																																																																																																																																																																													+-Applying beta-rule and splitting (1492), into two cases.
% 48.07/20.99  																																																																																																																																																																																													|-Branch one:
% 48.07/20.99  																																																																																																																																																																																													| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																													|
% 48.07/20.99  																																																																																																																																																																																														| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																														| (106) $false
% 48.07/20.99  																																																																																																																																																																																														|
% 48.07/20.99  																																																																																																																																																																																														|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																													|-Branch two:
% 48.07/20.99  																																																																																																																																																																																													| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																													| (1594) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/20.99  																																																																																																																																																																																													|
% 48.07/20.99  																																																																																																																																																																																														+-Applying beta-rule and splitting (1493), into two cases.
% 48.07/20.99  																																																																																																																																																																																														|-Branch one:
% 48.07/20.99  																																																																																																																																																																																														| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																														|
% 48.07/20.99  																																																																																																																																																																																															| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																															| (106) $false
% 48.07/20.99  																																																																																																																																																																																															|
% 48.07/20.99  																																																																																																																																																																																															|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																														|-Branch two:
% 48.07/20.99  																																																																																																																																																																																														| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																														| (1598) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/20.99  																																																																																																																																																																																														|
% 48.07/20.99  																																																																																																																																																																																															+-Applying beta-rule and splitting (1494), into two cases.
% 48.07/20.99  																																																																																																																																																																																															|-Branch one:
% 48.07/20.99  																																																																																																																																																																																															| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																															|
% 48.07/20.99  																																																																																																																																																																																																| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																| (106) $false
% 48.07/20.99  																																																																																																																																																																																																|
% 48.07/20.99  																																																																																																																																																																																																|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																															|-Branch two:
% 48.07/20.99  																																																																																																																																																																																															| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																															| (1602) 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))
% 48.07/20.99  																																																																																																																																																																																															|
% 48.07/20.99  																																																																																																																																																																																																+-Applying beta-rule and splitting (1542), into two cases.
% 48.07/20.99  																																																																																																																																																																																																|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																| (244) all_26_0_30 = 0
% 48.07/20.99  																																																																																																																																																																																																|
% 48.07/20.99  																																																																																																																																																																																																	| Equations (244) can reduce 84 to:
% 48.07/20.99  																																																																																																																																																																																																	| (106) $false
% 48.07/20.99  																																																																																																																																																																																																	|
% 48.07/20.99  																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																| (84)  ~ (all_26_0_30 = 0)
% 48.07/20.99  																																																																																																																																																																																																| (1606)  ? [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))
% 48.07/20.99  																																																																																																																																																																																																|
% 48.07/20.99  																																																																																																																																																																																																	+-Applying beta-rule and splitting (1546), into two cases.
% 48.07/20.99  																																																																																																																																																																																																	|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																	| (523) all_20_0_24 = 0
% 48.07/20.99  																																																																																																																																																																																																	|
% 48.07/20.99  																																																																																																																																																																																																		| Equations (523) can reduce 72 to:
% 48.07/20.99  																																																																																																																																																																																																		| (106) $false
% 48.07/20.99  																																																																																																																																																																																																		|
% 48.07/20.99  																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																	|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																	| (72)  ~ (all_20_0_24 = 0)
% 48.07/20.99  																																																																																																																																																																																																	| (1610)  ? [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))
% 48.07/20.99  																																																																																																																																																																																																	|
% 48.07/20.99  																																																																																																																																																																																																		+-Applying beta-rule and splitting (1503), into two cases.
% 48.07/20.99  																																																																																																																																																																																																		|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																		| (244) all_26_0_30 = 0
% 48.07/20.99  																																																																																																																																																																																																		|
% 48.07/20.99  																																																																																																																																																																																																			| Equations (244) can reduce 84 to:
% 48.07/20.99  																																																																																																																																																																																																			| (106) $false
% 48.07/20.99  																																																																																																																																																																																																			|
% 48.07/20.99  																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																		|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																		| (84)  ~ (all_26_0_30 = 0)
% 48.07/20.99  																																																																																																																																																																																																		| (1614) 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_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_3_3) = v0))
% 48.07/20.99  																																																																																																																																																																																																		|
% 48.07/20.99  																																																																																																																																																																																																			+-Applying beta-rule and splitting (1502), into two cases.
% 48.07/20.99  																																																																																																																																																																																																			|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																			| (105) all_0_1_1 = 0
% 48.07/20.99  																																																																																																																																																																																																			|
% 48.07/20.99  																																																																																																																																																																																																				| Equations (105) can reduce 33 to:
% 48.07/20.99  																																																																																																																																																																																																				| (106) $false
% 48.07/20.99  																																																																																																																																																																																																				|
% 48.07/20.99  																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																			|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																			| (33)  ~ (all_0_1_1 = 0)
% 48.07/20.99  																																																																																																																																																																																																			| (1618)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.99  																																																																																																																																																																																																			|
% 48.07/20.99  																																																																																																																																																																																																				+-Applying beta-rule and splitting (1468), into two cases.
