%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO198+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n029.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 03:48:34 EDT 2022

% Result   : Theorem 5.29s 1.91s
% Output   : Proof 23.84s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO198+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.33  % Computer : n029.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 18:59:59 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.58/0.57          ____       _                          
% 0.58/0.57    ___  / __ \_____(_)___  ________  __________
% 0.58/0.57   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.57  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.57  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.57  
% 0.58/0.57  A Theorem Prover for First-Order Logic
% 0.58/0.57  (ePrincess v.1.0)
% 0.58/0.57  
% 0.58/0.57  (c) Philipp Rümmer, 2009-2015
% 0.58/0.57  (c) Peter Backeman, 2014-2015
% 0.58/0.57  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.57  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.57  Bug reports to peter@backeman.se
% 0.58/0.57  
% 0.58/0.57  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.57  
% 0.58/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.58/0.62  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.59/0.87  Prover 0: Preprocessing ...
% 1.80/0.99  Prover 0: Warning: ignoring some quantifiers
% 1.80/1.01  Prover 0: Constructing countermodel ...
% 2.98/1.33  Prover 0: gave up
% 2.98/1.33  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.98/1.35  Prover 1: Preprocessing ...
% 3.18/1.43  Prover 1: Constructing countermodel ...
% 3.51/1.47  Prover 1: gave up
% 3.51/1.47  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.68/1.49  Prover 2: Preprocessing ...
% 4.00/1.61  Prover 2: Warning: ignoring some quantifiers
% 4.00/1.61  Prover 2: Constructing countermodel ...
% 5.29/1.91  Prover 2: proved (435ms)
% 5.29/1.91  
% 5.29/1.91  No countermodel exists, formula is valid
% 5.29/1.91  % SZS status Theorem for theBenchmark
% 5.29/1.91  
% 5.29/1.91  Generating proof ... Warning: ignoring some quantifiers
% 22.62/6.73  found it (size 550)
% 22.62/6.73  
% 22.62/6.73  % SZS output start Proof for theBenchmark
% 22.62/6.73  Assumed formulas after preprocessing and simplification: 
% 22.62/6.73  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] : ( ~ (v4 = 0) & intersection_point(v0, v2) = v5 & intersection_point(v0, v1) = v3 & apart_point_and_line(v5, v1) = 0 & apart_point_and_line(v3, v2) = v4 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(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)
% 22.89/6.79  | 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:
% 22.89/6.79  | (1)  ~ (all_0_1_1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_0_0_0 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1 & convergent_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0 & convergent_lines(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
% 22.89/6.80  |
% 22.89/6.80  | Applying alpha-rule on (1) yields:
% 22.89/6.80  | (2)  ! [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)
% 22.89/6.80  | (3)  ! [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)
% 22.89/6.80  | (4)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 22.89/6.80  | (5) convergent_lines(all_0_5_5, all_0_3_3) = 0
% 22.89/6.80  | (6) apart_point_and_line(all_0_0_0, all_0_4_4) = 0
% 22.89/6.80  | (7)  ! [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))
% 22.89/6.81  | (8)  ! [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)))
% 22.89/6.81  | (9)  ! [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))
% 22.89/6.81  | (10)  ! [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)))
% 22.89/6.81  | (11)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 22.89/6.81  | (12)  ! [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))
% 23.15/6.81  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 23.15/6.81  | (14)  ! [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)))
% 23.15/6.81  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 23.15/6.81  | (16)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 23.15/6.81  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 23.15/6.81  | (18)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 23.15/6.81  | (19)  ~ (all_0_1_1 = 0)
% 23.15/6.81  | (20)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 23.15/6.81  | (21)  ! [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)
% 23.15/6.81  | (22)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 23.15/6.81  | (23) apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1
% 23.15/6.81  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.15/6.81  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 23.15/6.81  | (26)  ! [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)))
% 23.15/6.81  | (27)  ! [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)))
% 23.15/6.81  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 23.15/6.81  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 23.15/6.81  | (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))
% 23.15/6.81  | (31)  ! [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))
% 23.15/6.81  | (32)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 23.15/6.82  | (33)  ! [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)))
% 23.15/6.82  | (34)  ! [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))
% 23.15/6.82  | (35)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 23.15/6.82  | (36) intersection_point(all_0_5_5, all_0_3_3) = all_0_0_0
% 23.15/6.82  | (37)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 23.15/6.82  | (38)  ! [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)
% 23.15/6.82  | (39)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 23.15/6.82  | (40)  ! [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)))
% 23.15/6.82  | (41) convergent_lines(all_0_3_3, all_0_4_4) = 0
% 23.15/6.82  | (42)  ! [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)))
% 23.15/6.82  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 23.15/6.82  | (44)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 23.15/6.82  | (45) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2
% 23.15/6.82  | (46)  ! [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)))
% 23.15/6.82  | (47) convergent_lines(all_0_5_5, all_0_4_4) = 0
% 23.15/6.82  | (48)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 23.15/6.82  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 23.15/6.82  | (50)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 23.15/6.82  | (51)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 23.15/6.82  | (52)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 23.15/6.82  | (53)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 23.15/6.82  | (54)  ! [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)))
% 23.15/6.82  | (55)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 23.15/6.82  | (56)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 23.15/6.82  | (57)  ! [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)))
% 23.15/6.82  |
% 23.15/6.82  | Instantiating formula (46) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 23.15/6.82  | (58)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0))
% 23.15/6.82  |
% 23.15/6.83  | Instantiating formula (42) with all_0_0_0, all_0_3_3, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 23.15/6.83  | (59)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_0_0, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = v0))
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (46) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 23.15/6.83  | (60)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0))
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (42) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 23.15/6.83  | (61)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0))
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (8) with all_0_1_1, all_0_1_1, all_0_3_3, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.83  | (62) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (4) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 23.15/6.83  | (63)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (53) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields:
% 23.15/6.83  | (64)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (4) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 23.15/6.83  | (65)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (53) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 23.15/6.83  | (66)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (4) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 23.15/6.83  | (67)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating formula (53) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 23.15/6.83  | (68)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (68) with all_20_0_24, all_20_1_25 yields:
% 23.15/6.83  | (69)  ~ (all_20_0_24 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25 & apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24
% 23.15/6.83  |
% 23.15/6.83  | Applying alpha-rule on (69) yields:
% 23.15/6.83  | (70)  ~ (all_20_0_24 = 0)
% 23.15/6.83  | (71) intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25
% 23.15/6.83  | (72) apart_point_and_line(all_20_1_25, all_0_5_5) = all_20_0_24
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (65) with all_22_0_26, all_22_1_27 yields:
% 23.15/6.83  | (73)  ~ (all_22_0_26 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27 & apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26
% 23.15/6.83  |
% 23.15/6.83  | Applying alpha-rule on (73) yields:
% 23.15/6.83  | (74)  ~ (all_22_0_26 = 0)
% 23.15/6.83  | (75) intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27
% 23.15/6.83  | (76) apart_point_and_line(all_22_1_27, all_0_3_3) = all_22_0_26
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (64) with all_24_0_28, all_24_1_29 yields:
% 23.15/6.83  | (77)  ~ (all_24_0_28 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29 & apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28
% 23.15/6.83  |
% 23.15/6.83  | Applying alpha-rule on (77) yields:
% 23.15/6.83  | (78)  ~ (all_24_0_28 = 0)
% 23.15/6.83  | (79) intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29
% 23.15/6.83  | (80) apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (63) with all_26_0_30, all_26_1_31 yields:
% 23.15/6.83  | (81)  ~ (all_26_0_30 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31 & apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30
% 23.15/6.83  |
% 23.15/6.83  | Applying alpha-rule on (81) yields:
% 23.15/6.83  | (82)  ~ (all_26_0_30 = 0)
% 23.15/6.83  | (83) intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31
% 23.15/6.83  | (84) apart_point_and_line(all_26_1_31, all_0_4_4) = all_26_0_30
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (67) with all_28_0_32, all_28_1_33 yields:
% 23.15/6.83  | (85)  ~ (all_28_0_32 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33 & apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32
% 23.15/6.83  |
% 23.15/6.83  | Applying alpha-rule on (85) yields:
% 23.15/6.83  | (86)  ~ (all_28_0_32 = 0)
% 23.15/6.83  | (87) intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33
% 23.15/6.83  | (88) apart_point_and_line(all_28_1_33, all_0_4_4) = all_28_0_32
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (61) with all_30_0_34 yields:
% 23.15/6.83  | (89) ( ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34) | ( ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (60) with all_31_0_35 yields:
% 23.15/6.83  | (90) ( ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35) | ( ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (66) with all_32_0_36, all_32_1_37 yields:
% 23.15/6.83  | (91)  ~ (all_32_0_36 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37 & apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36
% 23.15/6.83  |
% 23.15/6.83  | Applying alpha-rule on (91) yields:
% 23.15/6.83  | (92)  ~ (all_32_0_36 = 0)
% 23.15/6.83  | (93) intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37
% 23.15/6.83  | (94) apart_point_and_line(all_32_1_37, all_0_5_5) = all_32_0_36
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (59) with all_34_0_38 yields:
% 23.15/6.83  | (95) ( ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_0_0, all_0_5_5) = all_34_0_38) | ( ~ (all_34_0_38 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38)
% 23.15/6.83  |
% 23.15/6.83  | Instantiating (58) with all_35_0_39 yields:
% 23.15/6.84  | (96) ( ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_35_0_39) | ( ~ (all_35_0_39 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39)
% 23.15/6.84  |
% 23.15/6.84  +-Applying beta-rule and splitting (96), into two cases.
% 23.15/6.84  |-Branch one:
% 23.15/6.84  | (97)  ~ (all_35_0_39 = 0) & apart_point_and_line(all_0_0_0, all_0_3_3) = all_35_0_39
% 23.15/6.84  |
% 23.15/6.84  	| Applying alpha-rule on (97) yields:
% 23.15/6.84  	| (98)  ~ (all_35_0_39 = 0)
% 23.15/6.84  	| (99) apart_point_and_line(all_0_0_0, all_0_3_3) = all_35_0_39
% 23.15/6.84  	|
% 23.15/6.84  	+-Applying beta-rule and splitting (62), into two cases.
% 23.15/6.84  	|-Branch one:
% 23.15/6.84  	| (100) all_0_1_1 = 0
% 23.15/6.84  	|
% 23.15/6.84  		| Equations (100) can reduce 19 to:
% 23.15/6.84  		| (101) $false
% 23.15/6.84  		|
% 23.15/6.84  		|-The branch is then unsatisfiable
% 23.15/6.84  	|-Branch two:
% 23.15/6.84  	| (19)  ~ (all_0_1_1 = 0)
% 23.15/6.84  	| (103)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.15/6.84  	|
% 23.15/6.84  		+-Applying beta-rule and splitting (89), into two cases.
% 23.15/6.84  		|-Branch one:
% 23.15/6.84  		| (104)  ~ (all_30_0_34 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34
% 23.15/6.84  		|
% 23.15/6.84  			| Applying alpha-rule on (104) yields:
% 23.15/6.84  			| (105)  ~ (all_30_0_34 = 0)
% 23.15/6.84  			| (106) apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34
% 23.15/6.84  			|
% 23.15/6.84  			+-Applying beta-rule and splitting (95), into two cases.
% 23.15/6.84  			|-Branch one:
% 23.15/6.84  			| (107)  ~ (all_34_0_38 = 0) & apart_point_and_line(all_0_0_0, all_0_5_5) = all_34_0_38
% 23.15/6.84  			|
% 23.15/6.84  				| Applying alpha-rule on (107) yields:
% 23.15/6.84  				| (108)  ~ (all_34_0_38 = 0)
% 23.15/6.84  				| (109) apart_point_and_line(all_0_0_0, all_0_5_5) = all_34_0_38
% 23.15/6.84  				|
% 23.15/6.84  				+-Applying beta-rule and splitting (90), into two cases.
