TSTP Solution File: GEO196+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sat Jul 16 03:48:32 EDT 2022

% Result   : Theorem 6.04s 2.11s
% Output   : Proof 27.04s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : GEO196+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jun 17 18:11:42 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.59/0.59          ____       _                          
% 0.59/0.59    ___  / __ \_____(_)___  ________  __________
% 0.59/0.59   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.59/0.59  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.59/0.59  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.59/0.59  
% 0.59/0.59  A Theorem Prover for First-Order Logic
% 0.59/0.60  (ePrincess v.1.0)
% 0.59/0.60  
% 0.59/0.60  (c) Philipp Rümmer, 2009-2015
% 0.59/0.60  (c) Peter Backeman, 2014-2015
% 0.59/0.60  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.59/0.60  Free software under GNU Lesser General Public License (LGPL).
% 0.59/0.60  Bug reports to peter@backeman.se
% 0.59/0.60  
% 0.59/0.60  For more information, visit http://user.uu.se/~petba168/breu/
% 0.59/0.60  
% 0.59/0.60  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.70/0.64  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.57/0.91  Prover 0: Preprocessing ...
% 1.85/1.04  Prover 0: Warning: ignoring some quantifiers
% 1.85/1.06  Prover 0: Constructing countermodel ...
% 3.16/1.42  Prover 0: gave up
% 3.16/1.42  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 3.16/1.44  Prover 1: Preprocessing ...
% 3.63/1.53  Prover 1: Constructing countermodel ...
% 3.63/1.59  Prover 1: gave up
% 3.63/1.59  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.63/1.62  Prover 2: Preprocessing ...
% 4.38/1.76  Prover 2: Warning: ignoring some quantifiers
% 4.38/1.77  Prover 2: Constructing countermodel ...
% 6.04/2.11  Prover 2: proved (519ms)
% 6.04/2.11  
% 6.04/2.11  No countermodel exists, formula is valid
% 6.04/2.11  % SZS status Theorem for theBenchmark
% 6.04/2.11  
% 6.04/2.11  Generating proof ... Warning: ignoring some quantifiers
% 25.71/8.41  found it (size 771)
% 25.71/8.41  
% 25.71/8.41  % SZS output start Proof for theBenchmark
% 25.71/8.41  Assumed formulas after preprocessing and simplification: 
% 25.71/8.41  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] :  ? [v8] :  ? [v9] : ( ~ (v6 = 0) &  ~ (v5 = 0) & intersection_point(v2, v3) = v7 & intersection_point(v0, v1) = v4 & apart_point_and_line(v4, v3) = v6 & apart_point_and_line(v4, v2) = v5 & convergent_lines(v2, v3) = 0 & convergent_lines(v0, v1) = 0 &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 | v14 = 0 |  ~ (apart_point_and_line(v11, v13) = v15) |  ~ (apart_point_and_line(v11, v12) = v14) |  ~ (distinct_points(v10, v11) = 0) |  ? [v16] : ((v16 = 0 & apart_point_and_line(v10, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 | v14 = 0 |  ~ (apart_point_and_line(v11, v13) = v15) |  ~ (apart_point_and_line(v10, v13) = v14) |  ~ (distinct_lines(v12, v13) = 0) |  ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 | v14 = 0 |  ~ (apart_point_and_line(v11, v13) = v15) |  ~ (apart_point_and_line(v10, v12) = v14) |  ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v12) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 | v14 = 0 |  ~ (apart_point_and_line(v11, v12) = v15) |  ~ (apart_point_and_line(v10, v13) = v14) |  ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 | v14 = 0 |  ~ (apart_point_and_line(v11, v12) = v15) |  ~ (apart_point_and_line(v10, v12) = v14) |  ~ (distinct_lines(v12, v13) = 0) |  ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v10, v13) = 0) | ( ~ (v16 = 0) & distinct_points(v10, v11) = v16))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] :  ! [v15] : (v15 = 0 | v14 = 0 |  ~ (apart_point_and_line(v10, v13) = v15) |  ~ (apart_point_and_line(v10, v12) = v14) |  ~ (distinct_points(v10, v11) = 0) |  ? [v16] : ((v16 = 0 & apart_point_and_line(v11, v13) = 0) | (v16 = 0 & apart_point_and_line(v11, v12) = 0) | ( ~ (v16 = 0) & distinct_lines(v12, v13) = v16))) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 | v13 = 0 |  ~ (apart_point_and_line(v12, v11) = v14) |  ~ (distinct_points(v10, v12) = v13) |  ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 | v13 = 0 |  ~ (apart_point_and_line(v10, v12) = v14) |  ~ (distinct_lines(v11, v12) = v13) |  ? [v15] : ( ~ (v15 = 0) & apart_point_and_line(v10, v11) = v15)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 | v13 = 0 |  ~ (convergent_lines(v11, v12) = v14) |  ~ (convergent_lines(v10, v12) = v13) |  ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 | v13 = 0 |  ~ (convergent_lines(v10, v12) = v14) |  ~ (distinct_lines(v11, v12) = v13) |  ? [v15] : ( ~ (v15 = 0) & convergent_lines(v10, v11) = v15)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 | v13 = 0 |  ~ (distinct_lines(v11, v12) = v14) |  ~ (distinct_lines(v10, v12) = v13) |  ? [v15] : ( ~ (v15 = 0) & distinct_lines(v10, v11) = v15)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] :  ! [v14] : (v14 = 0 | v13 = 0 |  ~ (distinct_points(v11, v12) = v14) |  ~ (distinct_points(v10, v12) = v13) |  ? [v15] : ( ~ (v15 = 0) & distinct_points(v10, v11) = v15)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (apart_point_and_line(v12, v11) = v13) |  ~ (apart_point_and_line(v10, v11) = 0) | distinct_points(v10, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (apart_point_and_line(v10, v12) = v13) |  ~ (apart_point_and_line(v10, v11) = 0) | distinct_lines(v11, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (apart_point_and_line(v10, v11) = 0) |  ~ (distinct_lines(v11, v12) = v13) | apart_point_and_line(v10, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (apart_point_and_line(v10, v11) = 0) |  ~ (distinct_points(v10, v12) = v13) | apart_point_and_line(v12, v11) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (convergent_lines(v11, v12) = v13) |  ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v10, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (convergent_lines(v10, v12) = v13) |  ~ (convergent_lines(v10, v11) = 0) | convergent_lines(v11, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (convergent_lines(v10, v12) = v13) |  ~ (convergent_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (convergent_lines(v10, v11) = 0) |  ~ (distinct_lines(v11, v12) = v13) | convergent_lines(v10, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (distinct_lines(v11, v12) = v13) |  ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v10, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (distinct_lines(v10, v12) = v13) |  ~ (distinct_lines(v10, v11) = 0) | distinct_lines(v11, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (distinct_points(v11, v12) = v13) |  ~ (distinct_points(v10, v11) = 0) | distinct_points(v10, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 |  ~ (distinct_points(v10, v12) = v13) |  ~ (distinct_points(v10, v11) = 0) | distinct_points(v11, v12) = 0) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (intersection_point(v13, v12) = v11) |  ~ (intersection_point(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (line_connecting(v13, v12) = v11) |  ~ (line_connecting(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (apart_point_and_line(v13, v12) = v11) |  ~ (apart_point_and_line(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (convergent_lines(v13, v12) = v11) |  ~ (convergent_lines(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (distinct_lines(v13, v12) = v11) |  ~ (distinct_lines(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v11 = v10 |  ~ (distinct_points(v13, v12) = v11) |  ~ (distinct_points(v13, v12) = v10)) &  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : ( ~ (distinct_lines(v12, v13) = 0) |  ~ (distinct_points(v10, v11) = 0) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v11, v13) = 0) | (v14 = 0 & apart_point_and_line(v11, v12) = 0) | (v14 = 0 & apart_point_and_line(v10, v13) = 0) | (v14 = 0 & apart_point_and_line(v10, v12) = 0))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (intersection_point(v10, v11) = v12) |  ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v11) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (intersection_point(v10, v11) = v12) |  ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v12, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v10, v11) = v13))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (line_connecting(v10, v11) = v12) |  ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v11, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) &  ! [v10] :  ! [v11] :  ! [v12] : ( ~ (line_connecting(v10, v11) = v12) |  ? [v13] : (( ~ (v13 = 0) & apart_point_and_line(v10, v12) = v13) | ( ~ (v13 = 0) & distinct_points(v10, v11) = v13))) &  ! [v10] :  ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v11) = v13)) &  ! [v10] :  ! [v11] : ( ~ (convergent_lines(v10, v11) = 0) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & intersection_point(v10, v11) = v12 & apart_point_and_line(v12, v10) = v13)) &  ! [v10] :  ! [v11] : ( ~ (distinct_points(v10, v11) = 0) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v11, v12) = v13)) &  ! [v10] :  ! [v11] : ( ~ (distinct_points(v10, v11) = 0) |  ? [v12] :  ? [v13] : ( ~ (v13 = 0) & line_connecting(v10, v11) = v12 & apart_point_and_line(v10, v12) = v13)) &  ! [v10] :  ~ (convergent_lines(v10, v10) = 0) &  ! [v10] :  ~ (distinct_lines(v10, v10) = 0) &  ! [v10] :  ~ (distinct_points(v10, v10) = 0) &  ? [v10] :  ? [v11] :  ? [v12] : intersection_point(v11, v10) = v12 &  ? [v10] :  ? [v11] :  ? [v12] : line_connecting(v11, v10) = v12 &  ? [v10] :  ? [v11] :  ? [v12] : apart_point_and_line(v11, v10) = v12 &  ? [v10] :  ? [v11] :  ? [v12] : convergent_lines(v11, v10) = v12 &  ? [v10] :  ? [v11] :  ? [v12] : distinct_lines(v11, v10) = v12 &  ? [v10] :  ? [v11] :  ? [v12] : distinct_points(v11, v10) = v12 & ((v9 = 0 & apart_point_and_line(v7, v1) = 0) | (v8 = 0 & apart_point_and_line(v7, v0) = 0)))
% 26.05/8.46  | 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, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 26.05/8.46  | (1)  ~ (all_0_3_3 = 0) &  ~ (all_0_4_4 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5 & apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3 & apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4 & convergent_lines(all_0_7_7, all_0_6_6) = 0 & convergent_lines(all_0_9_9, all_0_8_8) = 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 & ((all_0_0_0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_0_1_1 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0))
% 26.05/8.48  |
% 26.05/8.48  | Applying alpha-rule on (1) yields:
% 26.05/8.48  | (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)
% 26.05/8.48  | (3)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 26.05/8.48  | (4)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 26.05/8.48  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 26.05/8.48  | (6)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 26.05/8.48  | (7)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 26.05/8.48  | (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)))
% 26.05/8.48  | (9) (all_0_0_0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (all_0_1_1 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0)
% 26.05/8.48  | (10)  ! [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)))
% 26.05/8.48  | (11)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 26.05/8.48  | (12)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 26.05/8.48  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 26.05/8.49  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 26.05/8.49  | (15)  ! [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)))
% 26.05/8.49  | (16)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 26.05/8.49  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 26.05/8.49  | (18)  ! [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)))
% 26.05/8.49  | (19)  ~ (all_0_3_3 = 0)
% 26.05/8.49  | (20)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 26.05/8.49  | (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)
% 26.05/8.49  | (22)  ! [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)
% 26.05/8.49  | (23)  ! [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)))
% 26.05/8.49  | (24) convergent_lines(all_0_9_9, all_0_8_8) = 0
% 26.21/8.49  | (25)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 26.21/8.49  | (26)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 26.21/8.49  | (27) apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3
% 26.21/8.49  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 26.21/8.49  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (convergent_lines(v1, v2) = v4) |  ~ (convergent_lines(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))
% 26.21/8.49  | (30) intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5
% 26.21/8.49  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 26.21/8.49  | (32)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 26.21/8.49  | (33)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 26.21/8.49  | (34)  ! [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))
% 26.21/8.49  | (35)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 26.21/8.49  | (36)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 26.21/8.49  | (37)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 26.21/8.49  | (38) intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2
% 26.21/8.49  | (39)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 26.21/8.49  | (40)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 26.21/8.49  | (41)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 26.21/8.49  | (42)  ! [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))
% 26.21/8.49  | (43)  ! [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)))
% 26.21/8.50  | (44)  ! [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))
% 26.21/8.50  | (45)  ~ (all_0_4_4 = 0)
% 26.21/8.50  | (46)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 26.21/8.50  | (47)  ! [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))
% 26.21/8.50  | (48) apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4
% 26.21/8.50  | (49)  ! [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)))
% 26.21/8.50  | (50) convergent_lines(all_0_7_7, all_0_6_6) = 0
% 26.21/8.50  | (51)  ! [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)))
% 26.21/8.50  | (52)  ! [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)
% 26.21/8.50  | (53)  ! [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)))
% 26.21/8.50  | (54)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 26.21/8.50  | (55)  ! [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)))
% 26.21/8.50  | (56)  ! [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))
% 26.21/8.50  | (57)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 26.21/8.50  | (58)  ! [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)))
% 26.21/8.50  |
% 26.21/8.50  | Instantiating formula (10) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 26.21/8.50  | (59)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = v0))
% 26.21/8.50  |
% 26.21/8.50  | Instantiating formula (55) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 26.21/8.50  | (60)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = v0))
% 26.21/8.50  |
% 26.21/8.50  | Instantiating formula (10) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 26.21/8.50  | (61)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = v0))
% 26.21/8.50  |
% 26.21/8.50  | Instantiating formula (55) with all_0_5_5, all_0_8_8, all_0_9_9 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 26.21/8.50  | (62)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = v0))
% 26.21/8.50  |
% 26.21/8.50  | Instantiating formula (8) with all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.21/8.50  | (63) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.50  |
% 26.21/8.50  | Instantiating formula (8) with all_0_4_4, all_0_3_3, all_0_7_7, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.21/8.50  | (64) all_0_3_3 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.51  |
% 26.21/8.51  | Instantiating formula (8) with all_0_3_3, all_0_4_4, all_0_6_6, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.21/8.51  | (65) all_0_3_3 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.51  |
% 26.21/8.51  | Instantiating formula (8) with all_0_4_4, all_0_4_4, all_0_7_7, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.21/8.51  | (66) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.51  |
% 26.21/8.51  | Instantiating formula (20) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 26.21/8.51  | (67)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_6_6) = v1)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating formula (7) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 26.21/8.51  | (68)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(v0, all_0_7_7) = v1)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating formula (20) with all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 26.21/8.51  | (69)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(v0, all_0_8_8) = v1)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating formula (7) with all_0_8_8, all_0_9_9 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 26.21/8.51  | (70)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_9_9, all_0_8_8) = v0 & apart_point_and_line(v0, all_0_9_9) = v1)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (70) with all_20_0_28, all_20_1_29 yields:
% 26.21/8.51  | (71)  ~ (all_20_0_28 = 0) & intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29 & apart_point_and_line(all_20_1_29, all_0_9_9) = all_20_0_28
% 26.21/8.51  |
% 26.21/8.51  | Applying alpha-rule on (71) yields:
% 26.21/8.51  | (72)  ~ (all_20_0_28 = 0)
% 26.21/8.51  | (73) intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29
% 26.21/8.51  | (74) apart_point_and_line(all_20_1_29, all_0_9_9) = all_20_0_28
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (62) with all_22_0_30 yields:
% 26.21/8.51  | (75) ( ~ (all_22_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30) | ( ~ (all_22_0_30 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (61) with all_23_0_31 yields:
% 26.21/8.51  | (76) ( ~ (all_23_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31) | ( ~ (all_23_0_31 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (59) with all_24_0_32 yields:
% 26.21/8.51  | (77) ( ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32) | ( ~ (all_24_0_32 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (60) with all_25_0_33 yields:
% 26.21/8.51  | (78) ( ~ (all_25_0_33 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33) | ( ~ (all_25_0_33 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33)
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (69) with all_26_0_34, all_26_1_35 yields:
% 26.21/8.51  | (79)  ~ (all_26_0_34 = 0) & intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35 & apart_point_and_line(all_26_1_35, all_0_8_8) = all_26_0_34
% 26.21/8.51  |
% 26.21/8.51  | Applying alpha-rule on (79) yields:
% 26.21/8.51  | (80)  ~ (all_26_0_34 = 0)
% 26.21/8.51  | (81) intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35
% 26.21/8.51  | (82) apart_point_and_line(all_26_1_35, all_0_8_8) = all_26_0_34
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (67) with all_28_0_36, all_28_1_37 yields:
% 26.21/8.51  | (83)  ~ (all_28_0_36 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37 & apart_point_and_line(all_28_1_37, all_0_6_6) = all_28_0_36
% 26.21/8.51  |
% 26.21/8.51  | Applying alpha-rule on (83) yields:
% 26.21/8.51  | (84)  ~ (all_28_0_36 = 0)
% 26.21/8.51  | (85) intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37
% 26.21/8.51  | (86) apart_point_and_line(all_28_1_37, all_0_6_6) = all_28_0_36
% 26.21/8.51  |
% 26.21/8.51  | Instantiating (68) with all_30_0_38, all_30_1_39 yields:
% 26.21/8.51  | (87)  ~ (all_30_0_38 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39 & apart_point_and_line(all_30_1_39, all_0_7_7) = all_30_0_38
% 26.21/8.51  |
% 26.21/8.51  | Applying alpha-rule on (87) yields:
% 26.21/8.51  | (88)  ~ (all_30_0_38 = 0)
% 26.21/8.51  | (89) intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39
% 26.21/8.51  | (90) apart_point_and_line(all_30_1_39, all_0_7_7) = all_30_0_38
% 26.21/8.51  |
% 26.21/8.51  +-Applying beta-rule and splitting (75), into two cases.
% 26.21/8.51  |-Branch one:
% 26.21/8.51  | (91)  ~ (all_22_0_30 = 0) & apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30
% 26.21/8.51  |
% 26.21/8.51  	| Applying alpha-rule on (91) yields:
% 26.21/8.51  	| (92)  ~ (all_22_0_30 = 0)
% 26.21/8.51  	| (93) apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30
% 26.21/8.51  	|
% 26.21/8.51  	+-Applying beta-rule and splitting (76), into two cases.
% 26.21/8.51  	|-Branch one:
% 26.21/8.51  	| (94)  ~ (all_23_0_31 = 0) & apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31
% 26.21/8.51  	|
% 26.21/8.51  		| Applying alpha-rule on (94) yields:
% 26.21/8.51  		| (95)  ~ (all_23_0_31 = 0)
% 26.21/8.51  		| (96) apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31
% 26.21/8.51  		|
% 26.21/8.51  		+-Applying beta-rule and splitting (77), into two cases.
% 26.21/8.51  		|-Branch one:
% 26.21/8.51  		| (97)  ~ (all_24_0_32 = 0) & apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32
% 26.21/8.51  		|
% 26.21/8.51  			| Applying alpha-rule on (97) yields:
% 26.21/8.51  			| (98)  ~ (all_24_0_32 = 0)
% 26.21/8.51  			| (99) apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32
% 26.21/8.51  			|
% 26.21/8.51  			+-Applying beta-rule and splitting (66), into two cases.
% 26.21/8.51  			|-Branch one:
% 26.21/8.51  			| (100) all_0_4_4 = 0
% 26.21/8.51  			|
% 26.21/8.51  				| Equations (100) can reduce 45 to:
% 26.21/8.51  				| (101) $false
% 26.21/8.51  				|
% 26.21/8.51  				|-The branch is then unsatisfiable
% 26.21/8.51  			|-Branch two:
% 26.21/8.51  			| (45)  ~ (all_0_4_4 = 0)
% 26.21/8.51  			| (103)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52  			|
% 26.21/8.52  				+-Applying beta-rule and splitting (78), into two cases.
% 26.21/8.52  				|-Branch one:
% 26.21/8.52  				| (104)  ~ (all_25_0_33 = 0) & apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33
% 26.21/8.52  				|
% 26.21/8.52  					| Applying alpha-rule on (104) yields:
% 26.21/8.52  					| (105)  ~ (all_25_0_33 = 0)
% 26.21/8.52  					| (106) apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33
% 26.21/8.52  					|
% 26.21/8.52  					+-Applying beta-rule and splitting (63), into two cases.