% 48.07/20.99  																																																																																																																																																																																																				|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																				| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																				|
% 48.07/20.99  																																																																																																																																																																																																					| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																					| (106) $false
% 48.07/20.99  																																																																																																																																																																																																					|
% 48.07/20.99  																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																				|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																				| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																				| (1622) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0))
% 48.07/20.99  																																																																																																																																																																																																				|
% 48.07/20.99  																																																																																																																																																																																																					+-Applying beta-rule and splitting (1469), into two cases.
% 48.07/20.99  																																																																																																																																																																																																					|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																					| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																					|
% 48.07/20.99  																																																																																																																																																																																																						| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																						| (106) $false
% 48.07/20.99  																																																																																																																																																																																																						|
% 48.07/20.99  																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																					|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																					| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																					| (1626) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0))
% 48.07/20.99  																																																																																																																																																																																																					|
% 48.07/20.99  																																																																																																																																																																																																						+-Applying beta-rule and splitting (1470), into two cases.
% 48.07/20.99  																																																																																																																																																																																																						|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																						| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																						|
% 48.07/20.99  																																																																																																																																																																																																							| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																							| (106) $false
% 48.07/20.99  																																																																																																																																																																																																							|
% 48.07/20.99  																																																																																																																																																																																																							|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																						|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																						| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																						| (1630) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 0) | (v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_lines(all_28_1_33, all_0_0_0) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.99  																																																																																																																																																																																																						|
% 48.07/20.99  																																																																																																																																																																																																							+-Applying beta-rule and splitting (1473), into two cases.
% 48.07/20.99  																																																																																																																																																																																																							|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																							| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																							|
% 48.07/20.99  																																																																																																																																																																																																								| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																								| (106) $false
% 48.07/20.99  																																																																																																																																																																																																								|
% 48.07/20.99  																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																							|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																							| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																							| (1634) 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_0_0_0, all_22_1_27) = v0))
% 48.07/20.99  																																																																																																																																																																																																							|
% 48.07/20.99  																																																																																																																																																																																																								+-Applying beta-rule and splitting (1471), into two cases.
% 48.07/20.99  																																																																																																																																																																																																								|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																								| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																								|
% 48.07/20.99  																																																																																																																																																																																																									| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																									| (106) $false
% 48.07/20.99  																																																																																																																																																																																																									|
% 48.07/20.99  																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																								|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																								| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																								| (1638) all_30_0_34 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_28_1_33) = 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_28_1_33) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_3_3) = v0))
% 48.07/20.99  																																																																																																																																																																																																								|
% 48.07/20.99  																																																																																																																																																																																																									+-Applying beta-rule and splitting (1472), into two cases.
% 48.07/20.99  																																																																																																																																																																																																									|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																									| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																									|
% 48.07/20.99  																																																																																																																																																																																																										| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																										| (106) $false
% 48.07/20.99  																																																																																																																																																																																																										|
% 48.07/20.99  																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																									|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																									| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																									| (1642) 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))
% 48.07/20.99  																																																																																																																																																																																																									|
% 48.07/20.99  																																																																																																																																																																																																										+-Applying beta-rule and splitting (1474), into two cases.
% 48.07/20.99  																																																																																																																																																																																																										|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																										| (1515) all_33_0_37 = 0
% 48.07/20.99  																																																																																																																																																																																																										|
% 48.07/20.99  																																																																																																																																																																																																											| Equations (1515) can reduce 230 to:
% 48.07/20.99  																																																																																																																																																																																																											| (106) $false
% 48.07/20.99  																																																																																																																																																																																																											|
% 48.07/20.99  																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																										|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																										| (230)  ~ (all_33_0_37 = 0)
% 48.07/20.99  																																																																																																																																																																																																										| (1646) 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))
% 48.07/20.99  																																																																																																																																																																																																										|
% 48.07/20.99  																																																																																																																																																																																																											+-Applying beta-rule and splitting (1550), into two cases.
% 48.07/20.99  																																																																																																																																																																																																											|-Branch one:
% 48.07/20.99  																																																																																																																																																																																																											| (523) all_20_0_24 = 0
% 48.07/20.99  																																																																																																																																																																																																											|
% 48.07/20.99  																																																																																																																																																																																																												| Equations (523) can reduce 72 to:
% 48.07/20.99  																																																																																																																																																																																																												| (106) $false
% 48.07/20.99  																																																																																																																																																																																																												|
% 48.07/20.99  																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 48.07/20.99  																																																																																																																																																																																																											|-Branch two:
% 48.07/20.99  																																																																																																																																																																																																											| (72)  ~ (all_20_0_24 = 0)
% 48.07/21.00  																																																																																																																																																																																																											| (1650)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																											|
% 48.07/21.00  																																																																																																																																																																																																												+-Applying beta-rule and splitting (1602), into two cases.