% 23.15/6.84  				|-Branch one:
% 23.15/6.84  				| (110)  ~ (all_31_0_35 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35
% 23.15/6.84  				|
% 23.15/6.84  					| Applying alpha-rule on (110) yields:
% 23.15/6.84  					| (111)  ~ (all_31_0_35 = 0)
% 23.15/6.84  					| (112) apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (44) with all_0_3_3, all_0_4_4, all_24_1_29, all_26_1_31 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_26_1_31, intersection_point(all_0_3_3, all_0_4_4) = all_24_1_29, yields:
% 23.15/6.84  					| (113) all_26_1_31 = all_24_1_29
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (44) with all_0_5_5, all_0_3_3, all_32_1_37, all_0_0_0 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37, intersection_point(all_0_5_5, all_0_3_3) = all_0_0_0, yields:
% 23.15/6.84  					| (114) all_32_1_37 = all_0_0_0
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (44) with all_0_5_5, all_0_3_3, all_22_1_27, all_32_1_37 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_32_1_37, intersection_point(all_0_5_5, all_0_3_3) = all_22_1_27, yields:
% 23.15/6.84  					| (115) all_32_1_37 = all_22_1_27
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (44) with all_0_5_5, all_0_4_4, all_28_1_33, all_0_2_2 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33, intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields:
% 23.15/6.84  					| (116) all_28_1_33 = all_0_2_2
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (44) with all_0_5_5, all_0_4_4, all_20_1_25, all_28_1_33 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_28_1_33, intersection_point(all_0_5_5, all_0_4_4) = all_20_1_25, yields:
% 23.15/6.84  					| (117) all_28_1_33 = all_20_1_25
% 23.15/6.84  					|
% 23.15/6.84  					| Combining equations (115,114) yields a new equation:
% 23.15/6.84  					| (118) all_22_1_27 = all_0_0_0
% 23.15/6.84  					|
% 23.15/6.84  					| Simplifying 118 yields:
% 23.15/6.84  					| (119) all_22_1_27 = all_0_0_0
% 23.15/6.84  					|
% 23.15/6.84  					| Combining equations (116,117) yields a new equation:
% 23.15/6.84  					| (120) all_20_1_25 = all_0_2_2
% 23.15/6.84  					|
% 23.15/6.84  					| Combining equations (120,117) yields a new equation:
% 23.15/6.84  					| (116) all_28_1_33 = all_0_2_2
% 23.15/6.84  					|
% 23.15/6.84  					| From (114) and (94) follows:
% 23.15/6.84  					| (122) apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36
% 23.15/6.84  					|
% 23.15/6.84  					| From (116) and (88) follows:
% 23.15/6.84  					| (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32
% 23.15/6.84  					|
% 23.15/6.84  					| From (113) and (84) follows:
% 23.15/6.84  					| (124) apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30
% 23.15/6.84  					|
% 23.15/6.84  					| From (119) and (76) follows:
% 23.15/6.84  					| (125) apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26
% 23.15/6.84  					|
% 23.15/6.84  					| From (120) and (72) follows:
% 23.15/6.84  					| (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (17) with all_0_0_0, all_0_3_3, all_22_0_26, all_35_0_39 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_35_0_39, apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, yields:
% 23.15/6.84  					| (127) all_35_0_39 = all_22_0_26
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (17) with all_0_0_0, all_0_5_5, all_32_0_36, all_34_0_38 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_34_0_38, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.15/6.84  					| (128) all_34_0_38 = all_32_0_36
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (17) with all_0_2_2, all_0_4_4, all_28_0_32, all_31_0_35 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_31_0_35, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.15/6.84  					| (129) all_31_0_35 = all_28_0_32
% 23.15/6.84  					|
% 23.15/6.84  					| Instantiating formula (17) with all_0_2_2, all_0_5_5, all_20_0_24, all_30_0_34 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_30_0_34, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.15/6.84  					| (130) all_30_0_34 = all_20_0_24
% 23.15/6.84  					|
% 23.15/6.84  					| Equations (127) can reduce 98 to:
% 23.15/6.84  					| (74)  ~ (all_22_0_26 = 0)
% 23.15/6.84  					|
% 23.15/6.84  					| Equations (128) can reduce 108 to:
% 23.15/6.84  					| (92)  ~ (all_32_0_36 = 0)
% 23.15/6.84  					|
% 23.15/6.84  					| Equations (129) can reduce 111 to:
% 23.15/6.84  					| (86)  ~ (all_28_0_32 = 0)
% 23.15/6.84  					|
% 23.15/6.84  					| Equations (130) can reduce 105 to:
% 23.15/6.84  					| (70)  ~ (all_20_0_24 = 0)
% 23.15/6.84  					|
% 23.15/6.84  					| From (127) and (99) follows:
% 23.15/6.85  					| (125) apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26
% 23.15/6.85  					|
% 23.15/6.85  					| From (128) and (109) follows:
% 23.15/6.85  					| (122) apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36
% 23.15/6.85  					|
% 23.15/6.85  					| From (129) and (112) follows:
% 23.15/6.85  					| (123) apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32
% 23.15/6.85  					|
% 23.15/6.85  					| From (130) and (106) follows:
% 23.15/6.85  					| (126) apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_24_0_28, all_0_1_1, all_0_3_3, all_0_3_3, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (139) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_0_1_1, all_24_0_28, all_0_3_3, all_0_3_3, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (140) all_24_0_28 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_24_0_28, all_24_0_28, all_0_3_3, all_0_3_3, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, yields:
% 23.15/6.85  					| (141) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_26_0_30, all_0_1_1, all_0_4_4, all_0_3_3, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (142) all_26_0_30 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_0_1_1, all_26_0_30, all_0_3_3, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (143) all_26_0_30 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (14) with all_26_0_30, all_0_1_1, all_0_3_3, all_0_4_4, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (144) all_26_0_30 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (14) with all_0_1_1, all_26_0_30, all_0_4_4, all_0_3_3, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (145) all_26_0_30 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_26_0_30, all_24_0_28, all_0_4_4, all_0_3_3, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, yields:
% 23.15/6.85  					| (146) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_24_0_28, all_26_0_30, all_0_3_3, all_0_4_4, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, yields:
% 23.15/6.85  					| (147) all_26_0_30 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_26_0_30, all_26_0_30, all_0_4_4, all_0_4_4, all_24_1_29, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, yields:
% 23.15/6.85  					| (148) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_22_0_26, all_0_1_1, all_0_3_3, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (149) all_22_0_26 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.15/6.85  					|
% 23.15/6.85  					| Instantiating formula (8) with all_0_1_1, all_22_0_26, all_0_3_3, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.85  					| (150) all_22_0_26 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_22_0_26, all_24_0_28, all_0_3_3, all_0_3_3, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, yields:
% 23.15/6.86  					| (151) all_24_0_28 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_22_0_26, all_26_0_30, all_0_3_3, all_0_4_4, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, yields:
% 23.15/6.86  					| (152) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_26_0_30, all_22_0_26, all_0_4_4, all_0_3_3, all_24_1_29, all_0_0_0 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, yields:
% 23.15/6.86  					| (153) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (14) with all_22_0_26, all_26_0_30, all_0_4_4, all_0_3_3, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, yields:
% 23.15/6.86  					| (154) all_26_0_30 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_22_0_26, all_22_0_26, all_0_3_3, all_0_3_3, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, yields:
% 23.15/6.86  					| (155) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_32_0_36, all_0_1_1, all_0_5_5, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.86  					| (156) all_32_0_36 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_0_1_1, all_32_0_36, all_0_3_3, all_0_5_5, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.86  					| (157) all_32_0_36 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (14) with all_32_0_36, all_0_1_1, all_0_3_3, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.86  					| (158) all_32_0_36 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (14) with all_0_1_1, all_32_0_36, all_0_5_5, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, yields:
% 23.15/6.86  					| (159) all_32_0_36 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_32_0_36, all_24_0_28, all_0_5_5, all_0_3_3, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.15/6.86  					| (160) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.15/6.86  					|
% 23.15/6.86  					| Instantiating formula (8) with all_24_0_28, all_32_0_36, all_0_3_3, all_0_5_5, all_24_1_29, all_0_0_0 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.15/6.86  					| (161) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.86  					|
% 23.42/6.86  					| Instantiating formula (14) with all_32_0_36, all_24_0_28, all_0_3_3, all_0_5_5, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.86  					| (162) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (14) with all_24_0_28, all_32_0_36, all_0_5_5, all_0_3_3, all_24_1_29, all_0_0_0 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (163) all_32_0_36 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_32_0_36, all_26_0_30, all_0_5_5, all_0_4_4, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (164) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_26_0_30, all_32_0_36, all_0_4_4, all_0_5_5, all_24_1_29, all_0_0_0 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (165) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (14) with all_32_0_36, all_26_0_30, all_0_4_4, all_0_5_5, all_0_0_0, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (166) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (14) with all_26_0_30, all_32_0_36, all_0_5_5, all_0_4_4, all_24_1_29, all_0_0_0 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (167) all_32_0_36 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_32_0_36, all_22_0_26, all_0_5_5, all_0_3_3, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (168) all_32_0_36 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_22_0_26, all_32_0_36, all_0_3_3, all_0_5_5, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (169) all_32_0_36 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_32_0_36, all_32_0_36, all_0_5_5, all_0_5_5, all_0_0_0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, yields:
% 23.42/6.87  					| (170) all_32_0_36 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (2) with all_28_0_32, all_0_2_2, all_0_4_4, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_4_4) = 0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.87  					| (171) all_28_0_32 = 0 | distinct_points(all_0_0_0, all_0_2_2) = 0
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_28_0_32, all_0_1_1, all_0_4_4, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.87  					| (172) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_0_1_1, all_28_0_32, all_0_3_3, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.87  					| (173) all_28_0_32 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.87  					|
% 23.42/6.87  					| Instantiating formula (8) with all_24_0_28, all_28_0_32, all_0_3_3, all_0_4_4, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.87  					| (174) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (14) with all_28_0_32, all_24_0_28, all_0_3_3, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (175) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (14) with all_24_0_28, all_28_0_32, all_0_4_4, all_0_3_3, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (176) all_28_0_32 = 0 | all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_28_0_32, all_26_0_30, all_0_4_4, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (177) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_26_0_30, all_28_0_32, all_0_4_4, all_0_4_4, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (178) all_28_0_32 = 0 | all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_28_0_32, all_22_0_26, all_0_4_4, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (179) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_22_0_26, all_28_0_32, all_0_3_3, all_0_4_4, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (180) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (14) with all_28_0_32, all_22_0_26, all_0_3_3, all_0_4_4, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (181) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (14) with all_22_0_26, all_28_0_32, all_0_4_4, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (182) all_28_0_32 = 0 | all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_28_0_32, all_32_0_36, all_0_4_4, all_0_5_5, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (183) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_32_0_36, all_28_0_32, all_0_5_5, all_0_4_4, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (184) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (14) with all_28_0_32, all_32_0_36, all_0_5_5, all_0_4_4, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (185) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (14) with all_32_0_36, all_28_0_32, all_0_4_4, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (186) all_32_0_36 = 0 | all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_28_0_32, all_28_0_32, all_0_4_4, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, yields:
% 23.42/6.88  					| (187) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_20_0_24, all_0_1_1, all_0_5_5, all_0_3_3, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.88  					| (188) all_20_0_24 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_0_1_1, all_20_0_24, all_0_3_3, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.88  					| (189) all_20_0_24 = 0 | all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.88  					|
% 23.42/6.88  					| Instantiating formula (8) with all_20_0_24, all_24_0_28, all_0_5_5, all_0_3_3, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (190) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_24_0_28, all_20_0_24, all_0_3_3, all_0_5_5, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (191) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (14) with all_20_0_24, all_24_0_28, all_0_3_3, all_0_5_5, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (192) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (14) with all_24_0_28, all_20_0_24, all_0_5_5, all_0_3_3, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_3_3) = all_24_0_28, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (193) all_24_0_28 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_20_0_24, all_26_0_30, all_0_5_5, all_0_4_4, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (194) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_26_0_30, all_20_0_24, all_0_4_4, all_0_5_5, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (195) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (14) with all_20_0_24, all_26_0_30, all_0_4_4, all_0_5_5, all_0_2_2, all_24_1_29 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (196) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (14) with all_26_0_30, all_20_0_24, all_0_5_5, all_0_4_4, all_24_1_29, all_0_2_2 and discharging atoms apart_point_and_line(all_24_1_29, all_0_4_4) = all_26_0_30, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (197) all_26_0_30 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_20_0_24, all_22_0_26, all_0_5_5, all_0_3_3, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (198) all_22_0_26 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_22_0_26, all_20_0_24, all_0_3_3, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (199) all_22_0_26 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (14) with all_20_0_24, all_22_0_26, all_0_3_3, all_0_5_5, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (200) all_22_0_26 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (14) with all_22_0_26, all_20_0_24, all_0_5_5, all_0_3_3, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (201) all_22_0_26 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_20_0_24, all_32_0_36, all_0_5_5, all_0_5_5, all_0_2_2, all_0_0_0 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (202) all_32_0_36 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_32_0_36, all_20_0_24, all_0_5_5, all_0_5_5, all_0_0_0, all_0_2_2 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (203) all_32_0_36 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_20_0_24, all_28_0_32, all_0_5_5, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (204) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_28_0_32, all_20_0_24, all_0_4_4, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_28_0_32, apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (205) all_28_0_32 = 0 | all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					| Instantiating formula (8) with all_20_0_24, all_20_0_24, all_0_5_5, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, yields:
% 23.42/6.89  					| (206) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.89  					|
% 23.42/6.89  					+-Applying beta-rule and splitting (141), into two cases.
% 23.42/6.89  					|-Branch one:
% 23.42/6.89  					| (207) all_24_0_28 = 0
% 23.42/6.89  					|
% 23.42/6.89  						| Equations (207) can reduce 78 to:
% 23.42/6.89  						| (101) $false
% 23.42/6.89  						|
% 23.42/6.89  						|-The branch is then unsatisfiable
% 23.42/6.89  					|-Branch two:
% 23.42/6.89  					| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.89  					| (210)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.42/6.90  					|
% 23.42/6.90  						+-Applying beta-rule and splitting (148), into two cases.
% 23.42/6.90  						|-Branch one:
% 23.42/6.90  						| (211) all_26_0_30 = 0
% 23.42/6.90  						|
% 23.42/6.90  							| Equations (211) can reduce 82 to:
% 23.42/6.90  							| (101) $false
% 23.42/6.90  							|
% 23.42/6.90  							|-The branch is then unsatisfiable
% 23.42/6.90  						|-Branch two:
% 23.42/6.90  						| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.90  						| (214)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.42/6.90  						|
% 23.42/6.90  							+-Applying beta-rule and splitting (187), into two cases.
% 23.42/6.90  							|-Branch one:
% 23.42/6.90  							| (215) all_28_0_32 = 0
% 23.42/6.90  							|
% 23.42/6.90  								| Equations (215) can reduce 86 to:
% 23.42/6.90  								| (101) $false
% 23.42/6.90  								|
% 23.42/6.90  								|-The branch is then unsatisfiable
% 23.42/6.90  							|-Branch two:
% 23.42/6.90  							| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.90  							| (218)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.90  							|
% 23.42/6.90  								+-Applying beta-rule and splitting (146), into two cases.
% 23.42/6.90  								|-Branch one:
% 23.42/6.90  								| (211) all_26_0_30 = 0
% 23.42/6.90  								|
% 23.42/6.90  									| Equations (211) can reduce 82 to:
% 23.42/6.90  									| (101) $false
% 23.42/6.90  									|
% 23.42/6.90  									|-The branch is then unsatisfiable
% 23.42/6.90  								|-Branch two:
% 23.42/6.90  								| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.90  								| (222) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.42/6.90  								|
% 23.42/6.90  									+-Applying beta-rule and splitting (145), into two cases.
% 23.42/6.90  									|-Branch one:
% 23.42/6.90  									| (211) all_26_0_30 = 0
% 23.42/6.90  									|
% 23.42/6.90  										| Equations (211) can reduce 82 to:
% 23.42/6.90  										| (101) $false
% 23.42/6.90  										|
% 23.42/6.90  										|-The branch is then unsatisfiable
% 23.42/6.90  									|-Branch two:
% 23.42/6.90  									| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.90  									| (226) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.90  									|
% 23.42/6.90  										+-Applying beta-rule and splitting (140), into two cases.
% 23.42/6.90  										|-Branch one:
% 23.42/6.90  										| (207) all_24_0_28 = 0
% 23.42/6.90  										|
% 23.42/6.90  											| Equations (207) can reduce 78 to:
% 23.42/6.90  											| (101) $false
% 23.42/6.90  											|
% 23.42/6.90  											|-The branch is then unsatisfiable
% 23.42/6.90  										|-Branch two:
% 23.42/6.90  										| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.90  										| (230) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.90  										|
% 23.42/6.90  											+-Applying beta-rule and splitting (155), into two cases.