% 26.21/8.52  					|-Branch one:
% 26.21/8.52  					| (107) all_0_3_3 = 0
% 26.21/8.52  					|
% 26.21/8.52  						| Equations (107) can reduce 19 to:
% 26.21/8.52  						| (101) $false
% 26.21/8.52  						|
% 26.21/8.52  						|-The branch is then unsatisfiable
% 26.21/8.52  					|-Branch two:
% 26.21/8.52  					| (19)  ~ (all_0_3_3 = 0)
% 26.21/8.52  					| (110)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52  					|
% 26.21/8.52  						+-Applying beta-rule and splitting (64), into two cases.
% 26.21/8.52  						|-Branch one:
% 26.21/8.52  						| (107) all_0_3_3 = 0
% 26.21/8.52  						|
% 26.21/8.52  							| Equations (107) can reduce 19 to:
% 26.21/8.52  							| (101) $false
% 26.21/8.52  							|
% 26.21/8.52  							|-The branch is then unsatisfiable
% 26.21/8.52  						|-Branch two:
% 26.21/8.52  						| (19)  ~ (all_0_3_3 = 0)
% 26.21/8.52  						| (114) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52  						|
% 26.21/8.52  							+-Applying beta-rule and splitting (65), into two cases.
% 26.21/8.52  							|-Branch one:
% 26.21/8.52  							| (107) all_0_3_3 = 0
% 26.21/8.52  							|
% 26.21/8.52  								| Equations (107) can reduce 19 to:
% 26.21/8.52  								| (101) $false
% 26.21/8.52  								|
% 26.21/8.52  								|-The branch is then unsatisfiable
% 26.21/8.52  							|-Branch two:
% 26.21/8.52  							| (19)  ~ (all_0_3_3 = 0)
% 26.21/8.52  							| (118) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52  							|
% 26.21/8.52  								+-Applying beta-rule and splitting (114), into two cases.
% 26.21/8.52  								|-Branch one:
% 26.21/8.52  								| (100) all_0_4_4 = 0
% 26.21/8.52  								|
% 26.21/8.52  									| Equations (100) can reduce 45 to:
% 26.21/8.52  									| (101) $false
% 26.21/8.52  									|
% 26.21/8.52  									|-The branch is then unsatisfiable
% 26.21/8.52  								|-Branch two:
% 26.21/8.52  								| (45)  ~ (all_0_4_4 = 0)
% 26.21/8.52  								| (122)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52  								|
% 26.21/8.52  									+-Applying beta-rule and splitting (118), into two cases.
% 26.21/8.52  									|-Branch one:
% 26.21/8.52  									| (100) all_0_4_4 = 0
% 26.21/8.52  									|
% 26.21/8.52  										| Equations (100) can reduce 45 to:
% 26.21/8.52  										| (101) $false
% 26.21/8.52  										|
% 26.21/8.52  										|-The branch is then unsatisfiable
% 26.21/8.52  									|-Branch two:
% 26.21/8.52  									| (45)  ~ (all_0_4_4 = 0)
% 26.21/8.52  									| (126)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.21/8.52  									|
% 26.21/8.52  										| Instantiating formula (39) with all_0_7_7, all_0_6_6, all_30_1_39, all_0_2_2 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39, intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 26.21/8.52  										| (127) all_30_1_39 = all_0_2_2
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (39) with all_0_7_7, all_0_6_6, all_28_1_37, all_30_1_39 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_30_1_39, intersection_point(all_0_7_7, all_0_6_6) = all_28_1_37, yields:
% 26.21/8.52  										| (128) all_30_1_39 = all_28_1_37
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (39) with all_0_9_9, all_0_8_8, all_26_1_35, all_0_5_5 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35, intersection_point(all_0_9_9, all_0_8_8) = all_0_5_5, yields:
% 26.21/8.52  										| (129) all_26_1_35 = all_0_5_5
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (39) with all_0_9_9, all_0_8_8, all_20_1_29, all_26_1_35 and discharging atoms intersection_point(all_0_9_9, all_0_8_8) = all_26_1_35, intersection_point(all_0_9_9, all_0_8_8) = all_20_1_29, yields:
% 26.21/8.52  										| (130) all_26_1_35 = all_20_1_29
% 26.21/8.52  										|
% 26.21/8.52  										| Combining equations (127,128) yields a new equation:
% 26.21/8.52  										| (131) all_28_1_37 = all_0_2_2
% 26.21/8.52  										|
% 26.21/8.52  										| Combining equations (130,129) yields a new equation:
% 26.21/8.52  										| (132) all_20_1_29 = all_0_5_5
% 26.21/8.52  										|
% 26.21/8.52  										| Simplifying 132 yields:
% 26.21/8.52  										| (133) all_20_1_29 = all_0_5_5
% 26.21/8.52  										|
% 26.21/8.52  										| Combining equations (131,128) yields a new equation:
% 26.21/8.52  										| (127) all_30_1_39 = all_0_2_2
% 26.21/8.52  										|
% 26.21/8.52  										| From (127) and (90) follows:
% 26.21/8.52  										| (135) apart_point_and_line(all_0_2_2, all_0_7_7) = all_30_0_38
% 26.21/8.52  										|
% 26.21/8.52  										| From (131) and (86) follows:
% 26.21/8.52  										| (136) apart_point_and_line(all_0_2_2, all_0_6_6) = all_28_0_36
% 26.21/8.52  										|
% 26.21/8.52  										| From (129) and (82) follows:
% 26.21/8.52  										| (137) apart_point_and_line(all_0_5_5, all_0_8_8) = all_26_0_34
% 26.21/8.52  										|
% 26.21/8.52  										| From (133) and (74) follows:
% 26.21/8.52  										| (138) apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (25) with all_0_2_2, all_0_6_6, all_28_0_36, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_28_0_36, apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, yields:
% 26.21/8.52  										| (139) all_28_0_36 = all_24_0_32
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (25) with all_0_2_2, all_0_7_7, all_30_0_38, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_30_0_38, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.21/8.52  										| (140) all_30_0_38 = all_25_0_33
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (25) with all_0_5_5, all_0_8_8, all_26_0_34, all_23_0_31 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_26_0_34, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.21/8.52  										| (141) all_26_0_34 = all_23_0_31
% 26.21/8.52  										|
% 26.21/8.52  										| Instantiating formula (25) with all_0_5_5, all_0_9_9, all_20_0_28, all_22_0_30 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_22_0_30, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.21/8.53  										| (142) all_22_0_30 = all_20_0_28
% 26.21/8.53  										|
% 26.21/8.53  										| Equations (140) can reduce 88 to:
% 26.21/8.53  										| (105)  ~ (all_25_0_33 = 0)
% 26.21/8.53  										|
% 26.21/8.53  										| Equations (139) can reduce 84 to:
% 26.21/8.53  										| (98)  ~ (all_24_0_32 = 0)
% 26.21/8.53  										|
% 26.21/8.53  										| Equations (141) can reduce 80 to:
% 26.21/8.53  										| (95)  ~ (all_23_0_31 = 0)
% 26.21/8.53  										|
% 26.21/8.53  										| Equations (142) can reduce 92 to:
% 26.21/8.53  										| (72)  ~ (all_20_0_28 = 0)
% 26.21/8.53  										|
% 26.21/8.53  										| From (139) and (136) follows:
% 26.21/8.53  										| (99) apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32
% 26.21/8.53  										|
% 26.21/8.53  										| From (140) and (135) follows:
% 26.21/8.53  										| (106) apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33
% 26.21/8.53  										|
% 26.21/8.53  										| From (141) and (137) follows:
% 26.21/8.53  										| (96) apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31
% 26.21/8.53  										|
% 26.21/8.53  										| From (142) and (93) follows:
% 26.21/8.53  										| (138) apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28
% 26.21/8.53  										|
% 26.21/8.53  										| Instantiating formula (8) with all_24_0_32, all_0_3_3, all_0_6_6, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.21/8.53  										| (151) all_24_0_32 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.21/8.53  										|
% 26.21/8.53  										| Instantiating formula (8) with all_0_3_3, all_24_0_32, all_0_6_6, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.21/8.53  										| (152) all_24_0_32 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (8) with all_24_0_32, all_0_4_4, all_0_6_6, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53  										| (153) all_24_0_32 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (8) with all_0_4_4, all_24_0_32, all_0_7_7, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53  										| (154) all_24_0_32 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (58) with all_24_0_32, all_0_4_4, all_0_7_7, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53  										| (155) all_24_0_32 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (58) with all_0_4_4, all_24_0_32, all_0_6_6, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.40/8.53  										| (156) all_24_0_32 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (8) with all_24_0_32, all_24_0_32, all_0_6_6, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, yields:
% 26.40/8.53  										| (157) all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (8) with all_25_0_33, all_0_3_3, all_0_7_7, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.53  										| (158) all_25_0_33 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (8) with all_0_3_3, all_25_0_33, all_0_6_6, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.53  										| (159) all_25_0_33 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.40/8.53  										|
% 26.40/8.53  										| Instantiating formula (58) with all_25_0_33, all_0_3_3, all_0_6_6, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.53  										| (160) all_25_0_33 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.40/8.54  										|
% 26.40/8.54  										| Instantiating formula (58) with all_0_3_3, all_25_0_33, all_0_7_7, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, yields:
% 26.40/8.54  										| (161) all_25_0_33 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_25_0_33, all_0_4_4, all_0_7_7, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.45/8.54  										| (162) all_25_0_33 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_0_4_4, all_25_0_33, all_0_7_7, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, yields:
% 26.45/8.54  										| (163) all_25_0_33 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_25_0_33, all_24_0_32, all_0_7_7, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.45/8.54  										| (164) all_25_0_33 = 0 | all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_24_0_32, all_25_0_33, all_0_6_6, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.45/8.54  										| (165) all_25_0_33 = 0 | all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_25_0_33, all_25_0_33, all_0_7_7, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, yields:
% 26.45/8.54  										| (166) all_25_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_23_0_31, all_0_3_3, all_0_8_8, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54  										| (167) all_23_0_31 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_0_3_3, all_23_0_31, all_0_6_6, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54  										| (168) all_23_0_31 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_23_0_31, all_0_4_4, all_0_8_8, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54  										| (169) all_23_0_31 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_0_4_4, all_23_0_31, all_0_7_7, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54  										| (170) all_23_0_31 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_23_0_31, all_24_0_32, all_0_8_8, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54  										| (171) all_24_0_32 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (8) with all_24_0_32, all_23_0_31, all_0_6_6, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.54  										| (172) all_24_0_32 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.54  										|
% 26.45/8.54  										| Instantiating formula (58) with all_23_0_31, all_24_0_32, all_0_6_6, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (173) all_24_0_32 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (58) with all_24_0_32, all_23_0_31, all_0_8_8, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (174) all_24_0_32 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_23_0_31, all_25_0_33, all_0_8_8, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (175) all_25_0_33 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_25_0_33, all_23_0_31, all_0_7_7, all_0_8_8, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (176) all_25_0_33 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (58) with all_23_0_31, all_25_0_33, all_0_7_7, all_0_8_8, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (177) all_25_0_33 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (58) with all_25_0_33, all_23_0_31, all_0_8_8, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (178) all_25_0_33 = 0 | all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_23_0_31, all_23_0_31, all_0_8_8, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.45/8.55  										| (179) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_20_0_28, all_0_3_3, all_0_9_9, all_0_6_6, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55  										| (180) all_20_0_28 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_0_3_3, all_20_0_28, all_0_6_6, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55  										| (181) all_20_0_28 = 0 | all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_20_0_28, all_0_4_4, all_0_9_9, all_0_7_7, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55  										| (182) all_20_0_28 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_0_4_4, all_20_0_28, all_0_7_7, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55  										| (183) all_20_0_28 = 0 | all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.55  										|
% 26.45/8.55  										| Instantiating formula (8) with all_20_0_28, all_24_0_32, all_0_9_9, all_0_6_6, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.55  										| (184) all_24_0_32 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (8) with all_24_0_32, all_20_0_28, all_0_6_6, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (185) all_24_0_32 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (58) with all_20_0_28, all_24_0_32, all_0_6_6, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (186) all_24_0_32 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (58) with all_24_0_32, all_20_0_28, all_0_9_9, all_0_6_6, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (187) all_24_0_32 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (8) with all_20_0_28, all_25_0_33, all_0_9_9, all_0_7_7, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (188) all_25_0_33 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (8) with all_25_0_33, all_20_0_28, all_0_7_7, all_0_9_9, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (189) all_25_0_33 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (58) with all_20_0_28, all_25_0_33, all_0_7_7, all_0_9_9, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (190) all_25_0_33 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (58) with all_25_0_33, all_20_0_28, all_0_9_9, all_0_7_7, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (191) all_25_0_33 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (8) with all_20_0_28, all_23_0_31, all_0_9_9, all_0_8_8, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (192) all_23_0_31 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (8) with all_23_0_31, all_20_0_28, all_0_8_8, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (193) all_23_0_31 = 0 | all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										| Instantiating formula (8) with all_20_0_28, all_20_0_28, all_0_9_9, all_0_9_9, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.45/8.56  										| (194) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56  										|
% 26.45/8.56  										+-Applying beta-rule and splitting (9), into two cases.
% 26.45/8.56  										|-Branch one:
% 26.45/8.56  										| (195) all_0_0_0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0
% 26.45/8.56  										|
% 26.45/8.56  											| Applying alpha-rule on (195) yields:
% 26.45/8.56  											| (196) all_0_0_0 = 0
% 26.45/8.56  											| (197) apart_point_and_line(all_0_2_2, all_0_8_8) = 0
% 26.45/8.56  											|
% 26.45/8.56  											+-Applying beta-rule and splitting (166), into two cases.
% 26.45/8.56  											|-Branch one:
% 26.45/8.56  											| (198) all_25_0_33 = 0
% 26.45/8.56  											|
% 26.45/8.56  												| Equations (198) can reduce 105 to:
% 26.45/8.56  												| (101) $false
% 26.45/8.56  												|
% 26.45/8.56  												|-The branch is then unsatisfiable
% 26.45/8.56  											|-Branch two:
% 26.45/8.56  											| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.56  											| (201)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.56  											|
% 26.45/8.56  												+-Applying beta-rule and splitting (157), into two cases.
% 26.45/8.56  												|-Branch one:
% 26.45/8.56  												| (202) all_24_0_32 = 0
% 26.45/8.56  												|
% 26.45/8.56  													| Equations (202) can reduce 98 to:
% 26.45/8.56  													| (101) $false
% 26.45/8.56  													|
% 26.45/8.56  													|-The branch is then unsatisfiable
% 26.45/8.56  												|-Branch two:
% 26.45/8.56  												| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.56  												| (205)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.56  												|
% 26.45/8.56  													+-Applying beta-rule and splitting (179), into two cases.
% 26.45/8.56  													|-Branch one:
% 26.45/8.56  													| (206) all_23_0_31 = 0
% 26.45/8.56  													|
% 26.45/8.56  														| Equations (206) can reduce 95 to:
% 26.45/8.56  														| (101) $false
% 26.45/8.56  														|
% 26.45/8.56  														|-The branch is then unsatisfiable
% 26.45/8.56  													|-Branch two:
% 26.45/8.56  													| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.56  													| (209)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.56  													|
% 26.45/8.56  														+-Applying beta-rule and splitting (194), into two cases.
% 26.45/8.56  														|-Branch one:
% 26.45/8.56  														| (210) all_20_0_28 = 0
% 26.45/8.56  														|
% 26.45/8.56  															| Equations (210) can reduce 72 to:
% 26.45/8.56  															| (101) $false
% 26.45/8.56  															|
% 26.45/8.56  															|-The branch is then unsatisfiable
% 26.45/8.56  														|-Branch two:
% 26.45/8.56  														| (72)  ~ (all_20_0_28 = 0)
% 26.45/8.56  														| (213)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57  														|
% 26.45/8.57  															+-Applying beta-rule and splitting (181), into two cases.
% 26.45/8.57  															|-Branch one:
% 26.45/8.57  															| (210) all_20_0_28 = 0
% 26.45/8.57  															|
% 26.45/8.57  																| Equations (210) can reduce 72 to:
% 26.45/8.57  																| (101) $false
% 26.45/8.57  																|
% 26.45/8.57  																|-The branch is then unsatisfiable
% 26.45/8.57  															|-Branch two:
% 26.45/8.57  															| (72)  ~ (all_20_0_28 = 0)
% 26.45/8.57  															| (217) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57  															|
% 26.45/8.57  																+-Applying beta-rule and splitting (182), into two cases.
% 26.45/8.57  																|-Branch one:
% 26.45/8.57  																| (210) all_20_0_28 = 0
% 26.45/8.57  																|
% 26.45/8.57  																	| Equations (210) can reduce 72 to:
% 26.45/8.57  																	| (101) $false
% 26.45/8.57  																	|
% 26.45/8.57  																	|-The branch is then unsatisfiable
% 26.45/8.57  																|-Branch two:
% 26.45/8.57  																| (72)  ~ (all_20_0_28 = 0)
% 26.45/8.57  																| (221) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57  																|
% 26.45/8.57  																	+-Applying beta-rule and splitting (187), into two cases.
% 26.45/8.57  																	|-Branch one:
% 26.45/8.57  																	| (202) all_24_0_32 = 0
% 26.45/8.57  																	|
% 26.45/8.57  																		| Equations (202) can reduce 98 to:
% 26.45/8.57  																		| (101) $false
% 26.45/8.57  																		|
% 26.45/8.57  																		|-The branch is then unsatisfiable
% 26.45/8.57  																	|-Branch two:
% 26.45/8.57  																	| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.57  																	| (225) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57  																	|
% 26.45/8.57  																		+-Applying beta-rule and splitting (188), into two cases.
% 26.45/8.57  																		|-Branch one:
% 26.45/8.57  																		| (198) all_25_0_33 = 0
% 26.45/8.57  																		|
% 26.45/8.57  																			| Equations (198) can reduce 105 to:
% 26.45/8.57  																			| (101) $false
% 26.45/8.57  																			|
% 26.45/8.57  																			|-The branch is then unsatisfiable
% 26.45/8.57  																		|-Branch two:
% 26.45/8.57  																		| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.57  																		| (229) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57  																		|
% 26.45/8.57  																			+-Applying beta-rule and splitting (191), into two cases.
% 26.45/8.57  																			|-Branch one:
% 26.45/8.57  																			| (198) all_25_0_33 = 0
% 26.45/8.57  																			|
% 26.45/8.57  																				| Equations (198) can reduce 105 to:
% 26.45/8.57  																				| (101) $false
% 26.45/8.57  																				|
% 26.45/8.57  																				|-The branch is then unsatisfiable
% 26.45/8.57  																			|-Branch two:
% 26.45/8.57  																			| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.57  																			| (233) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57  																			|
% 26.45/8.57  																				+-Applying beta-rule and splitting (151), into two cases.
% 26.45/8.57  																				|-Branch one:
% 26.45/8.57  																				| (202) all_24_0_32 = 0
% 26.45/8.57  																				|
% 26.45/8.57  																					| Equations (202) can reduce 98 to:
% 26.45/8.57  																					| (101) $false
% 26.45/8.57  																					|
% 26.45/8.57  																					|-The branch is then unsatisfiable
% 26.45/8.57  																				|-Branch two:
% 26.45/8.57  																				| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.57  																				| (237) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57  																				|
% 26.45/8.57  																					+-Applying beta-rule and splitting (163), into two cases.
% 26.45/8.57  																					|-Branch one:
% 26.45/8.57  																					| (198) all_25_0_33 = 0
% 26.45/8.57  																					|
% 26.45/8.57  																						| Equations (198) can reduce 105 to:
% 26.45/8.57  																						| (101) $false
% 26.45/8.57  																						|
% 26.45/8.57  																						|-The branch is then unsatisfiable
% 26.45/8.57  																					|-Branch two:
% 26.45/8.57  																					| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.57  																					| (241) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57  																					|
% 26.45/8.57  																						+-Applying beta-rule and splitting (164), into two cases.