% 48.07/21.00  																																																																																																																																																																																																												|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																												| (523) all_20_0_24 = 0
% 48.07/21.00  																																																																																																																																																																																																												|
% 48.07/21.00  																																																																																																																																																																																																													| Equations (523) can reduce 72 to:
% 48.07/21.00  																																																																																																																																																																																																													| (106) $false
% 48.07/21.00  																																																																																																																																																																																																													|
% 48.07/21.00  																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																												|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																												| (72)  ~ (all_20_0_24 = 0)
% 48.07/21.00  																																																																																																																																																																																																												| (1654)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																												|
% 48.07/21.00  																																																																																																																																																																																																													+-Applying beta-rule and splitting (1505), into two cases.
% 48.07/21.00  																																																																																																																																																																																																													|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																													| (244) all_26_0_30 = 0
% 48.07/21.00  																																																																																																																																																																																																													|
% 48.07/21.00  																																																																																																																																																																																																														| Equations (244) can reduce 84 to:
% 48.07/21.00  																																																																																																																																																																																																														| (106) $false
% 48.07/21.00  																																																																																																																																																																																																														|
% 48.07/21.00  																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																													|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																													| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.00  																																																																																																																																																																																																													| (1658)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 48.07/21.00  																																																																																																																																																																																																													|
% 48.07/21.00  																																																																																																																																																																																																														+-Applying beta-rule and splitting (1483), into two cases.
% 48.07/21.00  																																																																																																																																																																																																														|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																														| (1515) all_33_0_37 = 0
% 48.07/21.00  																																																																																																																																																																																																														|
% 48.07/21.00  																																																																																																																																																																																																															| Equations (1515) can reduce 230 to:
% 48.07/21.00  																																																																																																																																																																																																															| (106) $false
% 48.07/21.00  																																																																																																																																																																																																															|
% 48.07/21.00  																																																																																																																																																																																																															|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																														|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																														| (230)  ~ (all_33_0_37 = 0)
% 48.07/21.00  																																																																																																																																																																																																														| (1662) 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))
% 48.07/21.00  																																																																																																																																																																																																														|
% 48.07/21.00  																																																																																																																																																																																																															+-Applying beta-rule and splitting (1484), into two cases.
% 48.07/21.00  																																																																																																																																																																																																															|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																															| (1515) all_33_0_37 = 0
% 48.07/21.00  																																																																																																																																																																																																															|
% 48.07/21.00  																																																																																																																																																																																																																| Equations (1515) can reduce 230 to:
% 48.07/21.00  																																																																																																																																																																																																																| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																|
% 48.07/21.00  																																																																																																																																																																																																																|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																															|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																															| (230)  ~ (all_33_0_37 = 0)
% 48.07/21.00  																																																																																																																																																																																																															| (1666) 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))
% 48.07/21.00  																																																																																																																																																																																																															|
% 48.07/21.00  																																																																																																																																																																																																																+-Applying beta-rule and splitting (1485), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																| (1515) all_33_0_37 = 0
% 48.07/21.00  																																																																																																																																																																																																																|
% 48.07/21.00  																																																																																																																																																																																																																	| Equations (1515) can reduce 230 to:
% 48.07/21.00  																																																																																																																																																																																																																	| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																	|
% 48.07/21.00  																																																																																																																																																																																																																	|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																| (230)  ~ (all_33_0_37 = 0)
% 48.07/21.00  																																																																																																																																																																																																																| (1670) 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_4_4, all_0_3_3) = v0))
% 48.07/21.00  																																																																																																																																																																																																																|
% 48.07/21.00  																																																																																																																																																																																																																	+-Applying beta-rule and splitting (1486), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																	|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																	| (1515) all_33_0_37 = 0
% 48.07/21.00  																																																																																																																																																																																																																	|
% 48.07/21.00  																																																																																																																																																																																																																		| Equations (1515) can reduce 230 to:
% 48.07/21.00  																																																																																																																																																																																																																		| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																		|
% 48.07/21.00  																																																																																																																																																																																																																		|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																	|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																	| (230)  ~ (all_33_0_37 = 0)
% 48.07/21.00  																																																																																																																																																																																																																	| (1674) 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))
% 48.07/21.00  																																																																																																																																																																																																																	|
% 48.07/21.00  																																																																																																																																																																																																																		+-Applying beta-rule and splitting (1534), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																		|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																		| (244) all_26_0_30 = 0
% 48.07/21.00  																																																																																																																																																																																																																		|
% 48.07/21.00  																																																																																																																																																																																																																			| Equations (244) can reduce 84 to:
% 48.07/21.00  																																																																																																																																																																																																																			| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																			|