% 23.42/6.90  											|-Branch one:
% 23.42/6.90  											| (231) all_22_0_26 = 0
% 23.42/6.90  											|
% 23.42/6.90  												| Equations (231) can reduce 74 to:
% 23.42/6.90  												| (101) $false
% 23.42/6.90  												|
% 23.42/6.90  												|-The branch is then unsatisfiable
% 23.42/6.90  											|-Branch two:
% 23.42/6.90  											| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.90  											| (234)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.90  											|
% 23.42/6.90  												+-Applying beta-rule and splitting (206), into two cases.
% 23.42/6.90  												|-Branch one:
% 23.42/6.90  												| (235) all_20_0_24 = 0
% 23.42/6.90  												|
% 23.42/6.90  													| Equations (235) can reduce 70 to:
% 23.42/6.90  													| (101) $false
% 23.42/6.90  													|
% 23.42/6.90  													|-The branch is then unsatisfiable
% 23.42/6.90  												|-Branch two:
% 23.42/6.90  												| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.90  												| (238)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.90  												|
% 23.42/6.90  													+-Applying beta-rule and splitting (170), into two cases.
% 23.42/6.90  													|-Branch one:
% 23.42/6.90  													| (239) all_32_0_36 = 0
% 23.42/6.90  													|
% 23.42/6.90  														| Equations (239) can reduce 92 to:
% 23.42/6.90  														| (101) $false
% 23.42/6.90  														|
% 23.42/6.90  														|-The branch is then unsatisfiable
% 23.42/6.90  													|-Branch two:
% 23.42/6.90  													| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  													| (242)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.90  													|
% 23.42/6.90  														+-Applying beta-rule and splitting (165), into two cases.
% 23.42/6.90  														|-Branch one:
% 23.42/6.90  														| (239) all_32_0_36 = 0
% 23.42/6.90  														|
% 23.42/6.90  															| Equations (239) can reduce 92 to:
% 23.42/6.90  															| (101) $false
% 23.42/6.90  															|
% 23.42/6.90  															|-The branch is then unsatisfiable
% 23.42/6.90  														|-Branch two:
% 23.42/6.90  														| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  														| (246) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.90  														|
% 23.42/6.90  															+-Applying beta-rule and splitting (166), into two cases.
% 23.42/6.90  															|-Branch one:
% 23.42/6.90  															| (239) all_32_0_36 = 0
% 23.42/6.90  															|
% 23.42/6.90  																| Equations (239) can reduce 92 to:
% 23.42/6.90  																| (101) $false
% 23.42/6.90  																|
% 23.42/6.90  																|-The branch is then unsatisfiable
% 23.42/6.90  															|-Branch two:
% 23.42/6.90  															| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  															| (250) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.90  															|
% 23.42/6.90  																+-Applying beta-rule and splitting (167), into two cases.
% 23.42/6.90  																|-Branch one:
% 23.42/6.90  																| (239) all_32_0_36 = 0
% 23.42/6.90  																|
% 23.42/6.90  																	| Equations (239) can reduce 92 to:
% 23.42/6.90  																	| (101) $false
% 23.42/6.90  																	|
% 23.42/6.90  																	|-The branch is then unsatisfiable
% 23.42/6.90  																|-Branch two:
% 23.42/6.90  																| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  																| (254) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.90  																|
% 23.42/6.90  																	+-Applying beta-rule and splitting (169), into two cases.
% 23.42/6.90  																	|-Branch one:
% 23.42/6.90  																	| (239) all_32_0_36 = 0
% 23.42/6.90  																	|
% 23.42/6.90  																		| Equations (239) can reduce 92 to:
% 23.42/6.90  																		| (101) $false
% 23.42/6.90  																		|
% 23.42/6.90  																		|-The branch is then unsatisfiable
% 23.42/6.90  																	|-Branch two:
% 23.42/6.90  																	| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  																	| (258) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.90  																	|
% 23.42/6.90  																		+-Applying beta-rule and splitting (181), into two cases.
% 23.42/6.90  																		|-Branch one:
% 23.42/6.90  																		| (215) all_28_0_32 = 0
% 23.42/6.90  																		|
% 23.42/6.90  																			| Equations (215) can reduce 86 to:
% 23.42/6.90  																			| (101) $false
% 23.42/6.90  																			|
% 23.42/6.90  																			|-The branch is then unsatisfiable
% 23.42/6.90  																		|-Branch two:
% 23.42/6.90  																		| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.90  																		| (262) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.90  																		|
% 23.42/6.90  																			+-Applying beta-rule and splitting (183), into two cases.
% 23.42/6.90  																			|-Branch one:
% 23.42/6.90  																			| (239) all_32_0_36 = 0
% 23.42/6.90  																			|
% 23.42/6.90  																				| Equations (239) can reduce 92 to:
% 23.42/6.90  																				| (101) $false
% 23.42/6.90  																				|
% 23.42/6.90  																				|-The branch is then unsatisfiable
% 23.42/6.90  																			|-Branch two:
% 23.42/6.90  																			| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  																			| (266) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.90  																			|
% 23.42/6.90  																				+-Applying beta-rule and splitting (168), into two cases.
% 23.42/6.90  																				|-Branch one:
% 23.42/6.90  																				| (239) all_32_0_36 = 0
% 23.42/6.90  																				|
% 23.42/6.90  																					| Equations (239) can reduce 92 to:
% 23.42/6.90  																					| (101) $false
% 23.42/6.90  																					|
% 23.42/6.90  																					|-The branch is then unsatisfiable
% 23.42/6.90  																				|-Branch two:
% 23.42/6.90  																				| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  																				| (270) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.90  																				|
% 23.42/6.90  																					+-Applying beta-rule and splitting (180), into two cases.
% 23.42/6.90  																					|-Branch one:
% 23.42/6.90  																					| (215) all_28_0_32 = 0
% 23.42/6.90  																					|
% 23.42/6.90  																						| Equations (215) can reduce 86 to:
% 23.42/6.90  																						| (101) $false
% 23.42/6.90  																						|
% 23.42/6.90  																						|-The branch is then unsatisfiable
% 23.42/6.90  																					|-Branch two:
% 23.42/6.90  																					| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.90  																					| (274) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.90  																					|
% 23.42/6.90  																						+-Applying beta-rule and splitting (182), into two cases.
% 23.42/6.90  																						|-Branch one:
% 23.42/6.90  																						| (215) all_28_0_32 = 0
% 23.42/6.90  																						|
% 23.42/6.90  																							| Equations (215) can reduce 86 to:
% 23.42/6.90  																							| (101) $false
% 23.42/6.90  																							|
% 23.42/6.90  																							|-The branch is then unsatisfiable
% 23.42/6.90  																						|-Branch two:
% 23.42/6.90  																						| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.90  																						| (278) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.90  																						|
% 23.42/6.90  																							+-Applying beta-rule and splitting (186), into two cases.
% 23.42/6.90  																							|-Branch one:
% 23.42/6.90  																							| (239) all_32_0_36 = 0
% 23.42/6.90  																							|
% 23.42/6.90  																								| Equations (239) can reduce 92 to:
% 23.42/6.90  																								| (101) $false
% 23.42/6.90  																								|
% 23.42/6.90  																								|-The branch is then unsatisfiable
% 23.42/6.90  																							|-Branch two:
% 23.42/6.90  																							| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.90  																							| (282) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.90  																							|
% 23.42/6.90  																								+-Applying beta-rule and splitting (188), into two cases.
% 23.42/6.90  																								|-Branch one:
% 23.42/6.90  																								| (235) all_20_0_24 = 0
% 23.42/6.90  																								|
% 23.42/6.90  																									| Equations (235) can reduce 70 to:
% 23.42/6.90  																									| (101) $false
% 23.42/6.90  																									|
% 23.42/6.90  																									|-The branch is then unsatisfiable
% 23.42/6.90  																								|-Branch two:
% 23.42/6.90  																								| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.90  																								| (286) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.91  																								|
% 23.42/6.91  																									+-Applying beta-rule and splitting (189), into two cases.
% 23.42/6.91  																									|-Branch one:
% 23.42/6.91  																									| (235) all_20_0_24 = 0
% 23.42/6.91  																									|
% 23.42/6.91  																										| Equations (235) can reduce 70 to:
% 23.42/6.91  																										| (101) $false
% 23.42/6.91  																										|
% 23.42/6.91  																										|-The branch is then unsatisfiable
% 23.42/6.91  																									|-Branch two:
% 23.42/6.91  																									| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.91  																									| (290) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.91  																									|
% 23.42/6.91  																										+-Applying beta-rule and splitting (190), into two cases.
% 23.42/6.91  																										|-Branch one:
% 23.42/6.91  																										| (207) all_24_0_28 = 0
% 23.42/6.91  																										|
% 23.42/6.91  																											| Equations (207) can reduce 78 to:
% 23.42/6.91  																											| (101) $false
% 23.42/6.91  																											|
% 23.42/6.91  																											|-The branch is then unsatisfiable
% 23.42/6.91  																										|-Branch two:
% 23.42/6.91  																										| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.91  																										| (294) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.91  																										|
% 23.42/6.91  																											+-Applying beta-rule and splitting (191), into two cases.
% 23.42/6.91  																											|-Branch one:
% 23.42/6.91  																											| (207) all_24_0_28 = 0
% 23.42/6.91  																											|
% 23.42/6.91  																												| Equations (207) can reduce 78 to:
% 23.42/6.91  																												| (101) $false
% 23.42/6.91  																												|
% 23.42/6.91  																												|-The branch is then unsatisfiable
% 23.42/6.91  																											|-Branch two:
% 23.42/6.91  																											| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.91  																											| (298) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.91  																											|
% 23.42/6.91  																												+-Applying beta-rule and splitting (150), into two cases.
% 23.42/6.91  																												|-Branch one:
% 23.42/6.91  																												| (231) all_22_0_26 = 0
% 23.42/6.91  																												|
% 23.42/6.91  																													| Equations (231) can reduce 74 to:
% 23.42/6.91  																													| (101) $false
% 23.42/6.91  																													|
% 23.42/6.91  																													|-The branch is then unsatisfiable
% 23.42/6.91  																												|-Branch two:
% 23.42/6.91  																												| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.91  																												| (302) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.91  																												|
% 23.42/6.91  																													+-Applying beta-rule and splitting (151), into two cases.
% 23.42/6.91  																													|-Branch one:
% 23.42/6.91  																													| (207) all_24_0_28 = 0
% 23.42/6.91  																													|
% 23.42/6.91  																														| Equations (207) can reduce 78 to:
% 23.42/6.91  																														| (101) $false
% 23.42/6.91  																														|
% 23.42/6.91  																														|-The branch is then unsatisfiable
% 23.42/6.91  																													|-Branch two:
% 23.42/6.91  																													| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.91  																													| (306) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.91  																													|
% 23.42/6.91  																														+-Applying beta-rule and splitting (194), into two cases.
% 23.42/6.91  																														|-Branch one:
% 23.42/6.91  																														| (211) all_26_0_30 = 0
% 23.42/6.91  																														|
% 23.42/6.91  																															| Equations (211) can reduce 82 to:
% 23.42/6.91  																															| (101) $false
% 23.42/6.91  																															|
% 23.42/6.91  																															|-The branch is then unsatisfiable
% 23.42/6.91  																														|-Branch two:
% 23.42/6.91  																														| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.91  																														| (310) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.91  																														|
% 23.42/6.91  																															+-Applying beta-rule and splitting (184), into two cases.
% 23.42/6.91  																															|-Branch one:
% 23.42/6.91  																															| (239) all_32_0_36 = 0
% 23.42/6.91  																															|
% 23.42/6.91  																																| Equations (239) can reduce 92 to:
% 23.42/6.91  																																| (101) $false
% 23.42/6.91  																																|
% 23.42/6.91  																																|-The branch is then unsatisfiable
% 23.42/6.91  																															|-Branch two:
% 23.42/6.91  																															| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.91  																															| (314) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.91  																															|
% 23.42/6.91  																																+-Applying beta-rule and splitting (185), into two cases.
% 23.42/6.91  																																|-Branch one:
% 23.42/6.91  																																| (239) all_32_0_36 = 0
% 23.42/6.91  																																|
% 23.42/6.91  																																	| Equations (239) can reduce 92 to:
% 23.42/6.91  																																	| (101) $false
% 23.42/6.91  																																	|
% 23.42/6.91  																																	|-The branch is then unsatisfiable
% 23.42/6.91  																																|-Branch two:
% 23.42/6.91  																																| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.91  																																| (318) all_28_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.91  																																|
% 23.42/6.91  																																	+-Applying beta-rule and splitting (192), into two cases.
% 23.42/6.91  																																	|-Branch one:
% 23.42/6.91  																																	| (207) all_24_0_28 = 0
% 23.42/6.91  																																	|
% 23.42/6.91  																																		| Equations (207) can reduce 78 to:
% 23.42/6.91  																																		| (101) $false
% 23.42/6.91  																																		|
% 23.42/6.91  																																		|-The branch is then unsatisfiable
% 23.42/6.91  																																	|-Branch two:
% 23.42/6.91  																																	| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.91  																																	| (322) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.91  																																	|
% 23.42/6.91  																																		+-Applying beta-rule and splitting (193), into two cases.
% 23.42/6.91  																																		|-Branch one:
% 23.42/6.91  																																		| (207) all_24_0_28 = 0
% 23.42/6.91  																																		|
% 23.42/6.91  																																			| Equations (207) can reduce 78 to:
% 23.42/6.91  																																			| (101) $false
% 23.42/6.91  																																			|
% 23.42/6.91  																																			|-The branch is then unsatisfiable
% 23.42/6.91  																																		|-Branch two:
% 23.42/6.91  																																		| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.91  																																		| (326) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.91  																																		|
% 23.42/6.91  																																			+-Applying beta-rule and splitting (195), into two cases.
% 23.42/6.91  																																			|-Branch one:
% 23.42/6.91  																																			| (211) all_26_0_30 = 0
% 23.42/6.91  																																			|
% 23.42/6.91  																																				| Equations (211) can reduce 82 to:
% 23.42/6.91  																																				| (101) $false
% 23.42/6.91  																																				|
% 23.42/6.91  																																				|-The branch is then unsatisfiable
% 23.42/6.91  																																			|-Branch two:
% 23.42/6.91  																																			| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.91  																																			| (330) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.91  																																			|
% 23.42/6.91  																																				+-Applying beta-rule and splitting (147), into two cases.
% 23.42/6.91  																																				|-Branch one:
% 23.42/6.91  																																				| (211) all_26_0_30 = 0
% 23.42/6.91  																																				|
% 23.42/6.91  																																					| Equations (211) can reduce 82 to:
% 23.42/6.91  																																					| (101) $false
% 23.42/6.91  																																					|
% 23.42/6.91  																																					|-The branch is then unsatisfiable
% 23.42/6.91  																																				|-Branch two:
% 23.42/6.91  																																				| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.91  																																				| (334) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.42/6.91  																																				|
% 23.42/6.91  																																					+-Applying beta-rule and splitting (149), into two cases.