% 26.45/8.57  																						|-Branch one:
% 26.45/8.57  																						| (198) all_25_0_33 = 0
% 26.45/8.57  																						|
% 26.45/8.57  																							| Equations (198) can reduce 105 to:
% 26.45/8.57  																							| (101) $false
% 26.45/8.57  																							|
% 26.45/8.57  																							|-The branch is then unsatisfiable
% 26.45/8.57  																						|-Branch two:
% 26.45/8.57  																						| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.57  																						| (245) all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.57  																						|
% 26.45/8.57  																							+-Applying beta-rule and splitting (192), into two cases.
% 26.45/8.57  																							|-Branch one:
% 26.45/8.57  																							| (206) all_23_0_31 = 0
% 26.45/8.57  																							|
% 26.45/8.57  																								| Equations (206) can reduce 95 to:
% 26.45/8.57  																								| (101) $false
% 26.45/8.57  																								|
% 26.45/8.57  																								|-The branch is then unsatisfiable
% 26.45/8.57  																							|-Branch two:
% 26.45/8.57  																							| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.57  																							| (249) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.57  																							|
% 26.45/8.57  																								+-Applying beta-rule and splitting (152), into two cases.
% 26.45/8.57  																								|-Branch one:
% 26.45/8.57  																								| (202) all_24_0_32 = 0
% 26.45/8.57  																								|
% 26.45/8.57  																									| Equations (202) can reduce 98 to:
% 26.45/8.57  																									| (101) $false
% 26.45/8.57  																									|
% 26.45/8.57  																									|-The branch is then unsatisfiable
% 26.45/8.57  																								|-Branch two:
% 26.45/8.57  																								| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.57  																								| (253) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57  																								|
% 26.45/8.57  																									+-Applying beta-rule and splitting (153), into two cases.
% 26.45/8.57  																									|-Branch one:
% 26.45/8.57  																									| (202) all_24_0_32 = 0
% 26.45/8.57  																									|
% 26.45/8.57  																										| Equations (202) can reduce 98 to:
% 26.45/8.57  																										| (101) $false
% 26.45/8.57  																										|
% 26.45/8.57  																										|-The branch is then unsatisfiable
% 26.45/8.57  																									|-Branch two:
% 26.45/8.57  																									| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.57  																									| (257) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57  																									|
% 26.45/8.57  																										+-Applying beta-rule and splitting (154), into two cases.
% 26.45/8.57  																										|-Branch one:
% 26.45/8.57  																										| (202) all_24_0_32 = 0
% 26.45/8.57  																										|
% 26.45/8.57  																											| Equations (202) can reduce 98 to:
% 26.45/8.57  																											| (101) $false
% 26.45/8.57  																											|
% 26.45/8.57  																											|-The branch is then unsatisfiable
% 26.45/8.57  																										|-Branch two:
% 26.45/8.57  																										| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.57  																										| (261) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.57  																										|
% 26.45/8.57  																											+-Applying beta-rule and splitting (158), into two cases.
% 26.45/8.57  																											|-Branch one:
% 26.45/8.57  																											| (198) all_25_0_33 = 0
% 26.45/8.57  																											|
% 26.45/8.57  																												| Equations (198) can reduce 105 to:
% 26.45/8.57  																												| (101) $false
% 26.45/8.57  																												|
% 26.45/8.57  																												|-The branch is then unsatisfiable
% 26.45/8.57  																											|-Branch two:
% 26.45/8.57  																											| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.57  																											| (265) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57  																											|
% 26.45/8.57  																												+-Applying beta-rule and splitting (155), into two cases.
% 26.45/8.57  																												|-Branch one:
% 26.45/8.57  																												| (202) all_24_0_32 = 0
% 26.45/8.57  																												|
% 26.45/8.57  																													| Equations (202) can reduce 98 to:
% 26.45/8.57  																													| (101) $false
% 26.45/8.57  																													|
% 26.45/8.57  																													|-The branch is then unsatisfiable
% 26.45/8.57  																												|-Branch two:
% 26.45/8.57  																												| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.57  																												| (269) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.57  																												|
% 26.45/8.57  																													+-Applying beta-rule and splitting (183), into two cases.
% 26.45/8.57  																													|-Branch one:
% 26.45/8.57  																													| (210) all_20_0_28 = 0
% 26.45/8.57  																													|
% 26.45/8.57  																														| Equations (210) can reduce 72 to:
% 26.45/8.57  																														| (101) $false
% 26.45/8.57  																														|
% 26.45/8.57  																														|-The branch is then unsatisfiable
% 26.45/8.57  																													|-Branch two:
% 26.45/8.57  																													| (72)  ~ (all_20_0_28 = 0)
% 26.45/8.57  																													| (273) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58  																													|
% 26.45/8.58  																														+-Applying beta-rule and splitting (171), into two cases.
% 26.45/8.58  																														|-Branch one:
% 26.45/8.58  																														| (202) all_24_0_32 = 0
% 26.45/8.58  																														|
% 26.45/8.58  																															| Equations (202) can reduce 98 to:
% 26.45/8.58  																															| (101) $false
% 26.45/8.58  																															|
% 26.45/8.58  																															|-The branch is then unsatisfiable
% 26.45/8.58  																														|-Branch two:
% 26.45/8.58  																														| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.58  																														| (277) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																														|
% 26.45/8.58  																															+-Applying beta-rule and splitting (184), into two cases.
% 26.45/8.58  																															|-Branch one:
% 26.45/8.58  																															| (202) all_24_0_32 = 0
% 26.45/8.58  																															|
% 26.45/8.58  																																| Equations (202) can reduce 98 to:
% 26.45/8.58  																																| (101) $false
% 26.45/8.58  																																|
% 26.45/8.58  																																|-The branch is then unsatisfiable
% 26.45/8.58  																															|-Branch two:
% 26.45/8.58  																															| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.58  																															| (281) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																															|
% 26.45/8.58  																																+-Applying beta-rule and splitting (156), into two cases.
% 26.45/8.58  																																|-Branch one:
% 26.45/8.58  																																| (202) all_24_0_32 = 0
% 26.45/8.58  																																|
% 26.45/8.58  																																	| Equations (202) can reduce 98 to:
% 26.45/8.58  																																	| (101) $false
% 26.45/8.58  																																	|
% 26.45/8.58  																																	|-The branch is then unsatisfiable
% 26.45/8.58  																																|-Branch two:
% 26.45/8.58  																																| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.58  																																| (285) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																																|
% 26.45/8.58  																																	+-Applying beta-rule and splitting (185), into two cases.
% 26.45/8.58  																																	|-Branch one:
% 26.45/8.58  																																	| (202) all_24_0_32 = 0
% 26.45/8.58  																																	|
% 26.45/8.58  																																		| Equations (202) can reduce 98 to:
% 26.45/8.58  																																		| (101) $false
% 26.45/8.58  																																		|
% 26.45/8.58  																																		|-The branch is then unsatisfiable
% 26.45/8.58  																																	|-Branch two:
% 26.45/8.58  																																	| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.58  																																	| (289) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58  																																	|
% 26.45/8.58  																																		+-Applying beta-rule and splitting (186), into two cases.
% 26.45/8.58  																																		|-Branch one:
% 26.45/8.58  																																		| (202) all_24_0_32 = 0
% 26.45/8.58  																																		|
% 26.45/8.58  																																			| Equations (202) can reduce 98 to:
% 26.45/8.58  																																			| (101) $false
% 26.45/8.58  																																			|
% 26.45/8.58  																																			|-The branch is then unsatisfiable
% 26.45/8.58  																																		|-Branch two:
% 26.45/8.58  																																		| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.58  																																		| (293) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																																		|
% 26.45/8.58  																																			+-Applying beta-rule and splitting (189), into two cases.
% 26.45/8.58  																																			|-Branch one:
% 26.45/8.58  																																			| (198) all_25_0_33 = 0
% 26.45/8.58  																																			|
% 26.45/8.58  																																				| Equations (198) can reduce 105 to:
% 26.45/8.58  																																				| (101) $false
% 26.45/8.58  																																				|
% 26.45/8.58  																																				|-The branch is then unsatisfiable
% 26.45/8.58  																																			|-Branch two:
% 26.45/8.58  																																			| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.58  																																			| (297) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58  																																			|
% 26.45/8.58  																																				+-Applying beta-rule and splitting (190), into two cases.
% 26.45/8.58  																																				|-Branch one:
% 26.45/8.58  																																				| (198) all_25_0_33 = 0
% 26.45/8.58  																																				|
% 26.45/8.58  																																					| Equations (198) can reduce 105 to:
% 26.45/8.58  																																					| (101) $false
% 26.45/8.58  																																					|
% 26.45/8.58  																																					|-The branch is then unsatisfiable
% 26.45/8.58  																																				|-Branch two:
% 26.45/8.58  																																				| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.58  																																				| (301) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																																				|
% 26.45/8.58  																																					+-Applying beta-rule and splitting (172), into two cases.
% 26.45/8.58  																																					|-Branch one:
% 26.45/8.58  																																					| (202) all_24_0_32 = 0
% 26.45/8.58  																																					|
% 26.45/8.58  																																						| Equations (202) can reduce 98 to:
% 26.45/8.58  																																						| (101) $false
% 26.45/8.58  																																						|
% 26.45/8.58  																																						|-The branch is then unsatisfiable
% 26.45/8.58  																																					|-Branch two:
% 26.45/8.58  																																					| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.58  																																					| (305) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58  																																					|
% 26.45/8.58  																																						+-Applying beta-rule and splitting (175), into two cases.
% 26.45/8.58  																																						|-Branch one:
% 26.45/8.58  																																						| (198) all_25_0_33 = 0
% 26.45/8.58  																																						|
% 26.45/8.58  																																							| Equations (198) can reduce 105 to:
% 26.45/8.58  																																							| (101) $false
% 26.45/8.58  																																							|
% 26.45/8.58  																																							|-The branch is then unsatisfiable
% 26.45/8.58  																																						|-Branch two:
% 26.45/8.58  																																						| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.58  																																						| (309) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																																						|
% 26.45/8.58  																																							+-Applying beta-rule and splitting (176), into two cases.
% 26.45/8.58  																																							|-Branch one:
% 26.45/8.58  																																							| (198) all_25_0_33 = 0
% 26.45/8.58  																																							|
% 26.45/8.58  																																								| Equations (198) can reduce 105 to:
% 26.45/8.58  																																								| (101) $false
% 26.45/8.58  																																								|
% 26.45/8.58  																																								|-The branch is then unsatisfiable
% 26.45/8.58  																																							|-Branch two:
% 26.45/8.58  																																							| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.58  																																							| (313) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58  																																							|
% 26.45/8.58  																																								+-Applying beta-rule and splitting (177), into two cases.
% 26.45/8.58  																																								|-Branch one:
% 26.45/8.58  																																								| (198) all_25_0_33 = 0
% 26.45/8.58  																																								|
% 26.45/8.58  																																									| Equations (198) can reduce 105 to:
% 26.45/8.58  																																									| (101) $false
% 26.45/8.58  																																									|
% 26.45/8.58  																																									|-The branch is then unsatisfiable
% 26.45/8.58  																																								|-Branch two:
% 26.45/8.58  																																								| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.58  																																								| (317) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.58  																																								|
% 26.45/8.58  																																									+-Applying beta-rule and splitting (178), into two cases.
% 26.45/8.58  																																									|-Branch one:
% 26.45/8.58  																																									| (198) all_25_0_33 = 0
% 26.45/8.58  																																									|
% 26.45/8.58  																																										| Equations (198) can reduce 105 to:
% 26.45/8.58  																																										| (101) $false
% 26.45/8.58  																																										|
% 26.45/8.58  																																										|-The branch is then unsatisfiable
% 26.45/8.58  																																									|-Branch two:
% 26.45/8.58  																																									| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.58  																																									| (321) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.58  																																									|
% 26.45/8.58  																																										+-Applying beta-rule and splitting (180), into two cases.
% 26.45/8.58  																																										|-Branch one:
% 26.45/8.58  																																										| (210) all_20_0_28 = 0
% 26.45/8.58  																																										|
% 26.45/8.58  																																											| Equations (210) can reduce 72 to:
% 26.45/8.58  																																											| (101) $false
% 26.45/8.58  																																											|
% 26.45/8.58  																																											|-The branch is then unsatisfiable
% 26.45/8.58  																																										|-Branch two:
% 26.45/8.58  																																										| (72)  ~ (all_20_0_28 = 0)
% 26.45/8.58  																																										| (325) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58  																																										|
% 26.45/8.58  																																											+-Applying beta-rule and splitting (193), into two cases.
% 26.45/8.58  																																											|-Branch one:
% 26.45/8.58  																																											| (206) all_23_0_31 = 0
% 26.45/8.58  																																											|
% 26.45/8.58  																																												| Equations (206) can reduce 95 to:
% 26.45/8.58  																																												| (101) $false
% 26.45/8.58  																																												|
% 26.45/8.58  																																												|-The branch is then unsatisfiable
% 26.45/8.58  																																											|-Branch two:
% 26.45/8.58  																																											| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.58  																																											| (329) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58  																																											|
% 26.45/8.58  																																												+-Applying beta-rule and splitting (167), into two cases.
% 26.45/8.58  																																												|-Branch one:
% 26.45/8.58  																																												| (206) all_23_0_31 = 0
% 26.45/8.58  																																												|
% 26.45/8.58  																																													| Equations (206) can reduce 95 to:
% 26.45/8.58  																																													| (101) $false
% 26.45/8.58  																																													|
% 26.45/8.58  																																													|-The branch is then unsatisfiable
% 26.45/8.58  																																												|-Branch two:
% 26.45/8.58  																																												| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.58  																																												| (333) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58  																																												|
% 26.45/8.58  																																													+-Applying beta-rule and splitting (168), into two cases.
% 26.45/8.58  																																													|-Branch one:
% 26.45/8.58  																																													| (206) all_23_0_31 = 0
% 26.45/8.58  																																													|
% 26.45/8.58  																																														| Equations (206) can reduce 95 to:
% 26.45/8.58  																																														| (101) $false
% 26.45/8.58  																																														|
% 26.45/8.58  																																														|-The branch is then unsatisfiable
% 26.45/8.58  																																													|-Branch two:
% 26.45/8.58  																																													| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.58  																																													| (337) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.58  																																													|
% 26.45/8.58  																																														+-Applying beta-rule and splitting (169), into two cases.
% 26.45/8.58  																																														|-Branch one:
% 26.45/8.58  																																														| (206) all_23_0_31 = 0
% 26.45/8.58  																																														|
% 26.45/8.58  																																															| Equations (206) can reduce 95 to:
% 26.45/8.58  																																															| (101) $false
% 26.45/8.58  																																															|
% 26.45/8.58  																																															|-The branch is then unsatisfiable
% 26.45/8.58  																																														|-Branch two:
% 26.45/8.58  																																														| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.58  																																														| (341) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59  																																														|
% 26.45/8.59  																																															+-Applying beta-rule and splitting (170), into two cases.
% 26.45/8.59  																																															|-Branch one:
% 26.45/8.59  																																															| (206) all_23_0_31 = 0
% 26.45/8.59  																																															|
% 26.45/8.59  																																																| Equations (206) can reduce 95 to:
% 26.45/8.59  																																																| (101) $false
% 26.45/8.59  																																																|
% 26.45/8.59  																																																|-The branch is then unsatisfiable
% 26.45/8.59  																																															|-Branch two:
% 26.45/8.59  																																															| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.59  																																															| (345) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59  																																															|
% 26.45/8.59  																																																+-Applying beta-rule and splitting (173), into two cases.
% 26.45/8.59  																																																|-Branch one:
% 26.45/8.59  																																																| (202) all_24_0_32 = 0
% 26.45/8.59  																																																|
% 26.45/8.59  																																																	| Equations (202) can reduce 98 to:
% 26.45/8.59  																																																	| (101) $false
% 26.45/8.59  																																																	|
% 26.45/8.59  																																																	|-The branch is then unsatisfiable
% 26.45/8.59  																																																|-Branch two:
% 26.45/8.59  																																																| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.59  																																																| (349) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59  																																																|
% 26.45/8.59  																																																	+-Applying beta-rule and splitting (174), into two cases.
% 26.45/8.59  																																																	|-Branch one:
% 26.45/8.59  																																																	| (202) all_24_0_32 = 0
% 26.45/8.59  																																																	|
% 26.45/8.59  																																																		| Equations (202) can reduce 98 to:
% 26.45/8.59  																																																		| (101) $false
% 26.45/8.59  																																																		|
% 26.45/8.59  																																																		|-The branch is then unsatisfiable
% 26.45/8.59  																																																	|-Branch two:
% 26.45/8.59  																																																	| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.59  																																																	| (353) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59  																																																	|
% 26.45/8.59  																																																		+-Applying beta-rule and splitting (159), into two cases.
% 26.45/8.59  																																																		|-Branch one:
% 26.45/8.59  																																																		| (198) all_25_0_33 = 0
% 26.45/8.59  																																																		|
% 26.45/8.59  																																																			| Equations (198) can reduce 105 to:
% 26.45/8.59  																																																			| (101) $false
% 26.45/8.59  																																																			|
% 26.45/8.59  																																																			|-The branch is then unsatisfiable
% 26.45/8.59  																																																		|-Branch two:
% 26.45/8.59  																																																		| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.59  																																																		| (357) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59  																																																		|
% 26.45/8.59  																																																			+-Applying beta-rule and splitting (160), into two cases.
% 26.45/8.59  																																																			|-Branch one:
% 26.45/8.59  																																																			| (198) all_25_0_33 = 0
% 26.45/8.59  																																																			|
% 26.45/8.59  																																																				| Equations (198) can reduce 105 to:
% 26.45/8.59  																																																				| (101) $false
% 26.45/8.59  																																																				|
% 26.45/8.59  																																																				|-The branch is then unsatisfiable
% 26.45/8.59  																																																			|-Branch two:
% 26.45/8.59  																																																			| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.59  																																																			| (361) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59  																																																			|
% 26.45/8.59  																																																				+-Applying beta-rule and splitting (161), into two cases.
% 26.45/8.59  																																																				|-Branch one:
% 26.45/8.59  																																																				| (198) all_25_0_33 = 0
% 26.45/8.59  																																																				|
% 26.45/8.59  																																																					| Equations (198) can reduce 105 to:
% 26.45/8.59  																																																					| (101) $false
% 26.45/8.59  																																																					|
% 26.45/8.59  																																																					|-The branch is then unsatisfiable
% 26.45/8.59  																																																				|-Branch two:
% 26.45/8.59  																																																				| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.59  																																																				| (365) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59  																																																				|
% 26.45/8.59  																																																					+-Applying beta-rule and splitting (162), into two cases.
% 26.45/8.59  																																																					|-Branch one:
% 26.45/8.59  																																																					| (198) all_25_0_33 = 0
% 26.45/8.59  																																																					|
% 26.45/8.59  																																																						| Equations (198) can reduce 105 to:
% 26.45/8.59  																																																						| (101) $false
% 26.45/8.59  																																																						|
% 26.45/8.59  																																																						|-The branch is then unsatisfiable
% 26.45/8.59  																																																					|-Branch two:
% 26.45/8.59  																																																					| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.59  																																																					| (369) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59  																																																					|
% 26.45/8.59  																																																						+-Applying beta-rule and splitting (165), into two cases.
% 26.45/8.59  																																																						|-Branch one:
% 26.45/8.59  																																																						| (198) all_25_0_33 = 0
% 26.45/8.59  																																																						|
% 26.45/8.59  																																																							| Equations (198) can reduce 105 to:
% 26.45/8.59  																																																							| (101) $false
% 26.45/8.59  																																																							|
% 26.45/8.59  																																																							|-The branch is then unsatisfiable
% 26.45/8.59  																																																						|-Branch two:
% 26.45/8.59  																																																						| (105)  ~ (all_25_0_33 = 0)
% 26.45/8.59  																																																						| (373) all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.59  																																																						|
% 26.45/8.59  																																																							+-Applying beta-rule and splitting (217), into two cases.