% 48.07/21.00  																																																																																																																																																																																																																			|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																		|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																		| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.00  																																																																																																																																																																																																																		| (1678)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																																		|
% 48.07/21.00  																																																																																																																																																																																																																			+-Applying beta-rule and splitting (1538), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																			|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																			| (244) all_26_0_30 = 0
% 48.07/21.00  																																																																																																																																																																																																																			|
% 48.07/21.00  																																																																																																																																																																																																																				| Equations (244) can reduce 84 to:
% 48.07/21.00  																																																																																																																																																																																																																				| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																				|
% 48.07/21.00  																																																																																																																																																																																																																				|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																			|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																			| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.00  																																																																																																																																																																																																																			| (1682)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																																			|
% 48.07/21.00  																																																																																																																																																																																																																				+-Applying beta-rule and splitting (1562), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																				|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																				| (105) all_0_1_1 = 0
% 48.07/21.00  																																																																																																																																																																																																																				|
% 48.07/21.00  																																																																																																																																																																																																																					| Equations (105) can reduce 33 to:
% 48.07/21.00  																																																																																																																																																																																																																					| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																					|
% 48.07/21.00  																																																																																																																																																																																																																					|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																				|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																				| (33)  ~ (all_0_1_1 = 0)
% 48.07/21.00  																																																																																																																																																																																																																				| (1686)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																																				|
% 48.07/21.00  																																																																																																																																																																																																																					+-Applying beta-rule and splitting (1582), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																					|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																					| (105) all_0_1_1 = 0
% 48.07/21.00  																																																																																																																																																																																																																					|
% 48.07/21.00  																																																																																																																																																																																																																						| Equations (105) can reduce 33 to:
% 48.07/21.00  																																																																																																																																																																																																																						| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																						|
% 48.07/21.00  																																																																																																																																																																																																																						|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																					|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																					| (33)  ~ (all_0_1_1 = 0)
% 48.07/21.00  																																																																																																																																																																																																																					| (1690)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																																					|
% 48.07/21.00  																																																																																																																																																																																																																						+-Applying beta-rule and splitting (1511), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																						|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																						| (1691) (all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0) | (all_735_0_2478 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0)
% 48.07/21.00  																																																																																																																																																																																																																						|
% 48.07/21.00  																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1691), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																							|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																							| (1692) (all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0)
% 48.07/21.00  																																																																																																																																																																																																																							|
% 48.07/21.00  																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1692), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																								|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																								| (1693) all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																									| Applying alpha-rule on (1693) yields:
% 48.07/21.00  																																																																																																																																																																																																																									| (1694) all_735_0_2478 = 0
% 48.07/21.00  																																																																																																																																																																																																																									| (1695) apart_point_and_line(all_0_3_3, all_0_0_0) = 0
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1499), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																									|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																									| (1515) all_33_0_37 = 0
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																										| Equations (1515) can reduce 230 to:
% 48.07/21.00  																																																																																																																																																																																																																										| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																									|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																									| (230)  ~ (all_33_0_37 = 0)
% 48.07/21.00  																																																																																																																																																																																																																									| (1699)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																										| Instantiating formula (42) with all_0_3_3, all_0_0_0, 0, all_33_0_37 and discharging atoms apart_point_and_line(all_0_3_3, all_0_0_0) = all_33_0_37, apart_point_and_line(all_0_3_3, all_0_0_0) = 0, yields:
% 48.07/21.00  																																																																																																																																																																																																																										| (1515) all_33_0_37 = 0
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																										| Equations (1515) can reduce 230 to:
% 48.07/21.00  																																																																																																																																																																																																																										| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																								|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																								| (1702) all_735_0_2478 = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																									| Applying alpha-rule on (1702) yields:
% 48.07/21.00  																																																																																																																																																																																																																									| (1694) all_735_0_2478 = 0
% 48.07/21.00  																																																																																																																																																																																																																									| (510) apart_point_and_line(all_0_3_3, all_0_2_2) = 0
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1504), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																									|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																									| (244) all_26_0_30 = 0
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																										| Equations (244) can reduce 84 to:
% 48.07/21.00  																																																																																																																																																																																																																										| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																									|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																									| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.00  																																																																																																																																																																																																																									| (1708) 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_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1506), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																										|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																										| (523) all_20_0_24 = 0
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																											| Equations (523) can reduce 72 to:
% 48.07/21.00  																																																																																																																																																																																																																											| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																											|
% 48.07/21.00  																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																										|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																										| (72)  ~ (all_20_0_24 = 0)
% 48.07/21.00  																																																																																																																																																																																																																										| (1712) 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_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1578), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																											|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																											| (105) all_0_1_1 = 0
% 48.07/21.00  																																																																																																																																																																																																																											|
% 48.07/21.00  																																																																																																																																																																																																																												| Equations (105) can reduce 33 to:
% 48.07/21.00  																																																																																																																																																																																																																												| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																												|