% 23.42/6.91  																																					|-Branch one:
% 23.42/6.91  																																					| (231) all_22_0_26 = 0
% 23.42/6.91  																																					|
% 23.42/6.91  																																						| Equations (231) can reduce 74 to:
% 23.42/6.91  																																						| (101) $false
% 23.42/6.91  																																						|
% 23.42/6.91  																																						|-The branch is then unsatisfiable
% 23.42/6.91  																																					|-Branch two:
% 23.42/6.91  																																					| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.91  																																					| (338) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.91  																																					|
% 23.42/6.91  																																						+-Applying beta-rule and splitting (222), into two cases.
% 23.42/6.91  																																						|-Branch one:
% 23.42/6.91  																																						| (207) all_24_0_28 = 0
% 23.42/6.91  																																						|
% 23.42/6.91  																																							| Equations (207) can reduce 78 to:
% 23.42/6.91  																																							| (101) $false
% 23.42/6.91  																																							|
% 23.42/6.91  																																							|-The branch is then unsatisfiable
% 23.42/6.91  																																						|-Branch two:
% 23.42/6.91  																																						| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.91  																																						| (342)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.42/6.91  																																						|
% 23.42/6.91  																																							+-Applying beta-rule and splitting (230), into two cases.
% 23.42/6.91  																																							|-Branch one:
% 23.42/6.91  																																							| (100) all_0_1_1 = 0
% 23.42/6.91  																																							|
% 23.42/6.91  																																								| Equations (100) can reduce 19 to:
% 23.42/6.91  																																								| (101) $false
% 23.42/6.91  																																								|
% 23.42/6.91  																																								|-The branch is then unsatisfiable
% 23.42/6.91  																																							|-Branch two:
% 23.42/6.91  																																							| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.91  																																							| (346)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.91  																																							|
% 23.42/6.91  																																								+-Applying beta-rule and splitting (171), into two cases.
% 23.42/6.91  																																								|-Branch one:
% 23.42/6.91  																																								| (347) distinct_points(all_0_0_0, all_0_2_2) = 0
% 23.42/6.91  																																								|
% 23.42/6.91  																																									+-Applying beta-rule and splitting (246), into two cases.
% 23.42/6.91  																																									|-Branch one:
% 23.42/6.91  																																									| (211) all_26_0_30 = 0
% 23.42/6.91  																																									|
% 23.42/6.91  																																										| Equations (211) can reduce 82 to:
% 23.42/6.91  																																										| (101) $false
% 23.42/6.91  																																										|
% 23.42/6.91  																																										|-The branch is then unsatisfiable
% 23.42/6.91  																																									|-Branch two:
% 23.42/6.91  																																									| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.91  																																									| (351)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.91  																																									|
% 23.42/6.91  																																										+-Applying beta-rule and splitting (250), into two cases.
% 23.42/6.91  																																										|-Branch one:
% 23.42/6.91  																																										| (211) all_26_0_30 = 0
% 23.42/6.91  																																										|
% 23.42/6.91  																																											| Equations (211) can reduce 82 to:
% 23.42/6.91  																																											| (101) $false
% 23.42/6.91  																																											|
% 23.42/6.91  																																											|-The branch is then unsatisfiable
% 23.42/6.91  																																										|-Branch two:
% 23.42/6.91  																																										| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.91  																																										| (355)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.91  																																										|
% 23.42/6.91  																																											+-Applying beta-rule and splitting (254), into two cases.
% 23.42/6.91  																																											|-Branch one:
% 23.42/6.91  																																											| (211) all_26_0_30 = 0
% 23.42/6.91  																																											|
% 23.42/6.91  																																												| Equations (211) can reduce 82 to:
% 23.42/6.91  																																												| (101) $false
% 23.42/6.91  																																												|
% 23.42/6.91  																																												|-The branch is then unsatisfiable
% 23.42/6.91  																																											|-Branch two:
% 23.42/6.91  																																											| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.91  																																											| (359)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.91  																																											|
% 23.42/6.91  																																												+-Applying beta-rule and splitting (258), into two cases.
% 23.42/6.91  																																												|-Branch one:
% 23.42/6.91  																																												| (231) all_22_0_26 = 0
% 23.42/6.91  																																												|
% 23.42/6.91  																																													| Equations (231) can reduce 74 to:
% 23.42/6.91  																																													| (101) $false
% 23.42/6.91  																																													|
% 23.42/6.91  																																													|-The branch is then unsatisfiable
% 23.42/6.91  																																												|-Branch two:
% 23.42/6.91  																																												| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.91  																																												| (363)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.91  																																												|
% 23.42/6.91  																																													+-Applying beta-rule and splitting (262), into two cases.
% 23.42/6.91  																																													|-Branch one:
% 23.42/6.91  																																													| (231) all_22_0_26 = 0
% 23.42/6.91  																																													|
% 23.42/6.91  																																														| Equations (231) can reduce 74 to:
% 23.42/6.91  																																														| (101) $false
% 23.42/6.91  																																														|
% 23.42/6.91  																																														|-The branch is then unsatisfiable
% 23.42/6.91  																																													|-Branch two:
% 23.42/6.91  																																													| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.91  																																													| (367)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.91  																																													|
% 23.42/6.91  																																														+-Applying beta-rule and splitting (266), into two cases.
% 23.42/6.91  																																														|-Branch one:
% 23.42/6.91  																																														| (215) all_28_0_32 = 0
% 23.42/6.91  																																														|
% 23.42/6.92  																																															| Equations (215) can reduce 86 to:
% 23.42/6.92  																																															| (101) $false
% 23.42/6.92  																																															|
% 23.42/6.92  																																															|-The branch is then unsatisfiable
% 23.42/6.92  																																														|-Branch two:
% 23.42/6.92  																																														| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.92  																																														| (371)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.92  																																														|
% 23.42/6.92  																																															+-Applying beta-rule and splitting (274), into two cases.
% 23.42/6.92  																																															|-Branch one:
% 23.42/6.92  																																															| (231) all_22_0_26 = 0
% 23.42/6.92  																																															|
% 23.42/6.92  																																																| Equations (231) can reduce 74 to:
% 23.42/6.92  																																																| (101) $false
% 23.42/6.92  																																																|
% 23.42/6.92  																																																|-The branch is then unsatisfiable
% 23.42/6.92  																																															|-Branch two:
% 23.42/6.92  																																															| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.92  																																															| (375)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																															|
% 23.42/6.92  																																																+-Applying beta-rule and splitting (282), into two cases.
% 23.42/6.92  																																																|-Branch one:
% 23.42/6.92  																																																| (215) all_28_0_32 = 0
% 23.42/6.92  																																																|
% 23.42/6.92  																																																	| Equations (215) can reduce 86 to:
% 23.42/6.92  																																																	| (101) $false
% 23.42/6.92  																																																	|
% 23.42/6.92  																																																	|-The branch is then unsatisfiable
% 23.42/6.92  																																																|-Branch two:
% 23.42/6.92  																																																| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.92  																																																| (379)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																																|
% 23.42/6.92  																																																	+-Applying beta-rule and splitting (290), into two cases.
% 23.42/6.92  																																																	|-Branch one:
% 23.42/6.92  																																																	| (100) all_0_1_1 = 0
% 23.42/6.92  																																																	|
% 23.42/6.92  																																																		| Equations (100) can reduce 19 to:
% 23.42/6.92  																																																		| (101) $false
% 23.42/6.92  																																																		|
% 23.42/6.92  																																																		|-The branch is then unsatisfiable
% 23.42/6.92  																																																	|-Branch two:
% 23.42/6.92  																																																	| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.92  																																																	| (383)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.92  																																																	|
% 23.42/6.92  																																																		+-Applying beta-rule and splitting (294), into two cases.
% 23.42/6.92  																																																		|-Branch one:
% 23.42/6.92  																																																		| (235) all_20_0_24 = 0
% 23.42/6.92  																																																		|
% 23.42/6.92  																																																			| Equations (235) can reduce 70 to:
% 23.42/6.92  																																																			| (101) $false
% 23.42/6.92  																																																			|
% 23.42/6.92  																																																			|-The branch is then unsatisfiable
% 23.42/6.92  																																																		|-Branch two:
% 23.42/6.92  																																																		| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.92  																																																		| (387)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.92  																																																		|
% 23.42/6.92  																																																			+-Applying beta-rule and splitting (298), into two cases.
% 23.42/6.92  																																																			|-Branch one:
% 23.42/6.92  																																																			| (235) all_20_0_24 = 0
% 23.42/6.92  																																																			|
% 23.42/6.92  																																																				| Equations (235) can reduce 70 to:
% 23.42/6.92  																																																				| (101) $false
% 23.42/6.92  																																																				|
% 23.42/6.92  																																																				|-The branch is then unsatisfiable
% 23.42/6.92  																																																			|-Branch two:
% 23.42/6.92  																																																			| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.92  																																																			| (391)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.92  																																																			|
% 23.42/6.92  																																																				+-Applying beta-rule and splitting (302), into two cases.
% 23.42/6.92  																																																				|-Branch one:
% 23.42/6.92  																																																				| (100) all_0_1_1 = 0
% 23.42/6.92  																																																				|
% 23.42/6.92  																																																					| Equations (100) can reduce 19 to:
% 23.42/6.92  																																																					| (101) $false
% 23.42/6.92  																																																					|
% 23.42/6.92  																																																					|-The branch is then unsatisfiable
% 23.42/6.92  																																																				|-Branch two:
% 23.42/6.92  																																																				| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.92  																																																				| (395)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.92  																																																				|
% 23.42/6.92  																																																					+-Applying beta-rule and splitting (306), into two cases.
% 23.42/6.92  																																																					|-Branch one:
% 23.42/6.92  																																																					| (231) all_22_0_26 = 0
% 23.42/6.92  																																																					|
% 23.42/6.92  																																																						| Equations (231) can reduce 74 to:
% 23.42/6.92  																																																						| (101) $false
% 23.42/6.92  																																																						|
% 23.42/6.92  																																																						|-The branch is then unsatisfiable
% 23.42/6.92  																																																					|-Branch two:
% 23.42/6.92  																																																					| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.92  																																																					| (399)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.92  																																																					|
% 23.42/6.92  																																																						+-Applying beta-rule and splitting (310), into two cases.
% 23.42/6.92  																																																						|-Branch one:
% 23.42/6.92  																																																						| (235) all_20_0_24 = 0
% 23.42/6.92  																																																						|
% 23.42/6.92  																																																							| Equations (235) can reduce 70 to:
% 23.42/6.92  																																																							| (101) $false
% 23.42/6.92  																																																							|
% 23.42/6.92  																																																							|-The branch is then unsatisfiable
% 23.42/6.92  																																																						|-Branch two:
% 23.42/6.92  																																																						| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.92  																																																						| (403)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.92  																																																						|
% 23.42/6.92  																																																							+-Applying beta-rule and splitting (314), into two cases.
% 23.42/6.92  																																																							|-Branch one:
% 23.42/6.92  																																																							| (215) all_28_0_32 = 0
% 23.42/6.92  																																																							|
% 23.42/6.92  																																																								| Equations (215) can reduce 86 to:
% 23.42/6.92  																																																								| (101) $false
% 23.42/6.92  																																																								|
% 23.42/6.92  																																																								|-The branch is then unsatisfiable
% 23.42/6.92  																																																							|-Branch two:
% 23.42/6.92  																																																							| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.92  																																																							| (407)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																																							|
% 23.42/6.92  																																																								+-Applying beta-rule and splitting (326), into two cases.
% 23.42/6.92  																																																								|-Branch one:
% 23.42/6.92  																																																								| (235) all_20_0_24 = 0
% 23.42/6.92  																																																								|
% 23.42/6.92  																																																									| Equations (235) can reduce 70 to:
% 23.42/6.92  																																																									| (101) $false
% 23.42/6.92  																																																									|
% 23.42/6.92  																																																									|-The branch is then unsatisfiable
% 23.42/6.92  																																																								|-Branch two:
% 23.42/6.92  																																																								| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.92  																																																								| (411)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.92  																																																								|
% 23.42/6.92  																																																									+-Applying beta-rule and splitting (334), into two cases.
% 23.42/6.92  																																																									|-Branch one:
% 23.42/6.92  																																																									| (207) all_24_0_28 = 0
% 23.42/6.92  																																																									|
% 23.42/6.92  																																																										| Equations (207) can reduce 78 to:
% 23.42/6.92  																																																										| (101) $false
% 23.42/6.92  																																																										|
% 23.42/6.92  																																																										|-The branch is then unsatisfiable
% 23.42/6.92  																																																									|-Branch two:
% 23.42/6.92  																																																									| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.92  																																																									| (415)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_24_1_29) = v0))
% 23.42/6.92  																																																									|
% 23.42/6.92  																																																										+-Applying beta-rule and splitting (338), into two cases.
% 23.42/6.92  																																																										|-Branch one:
% 23.42/6.92  																																																										| (100) all_0_1_1 = 0
% 23.42/6.92  																																																										|
% 23.42/6.92  																																																											| Equations (100) can reduce 19 to:
% 23.42/6.92  																																																											| (101) $false
% 23.42/6.92  																																																											|
% 23.42/6.92  																																																											|-The branch is then unsatisfiable
% 23.42/6.92  																																																										|-Branch two:
% 23.42/6.92  																																																										| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.92  																																																										| (419)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																																										|
% 23.42/6.92  																																																											+-Applying beta-rule and splitting (196), into two cases.
% 23.42/6.92  																																																											|-Branch one:
% 23.42/6.92  																																																											| (211) all_26_0_30 = 0
% 23.42/6.92  																																																											|
% 23.42/6.92  																																																												| Equations (211) can reduce 82 to:
% 23.42/6.92  																																																												| (101) $false
% 23.42/6.92  																																																												|
% 23.42/6.92  																																																												|-The branch is then unsatisfiable
% 23.42/6.92  																																																											|-Branch two:
% 23.42/6.92  																																																											| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.92  																																																											| (423) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.92  																																																											|
% 23.42/6.92  																																																												+-Applying beta-rule and splitting (197), into two cases.