% 26.45/8.59  																																																							|-Branch one:
% 26.45/8.59  																																																							| (107) all_0_3_3 = 0
% 26.45/8.59  																																																							|
% 26.45/8.59  																																																								| Equations (107) can reduce 19 to:
% 26.45/8.59  																																																								| (101) $false
% 26.45/8.59  																																																								|
% 26.45/8.59  																																																								|-The branch is then unsatisfiable
% 26.45/8.59  																																																							|-Branch two:
% 26.45/8.59  																																																							| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.59  																																																							| (377)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59  																																																							|
% 26.45/8.59  																																																								+-Applying beta-rule and splitting (221), into two cases.
% 26.45/8.59  																																																								|-Branch one:
% 26.45/8.59  																																																								| (100) all_0_4_4 = 0
% 26.45/8.59  																																																								|
% 26.45/8.59  																																																									| Equations (100) can reduce 45 to:
% 26.45/8.59  																																																									| (101) $false
% 26.45/8.59  																																																									|
% 26.45/8.59  																																																									|-The branch is then unsatisfiable
% 26.45/8.59  																																																								|-Branch two:
% 26.45/8.59  																																																								| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.59  																																																								| (381)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.59  																																																								|
% 26.45/8.59  																																																									+-Applying beta-rule and splitting (237), into two cases.
% 26.45/8.59  																																																									|-Branch one:
% 26.45/8.59  																																																									| (107) all_0_3_3 = 0
% 26.45/8.59  																																																									|
% 26.45/8.59  																																																										| Equations (107) can reduce 19 to:
% 26.45/8.59  																																																										| (101) $false
% 26.45/8.59  																																																										|
% 26.45/8.59  																																																										|-The branch is then unsatisfiable
% 26.45/8.59  																																																									|-Branch two:
% 26.45/8.59  																																																									| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.59  																																																									| (385)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59  																																																									|
% 26.45/8.59  																																																										+-Applying beta-rule and splitting (241), into two cases.
% 26.45/8.59  																																																										|-Branch one:
% 26.45/8.59  																																																										| (100) all_0_4_4 = 0
% 26.45/8.59  																																																										|
% 26.45/8.59  																																																											| Equations (100) can reduce 45 to:
% 26.45/8.59  																																																											| (101) $false
% 26.45/8.59  																																																											|
% 26.45/8.59  																																																											|-The branch is then unsatisfiable
% 26.45/8.59  																																																										|-Branch two:
% 26.45/8.59  																																																										| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.59  																																																										| (389)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59  																																																										|
% 26.45/8.59  																																																											+-Applying beta-rule and splitting (245), into two cases.
% 26.45/8.59  																																																											|-Branch one:
% 26.45/8.59  																																																											| (202) all_24_0_32 = 0
% 26.45/8.59  																																																											|
% 26.45/8.59  																																																												| Equations (202) can reduce 98 to:
% 26.45/8.59  																																																												| (101) $false
% 26.45/8.59  																																																												|
% 26.45/8.59  																																																												|-The branch is then unsatisfiable
% 26.45/8.59  																																																											|-Branch two:
% 26.45/8.59  																																																											| (98)  ~ (all_24_0_32 = 0)
% 26.45/8.59  																																																											| (393)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.45/8.59  																																																											|
% 26.45/8.59  																																																												+-Applying beta-rule and splitting (253), into two cases.
% 26.45/8.59  																																																												|-Branch one:
% 26.45/8.59  																																																												| (107) all_0_3_3 = 0
% 26.45/8.59  																																																												|
% 26.45/8.59  																																																													| Equations (107) can reduce 19 to:
% 26.45/8.59  																																																													| (101) $false
% 26.45/8.59  																																																													|
% 26.45/8.59  																																																													|-The branch is then unsatisfiable
% 26.45/8.59  																																																												|-Branch two:
% 26.45/8.59  																																																												| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.59  																																																												| (397)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59  																																																												|
% 26.45/8.59  																																																													+-Applying beta-rule and splitting (257), into two cases.
% 26.45/8.59  																																																													|-Branch one:
% 26.45/8.59  																																																													| (100) all_0_4_4 = 0
% 26.45/8.59  																																																													|
% 26.45/8.59  																																																														| Equations (100) can reduce 45 to:
% 26.45/8.59  																																																														| (101) $false
% 26.45/8.59  																																																														|
% 26.45/8.59  																																																														|-The branch is then unsatisfiable
% 26.45/8.59  																																																													|-Branch two:
% 26.45/8.59  																																																													| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.59  																																																													| (401)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59  																																																													|
% 26.45/8.59  																																																														+-Applying beta-rule and splitting (261), into two cases.
% 26.45/8.59  																																																														|-Branch one:
% 26.45/8.59  																																																														| (100) all_0_4_4 = 0
% 26.45/8.59  																																																														|
% 26.45/8.59  																																																															| Equations (100) can reduce 45 to:
% 26.45/8.59  																																																															| (101) $false
% 26.45/8.59  																																																															|
% 26.45/8.59  																																																															|-The branch is then unsatisfiable
% 26.45/8.59  																																																														|-Branch two:
% 26.45/8.59  																																																														| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.59  																																																														| (405)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.59  																																																														|
% 26.45/8.59  																																																															| Instantiating (405) with all_272_0_59 yields:
% 26.45/8.59  																																																															| (406) (all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_59 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59) | ( ~ (all_272_0_59 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59)
% 26.45/8.59  																																																															|
% 26.45/8.59  																																																															+-Applying beta-rule and splitting (265), into two cases.
% 26.45/8.59  																																																															|-Branch one:
% 26.45/8.59  																																																															| (107) all_0_3_3 = 0
% 26.45/8.59  																																																															|
% 26.45/8.59  																																																																| Equations (107) can reduce 19 to:
% 26.45/8.59  																																																																| (101) $false
% 26.45/8.59  																																																																|
% 26.45/8.59  																																																																|-The branch is then unsatisfiable
% 26.45/8.59  																																																															|-Branch two:
% 26.45/8.59  																																																															| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.59  																																																															| (410)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.59  																																																															|
% 26.45/8.59  																																																																| Instantiating (410) with all_276_0_60 yields:
% 26.45/8.59  																																																																| (411) (all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_60 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60) | ( ~ (all_276_0_60 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60)
% 26.45/8.59  																																																																|
% 26.45/8.59  																																																																+-Applying beta-rule and splitting (269), into two cases.
% 26.45/8.59  																																																																|-Branch one:
% 26.45/8.59  																																																																| (100) all_0_4_4 = 0
% 26.45/8.59  																																																																|
% 26.45/8.59  																																																																	| Equations (100) can reduce 45 to:
% 26.45/8.59  																																																																	| (101) $false
% 26.45/8.59  																																																																	|
% 26.45/8.59  																																																																	|-The branch is then unsatisfiable
% 26.45/8.59  																																																																|-Branch two:
% 26.45/8.59  																																																																| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.59  																																																																| (415)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60  																																																																|
% 26.45/8.60  																																																																	| Instantiating (415) with all_280_0_61 yields:
% 26.45/8.60  																																																																	| (416) (all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_61 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61) | ( ~ (all_280_0_61 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61)
% 26.45/8.60  																																																																	|
% 26.45/8.60  																																																																	+-Applying beta-rule and splitting (273), into two cases.
% 26.45/8.60  																																																																	|-Branch one:
% 26.45/8.60  																																																																	| (100) all_0_4_4 = 0
% 26.45/8.60  																																																																	|
% 26.45/8.60  																																																																		| Equations (100) can reduce 45 to:
% 26.45/8.60  																																																																		| (101) $false
% 26.45/8.60  																																																																		|
% 26.45/8.60  																																																																		|-The branch is then unsatisfiable
% 26.45/8.60  																																																																	|-Branch two:
% 26.45/8.60  																																																																	| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.60  																																																																	| (420)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60  																																																																	|
% 26.45/8.60  																																																																		+-Applying beta-rule and splitting (277), into two cases.
% 26.45/8.60  																																																																		|-Branch one:
% 26.45/8.60  																																																																		| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																		|
% 26.45/8.60  																																																																			| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																			| (101) $false
% 26.45/8.60  																																																																			|
% 26.45/8.60  																																																																			|-The branch is then unsatisfiable
% 26.45/8.60  																																																																		|-Branch two:
% 26.45/8.60  																																																																		| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																		| (424)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																		|
% 26.45/8.60  																																																																			+-Applying beta-rule and splitting (285), into two cases.
% 26.45/8.60  																																																																			|-Branch one:
% 26.45/8.60  																																																																			| (100) all_0_4_4 = 0
% 26.45/8.60  																																																																			|
% 26.45/8.60  																																																																				| Equations (100) can reduce 45 to:
% 26.45/8.60  																																																																				| (101) $false
% 26.45/8.60  																																																																				|
% 26.45/8.60  																																																																				|-The branch is then unsatisfiable
% 26.45/8.60  																																																																			|-Branch two:
% 26.45/8.60  																																																																			| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.60  																																																																			| (428)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																			|
% 26.45/8.60  																																																																				+-Applying beta-rule and splitting (305), into two cases.
% 26.45/8.60  																																																																				|-Branch one:
% 26.45/8.60  																																																																				| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																				|
% 26.45/8.60  																																																																					| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																					| (101) $false
% 26.45/8.60  																																																																					|
% 26.45/8.60  																																																																					|-The branch is then unsatisfiable
% 26.45/8.60  																																																																				|-Branch two:
% 26.45/8.60  																																																																				| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																				| (432)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60  																																																																				|
% 26.45/8.60  																																																																					+-Applying beta-rule and splitting (309), into two cases.
% 26.45/8.60  																																																																					|-Branch one:
% 26.45/8.60  																																																																					| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																					|
% 26.45/8.60  																																																																						| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																						| (101) $false
% 26.45/8.60  																																																																						|
% 26.45/8.60  																																																																						|-The branch is then unsatisfiable
% 26.45/8.60  																																																																					|-Branch two:
% 26.45/8.60  																																																																					| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																					| (436)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																					|
% 26.45/8.60  																																																																						+-Applying beta-rule and splitting (313), into two cases.
% 26.45/8.60  																																																																						|-Branch one:
% 26.45/8.60  																																																																						| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																						|
% 26.45/8.60  																																																																							| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																							| (101) $false
% 26.45/8.60  																																																																							|
% 26.45/8.60  																																																																							|-The branch is then unsatisfiable
% 26.45/8.60  																																																																						|-Branch two:
% 26.45/8.60  																																																																						| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																						| (440)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60  																																																																						|
% 26.45/8.60  																																																																							+-Applying beta-rule and splitting (317), into two cases.
% 26.45/8.60  																																																																							|-Branch one:
% 26.45/8.60  																																																																							| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																							|
% 26.45/8.60  																																																																								| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																								| (101) $false
% 26.45/8.60  																																																																								|
% 26.45/8.60  																																																																								|-The branch is then unsatisfiable
% 26.45/8.60  																																																																							|-Branch two:
% 26.45/8.60  																																																																							| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																							| (444)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																							|
% 26.45/8.60  																																																																								+-Applying beta-rule and splitting (321), into two cases.
% 26.45/8.60  																																																																								|-Branch one:
% 26.45/8.60  																																																																								| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																								|
% 26.45/8.60  																																																																									| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																									| (101) $false
% 26.45/8.60  																																																																									|
% 26.45/8.60  																																																																									|-The branch is then unsatisfiable
% 26.45/8.60  																																																																								|-Branch two:
% 26.45/8.60  																																																																								| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																								| (448)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60  																																																																								|
% 26.45/8.60  																																																																									+-Applying beta-rule and splitting (325), into two cases.
% 26.45/8.60  																																																																									|-Branch one:
% 26.45/8.60  																																																																									| (107) all_0_3_3 = 0
% 26.45/8.60  																																																																									|
% 26.45/8.60  																																																																										| Equations (107) can reduce 19 to:
% 26.45/8.60  																																																																										| (101) $false
% 26.45/8.60  																																																																										|
% 26.45/8.60  																																																																										|-The branch is then unsatisfiable
% 26.45/8.60  																																																																									|-Branch two:
% 26.45/8.60  																																																																									| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.60  																																																																									| (452)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60  																																																																									|
% 26.45/8.60  																																																																										+-Applying beta-rule and splitting (333), into two cases.
% 26.45/8.60  																																																																										|-Branch one:
% 26.45/8.60  																																																																										| (107) all_0_3_3 = 0
% 26.45/8.60  																																																																										|
% 26.45/8.60  																																																																											| Equations (107) can reduce 19 to:
% 26.45/8.60  																																																																											| (101) $false
% 26.45/8.60  																																																																											|
% 26.45/8.60  																																																																											|-The branch is then unsatisfiable
% 26.45/8.60  																																																																										|-Branch two:
% 26.45/8.60  																																																																										| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.60  																																																																										| (456)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60  																																																																										|
% 26.45/8.60  																																																																											+-Applying beta-rule and splitting (337), into two cases.
% 26.45/8.60  																																																																											|-Branch one:
% 26.45/8.60  																																																																											| (107) all_0_3_3 = 0
% 26.45/8.60  																																																																											|
% 26.45/8.60  																																																																												| Equations (107) can reduce 19 to:
% 26.45/8.60  																																																																												| (101) $false
% 26.45/8.60  																																																																												|
% 26.45/8.60  																																																																												|-The branch is then unsatisfiable
% 26.45/8.60  																																																																											|-Branch two:
% 26.45/8.60  																																																																											| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.60  																																																																											| (460)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60  																																																																											|
% 26.45/8.60  																																																																												+-Applying beta-rule and splitting (341), into two cases.
% 26.45/8.60  																																																																												|-Branch one:
% 26.45/8.60  																																																																												| (100) all_0_4_4 = 0
% 26.45/8.60  																																																																												|
% 26.45/8.60  																																																																													| Equations (100) can reduce 45 to:
% 26.45/8.60  																																																																													| (101) $false
% 26.45/8.60  																																																																													|
% 26.45/8.60  																																																																													|-The branch is then unsatisfiable
% 26.45/8.60  																																																																												|-Branch two:
% 26.45/8.60  																																																																												| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.60  																																																																												| (464)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60  																																																																												|
% 26.45/8.60  																																																																													+-Applying beta-rule and splitting (345), into two cases.
% 26.45/8.60  																																																																													|-Branch one:
% 26.45/8.60  																																																																													| (100) all_0_4_4 = 0
% 26.45/8.60  																																																																													|
% 26.45/8.60  																																																																														| Equations (100) can reduce 45 to:
% 26.45/8.60  																																																																														| (101) $false
% 26.45/8.60  																																																																														|
% 26.45/8.60  																																																																														|-The branch is then unsatisfiable
% 26.45/8.60  																																																																													|-Branch two:
% 26.45/8.60  																																																																													| (45)  ~ (all_0_4_4 = 0)
% 26.45/8.60  																																																																													| (468)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.45/8.60  																																																																													|
% 26.45/8.60  																																																																														+-Applying beta-rule and splitting (349), into two cases.
% 26.45/8.60  																																																																														|-Branch one:
% 26.45/8.60  																																																																														| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																														|
% 26.45/8.60  																																																																															| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																															| (101) $false
% 26.45/8.60  																																																																															|
% 26.45/8.60  																																																																															|-The branch is then unsatisfiable
% 26.45/8.60  																																																																														|-Branch two:
% 26.45/8.60  																																																																														| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																														| (472)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																														|
% 26.45/8.60  																																																																															+-Applying beta-rule and splitting (353), into two cases.
% 26.45/8.60  																																																																															|-Branch one:
% 26.45/8.60  																																																																															| (206) all_23_0_31 = 0
% 26.45/8.60  																																																																															|
% 26.45/8.60  																																																																																| Equations (206) can reduce 95 to:
% 26.45/8.60  																																																																																| (101) $false
% 26.45/8.60  																																																																																|
% 26.45/8.60  																																																																																|-The branch is then unsatisfiable
% 26.45/8.60  																																																																															|-Branch two:
% 26.45/8.60  																																																																															| (95)  ~ (all_23_0_31 = 0)
% 26.45/8.60  																																																																															| (476)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60  																																																																															|
% 26.45/8.60  																																																																																+-Applying beta-rule and splitting (357), into two cases.
% 26.45/8.60  																																																																																|-Branch one:
% 26.45/8.60  																																																																																| (107) all_0_3_3 = 0
% 26.45/8.60  																																																																																|
% 26.45/8.60  																																																																																	| Equations (107) can reduce 19 to:
% 26.45/8.60  																																																																																	| (101) $false
% 26.45/8.60  																																																																																	|
% 26.45/8.60  																																																																																	|-The branch is then unsatisfiable
% 26.45/8.60  																																																																																|-Branch two:
% 26.45/8.60  																																																																																| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.60  																																																																																| (480)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																																|
% 26.45/8.60  																																																																																	+-Applying beta-rule and splitting (361), into two cases.
% 26.45/8.60  																																																																																	|-Branch one:
% 26.45/8.60  																																																																																	| (107) all_0_3_3 = 0
% 26.45/8.60  																																																																																	|
% 26.45/8.60  																																																																																		| Equations (107) can reduce 19 to:
% 26.45/8.60  																																																																																		| (101) $false
% 26.45/8.60  																																																																																		|
% 26.45/8.60  																																																																																		|-The branch is then unsatisfiable
% 26.45/8.60  																																																																																	|-Branch two:
% 26.45/8.60  																																																																																	| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.60  																																																																																	| (484)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.45/8.60  																																																																																	|
% 26.45/8.60  																																																																																		+-Applying beta-rule and splitting (365), into two cases.
% 26.45/8.60  																																																																																		|-Branch one:
% 26.45/8.60  																																																																																		| (107) all_0_3_3 = 0
% 26.45/8.60  																																																																																		|
% 26.45/8.60  																																																																																			| Equations (107) can reduce 19 to:
% 26.45/8.60  																																																																																			| (101) $false
% 26.45/8.60  																																																																																			|
% 26.45/8.60  																																																																																			|-The branch is then unsatisfiable
% 26.45/8.60  																																																																																		|-Branch two:
% 26.45/8.60  																																																																																		| (19)  ~ (all_0_3_3 = 0)
% 26.45/8.60  																																																																																		| (488)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.45/8.60  																																																																																		|
% 26.45/8.60  																																																																																			| Instantiating (488) with all_376_0_85 yields:
% 26.45/8.60  																																																																																			| (489) (all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_85 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85) | ( ~ (all_376_0_85 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85)
% 26.78/8.60  																																																																																			|
% 26.78/8.60  																																																																																			+-Applying beta-rule and splitting (369), into two cases.
% 26.78/8.60  																																																																																			|-Branch one:
% 26.78/8.60  																																																																																			| (100) all_0_4_4 = 0
% 26.78/8.60  																																																																																			|
% 26.78/8.60  																																																																																				| Equations (100) can reduce 45 to:
% 26.78/8.60  																																																																																				| (101) $false
% 26.78/8.60  																																																																																				|
% 26.78/8.60  																																																																																				|-The branch is then unsatisfiable
% 26.78/8.60  																																																																																			|-Branch two:
% 26.78/8.60  																																																																																			| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.60  																																																																																			| (493)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.60  																																																																																			|
% 26.78/8.60  																																																																																				+-Applying beta-rule and splitting (373), into two cases.
% 26.78/8.60  																																																																																				|-Branch one:
% 26.78/8.60  																																																																																				| (202) all_24_0_32 = 0
% 26.78/8.61  																																																																																				|
% 26.78/8.61  																																																																																					| Equations (202) can reduce 98 to:
% 26.78/8.61  																																																																																					| (101) $false
% 26.78/8.61  																																																																																					|
% 26.78/8.61  																																																																																					|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																				|-Branch two:
% 26.78/8.61  																																																																																				| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.61  																																																																																				| (497)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.61  																																																																																				|
% 26.78/8.61  																																																																																					| Instantiating formula (2) with all_23_0_31, all_0_5_5, all_0_8_8, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_8_8) = 0, apart_point_and_line(all_0_5_5, all_0_8_8) = all_23_0_31, yields:
% 26.78/8.61  																																																																																					| (498) all_23_0_31 = 0 | distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.61  																																																																																					|
% 26.78/8.61  																																																																																					+-Applying beta-rule and splitting (498), into two cases.
% 26.78/8.61  																																																																																					|-Branch one:
% 26.78/8.61  																																																																																					| (499) distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.61  																																																																																					|
% 26.78/8.61  																																																																																						+-Applying beta-rule and splitting (489), into two cases.