% 48.07/21.00  																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																											|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																											| (33)  ~ (all_0_1_1 = 0)
% 48.07/21.00  																																																																																																																																																																																																																											| (1716)  ? [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))
% 48.07/21.00  																																																																																																																																																																																																																											|
% 48.07/21.00  																																																																																																																																																																																																																												+-Applying beta-rule and splitting (1708), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																												|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																												| (105) all_0_1_1 = 0
% 48.07/21.00  																																																																																																																																																																																																																												|
% 48.07/21.00  																																																																																																																																																																																																																													| Equations (105) can reduce 33 to:
% 48.07/21.00  																																																																																																																																																																																																																													| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																													|
% 48.07/21.00  																																																																																																																																																																																																																													|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																												|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																												| (33)  ~ (all_0_1_1 = 0)
% 48.07/21.00  																																																																																																																																																																																																																												| (1720)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_3_3, all_0_0_0) = 0) | (v0 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 48.07/21.00  																																																																																																																																																																																																																												|
% 48.07/21.00  																																																																																																																																																																																																																													+-Applying beta-rule and splitting (1712), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																													|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																													| (105) all_0_1_1 = 0
% 48.07/21.00  																																																																																																																																																																																																																													|
% 48.07/21.00  																																																																																																																																																																																																																														| Equations (105) can reduce 33 to:
% 48.07/21.00  																																																																																																																																																																																																																														| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																														|
% 48.07/21.00  																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																													|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																													| (33)  ~ (all_0_1_1 = 0)
% 48.07/21.00  																																																																																																																																																																																																																													| (1724)  ? [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_points(all_0_3_3, all_0_5_5) = v0))
% 48.07/21.00  																																																																																																																																																																																																																													|
% 48.07/21.00  																																																																																																																																																																																																																														| Instantiating formula (42) 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:
% 48.07/21.00  																																																																																																																																																																																																																														| (105) all_0_1_1 = 0
% 48.07/21.00  																																																																																																																																																																																																																														|
% 48.07/21.00  																																																																																																																																																																																																																														| Equations (105) can reduce 33 to:
% 48.07/21.00  																																																																																																																																																																																																																														| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																														|
% 48.07/21.00  																																																																																																																																																																																																																														|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																							|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																							| (1727) all_735_0_2478 = 0 & apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 48.07/21.00  																																																																																																																																																																																																																							|
% 48.07/21.00  																																																																																																																																																																																																																								| Applying alpha-rule on (1727) yields:
% 48.07/21.00  																																																																																																																																																																																																																								| (1694) all_735_0_2478 = 0
% 48.07/21.00  																																																																																																																																																																																																																								| (1729) apart_point_and_line(all_0_4_4, all_0_0_0) = 0
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																								| Instantiating formula (42) with all_0_4_4, all_0_0_0, 0, all_34_0_38 and discharging atoms apart_point_and_line(all_0_4_4, all_0_0_0) = all_34_0_38, apart_point_and_line(all_0_4_4, all_0_0_0) = 0, yields:
% 48.07/21.00  																																																																																																																																																																																																																								| (1730) all_34_0_38 = 0
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																								| Equations (1730) can reduce 1513 to:
% 48.07/21.00  																																																																																																																																																																																																																								| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																						|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																						| (1732) all_735_0_2478 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 48.07/21.00  																																																																																																																																																																																																																						|
% 48.07/21.00  																																																																																																																																																																																																																							| Applying alpha-rule on (1732) yields:
% 48.07/21.00  																																																																																																																																																																																																																							| (1694) all_735_0_2478 = 0
% 48.07/21.00  																																																																																																																																																																																																																							| (1734) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 48.07/21.00  																																																																																																																																																																																																																							|
% 48.07/21.00  																																																																																																																																																																																																																							+-Applying beta-rule and splitting (1504), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																							|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																							| (244) all_26_0_30 = 0
% 48.07/21.00  																																																																																																																																																																																																																							|
% 48.07/21.00  																																																																																																																																																																																																																								| Equations (244) can reduce 84 to:
% 48.07/21.00  																																																																																																																																																																																																																								| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																								|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																							|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																							| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.00  																																																																																																																																																																																																																							| (1708) 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_4_4, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_3_3, all_0_4_4) = v0))
% 48.07/21.00  																																																																																																																																																																																																																							|
% 48.07/21.00  																																																																																																																																																																																																																								+-Applying beta-rule and splitting (1507), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																								|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																								| (244) all_26_0_30 = 0
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																									| Equations (244) can reduce 84 to:
% 48.07/21.00  																																																																																																																																																																																																																									| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																									|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																								|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																								| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.00  																																																																																																																																																																																																																								| (1742) 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_5_5, all_0_0_0) = 0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 48.07/21.00  																																																																																																																																																																																																																								|
% 48.07/21.00  																																																																																																																																																																																																																									+-Applying beta-rule and splitting (1501), into two cases.