% 23.42/6.92  																																																												|-Branch one:
% 23.42/6.92  																																																												| (211) all_26_0_30 = 0
% 23.42/6.92  																																																												|
% 23.42/6.92  																																																													| Equations (211) can reduce 82 to:
% 23.42/6.92  																																																													| (101) $false
% 23.42/6.92  																																																													|
% 23.42/6.92  																																																													|-The branch is then unsatisfiable
% 23.42/6.92  																																																												|-Branch two:
% 23.42/6.92  																																																												| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.92  																																																												| (427) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.92  																																																												|
% 23.42/6.92  																																																													+-Applying beta-rule and splitting (198), into two cases.
% 23.42/6.92  																																																													|-Branch one:
% 23.42/6.92  																																																													| (231) all_22_0_26 = 0
% 23.42/6.92  																																																													|
% 23.42/6.92  																																																														| Equations (231) can reduce 74 to:
% 23.42/6.92  																																																														| (101) $false
% 23.42/6.92  																																																														|
% 23.42/6.92  																																																														|-The branch is then unsatisfiable
% 23.42/6.92  																																																													|-Branch two:
% 23.42/6.92  																																																													| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.92  																																																													| (431) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.92  																																																													|
% 23.42/6.92  																																																														+-Applying beta-rule and splitting (199), into two cases.
% 23.42/6.92  																																																														|-Branch one:
% 23.42/6.92  																																																														| (231) all_22_0_26 = 0
% 23.42/6.92  																																																														|
% 23.42/6.92  																																																															| Equations (231) can reduce 74 to:
% 23.42/6.92  																																																															| (101) $false
% 23.42/6.92  																																																															|
% 23.42/6.92  																																																															|-The branch is then unsatisfiable
% 23.42/6.92  																																																														|-Branch two:
% 23.42/6.92  																																																														| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.92  																																																														| (435) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																																														|
% 23.42/6.92  																																																															+-Applying beta-rule and splitting (202), into two cases.
% 23.42/6.92  																																																															|-Branch one:
% 23.42/6.92  																																																															| (239) all_32_0_36 = 0
% 23.42/6.92  																																																															|
% 23.42/6.92  																																																																| Equations (239) can reduce 92 to:
% 23.42/6.92  																																																																| (101) $false
% 23.42/6.92  																																																																|
% 23.42/6.92  																																																																|-The branch is then unsatisfiable
% 23.42/6.92  																																																															|-Branch two:
% 23.42/6.92  																																																															| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.92  																																																															| (439) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.92  																																																															|
% 23.42/6.92  																																																																+-Applying beta-rule and splitting (200), into two cases.
% 23.42/6.92  																																																																|-Branch one:
% 23.42/6.92  																																																																| (231) all_22_0_26 = 0
% 23.42/6.92  																																																																|
% 23.42/6.92  																																																																	| Equations (231) can reduce 74 to:
% 23.42/6.92  																																																																	| (101) $false
% 23.42/6.92  																																																																	|
% 23.42/6.92  																																																																	|-The branch is then unsatisfiable
% 23.42/6.92  																																																																|-Branch two:
% 23.42/6.92  																																																																| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.92  																																																																| (443) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.92  																																																																|
% 23.42/6.92  																																																																	+-Applying beta-rule and splitting (201), into two cases.
% 23.42/6.92  																																																																	|-Branch one:
% 23.42/6.92  																																																																	| (231) all_22_0_26 = 0
% 23.42/6.92  																																																																	|
% 23.42/6.92  																																																																		| Equations (231) can reduce 74 to:
% 23.42/6.92  																																																																		| (101) $false
% 23.42/6.92  																																																																		|
% 23.42/6.92  																																																																		|-The branch is then unsatisfiable
% 23.42/6.92  																																																																	|-Branch two:
% 23.42/6.92  																																																																	| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.92  																																																																	| (447) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																																																	|
% 23.42/6.92  																																																																		+-Applying beta-rule and splitting (203), into two cases.
% 23.42/6.92  																																																																		|-Branch one:
% 23.42/6.92  																																																																		| (239) all_32_0_36 = 0
% 23.42/6.92  																																																																		|
% 23.42/6.92  																																																																			| Equations (239) can reduce 92 to:
% 23.42/6.92  																																																																			| (101) $false
% 23.42/6.92  																																																																			|
% 23.42/6.92  																																																																			|-The branch is then unsatisfiable
% 23.42/6.92  																																																																		|-Branch two:
% 23.42/6.92  																																																																		| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.92  																																																																		| (451) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.92  																																																																		|
% 23.42/6.92  																																																																			+-Applying beta-rule and splitting (172), into two cases.
% 23.42/6.92  																																																																			|-Branch one:
% 23.42/6.92  																																																																			| (215) all_28_0_32 = 0
% 23.42/6.92  																																																																			|
% 23.42/6.92  																																																																				| Equations (215) can reduce 86 to:
% 23.42/6.92  																																																																				| (101) $false
% 23.42/6.92  																																																																				|
% 23.42/6.92  																																																																				|-The branch is then unsatisfiable
% 23.42/6.92  																																																																			|-Branch two:
% 23.42/6.92  																																																																			| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.92  																																																																			| (455) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.93  																																																																			|
% 23.42/6.93  																																																																				+-Applying beta-rule and splitting (176), into two cases.
% 23.42/6.93  																																																																				|-Branch one:
% 23.42/6.93  																																																																				| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																				|
% 23.42/6.93  																																																																					| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																					| (101) $false
% 23.42/6.93  																																																																					|
% 23.42/6.93  																																																																					|-The branch is then unsatisfiable
% 23.42/6.93  																																																																				|-Branch two:
% 23.42/6.93  																																																																				| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																				| (459) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.93  																																																																				|
% 23.42/6.93  																																																																					+-Applying beta-rule and splitting (177), into two cases.
% 23.42/6.93  																																																																					|-Branch one:
% 23.42/6.93  																																																																					| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																					|
% 23.42/6.93  																																																																						| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																						| (101) $false
% 23.42/6.93  																																																																						|
% 23.42/6.93  																																																																						|-The branch is then unsatisfiable
% 23.42/6.93  																																																																					|-Branch two:
% 23.42/6.93  																																																																					| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																					| (463) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.93  																																																																					|
% 23.42/6.93  																																																																						+-Applying beta-rule and splitting (179), into two cases.
% 23.42/6.93  																																																																						|-Branch one:
% 23.42/6.93  																																																																						| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																						|
% 23.42/6.93  																																																																							| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																							| (101) $false
% 23.42/6.93  																																																																							|
% 23.42/6.93  																																																																							|-The branch is then unsatisfiable
% 23.42/6.93  																																																																						|-Branch two:
% 23.42/6.93  																																																																						| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																						| (467) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.93  																																																																						|
% 23.42/6.93  																																																																							+-Applying beta-rule and splitting (270), into two cases.
% 23.42/6.93  																																																																							|-Branch one:
% 23.42/6.93  																																																																							| (231) all_22_0_26 = 0
% 23.42/6.93  																																																																							|
% 23.42/6.93  																																																																								| Equations (231) can reduce 74 to:
% 23.42/6.93  																																																																								| (101) $false
% 23.42/6.93  																																																																								|
% 23.42/6.93  																																																																								|-The branch is then unsatisfiable
% 23.42/6.93  																																																																							|-Branch two:
% 23.42/6.93  																																																																							| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.93  																																																																							| (471)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_0_0) = v0))
% 23.42/6.93  																																																																							|
% 23.42/6.93  																																																																								+-Applying beta-rule and splitting (278), into two cases.
% 23.42/6.93  																																																																								|-Branch one:
% 23.42/6.93  																																																																								| (231) all_22_0_26 = 0
% 23.42/6.93  																																																																								|
% 23.42/6.93  																																																																									| Equations (231) can reduce 74 to:
% 23.42/6.93  																																																																									| (101) $false
% 23.42/6.93  																																																																									|
% 23.42/6.93  																																																																									|-The branch is then unsatisfiable
% 23.42/6.93  																																																																								|-Branch two:
% 23.42/6.93  																																																																								| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.93  																																																																								| (475)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.93  																																																																								|
% 23.42/6.93  																																																																									+-Applying beta-rule and splitting (174), into two cases.
% 23.42/6.93  																																																																									|-Branch one:
% 23.42/6.93  																																																																									| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																									|
% 23.42/6.93  																																																																										| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																										| (101) $false
% 23.42/6.93  																																																																										|
% 23.42/6.93  																																																																										|-The branch is then unsatisfiable
% 23.42/6.93  																																																																									|-Branch two:
% 23.42/6.93  																																																																									| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																									| (479) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.93  																																																																									|
% 23.42/6.93  																																																																										+-Applying beta-rule and splitting (175), into two cases.
% 23.42/6.93  																																																																										|-Branch one:
% 23.42/6.93  																																																																										| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																										|
% 23.42/6.93  																																																																											| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																											| (101) $false
% 23.42/6.93  																																																																											|
% 23.42/6.93  																																																																											|-The branch is then unsatisfiable
% 23.42/6.93  																																																																										|-Branch two:
% 23.42/6.93  																																																																										| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																										| (483) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.93  																																																																										|
% 23.42/6.93  																																																																											+-Applying beta-rule and splitting (178), into two cases.
% 23.42/6.93  																																																																											|-Branch one:
% 23.42/6.93  																																																																											| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																											|
% 23.42/6.93  																																																																												| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																												| (101) $false
% 23.42/6.93  																																																																												|
% 23.42/6.93  																																																																												|-The branch is then unsatisfiable
% 23.42/6.93  																																																																											|-Branch two:
% 23.42/6.93  																																																																											| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																											| (487) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.93  																																																																											|
% 23.42/6.93  																																																																												+-Applying beta-rule and splitting (153), into two cases.
% 23.42/6.93  																																																																												|-Branch one:
% 23.42/6.93  																																																																												| (211) all_26_0_30 = 0
% 23.42/6.93  																																																																												|
% 23.42/6.93  																																																																													| Equations (211) can reduce 82 to:
% 23.42/6.93  																																																																													| (101) $false
% 23.42/6.93  																																																																													|
% 23.42/6.93  																																																																													|-The branch is then unsatisfiable
% 23.42/6.93  																																																																												|-Branch two:
% 23.42/6.93  																																																																												| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.93  																																																																												| (491) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.93  																																																																												|
% 23.42/6.93  																																																																													+-Applying beta-rule and splitting (152), into two cases.
% 23.42/6.93  																																																																													|-Branch one:
% 23.42/6.93  																																																																													| (211) all_26_0_30 = 0
% 23.42/6.93  																																																																													|
% 23.42/6.93  																																																																														| Equations (211) can reduce 82 to:
% 23.42/6.93  																																																																														| (101) $false
% 23.42/6.93  																																																																														|
% 23.42/6.93  																																																																														|-The branch is then unsatisfiable
% 23.42/6.93  																																																																													|-Branch two:
% 23.42/6.93  																																																																													| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.93  																																																																													| (495) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.93  																																																																													|
% 23.42/6.93  																																																																														+-Applying beta-rule and splitting (154), into two cases.
% 23.42/6.93  																																																																														|-Branch one:
% 23.42/6.93  																																																																														| (211) all_26_0_30 = 0
% 23.42/6.93  																																																																														|
% 23.42/6.93  																																																																															| Equations (211) can reduce 82 to:
% 23.42/6.93  																																																																															| (101) $false
% 23.42/6.93  																																																																															|
% 23.42/6.93  																																																																															|-The branch is then unsatisfiable
% 23.42/6.93  																																																																														|-Branch two:
% 23.42/6.93  																																																																														| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.93  																																																																														| (499) all_22_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.93  																																																																														|
% 23.42/6.93  																																																																															+-Applying beta-rule and splitting (143), into two cases.
% 23.42/6.93  																																																																															|-Branch one:
% 23.42/6.93  																																																																															| (211) all_26_0_30 = 0
% 23.42/6.93  																																																																															|
% 23.42/6.93  																																																																																| Equations (211) can reduce 82 to:
% 23.42/6.93  																																																																																| (101) $false
% 23.42/6.93  																																																																																|
% 23.42/6.93  																																																																																|-The branch is then unsatisfiable
% 23.42/6.93  																																																																															|-Branch two:
% 23.42/6.93  																																																																															| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.93  																																																																															| (503) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.93  																																																																															|
% 23.42/6.93  																																																																																+-Applying beta-rule and splitting (204), into two cases.
% 23.42/6.93  																																																																																|-Branch one:
% 23.42/6.93  																																																																																| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																																|
% 23.42/6.93  																																																																																	| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																																	| (101) $false
% 23.42/6.93  																																																																																	|
% 23.42/6.93  																																																																																	|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																|-Branch two:
% 23.42/6.93  																																																																																| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																																| (507) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.93  																																																																																|
% 23.42/6.93  																																																																																	+-Applying beta-rule and splitting (156), into two cases.
% 23.42/6.93  																																																																																	|-Branch one:
% 23.42/6.93  																																																																																	| (239) all_32_0_36 = 0
% 23.42/6.93  																																																																																	|
% 23.42/6.93  																																																																																		| Equations (239) can reduce 92 to:
% 23.42/6.93  																																																																																		| (101) $false
% 23.42/6.93  																																																																																		|
% 23.42/6.93  																																																																																		|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																	|-Branch two:
% 23.42/6.93  																																																																																	| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.93  																																																																																	| (511) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.93  																																																																																	|
% 23.42/6.93  																																																																																		+-Applying beta-rule and splitting (205), into two cases.
% 23.42/6.93  																																																																																		|-Branch one:
% 23.42/6.93  																																																																																		| (215) all_28_0_32 = 0
% 23.42/6.93  																																																																																		|
% 23.42/6.93  																																																																																			| Equations (215) can reduce 86 to:
% 23.42/6.93  																																																																																			| (101) $false
% 23.42/6.93  																																																																																			|
% 23.42/6.93  																																																																																			|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																		|-Branch two:
% 23.42/6.93  																																																																																		| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.93  																																																																																		| (515) all_20_0_24 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.93  																																																																																		|
% 23.42/6.93  																																																																																			+-Applying beta-rule and splitting (144), into two cases.
% 23.42/6.93  																																																																																			|-Branch one:
% 23.42/6.93  																																																																																			| (211) all_26_0_30 = 0
% 23.42/6.93  																																																																																			|
% 23.42/6.93  																																																																																				| Equations (211) can reduce 82 to:
% 23.42/6.93  																																																																																				| (101) $false
% 23.42/6.93  																																																																																				|
% 23.42/6.93  																																																																																				|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																			|-Branch two:
% 23.42/6.93  																																																																																			| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.93  																																																																																			| (519) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.93  																																																																																			|
% 23.42/6.93  																																																																																				+-Applying beta-rule and splitting (226), into two cases.