% 26.78/8.61  																																																																																						|-Branch one:
% 26.78/8.61  																																																																																						| (500) (all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_85 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85)
% 26.78/8.61  																																																																																						|
% 26.78/8.61  																																																																																							+-Applying beta-rule and splitting (500), into two cases.
% 26.78/8.61  																																																																																							|-Branch one:
% 26.78/8.61  																																																																																							| (501) (all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.61  																																																																																							|
% 26.78/8.61  																																																																																								+-Applying beta-rule and splitting (501), into two cases.
% 26.78/8.61  																																																																																								|-Branch one:
% 26.78/8.61  																																																																																								| (502) all_376_0_85 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61  																																																																																								|
% 26.78/8.61  																																																																																									| Applying alpha-rule on (502) yields:
% 26.78/8.61  																																																																																									| (503) all_376_0_85 = 0
% 26.78/8.61  																																																																																									| (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																									| Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 26.78/8.61  																																																																																									| (202) all_24_0_32 = 0
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																									| Equations (202) can reduce 98 to:
% 26.78/8.61  																																																																																									| (101) $false
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																									|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																								|-Branch two:
% 26.78/8.61  																																																																																								| (507) all_376_0_85 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61  																																																																																								|
% 26.78/8.61  																																																																																									| Applying alpha-rule on (507) yields:
% 26.78/8.61  																																																																																									| (503) all_376_0_85 = 0
% 26.78/8.61  																																																																																									| (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																									| Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 26.78/8.61  																																																																																									| (100) all_0_4_4 = 0
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																									| Equations (100) can reduce 45 to:
% 26.78/8.61  																																																																																									| (101) $false
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																									|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																							|-Branch two:
% 26.78/8.61  																																																																																							| (512)  ~ (all_376_0_85 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85
% 26.78/8.61  																																																																																							|
% 26.78/8.61  																																																																																								| Applying alpha-rule on (512) yields:
% 26.78/8.61  																																																																																								| (513)  ~ (all_376_0_85 = 0)
% 26.78/8.61  																																																																																								| (514) distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85
% 26.78/8.61  																																																																																								|
% 26.78/8.61  																																																																																								+-Applying beta-rule and splitting (406), into two cases.
% 26.78/8.61  																																																																																								|-Branch one:
% 26.78/8.61  																																																																																								| (515) (all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_59 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59)
% 26.78/8.61  																																																																																								|
% 26.78/8.61  																																																																																									+-Applying beta-rule and splitting (515), into two cases.
% 26.78/8.61  																																																																																									|-Branch one:
% 26.78/8.61  																																																																																									| (516) (all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																										+-Applying beta-rule and splitting (516), into two cases.
% 26.78/8.61  																																																																																										|-Branch one:
% 26.78/8.61  																																																																																										| (517) all_272_0_59 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61  																																																																																										|
% 26.78/8.61  																																																																																											| Applying alpha-rule on (517) yields:
% 26.78/8.61  																																																																																											| (518) all_272_0_59 = 0
% 26.78/8.61  																																																																																											| (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																											| Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 26.78/8.61  																																																																																											| (198) all_25_0_33 = 0
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																											| Equations (198) can reduce 105 to:
% 26.78/8.61  																																																																																											| (101) $false
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																											|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																										|-Branch two:
% 26.78/8.61  																																																																																										| (522) all_272_0_59 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61  																																																																																										|
% 26.78/8.61  																																																																																											| Applying alpha-rule on (522) yields:
% 26.78/8.61  																																																																																											| (518) all_272_0_59 = 0
% 26.78/8.61  																																																																																											| (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																											| Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 26.78/8.61  																																																																																											| (107) all_0_3_3 = 0
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																											| Equations (107) can reduce 19 to:
% 26.78/8.61  																																																																																											| (101) $false
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																											|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																									|-Branch two:
% 26.78/8.61  																																																																																									| (527)  ~ (all_272_0_59 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61  																																																																																									|
% 26.78/8.61  																																																																																										| Applying alpha-rule on (527) yields:
% 26.78/8.61  																																																																																										| (528)  ~ (all_272_0_59 = 0)
% 26.78/8.61  																																																																																										| (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61  																																																																																										|
% 26.78/8.61  																																																																																										| Instantiating formula (28) with all_0_6_6, all_0_7_7, all_272_0_59, all_376_0_85 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_85, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.61  																																																																																										| (530) all_376_0_85 = all_272_0_59
% 26.78/8.61  																																																																																										|
% 26.78/8.61  																																																																																										| From (530) and (514) follows:
% 26.78/8.61  																																																																																										| (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61  																																																																																										|
% 26.78/8.61  																																																																																										+-Applying beta-rule and splitting (411), into two cases.
% 26.78/8.61  																																																																																										|-Branch one:
% 26.78/8.61  																																																																																										| (532) (all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_60 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60)
% 26.78/8.61  																																																																																										|
% 26.78/8.61  																																																																																											+-Applying beta-rule and splitting (532), into two cases.
% 26.78/8.61  																																																																																											|-Branch one:
% 26.78/8.61  																																																																																											| (533) (all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																												+-Applying beta-rule and splitting (533), into two cases.
% 26.78/8.61  																																																																																												|-Branch one:
% 26.78/8.61  																																																																																												| (534) all_276_0_60 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61  																																																																																												|
% 26.78/8.61  																																																																																													| Applying alpha-rule on (534) yields:
% 26.78/8.61  																																																																																													| (535) all_276_0_60 = 0
% 26.78/8.61  																																																																																													| (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																													| Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 26.78/8.61  																																																																																													| (202) all_24_0_32 = 0
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																													| Equations (202) can reduce 98 to:
% 26.78/8.61  																																																																																													| (101) $false
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																													|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																												|-Branch two:
% 26.78/8.61  																																																																																												| (539) all_276_0_60 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61  																																																																																												|
% 26.78/8.61  																																																																																													| Applying alpha-rule on (539) yields:
% 26.78/8.61  																																																																																													| (535) all_276_0_60 = 0
% 26.78/8.61  																																																																																													| (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																													| Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 26.78/8.61  																																																																																													| (100) all_0_4_4 = 0
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																													| Equations (100) can reduce 45 to:
% 26.78/8.61  																																																																																													| (101) $false
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																													|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																											|-Branch two:
% 26.78/8.61  																																																																																											| (544)  ~ (all_276_0_60 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60
% 26.78/8.61  																																																																																											|
% 26.78/8.61  																																																																																												| Applying alpha-rule on (544) yields:
% 26.78/8.61  																																																																																												| (545)  ~ (all_276_0_60 = 0)
% 26.78/8.61  																																																																																												| (546) distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60
% 26.78/8.61  																																																																																												|
% 26.78/8.61  																																																																																												| Instantiating formula (28) with all_0_6_6, all_0_7_7, all_276_0_60, all_272_0_59 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_60, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.61  																																																																																												| (547) all_276_0_60 = all_272_0_59
% 26.78/8.61  																																																																																												|
% 26.78/8.61  																																																																																												| From (547) and (546) follows:
% 26.78/8.61  																																																																																												| (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.61  																																																																																												|
% 26.78/8.61  																																																																																												+-Applying beta-rule and splitting (416), into two cases.
% 26.78/8.61  																																																																																												|-Branch one:
% 26.78/8.61  																																																																																												| (549) (all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_61 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61)
% 26.78/8.61  																																																																																												|
% 26.78/8.61  																																																																																													+-Applying beta-rule and splitting (549), into two cases.
% 26.78/8.61  																																																																																													|-Branch one:
% 26.78/8.61  																																																																																													| (550) (all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																														+-Applying beta-rule and splitting (550), into two cases.
% 26.78/8.61  																																																																																														|-Branch one:
% 26.78/8.61  																																																																																														| (551) all_280_0_61 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61  																																																																																														|
% 26.78/8.61  																																																																																															| Applying alpha-rule on (551) yields:
% 26.78/8.61  																																																																																															| (552) all_280_0_61 = 0
% 26.78/8.61  																																																																																															| (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.61  																																																																																															|
% 26.78/8.61  																																																																																															| Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 26.78/8.61  																																																																																															| (198) all_25_0_33 = 0
% 26.78/8.61  																																																																																															|
% 26.78/8.61  																																																																																															| Equations (198) can reduce 105 to:
% 26.78/8.61  																																																																																															| (101) $false
% 26.78/8.61  																																																																																															|
% 26.78/8.61  																																																																																															|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																														|-Branch two:
% 26.78/8.61  																																																																																														| (556) all_280_0_61 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61  																																																																																														|
% 26.78/8.61  																																																																																															| Applying alpha-rule on (556) yields:
% 26.78/8.61  																																																																																															| (552) all_280_0_61 = 0
% 26.78/8.61  																																																																																															| (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.61  																																																																																															|
% 26.78/8.61  																																																																																															| Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 26.78/8.61  																																																																																															| (107) all_0_3_3 = 0
% 26.78/8.61  																																																																																															|
% 26.78/8.61  																																																																																															| Equations (107) can reduce 19 to:
% 26.78/8.61  																																																																																															| (101) $false
% 26.78/8.61  																																																																																															|
% 26.78/8.61  																																																																																															|-The branch is then unsatisfiable
% 26.78/8.61  																																																																																													|-Branch two:
% 26.78/8.61  																																																																																													| (561)  ~ (all_280_0_61 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61
% 26.78/8.61  																																																																																													|
% 26.78/8.61  																																																																																														| Applying alpha-rule on (561) yields:
% 26.78/8.61  																																																																																														| (562)  ~ (all_280_0_61 = 0)
% 26.78/8.61  																																																																																														| (563) distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61
% 26.78/8.61  																																																																																														|
% 26.78/8.61  																																																																																														| Instantiating formula (28) with all_0_6_6, all_0_7_7, all_280_0_61, all_272_0_59 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_61, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.62  																																																																																														| (564) all_280_0_61 = all_272_0_59
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																														| Equations (564) can reduce 562 to:
% 26.78/8.62  																																																																																														| (528)  ~ (all_272_0_59 = 0)
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																														| From (564) and (563) follows:
% 26.78/8.62  																																																																																														| (529) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																														| Instantiating formula (17) with all_272_0_59, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_59, yields:
% 26.78/8.62  																																																																																														| (567) all_272_0_59 = 0 | convergent_lines(all_0_7_7, all_0_7_7) = 0
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																														+-Applying beta-rule and splitting (567), into two cases.
% 26.78/8.62  																																																																																														|-Branch one:
% 26.78/8.62  																																																																																														| (568) convergent_lines(all_0_7_7, all_0_7_7) = 0
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																															| Instantiating formula (4) with all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_7_7) = 0, yields:
% 26.78/8.62  																																																																																															| (569) $false
% 26.78/8.62  																																																																																															|
% 26.78/8.62  																																																																																															|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																														|-Branch two:
% 26.78/8.62  																																																																																														| (570)  ~ (convergent_lines(all_0_7_7, all_0_7_7) = 0)
% 26.78/8.62  																																																																																														| (518) all_272_0_59 = 0
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																															| Equations (518) can reduce 528 to:
% 26.78/8.62  																																																																																															| (101) $false
% 26.78/8.62  																																																																																															|
% 26.78/8.62  																																																																																															|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																												|-Branch two:
% 26.78/8.62  																																																																																												| (573)  ~ (all_280_0_61 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61
% 26.78/8.62  																																																																																												|
% 26.78/8.62  																																																																																													| Applying alpha-rule on (573) yields:
% 26.78/8.62  																																																																																													| (562)  ~ (all_280_0_61 = 0)
% 26.78/8.62  																																																																																													| (575) distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61
% 26.78/8.62  																																																																																													|
% 26.78/8.62  																																																																																													| Instantiating formula (32) with all_280_0_61, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_280_0_61, yields:
% 26.78/8.62  																																																																																													| (576) all_280_0_61 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62  																																																																																													|
% 26.78/8.62  																																																																																													+-Applying beta-rule and splitting (576), into two cases.
% 26.78/8.62  																																																																																													|-Branch one:
% 26.78/8.62  																																																																																													| (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62  																																																																																													|
% 26.78/8.62  																																																																																														| Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 26.78/8.62  																																																																																														| (569) $false
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																														|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																													|-Branch two:
% 26.78/8.62  																																																																																													| (579)  ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 26.78/8.62  																																																																																													| (552) all_280_0_61 = 0
% 26.78/8.62  																																																																																													|
% 26.78/8.62  																																																																																														| Equations (552) can reduce 562 to:
% 26.78/8.62  																																																																																														| (101) $false
% 26.78/8.62  																																																																																														|
% 26.78/8.62  																																																																																														|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																										|-Branch two:
% 26.78/8.62  																																																																																										| (582)  ~ (all_276_0_60 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60
% 26.78/8.62  																																																																																										|
% 26.78/8.62  																																																																																											| Applying alpha-rule on (582) yields:
% 26.78/8.62  																																																																																											| (545)  ~ (all_276_0_60 = 0)
% 26.78/8.62  																																																																																											| (584) distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60
% 26.78/8.62  																																																																																											|
% 26.78/8.62  																																																																																											| Instantiating formula (32) with all_276_0_60, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_276_0_60, yields:
% 26.78/8.62  																																																																																											| (585) all_276_0_60 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62  																																																																																											|
% 26.78/8.62  																																																																																											+-Applying beta-rule and splitting (585), into two cases.
% 26.78/8.62  																																																																																											|-Branch one:
% 26.78/8.62  																																																																																											| (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 26.78/8.62  																																																																																											|
% 26.78/8.62  																																																																																												| Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 26.78/8.62  																																																																																												| (569) $false
% 26.78/8.62  																																																																																												|
% 26.78/8.62  																																																																																												|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																											|-Branch two:
% 26.78/8.62  																																																																																											| (579)  ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 26.78/8.62  																																																																																											| (535) all_276_0_60 = 0
% 26.78/8.62  																																																																																											|
% 26.78/8.62  																																																																																												| Equations (535) can reduce 545 to:
% 26.78/8.62  																																																																																												| (101) $false
% 26.78/8.62  																																																																																												|
% 26.78/8.62  																																																																																												|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																								|-Branch two:
% 26.78/8.62  																																																																																								| (591)  ~ (all_272_0_59 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59
% 26.78/8.62  																																																																																								|
% 26.78/8.62  																																																																																									| Applying alpha-rule on (591) yields:
% 26.78/8.62  																																																																																									| (528)  ~ (all_272_0_59 = 0)
% 26.78/8.62  																																																																																									| (593) distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59
% 26.78/8.62  																																																																																									|
% 26.78/8.62  																																																																																									| Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_272_0_59 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_272_0_59, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 26.78/8.62  																																																																																									| (518) all_272_0_59 = 0
% 26.78/8.62  																																																																																									|
% 26.78/8.62  																																																																																									| Equations (518) can reduce 528 to:
% 26.78/8.62  																																																																																									| (101) $false
% 26.78/8.62  																																																																																									|
% 26.78/8.62  																																																																																									|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																						|-Branch two:
% 26.78/8.62  																																																																																						| (596)  ~ (all_376_0_85 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85
% 26.78/8.62  																																																																																						|
% 26.78/8.62  																																																																																							| Applying alpha-rule on (596) yields:
% 26.78/8.62  																																																																																							| (513)  ~ (all_376_0_85 = 0)
% 26.78/8.62  																																																																																							| (598) distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85
% 26.78/8.62  																																																																																							|
% 26.78/8.62  																																																																																							| Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_376_0_85 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_376_0_85, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 26.78/8.62  																																																																																							| (503) all_376_0_85 = 0
% 26.78/8.62  																																																																																							|
% 26.78/8.62  																																																																																							| Equations (503) can reduce 513 to:
% 26.78/8.62  																																																																																							| (101) $false
% 26.78/8.62  																																																																																							|
% 26.78/8.62  																																																																																							|-The branch is then unsatisfiable
% 26.78/8.62  																																																																																					|-Branch two:
% 26.78/8.62  																																																																																					| (601)  ~ (distinct_points(all_0_2_2, all_0_5_5) = 0)
% 26.78/8.62  																																																																																					| (206) all_23_0_31 = 0
% 26.78/8.62  																																																																																					|
% 26.78/8.62  																																																																																						| Equations (206) can reduce 95 to:
% 26.78/8.62  																																																																																						| (101) $false
% 26.78/8.62  																																																																																						|
% 26.78/8.62  																																																																																						|-The branch is then unsatisfiable
% 26.78/8.62  										|-Branch two:
% 26.78/8.62  										| (604) all_0_1_1 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0
% 26.78/8.62  										|
% 26.78/8.62  											| Applying alpha-rule on (604) yields:
% 26.78/8.62  											| (605) all_0_1_1 = 0
% 26.78/8.62  											| (606) apart_point_and_line(all_0_2_2, all_0_9_9) = 0
% 26.78/8.62  											|
% 26.78/8.62  											+-Applying beta-rule and splitting (166), into two cases.
% 26.78/8.62  											|-Branch one:
% 26.78/8.62  											| (198) all_25_0_33 = 0
% 26.78/8.62  											|
% 26.78/8.62  												| Equations (198) can reduce 105 to:
% 26.78/8.62  												| (101) $false
% 26.78/8.62  												|
% 26.78/8.62  												|-The branch is then unsatisfiable
% 26.78/8.62  											|-Branch two:
% 26.78/8.62  											| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.62  											| (201)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.62  											|
% 26.78/8.62  												+-Applying beta-rule and splitting (157), into two cases.
% 26.78/8.62  												|-Branch one:
% 26.78/8.62  												| (202) all_24_0_32 = 0
% 26.78/8.62  												|
% 26.78/8.62  													| Equations (202) can reduce 98 to:
% 26.78/8.62  													| (101) $false
% 26.78/8.62  													|
% 26.78/8.62  													|-The branch is then unsatisfiable
% 26.78/8.62  												|-Branch two:
% 26.78/8.62  												| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.62  												| (205)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.62  												|
% 26.78/8.62  													+-Applying beta-rule and splitting (179), into two cases.
% 26.78/8.62  													|-Branch one:
% 26.78/8.63  													| (206) all_23_0_31 = 0
% 26.78/8.63  													|
% 26.78/8.63  														| Equations (206) can reduce 95 to:
% 26.78/8.63  														| (101) $false
% 26.78/8.63  														|
% 26.78/8.63  														|-The branch is then unsatisfiable
% 26.78/8.63  													|-Branch two:
% 26.78/8.63  													| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.63  													| (209)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63  													|
% 26.78/8.63  														+-Applying beta-rule and splitting (194), into two cases.
% 26.78/8.63  														|-Branch one:
% 26.78/8.63  														| (210) all_20_0_28 = 0
% 26.78/8.63  														|
% 26.78/8.63  															| Equations (210) can reduce 72 to:
% 26.78/8.63  															| (101) $false
% 26.78/8.63  															|
% 26.78/8.63  															|-The branch is then unsatisfiable
% 26.78/8.63  														|-Branch two:
% 26.78/8.63  														| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.63  														| (213)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63  														|
% 26.78/8.63  															+-Applying beta-rule and splitting (181), into two cases.
% 26.78/8.63  															|-Branch one:
% 26.78/8.63  															| (210) all_20_0_28 = 0
% 26.78/8.63  															|
% 26.78/8.63  																| Equations (210) can reduce 72 to:
% 26.78/8.63  																| (101) $false
% 26.78/8.63  																|
% 26.78/8.63  																|-The branch is then unsatisfiable
% 26.78/8.63  															|-Branch two:
% 26.78/8.63  															| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.63  															| (217) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63  															|
% 26.78/8.63  																+-Applying beta-rule and splitting (182), into two cases.
% 26.78/8.63  																|-Branch one:
% 26.78/8.63  																| (210) all_20_0_28 = 0
% 26.78/8.63  																|
% 26.78/8.63  																	| Equations (210) can reduce 72 to:
% 26.78/8.63  																	| (101) $false
% 26.78/8.63  																	|
% 26.78/8.63  																	|-The branch is then unsatisfiable
% 26.78/8.63  																|-Branch two:
% 26.78/8.63  																| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.63  																| (221) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63  																|
% 26.78/8.63  																	+-Applying beta-rule and splitting (187), into two cases.