% 48.07/21.00  																																																																																																																																																																																																																									|-Branch one:
% 48.07/21.00  																																																																																																																																																																																																																									| (1435) all_382_0_1266 = 0
% 48.07/21.00  																																																																																																																																																																																																																									|
% 48.07/21.00  																																																																																																																																																																																																																										| Equations (1435) can reduce 1445 to:
% 48.07/21.00  																																																																																																																																																																																																																										| (106) $false
% 48.07/21.00  																																																																																																																																																																																																																										|
% 48.07/21.00  																																																																																																																																																																																																																										|-The branch is then unsatisfiable
% 48.07/21.00  																																																																																																																																																																																																																									|-Branch two:
% 48.07/21.00  																																																																																																																																																																																																																									| (1445)  ~ (all_382_0_1266 = 0)
% 48.07/21.00  																																																																																																																																																																																																																									| (1746) all_262_0_473 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_22_1_27, all_28_1_33) = v0)
% 48.07/21.01  																																																																																																																																																																																																																									|
% 48.07/21.01  																																																																																																																																																																																																																										+-Applying beta-rule and splitting (1500), into two cases.
% 48.07/21.01  																																																																																																																																																																																																																										|-Branch one:
% 48.07/21.01  																																																																																																																																																																																																																										| (1435) all_382_0_1266 = 0
% 48.07/21.01  																																																																																																																																																																																																																										|
% 48.07/21.01  																																																																																																																																																																																																																											| Equations (1435) can reduce 1445 to:
% 48.07/21.01  																																																																																																																																																																																																																											| (106) $false
% 48.07/21.01  																																																																																																																																																																																																																											|
% 48.07/21.01  																																																																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/21.01  																																																																																																																																																																																																																										|-Branch two:
% 48.07/21.01  																																																																																																																																																																																																																										| (1445)  ~ (all_382_0_1266 = 0)
% 48.07/21.01  																																																																																																																																																																																																																										| (1750) all_26_0_30 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_28_1_33) = v0)
% 48.07/21.01  																																																																																																																																																																																																																										|
% 48.07/21.01  																																																																																																																																																																																																																											+-Applying beta-rule and splitting (1750), into two cases.
% 48.07/21.01  																																																																																																																																																																																																																											|-Branch one:
% 48.07/21.01  																																																																																																																																																																																																																											| (244) all_26_0_30 = 0
% 48.07/21.01  																																																																																																																																																																																																																											|
% 48.07/21.01  																																																																																																																																																																																																																												| Equations (244) can reduce 84 to:
% 48.07/21.01  																																																																																																																																																																																																																												| (106) $false
% 48.07/21.01  																																																																																																																																																																																																																												|
% 48.07/21.01  																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 48.07/21.01  																																																																																																																																																																																																																											|-Branch two:
% 48.07/21.01  																																																																																																																																																																																																																											| (84)  ~ (all_26_0_30 = 0)
% 48.07/21.01  																																																																																																																																																																																																																											| (1754)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_28_1_33) = v0)
% 48.07/21.01  																																																																																																																																																																																																																											|
% 48.07/21.01  																																																																																																																																																																																																																												| Instantiating formula (42) with all_0_4_4, all_0_2_2, 0, all_26_0_30 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_4_4, all_0_2_2) = 0, yields:
% 48.07/21.01  																																																																																																																																																																																																																												| (244) all_26_0_30 = 0
% 48.07/21.01  																																																																																																																																																																																																																												|
% 48.07/21.01  																																																																																																																																																																																																																												| Equations (244) can reduce 84 to:
% 48.07/21.01  																																																																																																																																																																																																																												| (106) $false
% 48.07/21.01  																																																																																																																																																																																																																												|
% 48.07/21.01  																																																																																																																																																																																																																												|-The branch is then unsatisfiable
% 48.07/21.01  																																																																																																																																																																									|-Branch two:
% 48.07/21.01  																																																																																																																																																																									| (1757)  ~ (all_34_0_38 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_34_0_38
% 48.07/21.01  																																																																																																																																																																									|
% 48.07/21.01  																																																																																																																																																																										| Applying alpha-rule on (1757) yields:
% 48.07/21.01  																																																																																																																																																																										| (1513)  ~ (all_34_0_38 = 0)
% 48.07/21.01  																																																																																																																																																																										| (1759) distinct_points(all_0_3_3, all_0_4_4) = all_34_0_38
% 48.07/21.01  																																																																																																																																																																										|
% 48.07/21.01  																																																																																																																																																																										| Instantiating formula (38) with all_34_0_38, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_3_3, all_0_4_4) = all_34_0_38, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 48.07/21.01  																																																																																																																																																																										| (1760) all_34_0_38 = 0 | distinct_points(all_0_4_4, all_0_4_4) = 0
% 48.07/21.01  																																																																																																																																																																										|
% 48.07/21.01  																																																																																																																																																																										+-Applying beta-rule and splitting (1760), into two cases.