% 23.42/6.93  																																																																																				|-Branch one:
% 23.42/6.93  																																																																																				| (100) all_0_1_1 = 0
% 23.42/6.93  																																																																																				|
% 23.42/6.93  																																																																																					| Equations (100) can reduce 19 to:
% 23.42/6.93  																																																																																					| (101) $false
% 23.42/6.93  																																																																																					|
% 23.42/6.93  																																																																																					|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																				|-Branch two:
% 23.42/6.93  																																																																																				| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.93  																																																																																				| (523)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.93  																																																																																				|
% 23.42/6.93  																																																																																					+-Applying beta-rule and splitting (435), into two cases.
% 23.42/6.93  																																																																																					|-Branch one:
% 23.42/6.93  																																																																																					| (235) all_20_0_24 = 0
% 23.42/6.93  																																																																																					|
% 23.42/6.93  																																																																																						| Equations (235) can reduce 70 to:
% 23.42/6.93  																																																																																						| (101) $false
% 23.42/6.93  																																																																																						|
% 23.42/6.93  																																																																																						|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																					|-Branch two:
% 23.42/6.93  																																																																																					| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.93  																																																																																					| (527)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.93  																																																																																					|
% 23.42/6.93  																																																																																						+-Applying beta-rule and splitting (439), into two cases.
% 23.42/6.93  																																																																																						|-Branch one:
% 23.42/6.93  																																																																																						| (235) all_20_0_24 = 0
% 23.42/6.93  																																																																																						|
% 23.42/6.93  																																																																																							| Equations (235) can reduce 70 to:
% 23.42/6.93  																																																																																							| (101) $false
% 23.42/6.93  																																																																																							|
% 23.42/6.93  																																																																																							|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																						|-Branch two:
% 23.42/6.93  																																																																																						| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.93  																																																																																						| (531)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.93  																																																																																						|
% 23.42/6.93  																																																																																							+-Applying beta-rule and splitting (443), into two cases.
% 23.42/6.93  																																																																																							|-Branch one:
% 23.42/6.93  																																																																																							| (235) all_20_0_24 = 0
% 23.42/6.93  																																																																																							|
% 23.42/6.93  																																																																																								| Equations (235) can reduce 70 to:
% 23.42/6.93  																																																																																								| (101) $false
% 23.42/6.93  																																																																																								|
% 23.42/6.93  																																																																																								|-The branch is then unsatisfiable
% 23.42/6.93  																																																																																							|-Branch two:
% 23.42/6.93  																																																																																							| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.93  																																																																																							| (535)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.94  																																																																																							|
% 23.42/6.94  																																																																																								+-Applying beta-rule and splitting (447), into two cases.
% 23.42/6.94  																																																																																								|-Branch one:
% 23.42/6.94  																																																																																								| (235) all_20_0_24 = 0
% 23.42/6.94  																																																																																								|
% 23.42/6.94  																																																																																									| Equations (235) can reduce 70 to:
% 23.42/6.94  																																																																																									| (101) $false
% 23.42/6.94  																																																																																									|
% 23.42/6.94  																																																																																									|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																								|-Branch two:
% 23.42/6.94  																																																																																								| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.94  																																																																																								| (539)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.94  																																																																																								|
% 23.42/6.94  																																																																																									+-Applying beta-rule and splitting (451), into two cases.
% 23.42/6.94  																																																																																									|-Branch one:
% 23.42/6.94  																																																																																									| (235) all_20_0_24 = 0
% 23.42/6.94  																																																																																									|
% 23.42/6.94  																																																																																										| Equations (235) can reduce 70 to:
% 23.42/6.94  																																																																																										| (101) $false
% 23.42/6.94  																																																																																										|
% 23.42/6.94  																																																																																										|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																									|-Branch two:
% 23.42/6.94  																																																																																									| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.94  																																																																																									| (543)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.94  																																																																																									|
% 23.42/6.94  																																																																																										+-Applying beta-rule and splitting (455), into two cases.
% 23.42/6.94  																																																																																										|-Branch one:
% 23.42/6.94  																																																																																										| (100) all_0_1_1 = 0
% 23.42/6.94  																																																																																										|
% 23.42/6.94  																																																																																											| Equations (100) can reduce 19 to:
% 23.42/6.94  																																																																																											| (101) $false
% 23.42/6.94  																																																																																											|
% 23.42/6.94  																																																																																											|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																										|-Branch two:
% 23.42/6.94  																																																																																										| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.94  																																																																																										| (547)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.94  																																																																																										|
% 23.42/6.94  																																																																																											+-Applying beta-rule and splitting (459), into two cases.
% 23.42/6.94  																																																																																											|-Branch one:
% 23.42/6.94  																																																																																											| (207) all_24_0_28 = 0
% 23.42/6.94  																																																																																											|
% 23.42/6.94  																																																																																												| Equations (207) can reduce 78 to:
% 23.42/6.94  																																																																																												| (101) $false
% 23.42/6.94  																																																																																												|
% 23.42/6.94  																																																																																												|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																											|-Branch two:
% 23.42/6.94  																																																																																											| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.94  																																																																																											| (551)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.94  																																																																																											|
% 23.42/6.94  																																																																																												+-Applying beta-rule and splitting (173), into two cases.
% 23.42/6.94  																																																																																												|-Branch one:
% 23.42/6.94  																																																																																												| (215) all_28_0_32 = 0
% 23.42/6.94  																																																																																												|
% 23.42/6.94  																																																																																													| Equations (215) can reduce 86 to:
% 23.42/6.94  																																																																																													| (101) $false
% 23.42/6.94  																																																																																													|
% 23.42/6.94  																																																																																													|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																												|-Branch two:
% 23.42/6.94  																																																																																												| (86)  ~ (all_28_0_32 = 0)
% 23.42/6.94  																																																																																												| (555) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.94  																																																																																												|
% 23.42/6.94  																																																																																													+-Applying beta-rule and splitting (423), into two cases.
% 23.42/6.94  																																																																																													|-Branch one:
% 23.42/6.94  																																																																																													| (235) all_20_0_24 = 0
% 23.42/6.94  																																																																																													|
% 23.42/6.94  																																																																																														| Equations (235) can reduce 70 to:
% 23.42/6.94  																																																																																														| (101) $false
% 23.42/6.94  																																																																																														|
% 23.42/6.94  																																																																																														|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																													|-Branch two:
% 23.42/6.94  																																																																																													| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.94  																																																																																													| (559)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.94  																																																																																													|
% 23.42/6.94  																																																																																														+-Applying beta-rule and splitting (427), into two cases.
% 23.42/6.94  																																																																																														|-Branch one:
% 23.42/6.94  																																																																																														| (235) all_20_0_24 = 0
% 23.42/6.94  																																																																																														|
% 23.42/6.94  																																																																																															| Equations (235) can reduce 70 to:
% 23.42/6.94  																																																																																															| (101) $false
% 23.42/6.94  																																																																																															|
% 23.42/6.94  																																																																																															|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																														|-Branch two:
% 23.42/6.94  																																																																																														| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.94  																																																																																														| (563)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.94  																																																																																														|
% 23.42/6.94  																																																																																															+-Applying beta-rule and splitting (463), into two cases.
% 23.42/6.94  																																																																																															|-Branch one:
% 23.42/6.94  																																																																																															| (211) all_26_0_30 = 0
% 23.42/6.94  																																																																																															|
% 23.42/6.94  																																																																																																| Equations (211) can reduce 82 to:
% 23.42/6.94  																																																																																																| (101) $false
% 23.42/6.94  																																																																																																|
% 23.42/6.94  																																																																																																|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																															|-Branch two:
% 23.42/6.94  																																																																																															| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.94  																																																																																															| (567)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.94  																																																																																															|
% 23.42/6.94  																																																																																																+-Applying beta-rule and splitting (467), into two cases.
% 23.42/6.94  																																																																																																|-Branch one:
% 23.42/6.94  																																																																																																| (231) all_22_0_26 = 0
% 23.42/6.94  																																																																																																|
% 23.42/6.94  																																																																																																	| Equations (231) can reduce 74 to:
% 23.42/6.94  																																																																																																	| (101) $false
% 23.42/6.94  																																																																																																	|
% 23.42/6.94  																																																																																																	|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																|-Branch two:
% 23.42/6.94  																																																																																																| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.94  																																																																																																| (571)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.94  																																																																																																|
% 23.42/6.94  																																																																																																	+-Applying beta-rule and splitting (491), into two cases.
% 23.42/6.94  																																																																																																	|-Branch one:
% 23.42/6.94  																																																																																																	| (231) all_22_0_26 = 0
% 23.42/6.94  																																																																																																	|
% 23.42/6.94  																																																																																																		| Equations (231) can reduce 74 to:
% 23.42/6.94  																																																																																																		| (101) $false
% 23.42/6.94  																																																																																																		|
% 23.42/6.94  																																																																																																		|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																	|-Branch two:
% 23.42/6.94  																																																																																																	| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.94  																																																																																																	| (575)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.94  																																																																																																	|
% 23.42/6.94  																																																																																																		+-Applying beta-rule and splitting (139), into two cases.
% 23.42/6.94  																																																																																																		|-Branch one:
% 23.42/6.94  																																																																																																		| (207) all_24_0_28 = 0
% 23.42/6.94  																																																																																																		|
% 23.42/6.94  																																																																																																			| Equations (207) can reduce 78 to:
% 23.42/6.94  																																																																																																			| (101) $false
% 23.42/6.94  																																																																																																			|
% 23.42/6.94  																																																																																																			|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																		|-Branch two:
% 23.42/6.94  																																																																																																		| (78)  ~ (all_24_0_28 = 0)
% 23.42/6.94  																																																																																																		| (579) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.94  																																																																																																		|
% 23.42/6.94  																																																																																																			+-Applying beta-rule and splitting (161), into two cases.
% 23.42/6.94  																																																																																																			|-Branch one:
% 23.42/6.94  																																																																																																			| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																			|
% 23.42/6.94  																																																																																																				| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																				| (101) $false
% 23.42/6.94  																																																																																																				|
% 23.42/6.94  																																																																																																				|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																			|-Branch two:
% 23.42/6.94  																																																																																																			| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																			| (583) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.94  																																																																																																			|
% 23.42/6.94  																																																																																																				+-Applying beta-rule and splitting (162), into two cases.
% 23.42/6.94  																																																																																																				|-Branch one:
% 23.42/6.94  																																																																																																				| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																				|
% 23.42/6.94  																																																																																																					| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																					| (101) $false
% 23.42/6.94  																																																																																																					|
% 23.42/6.94  																																																																																																					|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																				|-Branch two:
% 23.42/6.94  																																																																																																				| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																				| (587) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.94  																																																																																																				|
% 23.42/6.94  																																																																																																					+-Applying beta-rule and splitting (157), into two cases.
% 23.42/6.94  																																																																																																					|-Branch one:
% 23.42/6.94  																																																																																																					| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																					|
% 23.42/6.94  																																																																																																						| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																						| (101) $false
% 23.42/6.94  																																																																																																						|
% 23.42/6.94  																																																																																																						|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																					|-Branch two:
% 23.42/6.94  																																																																																																					| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																					| (591) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.94  																																																																																																					|
% 23.42/6.94  																																																																																																						+-Applying beta-rule and splitting (158), into two cases.
% 23.42/6.94  																																																																																																						|-Branch one:
% 23.42/6.94  																																																																																																						| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																						|
% 23.42/6.94  																																																																																																							| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																							| (101) $false
% 23.42/6.94  																																																																																																							|
% 23.42/6.94  																																																																																																							|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																						|-Branch two:
% 23.42/6.94  																																																																																																						| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																						| (595) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.94  																																																																																																						|
% 23.42/6.94  																																																																																																							+-Applying beta-rule and splitting (159), into two cases.
% 23.42/6.94  																																																																																																							|-Branch one:
% 23.42/6.94  																																																																																																							| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																							|
% 23.42/6.94  																																																																																																								| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																								| (101) $false
% 23.42/6.94  																																																																																																								|
% 23.42/6.94  																																																																																																								|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																							|-Branch two:
% 23.42/6.94  																																																																																																							| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																							| (599) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.94  																																																																																																							|
% 23.42/6.94  																																																																																																								+-Applying beta-rule and splitting (160), into two cases.
% 23.42/6.94  																																																																																																								|-Branch one:
% 23.42/6.94  																																																																																																								| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																								|
% 23.42/6.94  																																																																																																									| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																									| (101) $false
% 23.42/6.94  																																																																																																									|
% 23.42/6.94  																																																																																																									|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																								|-Branch two:
% 23.42/6.94  																																																																																																								| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																								| (603) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.94  																																																																																																								|
% 23.42/6.94  																																																																																																									+-Applying beta-rule and splitting (163), into two cases.
% 23.42/6.94  																																																																																																									|-Branch one:
% 23.42/6.94  																																																																																																									| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																									|
% 23.42/6.94  																																																																																																										| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																										| (101) $false
% 23.42/6.94  																																																																																																										|
% 23.42/6.94  																																																																																																										|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																									|-Branch two:
% 23.42/6.94  																																																																																																									| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																									| (607) all_24_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_24_1_29) = v0))
% 23.42/6.94  																																																																																																									|
% 23.42/6.94  																																																																																																										+-Applying beta-rule and splitting (164), into two cases.
% 23.42/6.94  																																																																																																										|-Branch one:
% 23.42/6.94  																																																																																																										| (239) all_32_0_36 = 0
% 23.42/6.94  																																																																																																										|
% 23.42/6.94  																																																																																																											| Equations (239) can reduce 92 to:
% 23.42/6.94  																																																																																																											| (101) $false
% 23.42/6.94  																																																																																																											|
% 23.42/6.94  																																																																																																											|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																										|-Branch two:
% 23.42/6.94  																																																																																																										| (92)  ~ (all_32_0_36 = 0)
% 23.42/6.94  																																																																																																										| (611) all_26_0_30 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.94  																																																																																																										|
% 23.42/6.94  																																																																																																											+-Applying beta-rule and splitting (142), into two cases.
% 23.42/6.94  																																																																																																											|-Branch one:
% 23.42/6.94  																																																																																																											| (211) all_26_0_30 = 0
% 23.42/6.94  																																																																																																											|
% 23.42/6.94  																																																																																																												| Equations (211) can reduce 82 to:
% 23.42/6.94  																																																																																																												| (101) $false
% 23.42/6.94  																																																																																																												|
% 23.42/6.94  																																																																																																												|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																											|-Branch two:
% 23.42/6.94  																																																																																																											| (82)  ~ (all_26_0_30 = 0)
% 23.42/6.94  																																																																																																											| (615) all_0_1_1 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.94  																																																																																																											|
% 23.42/6.94  																																																																																																												+-Applying beta-rule and splitting (286), into two cases.