% 26.78/8.63  																	|-Branch one:
% 26.78/8.63  																	| (202) all_24_0_32 = 0
% 26.78/8.63  																	|
% 26.78/8.63  																		| Equations (202) can reduce 98 to:
% 26.78/8.63  																		| (101) $false
% 26.78/8.63  																		|
% 26.78/8.63  																		|-The branch is then unsatisfiable
% 26.78/8.63  																	|-Branch two:
% 26.78/8.63  																	| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																	| (225) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																	|
% 26.78/8.63  																		+-Applying beta-rule and splitting (188), into two cases.
% 26.78/8.63  																		|-Branch one:
% 26.78/8.63  																		| (198) all_25_0_33 = 0
% 26.78/8.63  																		|
% 26.78/8.63  																			| Equations (198) can reduce 105 to:
% 26.78/8.63  																			| (101) $false
% 26.78/8.63  																			|
% 26.78/8.63  																			|-The branch is then unsatisfiable
% 26.78/8.63  																		|-Branch two:
% 26.78/8.63  																		| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																		| (229) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																		|
% 26.78/8.63  																			+-Applying beta-rule and splitting (191), into two cases.
% 26.78/8.63  																			|-Branch one:
% 26.78/8.63  																			| (198) all_25_0_33 = 0
% 26.78/8.63  																			|
% 26.78/8.63  																				| Equations (198) can reduce 105 to:
% 26.78/8.63  																				| (101) $false
% 26.78/8.63  																				|
% 26.78/8.63  																				|-The branch is then unsatisfiable
% 26.78/8.63  																			|-Branch two:
% 26.78/8.63  																			| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																			| (233) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																			|
% 26.78/8.63  																				+-Applying beta-rule and splitting (151), into two cases.
% 26.78/8.63  																				|-Branch one:
% 26.78/8.63  																				| (202) all_24_0_32 = 0
% 26.78/8.63  																				|
% 26.78/8.63  																					| Equations (202) can reduce 98 to:
% 26.78/8.63  																					| (101) $false
% 26.78/8.63  																					|
% 26.78/8.63  																					|-The branch is then unsatisfiable
% 26.78/8.63  																				|-Branch two:
% 26.78/8.63  																				| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																				| (237) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																				|
% 26.78/8.63  																					+-Applying beta-rule and splitting (163), into two cases.
% 26.78/8.63  																					|-Branch one:
% 26.78/8.63  																					| (198) all_25_0_33 = 0
% 26.78/8.63  																					|
% 26.78/8.63  																						| Equations (198) can reduce 105 to:
% 26.78/8.63  																						| (101) $false
% 26.78/8.63  																						|
% 26.78/8.63  																						|-The branch is then unsatisfiable
% 26.78/8.63  																					|-Branch two:
% 26.78/8.63  																					| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																					| (241) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																					|
% 26.78/8.63  																						+-Applying beta-rule and splitting (164), into two cases.
% 26.78/8.63  																						|-Branch one:
% 26.78/8.63  																						| (198) all_25_0_33 = 0
% 26.78/8.63  																						|
% 26.78/8.63  																							| Equations (198) can reduce 105 to:
% 26.78/8.63  																							| (101) $false
% 26.78/8.63  																							|
% 26.78/8.63  																							|-The branch is then unsatisfiable
% 26.78/8.63  																						|-Branch two:
% 26.78/8.63  																						| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																						| (245) all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.63  																						|
% 26.78/8.63  																							+-Applying beta-rule and splitting (192), into two cases.
% 26.78/8.63  																							|-Branch one:
% 26.78/8.63  																							| (206) all_23_0_31 = 0
% 26.78/8.63  																							|
% 26.78/8.63  																								| Equations (206) can reduce 95 to:
% 26.78/8.63  																								| (101) $false
% 26.78/8.63  																								|
% 26.78/8.63  																								|-The branch is then unsatisfiable
% 26.78/8.63  																							|-Branch two:
% 26.78/8.63  																							| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.63  																							| (249) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63  																							|
% 26.78/8.63  																								+-Applying beta-rule and splitting (152), into two cases.
% 26.78/8.63  																								|-Branch one:
% 26.78/8.63  																								| (202) all_24_0_32 = 0
% 26.78/8.63  																								|
% 26.78/8.63  																									| Equations (202) can reduce 98 to:
% 26.78/8.63  																									| (101) $false
% 26.78/8.63  																									|
% 26.78/8.63  																									|-The branch is then unsatisfiable
% 26.78/8.63  																								|-Branch two:
% 26.78/8.63  																								| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																								| (253) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																								|
% 26.78/8.63  																									+-Applying beta-rule and splitting (153), into two cases.
% 26.78/8.63  																									|-Branch one:
% 26.78/8.63  																									| (202) all_24_0_32 = 0
% 26.78/8.63  																									|
% 26.78/8.63  																										| Equations (202) can reduce 98 to:
% 26.78/8.63  																										| (101) $false
% 26.78/8.63  																										|
% 26.78/8.63  																										|-The branch is then unsatisfiable
% 26.78/8.63  																									|-Branch two:
% 26.78/8.63  																									| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																									| (257) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																									|
% 26.78/8.63  																										+-Applying beta-rule and splitting (154), into two cases.
% 26.78/8.63  																										|-Branch one:
% 26.78/8.63  																										| (202) all_24_0_32 = 0
% 26.78/8.63  																										|
% 26.78/8.63  																											| Equations (202) can reduce 98 to:
% 26.78/8.63  																											| (101) $false
% 26.78/8.63  																											|
% 26.78/8.63  																											|-The branch is then unsatisfiable
% 26.78/8.63  																										|-Branch two:
% 26.78/8.63  																										| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																										| (261) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																										|
% 26.78/8.63  																											+-Applying beta-rule and splitting (158), into two cases.
% 26.78/8.63  																											|-Branch one:
% 26.78/8.63  																											| (198) all_25_0_33 = 0
% 26.78/8.63  																											|
% 26.78/8.63  																												| Equations (198) can reduce 105 to:
% 26.78/8.63  																												| (101) $false
% 26.78/8.63  																												|
% 26.78/8.63  																												|-The branch is then unsatisfiable
% 26.78/8.63  																											|-Branch two:
% 26.78/8.63  																											| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																											| (265) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																											|
% 26.78/8.63  																												+-Applying beta-rule and splitting (155), into two cases.
% 26.78/8.63  																												|-Branch one:
% 26.78/8.63  																												| (202) all_24_0_32 = 0
% 26.78/8.63  																												|
% 26.78/8.63  																													| Equations (202) can reduce 98 to:
% 26.78/8.63  																													| (101) $false
% 26.78/8.63  																													|
% 26.78/8.63  																													|-The branch is then unsatisfiable
% 26.78/8.63  																												|-Branch two:
% 26.78/8.63  																												| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																												| (269) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																												|
% 26.78/8.63  																													+-Applying beta-rule and splitting (183), into two cases.
% 26.78/8.63  																													|-Branch one:
% 26.78/8.63  																													| (210) all_20_0_28 = 0
% 26.78/8.63  																													|
% 26.78/8.63  																														| Equations (210) can reduce 72 to:
% 26.78/8.63  																														| (101) $false
% 26.78/8.63  																														|
% 26.78/8.63  																														|-The branch is then unsatisfiable
% 26.78/8.63  																													|-Branch two:
% 26.78/8.63  																													| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.63  																													| (273) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.63  																													|
% 26.78/8.63  																														+-Applying beta-rule and splitting (171), into two cases.
% 26.78/8.63  																														|-Branch one:
% 26.78/8.63  																														| (202) all_24_0_32 = 0
% 26.78/8.63  																														|
% 26.78/8.63  																															| Equations (202) can reduce 98 to:
% 26.78/8.63  																															| (101) $false
% 26.78/8.63  																															|
% 26.78/8.63  																															|-The branch is then unsatisfiable
% 26.78/8.63  																														|-Branch two:
% 26.78/8.63  																														| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																														| (277) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																														|
% 26.78/8.63  																															+-Applying beta-rule and splitting (184), into two cases.
% 26.78/8.63  																															|-Branch one:
% 26.78/8.63  																															| (202) all_24_0_32 = 0
% 26.78/8.63  																															|
% 26.78/8.63  																																| Equations (202) can reduce 98 to:
% 26.78/8.63  																																| (101) $false
% 26.78/8.63  																																|
% 26.78/8.63  																																|-The branch is then unsatisfiable
% 26.78/8.63  																															|-Branch two:
% 26.78/8.63  																															| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																															| (281) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																															|
% 26.78/8.63  																																+-Applying beta-rule and splitting (156), into two cases.
% 26.78/8.63  																																|-Branch one:
% 26.78/8.63  																																| (202) all_24_0_32 = 0
% 26.78/8.63  																																|
% 26.78/8.63  																																	| Equations (202) can reduce 98 to:
% 26.78/8.63  																																	| (101) $false
% 26.78/8.63  																																	|
% 26.78/8.63  																																	|-The branch is then unsatisfiable
% 26.78/8.63  																																|-Branch two:
% 26.78/8.63  																																| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																																| (285) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																																|
% 26.78/8.63  																																	+-Applying beta-rule and splitting (185), into two cases.
% 26.78/8.63  																																	|-Branch one:
% 26.78/8.63  																																	| (202) all_24_0_32 = 0
% 26.78/8.63  																																	|
% 26.78/8.63  																																		| Equations (202) can reduce 98 to:
% 26.78/8.63  																																		| (101) $false
% 26.78/8.63  																																		|
% 26.78/8.63  																																		|-The branch is then unsatisfiable
% 26.78/8.63  																																	|-Branch two:
% 26.78/8.63  																																	| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																																	| (289) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																																	|
% 26.78/8.63  																																		+-Applying beta-rule and splitting (186), into two cases.
% 26.78/8.63  																																		|-Branch one:
% 26.78/8.63  																																		| (202) all_24_0_32 = 0
% 26.78/8.63  																																		|
% 26.78/8.63  																																			| Equations (202) can reduce 98 to:
% 26.78/8.63  																																			| (101) $false
% 26.78/8.63  																																			|
% 26.78/8.63  																																			|-The branch is then unsatisfiable
% 26.78/8.63  																																		|-Branch two:
% 26.78/8.63  																																		| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.63  																																		| (293) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.63  																																		|
% 26.78/8.63  																																			+-Applying beta-rule and splitting (189), into two cases.
% 26.78/8.63  																																			|-Branch one:
% 26.78/8.63  																																			| (198) all_25_0_33 = 0
% 26.78/8.63  																																			|
% 26.78/8.63  																																				| Equations (198) can reduce 105 to:
% 26.78/8.63  																																				| (101) $false
% 26.78/8.63  																																				|
% 26.78/8.63  																																				|-The branch is then unsatisfiable
% 26.78/8.63  																																			|-Branch two:
% 26.78/8.63  																																			| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																																			| (297) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.63  																																			|
% 26.78/8.63  																																				+-Applying beta-rule and splitting (190), into two cases.
% 26.78/8.63  																																				|-Branch one:
% 26.78/8.63  																																				| (198) all_25_0_33 = 0
% 26.78/8.63  																																				|
% 26.78/8.63  																																					| Equations (198) can reduce 105 to:
% 26.78/8.63  																																					| (101) $false
% 26.78/8.63  																																					|
% 26.78/8.63  																																					|-The branch is then unsatisfiable
% 26.78/8.63  																																				|-Branch two:
% 26.78/8.63  																																				| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.63  																																				| (301) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64  																																				|
% 26.78/8.64  																																					+-Applying beta-rule and splitting (172), into two cases.
% 26.78/8.64  																																					|-Branch one:
% 26.78/8.64  																																					| (202) all_24_0_32 = 0
% 26.78/8.64  																																					|
% 26.78/8.64  																																						| Equations (202) can reduce 98 to:
% 26.78/8.64  																																						| (101) $false
% 26.78/8.64  																																						|
% 26.78/8.64  																																						|-The branch is then unsatisfiable
% 26.78/8.64  																																					|-Branch two:
% 26.78/8.64  																																					| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.64  																																					| (305) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																					|
% 26.78/8.64  																																						+-Applying beta-rule and splitting (175), into two cases.
% 26.78/8.64  																																						|-Branch one:
% 26.78/8.64  																																						| (198) all_25_0_33 = 0
% 26.78/8.64  																																						|
% 26.78/8.64  																																							| Equations (198) can reduce 105 to:
% 26.78/8.64  																																							| (101) $false
% 26.78/8.64  																																							|
% 26.78/8.64  																																							|-The branch is then unsatisfiable
% 26.78/8.64  																																						|-Branch two:
% 26.78/8.64  																																						| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																						| (309) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64  																																						|
% 26.78/8.64  																																							+-Applying beta-rule and splitting (176), into two cases.
% 26.78/8.64  																																							|-Branch one:
% 26.78/8.64  																																							| (198) all_25_0_33 = 0
% 26.78/8.64  																																							|
% 26.78/8.64  																																								| Equations (198) can reduce 105 to:
% 26.78/8.64  																																								| (101) $false
% 26.78/8.64  																																								|
% 26.78/8.64  																																								|-The branch is then unsatisfiable
% 26.78/8.64  																																							|-Branch two:
% 26.78/8.64  																																							| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																							| (313) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																							|
% 26.78/8.64  																																								+-Applying beta-rule and splitting (177), into two cases.
% 26.78/8.64  																																								|-Branch one:
% 26.78/8.64  																																								| (198) all_25_0_33 = 0
% 26.78/8.64  																																								|
% 26.78/8.64  																																									| Equations (198) can reduce 105 to:
% 26.78/8.64  																																									| (101) $false
% 26.78/8.64  																																									|
% 26.78/8.64  																																									|-The branch is then unsatisfiable
% 26.78/8.64  																																								|-Branch two:
% 26.78/8.64  																																								| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																								| (317) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64  																																								|
% 26.78/8.64  																																									+-Applying beta-rule and splitting (178), into two cases.
% 26.78/8.64  																																									|-Branch one:
% 26.78/8.64  																																									| (198) all_25_0_33 = 0
% 26.78/8.64  																																									|
% 26.78/8.64  																																										| Equations (198) can reduce 105 to:
% 26.78/8.64  																																										| (101) $false
% 26.78/8.64  																																										|
% 26.78/8.64  																																										|-The branch is then unsatisfiable
% 26.78/8.64  																																									|-Branch two:
% 26.78/8.64  																																									| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																									| (321) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																									|
% 26.78/8.64  																																										+-Applying beta-rule and splitting (180), into two cases.
% 26.78/8.64  																																										|-Branch one:
% 26.78/8.64  																																										| (210) all_20_0_28 = 0
% 26.78/8.64  																																										|
% 26.78/8.64  																																											| Equations (210) can reduce 72 to:
% 26.78/8.64  																																											| (101) $false
% 26.78/8.64  																																											|
% 26.78/8.64  																																											|-The branch is then unsatisfiable
% 26.78/8.64  																																										|-Branch two:
% 26.78/8.64  																																										| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.64  																																										| (325) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																										|
% 26.78/8.64  																																											+-Applying beta-rule and splitting (193), into two cases.
% 26.78/8.64  																																											|-Branch one:
% 26.78/8.64  																																											| (206) all_23_0_31 = 0
% 26.78/8.64  																																											|
% 26.78/8.64  																																												| Equations (206) can reduce 95 to:
% 26.78/8.64  																																												| (101) $false
% 26.78/8.64  																																												|
% 26.78/8.64  																																												|-The branch is then unsatisfiable
% 26.78/8.64  																																											|-Branch two:
% 26.78/8.64  																																											| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.64  																																											| (329) all_20_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																											|
% 26.78/8.64  																																												+-Applying beta-rule and splitting (167), into two cases.
% 26.78/8.64  																																												|-Branch one:
% 26.78/8.64  																																												| (206) all_23_0_31 = 0
% 26.78/8.64  																																												|
% 26.78/8.64  																																													| Equations (206) can reduce 95 to:
% 26.78/8.64  																																													| (101) $false
% 26.78/8.64  																																													|
% 26.78/8.64  																																													|-The branch is then unsatisfiable
% 26.78/8.64  																																												|-Branch two:
% 26.78/8.64  																																												| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.64  																																												| (333) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																												|
% 26.78/8.64  																																													+-Applying beta-rule and splitting (168), into two cases.
% 26.78/8.64  																																													|-Branch one:
% 26.78/8.64  																																													| (206) all_23_0_31 = 0
% 26.78/8.64  																																													|
% 26.78/8.64  																																														| Equations (206) can reduce 95 to:
% 26.78/8.64  																																														| (101) $false
% 26.78/8.64  																																														|
% 26.78/8.64  																																														|-The branch is then unsatisfiable
% 26.78/8.64  																																													|-Branch two:
% 26.78/8.64  																																													| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.64  																																													| (337) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																													|
% 26.78/8.64  																																														+-Applying beta-rule and splitting (169), into two cases.
% 26.78/8.64  																																														|-Branch one:
% 26.78/8.64  																																														| (206) all_23_0_31 = 0
% 26.78/8.64  																																														|
% 26.78/8.64  																																															| Equations (206) can reduce 95 to:
% 26.78/8.64  																																															| (101) $false
% 26.78/8.64  																																															|
% 26.78/8.64  																																															|-The branch is then unsatisfiable
% 26.78/8.64  																																														|-Branch two:
% 26.78/8.64  																																														| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.64  																																														| (341) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																														|
% 26.78/8.64  																																															+-Applying beta-rule and splitting (170), into two cases.
% 26.78/8.64  																																															|-Branch one:
% 26.78/8.64  																																															| (206) all_23_0_31 = 0
% 26.78/8.64  																																															|
% 26.78/8.64  																																																| Equations (206) can reduce 95 to:
% 26.78/8.64  																																																| (101) $false
% 26.78/8.64  																																																|
% 26.78/8.64  																																																|-The branch is then unsatisfiable
% 26.78/8.64  																																															|-Branch two:
% 26.78/8.64  																																															| (95)  ~ (all_23_0_31 = 0)
% 26.78/8.64  																																															| (345) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																															|
% 26.78/8.64  																																																+-Applying beta-rule and splitting (173), into two cases.
% 26.78/8.64  																																																|-Branch one:
% 26.78/8.64  																																																| (202) all_24_0_32 = 0
% 26.78/8.64  																																																|
% 26.78/8.64  																																																	| Equations (202) can reduce 98 to:
% 26.78/8.64  																																																	| (101) $false
% 26.78/8.64  																																																	|
% 26.78/8.64  																																																	|-The branch is then unsatisfiable
% 26.78/8.64  																																																|-Branch two:
% 26.78/8.64  																																																| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.64  																																																| (349) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64  																																																|
% 26.78/8.64  																																																	+-Applying beta-rule and splitting (174), into two cases.
% 26.78/8.64  																																																	|-Branch one:
% 26.78/8.64  																																																	| (202) all_24_0_32 = 0
% 26.78/8.64  																																																	|
% 26.78/8.64  																																																		| Equations (202) can reduce 98 to:
% 26.78/8.64  																																																		| (101) $false
% 26.78/8.64  																																																		|
% 26.78/8.64  																																																		|-The branch is then unsatisfiable
% 26.78/8.64  																																																	|-Branch two:
% 26.78/8.64  																																																	| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.64  																																																	| (353) all_23_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																																	|
% 26.78/8.64  																																																		+-Applying beta-rule and splitting (159), into two cases.
% 26.78/8.64  																																																		|-Branch one:
% 26.78/8.64  																																																		| (198) all_25_0_33 = 0
% 26.78/8.64  																																																		|
% 26.78/8.64  																																																			| Equations (198) can reduce 105 to:
% 26.78/8.64  																																																			| (101) $false
% 26.78/8.64  																																																			|
% 26.78/8.64  																																																			|-The branch is then unsatisfiable
% 26.78/8.64  																																																		|-Branch two:
% 26.78/8.64  																																																		| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																																		| (357) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64  																																																		|
% 26.78/8.64  																																																			+-Applying beta-rule and splitting (160), into two cases.
% 26.78/8.64  																																																			|-Branch one:
% 26.78/8.64  																																																			| (198) all_25_0_33 = 0
% 26.78/8.64  																																																			|
% 26.78/8.64  																																																				| Equations (198) can reduce 105 to:
% 26.78/8.64  																																																				| (101) $false
% 26.78/8.64  																																																				|
% 26.78/8.64  																																																				|-The branch is then unsatisfiable
% 26.78/8.64  																																																			|-Branch two:
% 26.78/8.64  																																																			| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																																			| (361) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																																			|
% 26.78/8.64  																																																				+-Applying beta-rule and splitting (161), into two cases.