% 48.07/21.01  																																																																																																																																																																										|-Branch one:
% 48.07/21.01  																																																																																																																																																																										| (1761) distinct_points(all_0_4_4, all_0_4_4) = 0
% 48.07/21.01  																																																																																																																																																																										|
% 48.07/21.01  																																																																																																																																																																											| Instantiating formula (3) with all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_4_4) = 0, yields:
% 48.07/21.01  																																																																																																																																																																											| (1762) $false
% 48.07/21.01  																																																																																																																																																																											|
% 48.07/21.01  																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/21.01  																																																																																																																																																																										|-Branch two:
% 48.07/21.01  																																																																																																																																																																										| (1763)  ~ (distinct_points(all_0_4_4, all_0_4_4) = 0)
% 48.07/21.01  																																																																																																																																																																										| (1730) all_34_0_38 = 0
% 48.07/21.01  																																																																																																																																																																										|
% 48.07/21.01  																																																																																																																																																																											| Equations (1730) can reduce 1513 to:
% 48.07/21.01  																																																																																																																																																																											| (106) $false
% 48.07/21.01  																																																																																																																																																																											|
% 48.07/21.01  																																																																																																																																																																											|-The branch is then unsatisfiable
% 48.07/21.01  																																																																																																																																																																			|-Branch two:
% 48.07/21.01  																																																																																																																																																																			| (1766)  ~ (all_382_0_1266 = 0) & distinct_points(all_0_5_5, all_0_3_3) = all_382_0_1266
% 48.07/21.01  																																																																																																																																																																			|
% 48.07/21.01  																																																																																																																																																																				| Applying alpha-rule on (1766) yields:
% 48.07/21.01  																																																																																																																																																																				| (1445)  ~ (all_382_0_1266 = 0)
% 48.07/21.01  																																																																																																																																																																				| (1768) distinct_points(all_0_5_5, all_0_3_3) = all_382_0_1266
% 48.07/21.01  																																																																																																																																																																				|
% 48.07/21.01  																																																																																																																																																																				| Instantiating formula (26) with all_0_5_5, all_0_3_3, all_382_0_1266, 0 and discharging atoms distinct_points(all_0_5_5, all_0_3_3) = all_382_0_1266, distinct_points(all_0_5_5, all_0_3_3) = 0, yields:
% 48.07/21.01  																																																																																																																																																																				| (1435) all_382_0_1266 = 0
% 48.07/21.01  																																																																																																																																																																				|
% 48.07/21.01  																																																																																																																																																																				| Equations (1435) can reduce 1445 to:
% 48.07/21.01  																																																																																																																																																																				| (106) $false
% 48.07/21.01  																																																																																																																																																																				|