% 23.42/6.94  																																																																																																												|-Branch one:
% 23.42/6.94  																																																																																																												| (100) all_0_1_1 = 0
% 23.42/6.94  																																																																																																												|
% 23.42/6.94  																																																																																																													| Equations (100) can reduce 19 to:
% 23.42/6.94  																																																																																																													| (101) $false
% 23.42/6.94  																																																																																																													|
% 23.42/6.94  																																																																																																													|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																												|-Branch two:
% 23.42/6.94  																																																																																																												| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.94  																																																																																																												| (619)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.94  																																																																																																												|
% 23.42/6.94  																																																																																																													+-Applying beta-rule and splitting (322), into two cases.
% 23.42/6.94  																																																																																																													|-Branch one:
% 23.42/6.94  																																																																																																													| (235) all_20_0_24 = 0
% 23.42/6.94  																																																																																																													|
% 23.42/6.94  																																																																																																														| Equations (235) can reduce 70 to:
% 23.42/6.94  																																																																																																														| (101) $false
% 23.42/6.94  																																																																																																														|
% 23.42/6.94  																																																																																																														|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																													|-Branch two:
% 23.42/6.94  																																																																																																													| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.94  																																																																																																													| (623)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.94  																																																																																																													|
% 23.42/6.94  																																																																																																														+-Applying beta-rule and splitting (330), into two cases.
% 23.42/6.94  																																																																																																														|-Branch one:
% 23.42/6.94  																																																																																																														| (235) all_20_0_24 = 0
% 23.42/6.94  																																																																																																														|
% 23.42/6.94  																																																																																																															| Equations (235) can reduce 70 to:
% 23.42/6.94  																																																																																																															| (101) $false
% 23.42/6.94  																																																																																																															|
% 23.42/6.94  																																																																																																															|-The branch is then unsatisfiable
% 23.42/6.94  																																																																																																														|-Branch two:
% 23.42/6.94  																																																																																																														| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.94  																																																																																																														| (627)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.95  																																																																																																														|
% 23.42/6.95  																																																																																																															+-Applying beta-rule and splitting (431), into two cases.
% 23.42/6.95  																																																																																																															|-Branch one:
% 23.42/6.95  																																																																																																															| (235) all_20_0_24 = 0
% 23.42/6.95  																																																																																																															|
% 23.42/6.95  																																																																																																																| Equations (235) can reduce 70 to:
% 23.42/6.95  																																																																																																																| (101) $false
% 23.42/6.95  																																																																																																																|
% 23.42/6.95  																																																																																																																|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																															|-Branch two:
% 23.42/6.95  																																																																																																															| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.95  																																																																																																															| (631)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.95  																																																																																																															|
% 23.42/6.95  																																																																																																																| Instantiating (631) with all_476_0_1167 yields:
% 23.42/6.95  																																																																																																																| (632) (all_476_0_1167 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (all_476_0_1167 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_476_0_1167 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167) | ( ~ (all_476_0_1167 = 0) & distinct_points(all_0_0_0, all_0_2_2) = all_476_0_1167)
% 23.42/6.95  																																																																																																																|
% 23.42/6.95  																																																																																																																+-Applying beta-rule and splitting (495), into two cases.
% 23.42/6.95  																																																																																																																|-Branch one:
% 23.42/6.95  																																																																																																																| (231) all_22_0_26 = 0
% 23.42/6.95  																																																																																																																|
% 23.42/6.95  																																																																																																																	| Equations (231) can reduce 74 to:
% 23.42/6.95  																																																																																																																	| (101) $false
% 23.42/6.95  																																																																																																																	|
% 23.42/6.95  																																																																																																																	|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																|-Branch two:
% 23.42/6.95  																																																																																																																| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.95  																																																																																																																| (636)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.95  																																																																																																																|
% 23.42/6.95  																																																																																																																	+-Applying beta-rule and splitting (499), into two cases.
% 23.42/6.95  																																																																																																																	|-Branch one:
% 23.42/6.95  																																																																																																																	| (231) all_22_0_26 = 0
% 23.42/6.95  																																																																																																																	|
% 23.42/6.95  																																																																																																																		| Equations (231) can reduce 74 to:
% 23.42/6.95  																																																																																																																		| (101) $false
% 23.42/6.95  																																																																																																																		|
% 23.42/6.95  																																																																																																																		|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																	|-Branch two:
% 23.42/6.95  																																																																																																																	| (74)  ~ (all_22_0_26 = 0)
% 23.42/6.95  																																																																																																																	| (640)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_0_0, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_0_0) = v0))
% 23.42/6.95  																																																																																																																	|
% 23.42/6.95  																																																																																																																		+-Applying beta-rule and splitting (503), into two cases.
% 23.42/6.95  																																																																																																																		|-Branch one:
% 23.42/6.95  																																																																																																																		| (100) all_0_1_1 = 0
% 23.42/6.95  																																																																																																																		|
% 23.42/6.95  																																																																																																																			| Equations (100) can reduce 19 to:
% 23.42/6.95  																																																																																																																			| (101) $false
% 23.42/6.95  																																																																																																																			|
% 23.42/6.95  																																																																																																																			|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																		|-Branch two:
% 23.42/6.95  																																																																																																																		| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.95  																																																																																																																		| (644)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_24_1_29, all_0_2_2) = v0))
% 23.42/6.95  																																																																																																																		|
% 23.42/6.95  																																																																																																																			+-Applying beta-rule and splitting (507), into two cases.
% 23.42/6.95  																																																																																																																			|-Branch one:
% 23.42/6.95  																																																																																																																			| (235) all_20_0_24 = 0
% 23.42/6.95  																																																																																																																			|
% 23.42/6.95  																																																																																																																				| Equations (235) can reduce 70 to:
% 23.42/6.95  																																																																																																																				| (101) $false
% 23.42/6.95  																																																																																																																				|
% 23.42/6.95  																																																																																																																				|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																			|-Branch two:
% 23.42/6.95  																																																																																																																			| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.95  																																																																																																																			| (648)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.95  																																																																																																																			|
% 23.42/6.95  																																																																																																																				+-Applying beta-rule and splitting (511), into two cases.
% 23.42/6.95  																																																																																																																				|-Branch one:
% 23.42/6.95  																																																																																																																				| (100) all_0_1_1 = 0
% 23.42/6.95  																																																																																																																				|
% 23.42/6.95  																																																																																																																					| Equations (100) can reduce 19 to:
% 23.42/6.95  																																																																																																																					| (101) $false
% 23.42/6.95  																																																																																																																					|
% 23.42/6.95  																																																																																																																					|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																				|-Branch two:
% 23.42/6.95  																																																																																																																				| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.95  																																																																																																																				| (652)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.95  																																																																																																																				|
% 23.42/6.95  																																																																																																																					+-Applying beta-rule and splitting (515), into two cases.
% 23.42/6.95  																																																																																																																					|-Branch one:
% 23.42/6.95  																																																																																																																					| (235) all_20_0_24 = 0
% 23.42/6.95  																																																																																																																					|
% 23.42/6.95  																																																																																																																						| Equations (235) can reduce 70 to:
% 23.42/6.95  																																																																																																																						| (101) $false
% 23.42/6.95  																																																																																																																						|
% 23.42/6.95  																																																																																																																						|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																					|-Branch two:
% 23.42/6.95  																																																																																																																					| (70)  ~ (all_20_0_24 = 0)
% 23.42/6.95  																																																																																																																					| (656)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.95  																																																																																																																					|
% 23.42/6.95  																																																																																																																						+-Applying beta-rule and splitting (519), into two cases.
% 23.42/6.95  																																																																																																																						|-Branch one:
% 23.42/6.95  																																																																																																																						| (100) all_0_1_1 = 0
% 23.42/6.95  																																																																																																																						|
% 23.42/6.95  																																																																																																																							| Equations (100) can reduce 19 to:
% 23.42/6.95  																																																																																																																							| (101) $false
% 23.42/6.95  																																																																																																																							|
% 23.42/6.95  																																																																																																																							|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																						|-Branch two:
% 23.42/6.95  																																																																																																																						| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.95  																																																																																																																						| (660)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.42/6.95  																																																																																																																						|
% 23.42/6.95  																																																																																																																							+-Applying beta-rule and splitting (555), into two cases.
% 23.42/6.95  																																																																																																																							|-Branch one:
% 23.42/6.95  																																																																																																																							| (100) all_0_1_1 = 0
% 23.42/6.95  																																																																																																																							|
% 23.42/6.95  																																																																																																																								| Equations (100) can reduce 19 to:
% 23.42/6.95  																																																																																																																								| (101) $false
% 23.42/6.95  																																																																																																																								|
% 23.42/6.95  																																																																																																																								|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																							|-Branch two:
% 23.42/6.95  																																																																																																																							| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.95  																																																																																																																							| (664)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.42/6.95  																																																																																																																							|
% 23.42/6.95  																																																																																																																								+-Applying beta-rule and splitting (595), into two cases.
% 23.42/6.95  																																																																																																																								|-Branch one:
% 23.42/6.95  																																																																																																																								| (100) all_0_1_1 = 0
% 23.42/6.95  																																																																																																																								|
% 23.42/6.95  																																																																																																																									| Equations (100) can reduce 19 to:
% 23.42/6.95  																																																																																																																									| (101) $false
% 23.42/6.95  																																																																																																																									|
% 23.42/6.95  																																																																																																																									|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																								|-Branch two:
% 23.42/6.95  																																																																																																																								| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.95  																																																																																																																								| (668)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_0_0) = v0))
% 23.42/6.95  																																																																																																																								|
% 23.42/6.95  																																																																																																																									+-Applying beta-rule and splitting (599), into two cases.
% 23.42/6.95  																																																																																																																									|-Branch one:
% 23.42/6.95  																																																																																																																									| (100) all_0_1_1 = 0
% 23.42/6.95  																																																																																																																									|
% 23.42/6.95  																																																																																																																										| Equations (100) can reduce 19 to:
% 23.42/6.95  																																																																																																																										| (101) $false
% 23.42/6.95  																																																																																																																										|
% 23.42/6.95  																																																																																																																										|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																									|-Branch two:
% 23.42/6.95  																																																																																																																									| (19)  ~ (all_0_1_1 = 0)
% 23.42/6.95  																																																																																																																									| (672)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_0_0, all_0_2_2) = v0))
% 23.42/6.95  																																																																																																																									|
% 23.42/6.95  																																																																																																																										| Instantiating (672) with all_536_0_1276 yields:
% 23.42/6.95  																																																																																																																										| (673) (all_536_0_1276 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (all_536_0_1276 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_536_0_1276 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_536_0_1276) | ( ~ (all_536_0_1276 = 0) & distinct_points(all_0_0_0, all_0_2_2) = all_536_0_1276)
% 23.42/6.95  																																																																																																																										|
% 23.42/6.95  																																																																																																																										+-Applying beta-rule and splitting (673), into two cases.
% 23.42/6.95  																																																																																																																										|-Branch one:
% 23.42/6.95  																																																																																																																										| (674) (all_536_0_1276 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (all_536_0_1276 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_536_0_1276 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_536_0_1276)
% 23.42/6.95  																																																																																																																										|
% 23.42/6.95  																																																																																																																											+-Applying beta-rule and splitting (674), into two cases.
% 23.42/6.95  																																																																																																																											|-Branch one:
% 23.42/6.95  																																																																																																																											| (675) (all_536_0_1276 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0) | (all_536_0_1276 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0)
% 23.42/6.95  																																																																																																																											|
% 23.42/6.95  																																																																																																																												+-Applying beta-rule and splitting (675), into two cases.
% 23.42/6.95  																																																																																																																												|-Branch one:
% 23.42/6.95  																																																																																																																												| (676) all_536_0_1276 = 0 & apart_point_and_line(all_0_0_0, all_0_3_3) = 0
% 23.42/6.95  																																																																																																																												|
% 23.42/6.95  																																																																																																																													| Applying alpha-rule on (676) yields:
% 23.42/6.95  																																																																																																																													| (677) all_536_0_1276 = 0
% 23.42/6.95  																																																																																																																													| (678) apart_point_and_line(all_0_0_0, all_0_3_3) = 0
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																													| Instantiating formula (17) with all_0_0_0, all_0_3_3, 0, all_22_0_26 and discharging atoms apart_point_and_line(all_0_0_0, all_0_3_3) = all_22_0_26, apart_point_and_line(all_0_0_0, all_0_3_3) = 0, yields:
% 23.42/6.95  																																																																																																																													| (231) all_22_0_26 = 0
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																													| Equations (231) can reduce 74 to:
% 23.42/6.95  																																																																																																																													| (101) $false
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																													|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																												|-Branch two:
% 23.42/6.95  																																																																																																																												| (681) all_536_0_1276 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 23.42/6.95  																																																																																																																												|
% 23.42/6.95  																																																																																																																													| Applying alpha-rule on (681) yields:
% 23.42/6.95  																																																																																																																													| (677) all_536_0_1276 = 0
% 23.42/6.95  																																																																																																																													| (683) apart_point_and_line(all_0_2_2, all_0_5_5) = 0
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																													| Instantiating formula (17) with all_0_2_2, all_0_5_5, 0, all_20_0_24 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_20_0_24, apart_point_and_line(all_0_2_2, all_0_5_5) = 0, yields:
% 23.42/6.95  																																																																																																																													| (235) all_20_0_24 = 0
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																													| Equations (235) can reduce 70 to:
% 23.42/6.95  																																																																																																																													| (101) $false
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																													|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																											|-Branch two:
% 23.42/6.95  																																																																																																																											| (686)  ~ (all_536_0_1276 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_536_0_1276
% 23.42/6.95  																																																																																																																											|
% 23.42/6.95  																																																																																																																												| Applying alpha-rule on (686) yields:
% 23.42/6.95  																																																																																																																												| (687)  ~ (all_536_0_1276 = 0)
% 23.42/6.95  																																																																																																																												| (688) distinct_lines(all_0_3_3, all_0_5_5) = all_536_0_1276
% 23.42/6.95  																																																																																																																												|
% 23.42/6.95  																																																																																																																												+-Applying beta-rule and splitting (632), into two cases.
% 23.42/6.95  																																																																																																																												|-Branch one:
% 23.42/6.95  																																																																																																																												| (689) (all_476_0_1167 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (all_476_0_1167 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_476_0_1167 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167)
% 23.42/6.95  																																																																																																																												|
% 23.42/6.95  																																																																																																																													+-Applying beta-rule and splitting (689), into two cases.