% 26.78/8.64  																																																				|-Branch one:
% 26.78/8.64  																																																				| (198) all_25_0_33 = 0
% 26.78/8.64  																																																				|
% 26.78/8.64  																																																					| Equations (198) can reduce 105 to:
% 26.78/8.64  																																																					| (101) $false
% 26.78/8.64  																																																					|
% 26.78/8.64  																																																					|-The branch is then unsatisfiable
% 26.78/8.64  																																																				|-Branch two:
% 26.78/8.64  																																																				| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																																				| (365) all_0_3_3 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.64  																																																				|
% 26.78/8.64  																																																					+-Applying beta-rule and splitting (162), into two cases.
% 26.78/8.64  																																																					|-Branch one:
% 26.78/8.64  																																																					| (198) all_25_0_33 = 0
% 26.78/8.64  																																																					|
% 26.78/8.64  																																																						| Equations (198) can reduce 105 to:
% 26.78/8.64  																																																						| (101) $false
% 26.78/8.64  																																																						|
% 26.78/8.64  																																																						|-The branch is then unsatisfiable
% 26.78/8.64  																																																					|-Branch two:
% 26.78/8.64  																																																					| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																																					| (369) all_0_4_4 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																																					|
% 26.78/8.64  																																																						+-Applying beta-rule and splitting (165), into two cases.
% 26.78/8.64  																																																						|-Branch one:
% 26.78/8.64  																																																						| (198) all_25_0_33 = 0
% 26.78/8.64  																																																						|
% 26.78/8.64  																																																							| Equations (198) can reduce 105 to:
% 26.78/8.64  																																																							| (101) $false
% 26.78/8.64  																																																							|
% 26.78/8.64  																																																							|-The branch is then unsatisfiable
% 26.78/8.64  																																																						|-Branch two:
% 26.78/8.64  																																																						| (105)  ~ (all_25_0_33 = 0)
% 26.78/8.64  																																																						| (373) all_24_0_32 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.64  																																																						|
% 26.78/8.64  																																																							+-Applying beta-rule and splitting (217), into two cases.
% 26.78/8.64  																																																							|-Branch one:
% 26.78/8.64  																																																							| (107) all_0_3_3 = 0
% 26.78/8.64  																																																							|
% 26.78/8.64  																																																								| Equations (107) can reduce 19 to:
% 26.78/8.64  																																																								| (101) $false
% 26.78/8.64  																																																								|
% 26.78/8.64  																																																								|-The branch is then unsatisfiable
% 26.78/8.64  																																																							|-Branch two:
% 26.78/8.64  																																																							| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.64  																																																							| (377)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																																							|
% 26.78/8.64  																																																								+-Applying beta-rule and splitting (221), into two cases.
% 26.78/8.64  																																																								|-Branch one:
% 26.78/8.64  																																																								| (100) all_0_4_4 = 0
% 26.78/8.64  																																																								|
% 26.78/8.64  																																																									| Equations (100) can reduce 45 to:
% 26.78/8.64  																																																									| (101) $false
% 26.78/8.64  																																																									|
% 26.78/8.64  																																																									|-The branch is then unsatisfiable
% 26.78/8.64  																																																								|-Branch two:
% 26.78/8.64  																																																								| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.64  																																																								| (381)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.64  																																																								|
% 26.78/8.64  																																																									+-Applying beta-rule and splitting (225), into two cases.
% 26.78/8.64  																																																									|-Branch one:
% 26.78/8.64  																																																									| (210) all_20_0_28 = 0
% 26.78/8.64  																																																									|
% 26.78/8.64  																																																										| Equations (210) can reduce 72 to:
% 26.78/8.64  																																																										| (101) $false
% 26.78/8.64  																																																										|
% 26.78/8.64  																																																										|-The branch is then unsatisfiable
% 26.78/8.64  																																																									|-Branch two:
% 26.78/8.64  																																																									| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.64  																																																									| (794)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.64  																																																									|
% 26.78/8.64  																																																										+-Applying beta-rule and splitting (229), into two cases.
% 26.78/8.64  																																																										|-Branch one:
% 26.78/8.64  																																																										| (210) all_20_0_28 = 0
% 26.78/8.64  																																																										|
% 26.78/8.64  																																																											| Equations (210) can reduce 72 to:
% 26.78/8.64  																																																											| (101) $false
% 26.78/8.64  																																																											|
% 26.78/8.64  																																																											|-The branch is then unsatisfiable
% 26.78/8.64  																																																										|-Branch two:
% 26.78/8.64  																																																										| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.64  																																																										| (798)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																										|
% 26.78/8.65  																																																											+-Applying beta-rule and splitting (233), into two cases.
% 26.78/8.65  																																																											|-Branch one:
% 26.78/8.65  																																																											| (210) all_20_0_28 = 0
% 26.78/8.65  																																																											|
% 26.78/8.65  																																																												| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																												| (101) $false
% 26.78/8.65  																																																												|
% 26.78/8.65  																																																												|-The branch is then unsatisfiable
% 26.78/8.65  																																																											|-Branch two:
% 26.78/8.65  																																																											| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																											| (802)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																											|
% 26.78/8.65  																																																												+-Applying beta-rule and splitting (237), into two cases.
% 26.78/8.65  																																																												|-Branch one:
% 26.78/8.65  																																																												| (107) all_0_3_3 = 0
% 26.78/8.65  																																																												|
% 26.78/8.65  																																																													| Equations (107) can reduce 19 to:
% 26.78/8.65  																																																													| (101) $false
% 26.78/8.65  																																																													|
% 26.78/8.65  																																																													|-The branch is then unsatisfiable
% 26.78/8.65  																																																												|-Branch two:
% 26.78/8.65  																																																												| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.65  																																																												| (385)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																												|
% 26.78/8.65  																																																													+-Applying beta-rule and splitting (241), into two cases.
% 26.78/8.65  																																																													|-Branch one:
% 26.78/8.65  																																																													| (100) all_0_4_4 = 0
% 26.78/8.65  																																																													|
% 26.78/8.65  																																																														| Equations (100) can reduce 45 to:
% 26.78/8.65  																																																														| (101) $false
% 26.78/8.65  																																																														|
% 26.78/8.65  																																																														|-The branch is then unsatisfiable
% 26.78/8.65  																																																													|-Branch two:
% 26.78/8.65  																																																													| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.65  																																																													| (389)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																													|
% 26.78/8.65  																																																														+-Applying beta-rule and splitting (245), into two cases.
% 26.78/8.65  																																																														|-Branch one:
% 26.78/8.65  																																																														| (202) all_24_0_32 = 0
% 26.78/8.65  																																																														|
% 26.78/8.65  																																																															| Equations (202) can reduce 98 to:
% 26.78/8.65  																																																															| (101) $false
% 26.78/8.65  																																																															|
% 26.78/8.65  																																																															|-The branch is then unsatisfiable
% 26.78/8.65  																																																														|-Branch two:
% 26.78/8.65  																																																														| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.65  																																																														| (393)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.65  																																																														|
% 26.78/8.65  																																																															+-Applying beta-rule and splitting (249), into two cases.
% 26.78/8.65  																																																															|-Branch one:
% 26.78/8.65  																																																															| (210) all_20_0_28 = 0
% 26.78/8.65  																																																															|
% 26.78/8.65  																																																																| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																| (101) $false
% 26.78/8.65  																																																																|
% 26.78/8.65  																																																																|-The branch is then unsatisfiable
% 26.78/8.65  																																																															|-Branch two:
% 26.78/8.65  																																																															| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																															| (818)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65  																																																															|
% 26.78/8.65  																																																																+-Applying beta-rule and splitting (253), into two cases.
% 26.78/8.65  																																																																|-Branch one:
% 26.78/8.65  																																																																| (107) all_0_3_3 = 0
% 26.78/8.65  																																																																|
% 26.78/8.65  																																																																	| Equations (107) can reduce 19 to:
% 26.78/8.65  																																																																	| (101) $false
% 26.78/8.65  																																																																	|
% 26.78/8.65  																																																																	|-The branch is then unsatisfiable
% 26.78/8.65  																																																																|-Branch two:
% 26.78/8.65  																																																																| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.65  																																																																| (397)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																																|
% 26.78/8.65  																																																																	+-Applying beta-rule and splitting (257), into two cases.
% 26.78/8.65  																																																																	|-Branch one:
% 26.78/8.65  																																																																	| (100) all_0_4_4 = 0
% 26.78/8.65  																																																																	|
% 26.78/8.65  																																																																		| Equations (100) can reduce 45 to:
% 26.78/8.65  																																																																		| (101) $false
% 26.78/8.65  																																																																		|
% 26.78/8.65  																																																																		|-The branch is then unsatisfiable
% 26.78/8.65  																																																																	|-Branch two:
% 26.78/8.65  																																																																	| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.65  																																																																	| (401)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																																	|
% 26.78/8.65  																																																																		+-Applying beta-rule and splitting (261), into two cases.
% 26.78/8.65  																																																																		|-Branch one:
% 26.78/8.65  																																																																		| (100) all_0_4_4 = 0
% 26.78/8.65  																																																																		|
% 26.78/8.65  																																																																			| Equations (100) can reduce 45 to:
% 26.78/8.65  																																																																			| (101) $false
% 26.78/8.65  																																																																			|
% 26.78/8.65  																																																																			|-The branch is then unsatisfiable
% 26.78/8.65  																																																																		|-Branch two:
% 26.78/8.65  																																																																		| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.65  																																																																		| (405)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																																		|
% 26.78/8.65  																																																																			| Instantiating (405) with all_272_0_417 yields:
% 26.78/8.65  																																																																			| (831) (all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_417 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417) | ( ~ (all_272_0_417 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417)
% 26.78/8.65  																																																																			|
% 26.78/8.65  																																																																			+-Applying beta-rule and splitting (265), into two cases.
% 26.78/8.65  																																																																			|-Branch one:
% 26.78/8.65  																																																																			| (107) all_0_3_3 = 0
% 26.78/8.65  																																																																			|
% 26.78/8.65  																																																																				| Equations (107) can reduce 19 to:
% 26.78/8.65  																																																																				| (101) $false
% 26.78/8.65  																																																																				|
% 26.78/8.65  																																																																				|-The branch is then unsatisfiable
% 26.78/8.65  																																																																			|-Branch two:
% 26.78/8.65  																																																																			| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.65  																																																																			| (410)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																																			|
% 26.78/8.65  																																																																				| Instantiating (410) with all_276_0_418 yields:
% 26.78/8.65  																																																																				| (836) (all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_418 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418) | ( ~ (all_276_0_418 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418)
% 26.78/8.65  																																																																				|
% 26.78/8.65  																																																																				+-Applying beta-rule and splitting (269), into two cases.
% 26.78/8.65  																																																																				|-Branch one:
% 26.78/8.65  																																																																				| (100) all_0_4_4 = 0
% 26.78/8.65  																																																																				|
% 26.78/8.65  																																																																					| Equations (100) can reduce 45 to:
% 26.78/8.65  																																																																					| (101) $false
% 26.78/8.65  																																																																					|
% 26.78/8.65  																																																																					|-The branch is then unsatisfiable
% 26.78/8.65  																																																																				|-Branch two:
% 26.78/8.65  																																																																				| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.65  																																																																				| (415)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																																				|
% 26.78/8.65  																																																																					| Instantiating (415) with all_280_0_419 yields:
% 26.78/8.65  																																																																					| (841) (all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_419 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419) | ( ~ (all_280_0_419 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419)
% 26.78/8.65  																																																																					|
% 26.78/8.65  																																																																					+-Applying beta-rule and splitting (273), into two cases.
% 26.78/8.65  																																																																					|-Branch one:
% 26.78/8.65  																																																																					| (100) all_0_4_4 = 0
% 26.78/8.65  																																																																					|
% 26.78/8.65  																																																																						| Equations (100) can reduce 45 to:
% 26.78/8.65  																																																																						| (101) $false
% 26.78/8.65  																																																																						|
% 26.78/8.65  																																																																						|-The branch is then unsatisfiable
% 26.78/8.65  																																																																					|-Branch two:
% 26.78/8.65  																																																																					| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.65  																																																																					| (420)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65  																																																																					|
% 26.78/8.65  																																																																						+-Applying beta-rule and splitting (281), into two cases.
% 26.78/8.65  																																																																						|-Branch one:
% 26.78/8.65  																																																																						| (210) all_20_0_28 = 0
% 26.78/8.65  																																																																						|
% 26.78/8.65  																																																																							| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																							| (101) $false
% 26.78/8.65  																																																																							|
% 26.78/8.65  																																																																							|-The branch is then unsatisfiable
% 26.78/8.65  																																																																						|-Branch two:
% 26.78/8.65  																																																																						| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																																						| (849)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																																						|
% 26.78/8.65  																																																																							+-Applying beta-rule and splitting (285), into two cases.
% 26.78/8.65  																																																																							|-Branch one:
% 26.78/8.65  																																																																							| (100) all_0_4_4 = 0
% 26.78/8.65  																																																																							|
% 26.78/8.65  																																																																								| Equations (100) can reduce 45 to:
% 26.78/8.65  																																																																								| (101) $false
% 26.78/8.65  																																																																								|
% 26.78/8.65  																																																																								|-The branch is then unsatisfiable
% 26.78/8.65  																																																																							|-Branch two:
% 26.78/8.65  																																																																							| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.65  																																																																							| (428)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																																							|
% 26.78/8.65  																																																																								+-Applying beta-rule and splitting (289), into two cases.
% 26.78/8.65  																																																																								|-Branch one:
% 26.78/8.65  																																																																								| (210) all_20_0_28 = 0
% 26.78/8.65  																																																																								|
% 26.78/8.65  																																																																									| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																									| (101) $false
% 26.78/8.65  																																																																									|
% 26.78/8.65  																																																																									|-The branch is then unsatisfiable
% 26.78/8.65  																																																																								|-Branch two:
% 26.78/8.65  																																																																								| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																																								| (857)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																																								|
% 26.78/8.65  																																																																									+-Applying beta-rule and splitting (293), into two cases.
% 26.78/8.65  																																																																									|-Branch one:
% 26.78/8.65  																																																																									| (210) all_20_0_28 = 0
% 26.78/8.65  																																																																									|
% 26.78/8.65  																																																																										| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																										| (101) $false
% 26.78/8.65  																																																																										|
% 26.78/8.65  																																																																										|-The branch is then unsatisfiable
% 26.78/8.65  																																																																									|-Branch two:
% 26.78/8.65  																																																																									| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																																									| (861)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																																									|
% 26.78/8.65  																																																																										+-Applying beta-rule and splitting (297), into two cases.
% 26.78/8.65  																																																																										|-Branch one:
% 26.78/8.65  																																																																										| (210) all_20_0_28 = 0
% 26.78/8.65  																																																																										|
% 26.78/8.65  																																																																											| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																											| (101) $false
% 26.78/8.65  																																																																											|
% 26.78/8.65  																																																																											|-The branch is then unsatisfiable
% 26.78/8.65  																																																																										|-Branch two:
% 26.78/8.65  																																																																										| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																																										| (865)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.65  																																																																										|
% 26.78/8.65  																																																																											+-Applying beta-rule and splitting (301), into two cases.
% 26.78/8.65  																																																																											|-Branch one:
% 26.78/8.65  																																																																											| (210) all_20_0_28 = 0
% 26.78/8.65  																																																																											|
% 26.78/8.65  																																																																												| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																												| (101) $false
% 26.78/8.65  																																																																												|
% 26.78/8.65  																																																																												|-The branch is then unsatisfiable
% 26.78/8.65  																																																																											|-Branch two:
% 26.78/8.65  																																																																											| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																																											| (869)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_9_9) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.65  																																																																											|
% 26.78/8.65  																																																																												+-Applying beta-rule and splitting (325), into two cases.
% 26.78/8.65  																																																																												|-Branch one:
% 26.78/8.65  																																																																												| (107) all_0_3_3 = 0
% 26.78/8.65  																																																																												|
% 26.78/8.65  																																																																													| Equations (107) can reduce 19 to:
% 26.78/8.65  																																																																													| (101) $false
% 26.78/8.65  																																																																													|
% 26.78/8.65  																																																																													|-The branch is then unsatisfiable
% 26.78/8.65  																																																																												|-Branch two:
% 26.78/8.65  																																																																												| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.65  																																																																												| (452)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_9_9) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65  																																																																												|
% 26.78/8.65  																																																																													+-Applying beta-rule and splitting (329), into two cases.
% 26.78/8.65  																																																																													|-Branch one:
% 26.78/8.65  																																																																													| (210) all_20_0_28 = 0
% 26.78/8.65  																																																																													|
% 26.78/8.65  																																																																														| Equations (210) can reduce 72 to:
% 26.78/8.65  																																																																														| (101) $false
% 26.78/8.65  																																																																														|
% 26.78/8.65  																																																																														|-The branch is then unsatisfiable
% 26.78/8.65  																																																																													|-Branch two:
% 26.78/8.65  																																																																													| (72)  ~ (all_20_0_28 = 0)
% 26.78/8.65  																																																																													| (877)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_9_9) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_9_9, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65  																																																																													|
% 26.78/8.65  																																																																														+-Applying beta-rule and splitting (333), into two cases.
% 26.78/8.65  																																																																														|-Branch one:
% 26.78/8.65  																																																																														| (107) all_0_3_3 = 0
% 26.78/8.65  																																																																														|
% 26.78/8.65  																																																																															| Equations (107) can reduce 19 to:
% 26.78/8.65  																																																																															| (101) $false
% 26.78/8.65  																																																																															|
% 26.78/8.65  																																																																															|-The branch is then unsatisfiable
% 26.78/8.65  																																																																														|-Branch two:
% 26.78/8.65  																																																																														| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.65  																																																																														| (456)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.65  																																																																														|
% 26.78/8.66  																																																																															+-Applying beta-rule and splitting (337), into two cases.
% 26.78/8.66  																																																																															|-Branch one:
% 26.78/8.66  																																																																															| (107) all_0_3_3 = 0
% 26.78/8.66  																																																																															|
% 26.78/8.66  																																																																																| Equations (107) can reduce 19 to:
% 26.78/8.66  																																																																																| (101) $false
% 26.78/8.66  																																																																																|
% 26.78/8.66  																																																																																|-The branch is then unsatisfiable
% 26.78/8.66  																																																																															|-Branch two:
% 26.78/8.66  																																																																															| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.66  																																																																															| (460)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.66  																																																																															|
% 26.78/8.66  																																																																																+-Applying beta-rule and splitting (341), into two cases.
% 26.78/8.66  																																																																																|-Branch one:
% 26.78/8.66  																																																																																| (100) all_0_4_4 = 0
% 26.78/8.66  																																																																																|
% 26.78/8.66  																																																																																	| Equations (100) can reduce 45 to:
% 26.78/8.66  																																																																																	| (101) $false
% 26.78/8.66  																																																																																	|
% 26.78/8.66  																																																																																	|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																|-Branch two:
% 26.78/8.66  																																																																																| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.66  																																																																																| (464)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_8_8) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.66  																																																																																|
% 26.78/8.66  																																																																																	+-Applying beta-rule and splitting (345), into two cases.
% 26.78/8.66  																																																																																	|-Branch one:
% 26.78/8.66  																																																																																	| (100) all_0_4_4 = 0
% 26.78/8.66  																																																																																	|
% 26.78/8.66  																																																																																		| Equations (100) can reduce 45 to:
% 26.78/8.66  																																																																																		| (101) $false
% 26.78/8.66  																																																																																		|
% 26.78/8.66  																																																																																		|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																	|-Branch two:
% 26.78/8.66  																																																																																	| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.66  																																																																																	| (468)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_8_8) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_8_8, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 26.78/8.66  																																																																																	|
% 26.78/8.66  																																																																																		+-Applying beta-rule and splitting (357), into two cases.