% 48.07/21.01  																																																																																																																																																																				|-The branch is then unsatisfiable
% 48.07/21.01  																																																																																														|-Branch two:
% 48.07/21.01  																																																																																														| (1771)  ~ (distinct_lines(all_0_0_0, all_0_2_2) = 0)
% 48.07/21.01  																																																																																														| (523) all_20_0_24 = 0
% 48.07/21.01  																																																																																														|
% 48.07/21.01  																																																																																															| Equations (523) can reduce 72 to:
% 48.07/21.01  																																																																																															| (106) $false
% 48.07/21.01  																																																																																															|
% 48.07/21.01  																																																																																															|-The branch is then unsatisfiable
% 48.07/21.01  																																																																										|-Branch two:
% 48.07/21.01  																																																																										| (1774)  ~ (all_262_0_473 = 0) & distinct_points(all_0_4_4, all_0_3_3) = all_262_0_473
% 48.07/21.01  																																																																										|
% 48.07/21.01  																																																																											| Applying alpha-rule on (1774) yields:
% 48.07/21.01  																																																																											| (727)  ~ (all_262_0_473 = 0)
% 48.07/21.01  																																																																											| (1776) distinct_points(all_0_4_4, all_0_3_3) = all_262_0_473
% 48.07/21.01  																																																																											|
% 48.07/21.01  																																																																											| Instantiating formula (26) with all_0_4_4, all_0_3_3, all_262_0_473, 0 and discharging atoms distinct_points(all_0_4_4, all_0_3_3) = all_262_0_473, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 48.07/21.01  																																																																											| (509) all_262_0_473 = 0
% 48.07/21.01  																																																																											|
% 48.07/21.01  																																																																											| Equations (509) can reduce 727 to:
% 48.07/21.01  																																																																											| (106) $false
% 48.07/21.01  																																																																											|
% 48.07/21.01  																																																																											|-The branch is then unsatisfiable
% 48.07/21.01  					|-Branch two:
% 48.07/21.01  					| (1779)  ~ (all_33_0_37 = 0) & distinct_points(all_0_3_3, all_0_4_4) = all_33_0_37
% 48.07/21.01  					|
% 48.07/21.01  						| Applying alpha-rule on (1779) yields:
% 48.07/21.01  						| (230)  ~ (all_33_0_37 = 0)
% 48.07/21.01  						| (1781) distinct_points(all_0_3_3, all_0_4_4) = all_33_0_37
% 48.07/21.01  						|
% 48.07/21.01  						| Instantiating formula (38) with all_33_0_37, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms distinct_points(all_0_3_3, all_0_4_4) = all_33_0_37, distinct_points(all_0_4_4, all_0_3_3) = 0, yields:
% 48.07/21.01  						| (1782) all_33_0_37 = 0 | distinct_points(all_0_4_4, all_0_4_4) = 0
% 48.07/21.01  						|
% 48.07/21.01  						+-Applying beta-rule and splitting (1782), into two cases.
% 48.07/21.01  						|-Branch one:
% 48.07/21.01  						| (1761) distinct_points(all_0_4_4, all_0_4_4) = 0
% 48.07/21.01  						|
% 48.07/21.01  							| Instantiating formula (3) with all_0_4_4 and discharging atoms distinct_points(all_0_4_4, all_0_4_4) = 0, yields:
% 48.07/21.01  							| (1762) $false
% 48.07/21.01  							|
% 48.07/21.01  							|-The branch is then unsatisfiable
% 48.07/21.01  						|-Branch two:
% 48.07/21.01  						| (1763)  ~ (distinct_points(all_0_4_4, all_0_4_4) = 0)
% 48.07/21.01  						| (1515) all_33_0_37 = 0
% 48.07/21.01  						|
% 48.07/21.01  							| Equations (1515) can reduce 230 to:
% 48.07/21.01  							| (106) $false
% 48.07/21.01  							|
% 48.07/21.01  							|-The branch is then unsatisfiable
% 48.07/21.01  	|-Branch two:
% 48.07/21.01  	| (1788)  ~ (all_32_0_36 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36
% 48.07/21.01  	|
% 48.07/21.01  		| Applying alpha-rule on (1788) yields:
% 48.07/21.01  		| (103)  ~ (all_32_0_36 = 0)
% 48.07/21.01  		| (1790) distinct_points(all_0_5_5, all_0_4_4) = all_32_0_36
% 48.07/21.01  		|
% 48.07/21.01  		| Instantiating formula (26) 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:
% 48.07/21.01  		| (1791) all_32_0_36 = 0
% 48.07/21.01  		|
% 48.07/21.01  		| Equations (1791) can reduce 103 to:
% 48.07/21.01  		| (106) $false
% 48.07/21.01  		|
% 48.07/21.01  		|-The branch is then unsatisfiable
% 48.07/21.01  |-Branch two:
% 48.07/21.01  | (1793)  ~ (all_35_0_39 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39
% 48.07/21.01  |
% 48.07/21.01  	| Applying alpha-rule on (1793) yields:
% 48.07/21.01  	| (100)  ~ (all_35_0_39 = 0)
% 48.07/21.01  	| (1795) distinct_points(all_0_5_5, all_0_4_4) = all_35_0_39
% 48.07/21.01  	|
% 48.07/21.01  	| Instantiating formula (26) 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:
% 48.07/21.01  	| (1796) all_35_0_39 = 0
% 48.07/21.01  	|
% 48.07/21.01  	| Equations (1796) can reduce 100 to:
% 48.07/21.01  	| (106) $false
% 48.07/21.01  	|
% 48.07/21.01  	|-The branch is then unsatisfiable
% 48.07/21.01  % SZS output end Proof for theBenchmark
% 48.07/21.02  
% 48.07/21.02  20429ms
%------------------------------------------------------------------------------