% 23.42/6.95  																																																																																																																													|-Branch one:
% 23.42/6.95  																																																																																																																													| (690) (all_476_0_1167 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0) | (all_476_0_1167 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0)
% 23.42/6.95  																																																																																																																													|
% 23.42/6.95  																																																																																																																														+-Applying beta-rule and splitting (690), into two cases.
% 23.42/6.95  																																																																																																																														|-Branch one:
% 23.42/6.95  																																																																																																																														| (691) all_476_0_1167 = 0 & apart_point_and_line(all_0_0_0, all_0_5_5) = 0
% 23.42/6.95  																																																																																																																														|
% 23.42/6.95  																																																																																																																															| Applying alpha-rule on (691) yields:
% 23.42/6.95  																																																																																																																															| (692) all_476_0_1167 = 0
% 23.42/6.95  																																																																																																																															| (693) apart_point_and_line(all_0_0_0, all_0_5_5) = 0
% 23.42/6.95  																																																																																																																															|
% 23.42/6.95  																																																																																																																															| Instantiating formula (17) with all_0_0_0, all_0_5_5, 0, all_32_0_36 and discharging atoms apart_point_and_line(all_0_0_0, all_0_5_5) = all_32_0_36, apart_point_and_line(all_0_0_0, all_0_5_5) = 0, yields:
% 23.42/6.95  																																																																																																																															| (239) all_32_0_36 = 0
% 23.42/6.95  																																																																																																																															|
% 23.42/6.95  																																																																																																																															| Equations (239) can reduce 92 to:
% 23.42/6.95  																																																																																																																															| (101) $false
% 23.42/6.95  																																																																																																																															|
% 23.42/6.95  																																																																																																																															|-The branch is then unsatisfiable
% 23.42/6.95  																																																																																																																														|-Branch two:
% 23.42/6.95  																																																																																																																														| (696) all_476_0_1167 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 23.42/6.95  																																																																																																																														|
% 23.42/6.95  																																																																																																																															| Applying alpha-rule on (696) yields:
% 23.42/6.95  																																																																																																																															| (692) all_476_0_1167 = 0
% 23.42/6.95  																																																																																																																															| (698) apart_point_and_line(all_0_2_2, all_0_3_3) = 0
% 23.42/6.95  																																																																																																																															|
% 23.42/6.95  																																																																																																																															+-Applying beta-rule and splitting (579), into two cases.
% 23.42/6.95  																																																																																																																															|-Branch one:
% 23.84/6.95  																																																																																																																															| (100) all_0_1_1 = 0
% 23.84/6.95  																																																																																																																															|
% 23.84/6.95  																																																																																																																																| Equations (100) can reduce 19 to:
% 23.84/6.95  																																																																																																																																| (101) $false
% 23.84/6.95  																																																																																																																																|
% 23.84/6.95  																																																																																																																																|-The branch is then unsatisfiable
% 23.84/6.95  																																																																																																																															|-Branch two:
% 23.84/6.95  																																																																																																																															| (19)  ~ (all_0_1_1 = 0)
% 23.84/6.95  																																																																																																																															| (702)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.84/6.95  																																																																																																																															|
% 23.84/6.95  																																																																																																																																+-Applying beta-rule and splitting (615), into two cases.
% 23.84/6.95  																																																																																																																																|-Branch one:
% 23.84/6.95  																																																																																																																																| (100) all_0_1_1 = 0
% 23.84/6.95  																																																																																																																																|
% 23.84/6.95  																																																																																																																																	| Equations (100) can reduce 19 to:
% 23.84/6.95  																																																																																																																																	| (101) $false
% 23.84/6.95  																																																																																																																																	|
% 23.84/6.95  																																																																																																																																	|-The branch is then unsatisfiable
% 23.84/6.95  																																																																																																																																|-Branch two:
% 23.84/6.95  																																																																																																																																| (19)  ~ (all_0_1_1 = 0)
% 23.84/6.95  																																																																																																																																| (706)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_24_1_29, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_24_1_29) = v0))
% 23.84/6.95  																																																																																																																																|
% 23.84/6.95  																																																																																																																																	| Instantiating formula (17) with all_0_2_2, all_0_3_3, 0, all_0_1_1 and discharging atoms apart_point_and_line(all_0_2_2, all_0_3_3) = all_0_1_1, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields:
% 23.84/6.95  																																																																																																																																	| (100) all_0_1_1 = 0
% 23.84/6.95  																																																																																																																																	|
% 23.84/6.95  																																																																																																																																	| Equations (100) can reduce 19 to:
% 23.84/6.95  																																																																																																																																	| (101) $false
% 23.84/6.95  																																																																																																																																	|
% 23.84/6.95  																																																																																																																																	|-The branch is then unsatisfiable
% 23.84/6.95  																																																																																																																													|-Branch two:
% 23.84/6.95  																																																																																																																													| (709)  ~ (all_476_0_1167 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167
% 23.84/6.95  																																																																																																																													|
% 23.84/6.95  																																																																																																																														| Applying alpha-rule on (709) yields:
% 23.84/6.95  																																																																																																																														| (710)  ~ (all_476_0_1167 = 0)
% 23.84/6.95  																																																																																																																														| (711) distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167
% 23.84/6.95  																																																																																																																														|
% 23.84/6.95  																																																																																																																														| Instantiating formula (51) with all_0_3_3, all_0_5_5, all_476_0_1167, all_536_0_1276 and discharging atoms distinct_lines(all_0_3_3, all_0_5_5) = all_536_0_1276, distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167, yields:
% 23.84/6.95  																																																																																																																														| (712) all_536_0_1276 = all_476_0_1167
% 23.84/6.95  																																																																																																																														|
% 23.84/6.95  																																																																																																																														| Equations (712) can reduce 687 to:
% 23.84/6.95  																																																																																																																														| (710)  ~ (all_476_0_1167 = 0)
% 23.84/6.95  																																																																																																																														|
% 23.84/6.95  																																																																																																																														| From (712) and (688) follows:
% 23.84/6.95  																																																																																																																														| (711) distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167
% 23.84/6.95  																																																																																																																														|
% 23.84/6.95  																																																																																																																														| Instantiating formula (11) with all_476_0_1167, all_0_5_5, all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, distinct_lines(all_0_3_3, all_0_5_5) = all_476_0_1167, yields:
% 23.84/6.95  																																																																																																																														| (715) all_476_0_1167 = 0 | convergent_lines(all_0_5_5, all_0_5_5) = 0
% 23.84/6.95  																																																																																																																														|
% 23.84/6.96  																																																																																																																														+-Applying beta-rule and splitting (715), into two cases.
% 23.84/6.96  																																																																																																																														|-Branch one:
% 23.84/6.96  																																																																																																																														| (716) convergent_lines(all_0_5_5, all_0_5_5) = 0
% 23.84/6.96  																																																																																																																														|
% 23.84/6.96  																																																																																																																															| Instantiating formula (32) with all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_5_5) = 0, yields:
% 23.84/6.96  																																																																																																																															| (717) $false
% 23.84/6.96  																																																																																																																															|
% 23.84/6.96  																																																																																																																															|-The branch is then unsatisfiable
% 23.84/6.96  																																																																																																																														|-Branch two:
% 23.84/6.96  																																																																																																																														| (718)  ~ (convergent_lines(all_0_5_5, all_0_5_5) = 0)
% 23.84/6.96  																																																																																																																														| (692) all_476_0_1167 = 0
% 23.84/6.96  																																																																																																																														|
% 23.84/6.96  																																																																																																																															| Equations (692) can reduce 710 to:
% 23.84/6.96  																																																																																																																															| (101) $false
% 23.84/6.96  																																																																																																																															|
% 23.84/6.96  																																																																																																																															|-The branch is then unsatisfiable
% 23.84/6.96  																																																																																																																												|-Branch two:
% 23.84/6.96  																																																																																																																												| (721)  ~ (all_476_0_1167 = 0) & distinct_points(all_0_0_0, all_0_2_2) = all_476_0_1167
% 23.84/6.96  																																																																																																																												|
% 23.84/6.96  																																																																																																																													| Applying alpha-rule on (721) yields:
% 23.84/6.96  																																																																																																																													| (710)  ~ (all_476_0_1167 = 0)
% 23.84/6.96  																																																																																																																													| (723) distinct_points(all_0_0_0, all_0_2_2) = all_476_0_1167
% 23.84/6.96  																																																																																																																													|
% 23.84/6.96  																																																																																																																													| Instantiating formula (43) with all_0_0_0, all_0_2_2, 0, all_476_0_1167 and discharging atoms distinct_points(all_0_0_0, all_0_2_2) = all_476_0_1167, distinct_points(all_0_0_0, all_0_2_2) = 0, yields:
% 23.84/6.96  																																																																																																																													| (692) all_476_0_1167 = 0
% 23.84/6.96  																																																																																																																													|
% 23.84/6.96  																																																																																																																													| Equations (692) can reduce 710 to:
% 23.84/6.96  																																																																																																																													| (101) $false
% 23.84/6.96  																																																																																																																													|
% 23.84/6.96  																																																																																																																													|-The branch is then unsatisfiable
% 23.84/6.96  																																																																																																																										|-Branch two:
% 23.84/6.96  																																																																																																																										| (726)  ~ (all_536_0_1276 = 0) & distinct_points(all_0_0_0, all_0_2_2) = all_536_0_1276
% 23.84/6.96  																																																																																																																										|
% 23.84/6.96  																																																																																																																											| Applying alpha-rule on (726) yields:
% 23.84/6.96  																																																																																																																											| (687)  ~ (all_536_0_1276 = 0)
% 23.84/6.96  																																																																																																																											| (728) distinct_points(all_0_0_0, all_0_2_2) = all_536_0_1276
% 23.84/6.96  																																																																																																																											|
% 23.84/6.96  																																																																																																																											| Instantiating formula (43) with all_0_0_0, all_0_2_2, 0, all_536_0_1276 and discharging atoms distinct_points(all_0_0_0, all_0_2_2) = all_536_0_1276, distinct_points(all_0_0_0, all_0_2_2) = 0, yields:
% 23.84/6.96  																																																																																																																											| (677) all_536_0_1276 = 0
% 23.84/6.96  																																																																																																																											|
% 23.84/6.96  																																																																																																																											| Equations (677) can reduce 687 to:
% 23.84/6.96  																																																																																																																											| (101) $false
% 23.84/6.96  																																																																																																																											|
% 23.84/6.96  																																																																																																																											|-The branch is then unsatisfiable
% 23.84/6.96  																																								|-Branch two:
% 23.84/6.96  																																								| (731)  ~ (distinct_points(all_0_0_0, all_0_2_2) = 0)
% 23.84/6.96  																																								| (215) all_28_0_32 = 0
% 23.84/6.96  																																								|
% 23.84/6.96  																																									| Equations (215) can reduce 86 to:
% 23.84/6.96  																																									| (101) $false
% 23.84/6.96  																																									|
% 23.84/6.96  																																									|-The branch is then unsatisfiable
% 23.84/6.96  				|-Branch two:
% 23.84/6.96  				| (734)  ~ (all_31_0_35 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35
% 23.84/6.96  				|
% 23.84/6.96  					| Applying alpha-rule on (734) yields:
% 23.84/6.96  					| (111)  ~ (all_31_0_35 = 0)
% 23.84/6.96  					| (736) convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35
% 23.84/6.96  					|
% 23.84/6.96  					| Instantiating formula (13) with all_0_5_5, all_0_4_4, all_31_0_35, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_31_0_35, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 23.84/6.96  					| (737) all_31_0_35 = 0
% 23.84/6.96  					|
% 23.84/6.96  					| Equations (737) can reduce 111 to:
% 23.84/6.96  					| (101) $false
% 23.84/6.96  					|
% 23.84/6.96  					|-The branch is then unsatisfiable
% 23.84/6.96  			|-Branch two:
% 23.84/6.96  			| (739)  ~ (all_34_0_38 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38
% 23.84/6.96  			|
% 23.84/6.96  				| Applying alpha-rule on (739) yields:
% 23.84/6.96  				| (108)  ~ (all_34_0_38 = 0)
% 23.84/6.96  				| (741) convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38
% 23.84/6.96  				|
% 23.84/6.96  				| Instantiating formula (13) with all_0_5_5, all_0_3_3, all_34_0_38, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_34_0_38, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 23.84/6.96  				| (742) all_34_0_38 = 0
% 23.84/6.96  				|
% 23.84/6.96  				| Equations (742) can reduce 108 to:
% 23.84/6.96  				| (101) $false
% 23.84/6.96  				|
% 23.84/6.96  				|-The branch is then unsatisfiable
% 23.84/6.96  		|-Branch two:
% 23.84/6.96  		| (744)  ~ (all_30_0_34 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34
% 23.84/6.96  		|
% 23.84/6.96  			| Applying alpha-rule on (744) yields:
% 23.84/6.96  			| (105)  ~ (all_30_0_34 = 0)
% 23.84/6.96  			| (746) convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34
% 23.84/6.96  			|
% 23.84/6.96  			| Instantiating formula (13) with all_0_5_5, all_0_4_4, all_30_0_34, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_30_0_34, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields:
% 23.84/6.96  			| (747) all_30_0_34 = 0
% 23.84/6.96  			|
% 23.84/6.96  			| Equations (747) can reduce 105 to:
% 23.84/6.96  			| (101) $false
% 23.84/6.96  			|
% 23.84/6.96  			|-The branch is then unsatisfiable
% 23.84/6.96  |-Branch two:
% 23.84/6.96  | (749)  ~ (all_35_0_39 = 0) & convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39
% 23.84/6.96  |
% 23.84/6.96  	| Applying alpha-rule on (749) yields:
% 23.84/6.96  	| (98)  ~ (all_35_0_39 = 0)
% 23.84/6.96  	| (751) convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39
% 23.84/6.96  	|
% 23.84/6.96  	| Instantiating formula (13) with all_0_5_5, all_0_3_3, all_35_0_39, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = all_35_0_39, convergent_lines(all_0_5_5, all_0_3_3) = 0, yields:
% 23.84/6.96  	| (752) all_35_0_39 = 0
% 23.84/6.96  	|
% 23.84/6.96  	| Equations (752) can reduce 98 to:
% 23.84/6.96  	| (101) $false
% 23.84/6.96  	|
% 23.84/6.96  	|-The branch is then unsatisfiable
% 23.84/6.96  % SZS output end Proof for theBenchmark
% 23.84/6.96  
% 23.84/6.96  6375ms
%------------------------------------------------------------------------------