% 26.78/8.66  																																																																																		|-Branch one:
% 26.78/8.66  																																																																																		| (107) all_0_3_3 = 0
% 26.78/8.66  																																																																																		|
% 26.78/8.66  																																																																																			| Equations (107) can reduce 19 to:
% 26.78/8.66  																																																																																			| (101) $false
% 26.78/8.66  																																																																																			|
% 26.78/8.66  																																																																																			|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																		|-Branch two:
% 26.78/8.66  																																																																																		| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.66  																																																																																		| (480)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.66  																																																																																		|
% 26.78/8.66  																																																																																			+-Applying beta-rule and splitting (361), into two cases.
% 26.78/8.66  																																																																																			|-Branch one:
% 26.78/8.66  																																																																																			| (107) all_0_3_3 = 0
% 26.78/8.66  																																																																																			|
% 26.78/8.66  																																																																																				| Equations (107) can reduce 19 to:
% 26.78/8.66  																																																																																				| (101) $false
% 26.78/8.66  																																																																																				|
% 26.78/8.66  																																																																																				|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																			|-Branch two:
% 26.78/8.66  																																																																																			| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.66  																																																																																			| (484)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.66  																																																																																			|
% 26.78/8.66  																																																																																				+-Applying beta-rule and splitting (365), into two cases.
% 26.78/8.66  																																																																																				|-Branch one:
% 26.78/8.66  																																																																																				| (107) all_0_3_3 = 0
% 26.78/8.66  																																																																																				|
% 26.78/8.66  																																																																																					| Equations (107) can reduce 19 to:
% 26.78/8.66  																																																																																					| (101) $false
% 26.78/8.66  																																																																																					|
% 26.78/8.66  																																																																																					|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																				|-Branch two:
% 26.78/8.66  																																																																																				| (19)  ~ (all_0_3_3 = 0)
% 26.78/8.66  																																																																																				| (488)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_5_5) = v0))
% 26.78/8.66  																																																																																				|
% 26.78/8.66  																																																																																					| Instantiating (488) with all_376_0_443 yields:
% 26.78/8.66  																																																																																					| (906) (all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_443 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443) | ( ~ (all_376_0_443 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443)
% 26.78/8.66  																																																																																					|
% 26.78/8.66  																																																																																					+-Applying beta-rule and splitting (369), into two cases.
% 26.78/8.66  																																																																																					|-Branch one:
% 26.78/8.66  																																																																																					| (100) all_0_4_4 = 0
% 26.78/8.66  																																																																																					|
% 26.78/8.66  																																																																																						| Equations (100) can reduce 45 to:
% 26.78/8.66  																																																																																						| (101) $false
% 26.78/8.66  																																																																																						|
% 26.78/8.66  																																																																																						|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																					|-Branch two:
% 26.78/8.66  																																																																																					| (45)  ~ (all_0_4_4 = 0)
% 26.78/8.66  																																																																																					| (493)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_2_2) = v0))
% 26.78/8.66  																																																																																					|
% 26.78/8.66  																																																																																						+-Applying beta-rule and splitting (373), into two cases.
% 26.78/8.66  																																																																																						|-Branch one:
% 26.78/8.66  																																																																																						| (202) all_24_0_32 = 0
% 26.78/8.66  																																																																																						|
% 26.78/8.66  																																																																																							| Equations (202) can reduce 98 to:
% 26.78/8.66  																																																																																							| (101) $false
% 26.78/8.66  																																																																																							|
% 26.78/8.66  																																																																																							|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																						|-Branch two:
% 26.78/8.66  																																																																																						| (98)  ~ (all_24_0_32 = 0)
% 26.78/8.66  																																																																																						| (497)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 26.78/8.66  																																																																																						|
% 26.78/8.66  																																																																																							| Instantiating formula (2) with all_20_0_28, all_0_5_5, all_0_9_9, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_9_9) = 0, apart_point_and_line(all_0_5_5, all_0_9_9) = all_20_0_28, yields:
% 26.78/8.66  																																																																																							| (915) all_20_0_28 = 0 | distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.66  																																																																																							|
% 26.78/8.66  																																																																																							+-Applying beta-rule and splitting (915), into two cases.
% 26.78/8.66  																																																																																							|-Branch one:
% 26.78/8.66  																																																																																							| (499) distinct_points(all_0_2_2, all_0_5_5) = 0
% 26.78/8.66  																																																																																							|
% 26.78/8.66  																																																																																								+-Applying beta-rule and splitting (831), into two cases.
% 26.78/8.66  																																																																																								|-Branch one:
% 26.78/8.66  																																																																																								| (917) (all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_272_0_417 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417)
% 26.78/8.66  																																																																																								|
% 26.78/8.66  																																																																																									+-Applying beta-rule and splitting (917), into two cases.
% 26.78/8.66  																																																																																									|-Branch one:
% 26.78/8.66  																																																																																									| (918) (all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 26.78/8.66  																																																																																									|
% 26.78/8.66  																																																																																										+-Applying beta-rule and splitting (918), into two cases.
% 26.78/8.66  																																																																																										|-Branch one:
% 26.78/8.66  																																																																																										| (919) all_272_0_417 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.66  																																																																																										|
% 26.78/8.66  																																																																																											| Applying alpha-rule on (919) yields:
% 26.78/8.66  																																																																																											| (920) all_272_0_417 = 0
% 26.78/8.66  																																																																																											| (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																											| Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 26.78/8.66  																																																																																											| (198) all_25_0_33 = 0
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																											| Equations (198) can reduce 105 to:
% 26.78/8.66  																																																																																											| (101) $false
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																											|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																										|-Branch two:
% 26.78/8.66  																																																																																										| (924) all_272_0_417 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.66  																																																																																										|
% 26.78/8.66  																																																																																											| Applying alpha-rule on (924) yields:
% 26.78/8.66  																																																																																											| (920) all_272_0_417 = 0
% 26.78/8.66  																																																																																											| (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																											| Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 26.78/8.66  																																																																																											| (107) all_0_3_3 = 0
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																											| Equations (107) can reduce 19 to:
% 26.78/8.66  																																																																																											| (101) $false
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																											|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																									|-Branch two:
% 26.78/8.66  																																																																																									| (929)  ~ (all_272_0_417 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 26.78/8.66  																																																																																									|
% 26.78/8.66  																																																																																										| Applying alpha-rule on (929) yields:
% 26.78/8.66  																																																																																										| (930)  ~ (all_272_0_417 = 0)
% 26.78/8.66  																																																																																										| (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 26.78/8.66  																																																																																										|
% 26.78/8.66  																																																																																										+-Applying beta-rule and splitting (906), into two cases.
% 26.78/8.66  																																																																																										|-Branch one:
% 26.78/8.66  																																																																																										| (932) (all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_376_0_443 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443)
% 26.78/8.66  																																																																																										|
% 26.78/8.66  																																																																																											+-Applying beta-rule and splitting (932), into two cases.
% 26.78/8.66  																																																																																											|-Branch one:
% 26.78/8.66  																																																																																											| (933) (all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																												+-Applying beta-rule and splitting (933), into two cases.
% 26.78/8.66  																																																																																												|-Branch one:
% 26.78/8.66  																																																																																												| (934) all_376_0_443 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.66  																																																																																												|
% 26.78/8.66  																																																																																													| Applying alpha-rule on (934) yields:
% 26.78/8.66  																																																																																													| (935) all_376_0_443 = 0
% 26.78/8.66  																																																																																													| (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.66  																																																																																													|
% 26.78/8.66  																																																																																													| Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 26.78/8.66  																																																																																													| (202) all_24_0_32 = 0
% 26.78/8.66  																																																																																													|
% 26.78/8.66  																																																																																													| Equations (202) can reduce 98 to:
% 26.78/8.66  																																																																																													| (101) $false
% 26.78/8.66  																																																																																													|
% 26.78/8.66  																																																																																													|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																												|-Branch two:
% 26.78/8.66  																																																																																												| (939) all_376_0_443 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.66  																																																																																												|
% 26.78/8.66  																																																																																													| Applying alpha-rule on (939) yields:
% 26.78/8.66  																																																																																													| (935) all_376_0_443 = 0
% 26.78/8.66  																																																																																													| (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 26.78/8.66  																																																																																													|
% 26.78/8.66  																																																																																													| Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 26.78/8.66  																																																																																													| (100) all_0_4_4 = 0
% 26.78/8.66  																																																																																													|
% 26.78/8.66  																																																																																													| Equations (100) can reduce 45 to:
% 26.78/8.66  																																																																																													| (101) $false
% 26.78/8.66  																																																																																													|
% 26.78/8.66  																																																																																													|-The branch is then unsatisfiable
% 26.78/8.66  																																																																																											|-Branch two:
% 26.78/8.66  																																																																																											| (944)  ~ (all_376_0_443 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443
% 26.78/8.66  																																																																																											|
% 26.78/8.66  																																																																																												| Applying alpha-rule on (944) yields:
% 26.78/8.66  																																																																																												| (945)  ~ (all_376_0_443 = 0)
% 26.78/8.66  																																																																																												| (946) distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443
% 26.78/8.66  																																																																																												|
% 26.78/8.66  																																																																																												| Instantiating formula (28) with all_0_6_6, all_0_7_7, all_272_0_417, all_376_0_443 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_376_0_443, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 26.78/8.66  																																																																																												| (947) all_376_0_443 = all_272_0_417
% 26.78/8.66  																																																																																												|
% 26.78/8.66  																																																																																												| From (947) and (946) follows:
% 26.78/8.66  																																																																																												| (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 26.78/8.66  																																																																																												|
% 26.78/8.66  																																																																																												+-Applying beta-rule and splitting (836), into two cases.
% 26.78/8.66  																																																																																												|-Branch one:
% 26.78/8.66  																																																																																												| (949) (all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0) | ( ~ (all_276_0_418 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418)
% 26.78/8.66  																																																																																												|
% 26.78/8.66  																																																																																													+-Applying beta-rule and splitting (949), into two cases.
% 26.78/8.66  																																																																																													|-Branch one:
% 26.78/8.66  																																																																																													| (950) (all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | (all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0)
% 26.78/8.67  																																																																																													|
% 26.78/8.67  																																																																																														+-Applying beta-rule and splitting (950), into two cases.
% 26.78/8.67  																																																																																														|-Branch one:
% 26.78/8.67  																																																																																														| (951) all_276_0_418 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 26.78/8.67  																																																																																														|
% 26.78/8.67  																																																																																															| Applying alpha-rule on (951) yields:
% 26.78/8.67  																																																																																															| (952) all_276_0_418 = 0
% 27.04/8.67  																																																																																															| (504) apart_point_and_line(all_0_2_2, all_0_6_6) = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															| Instantiating formula (25) with all_0_2_2, all_0_6_6, 0, all_24_0_32 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_24_0_32, apart_point_and_line(all_0_2_2, all_0_6_6) = 0, yields:
% 27.04/8.67  																																																																																															| (202) all_24_0_32 = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															| Equations (202) can reduce 98 to:
% 27.04/8.67  																																																																																															| (101) $false
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																														|-Branch two:
% 27.04/8.67  																																																																																														| (956) all_276_0_418 = 0 & apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																															| Applying alpha-rule on (956) yields:
% 27.04/8.67  																																																																																															| (952) all_276_0_418 = 0
% 27.04/8.67  																																																																																															| (509) apart_point_and_line(all_0_5_5, all_0_7_7) = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															| Instantiating formula (25) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms apart_point_and_line(all_0_5_5, all_0_7_7) = all_0_4_4, apart_point_and_line(all_0_5_5, all_0_7_7) = 0, yields:
% 27.04/8.67  																																																																																															| (100) all_0_4_4 = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															| Equations (100) can reduce 45 to:
% 27.04/8.67  																																																																																															| (101) $false
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																													|-Branch two:
% 27.04/8.67  																																																																																													| (961)  ~ (all_276_0_418 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418
% 27.04/8.67  																																																																																													|
% 27.04/8.67  																																																																																														| Applying alpha-rule on (961) yields:
% 27.04/8.67  																																																																																														| (962)  ~ (all_276_0_418 = 0)
% 27.04/8.67  																																																																																														| (963) distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																														| Instantiating formula (28) with all_0_6_6, all_0_7_7, all_276_0_418, all_272_0_417 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_276_0_418, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 27.04/8.67  																																																																																														| (964) all_276_0_418 = all_272_0_417
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																														| From (964) and (963) follows:
% 27.04/8.67  																																																																																														| (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																														+-Applying beta-rule and splitting (841), into two cases.
% 27.04/8.67  																																																																																														|-Branch one:
% 27.04/8.67  																																																																																														| (966) (all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0) | ( ~ (all_280_0_419 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419)
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																															+-Applying beta-rule and splitting (966), into two cases.
% 27.04/8.67  																																																																																															|-Branch one:
% 27.04/8.67  																																																																																															| (967) (all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | (all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0)
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																																+-Applying beta-rule and splitting (967), into two cases.
% 27.04/8.67  																																																																																																|-Branch one:
% 27.04/8.67  																																																																																																| (968) all_280_0_419 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																	| Applying alpha-rule on (968) yields:
% 27.04/8.67  																																																																																																	| (969) all_280_0_419 = 0
% 27.04/8.67  																																																																																																	| (519) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	| Instantiating formula (25) with all_0_2_2, all_0_7_7, 0, all_25_0_33 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_25_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 27.04/8.67  																																																																																																	| (198) all_25_0_33 = 0
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	| Equations (198) can reduce 105 to:
% 27.04/8.67  																																																																																																	| (101) $false
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																																|-Branch two:
% 27.04/8.67  																																																																																																| (973) all_280_0_419 = 0 & apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																	| Applying alpha-rule on (973) yields:
% 27.04/8.67  																																																																																																	| (969) all_280_0_419 = 0
% 27.04/8.67  																																																																																																	| (524) apart_point_and_line(all_0_5_5, all_0_6_6) = 0
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	| Instantiating formula (25) with all_0_5_5, all_0_6_6, 0, all_0_3_3 and discharging atoms apart_point_and_line(all_0_5_5, all_0_6_6) = all_0_3_3, apart_point_and_line(all_0_5_5, all_0_6_6) = 0, yields:
% 27.04/8.67  																																																																																																	| (107) all_0_3_3 = 0
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	| Equations (107) can reduce 19 to:
% 27.04/8.67  																																																																																																	| (101) $false
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																															|-Branch two:
% 27.04/8.67  																																																																																															| (978)  ~ (all_280_0_419 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																																| Applying alpha-rule on (978) yields:
% 27.04/8.67  																																																																																																| (979)  ~ (all_280_0_419 = 0)
% 27.04/8.67  																																																																																																| (980) distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																| Instantiating formula (28) with all_0_6_6, all_0_7_7, all_280_0_419, all_272_0_417 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_280_0_419, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 27.04/8.67  																																																																																																| (981) all_280_0_419 = all_272_0_417
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																| Equations (981) can reduce 979 to:
% 27.04/8.67  																																																																																																| (930)  ~ (all_272_0_417 = 0)
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																| From (981) and (980) follows:
% 27.04/8.67  																																																																																																| (931) distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																| Instantiating formula (17) with all_272_0_417, all_0_7_7, all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, distinct_lines(all_0_6_6, all_0_7_7) = all_272_0_417, yields:
% 27.04/8.67  																																																																																																| (984) all_272_0_417 = 0 | convergent_lines(all_0_7_7, all_0_7_7) = 0
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																+-Applying beta-rule and splitting (984), into two cases.
% 27.04/8.67  																																																																																																|-Branch one:
% 27.04/8.67  																																																																																																| (568) convergent_lines(all_0_7_7, all_0_7_7) = 0
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																	| Instantiating formula (4) with all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_7_7) = 0, yields:
% 27.04/8.67  																																																																																																	| (569) $false
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																																|-Branch two:
% 27.04/8.67  																																																																																																| (570)  ~ (convergent_lines(all_0_7_7, all_0_7_7) = 0)
% 27.04/8.67  																																																																																																| (920) all_272_0_417 = 0
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																	| Equations (920) can reduce 930 to:
% 27.04/8.67  																																																																																																	| (101) $false
% 27.04/8.67  																																																																																																	|
% 27.04/8.67  																																																																																																	|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																														|-Branch two:
% 27.04/8.67  																																																																																														| (990)  ~ (all_280_0_419 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																															| Applying alpha-rule on (990) yields:
% 27.04/8.67  																																																																																															| (979)  ~ (all_280_0_419 = 0)
% 27.04/8.67  																																																																																															| (992) distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															| Instantiating formula (32) with all_280_0_419, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_280_0_419, yields:
% 27.04/8.67  																																																																																															| (993) all_280_0_419 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																															+-Applying beta-rule and splitting (993), into two cases.
% 27.04/8.67  																																																																																															|-Branch one:
% 27.04/8.67  																																																																																															| (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																																| Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 27.04/8.67  																																																																																																| (569) $false
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																															|-Branch two:
% 27.04/8.67  																																																																																															| (579)  ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 27.04/8.67  																																																																																															| (969) all_280_0_419 = 0
% 27.04/8.67  																																																																																															|
% 27.04/8.67  																																																																																																| Equations (969) can reduce 979 to:
% 27.04/8.67  																																																																																																| (101) $false
% 27.04/8.67  																																																																																																|
% 27.04/8.67  																																																																																																|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																												|-Branch two:
% 27.04/8.67  																																																																																												| (999)  ~ (all_276_0_418 = 0) & distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418
% 27.04/8.67  																																																																																												|
% 27.04/8.67  																																																																																													| Applying alpha-rule on (999) yields:
% 27.04/8.67  																																																																																													| (962)  ~ (all_276_0_418 = 0)
% 27.04/8.67  																																																																																													| (1001) distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418
% 27.04/8.67  																																																																																													|
% 27.04/8.67  																																																																																													| Instantiating formula (32) with all_276_0_418, all_0_2_2, all_0_5_5, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = 0, distinct_points(all_0_5_5, all_0_2_2) = all_276_0_418, yields:
% 27.04/8.67  																																																																																													| (1002) all_276_0_418 = 0 | distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67  																																																																																													|
% 27.04/8.67  																																																																																													+-Applying beta-rule and splitting (1002), into two cases.
% 27.04/8.67  																																																																																													|-Branch one:
% 27.04/8.67  																																																																																													| (577) distinct_points(all_0_2_2, all_0_2_2) = 0
% 27.04/8.67  																																																																																													|
% 27.04/8.67  																																																																																														| Instantiating formula (26) with all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_2_2) = 0, yields:
% 27.04/8.67  																																																																																														| (569) $false
% 27.04/8.67  																																																																																														|
% 27.04/8.67  																																																																																														|-The branch is then unsatisfiable
% 27.04/8.67  																																																																																													|-Branch two:
% 27.04/8.67  																																																																																													| (579)  ~ (distinct_points(all_0_2_2, all_0_2_2) = 0)
% 27.04/8.67  																																																																																													| (952) all_276_0_418 = 0
% 27.04/8.68  																																																																																													|
% 27.04/8.68  																																																																																														| Equations (952) can reduce 962 to:
% 27.04/8.68  																																																																																														| (101) $false
% 27.04/8.68  																																																																																														|
% 27.04/8.68  																																																																																														|-The branch is then unsatisfiable
% 27.04/8.68  																																																																																										|-Branch two:
% 27.04/8.68  																																																																																										| (1008)  ~ (all_376_0_443 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443
% 27.04/8.68  																																																																																										|
% 27.04/8.68  																																																																																											| Applying alpha-rule on (1008) yields:
% 27.04/8.68  																																																																																											| (945)  ~ (all_376_0_443 = 0)
% 27.04/8.68  																																																																																											| (1010) distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443
% 27.04/8.68  																																																																																											|
% 27.04/8.68  																																																																																											| Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_376_0_443 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_376_0_443, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 27.04/8.68  																																																																																											| (935) all_376_0_443 = 0
% 27.04/8.68  																																																																																											|
% 27.04/8.68  																																																																																											| Equations (935) can reduce 945 to:
% 27.04/8.68  																																																																																											| (101) $false
% 27.04/8.68  																																																																																											|
% 27.04/8.68  																																																																																											|-The branch is then unsatisfiable
% 27.04/8.68  																																																																																								|-Branch two:
% 27.04/8.68  																																																																																								| (1013)  ~ (all_272_0_417 = 0) & distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417
% 27.04/8.68  																																																																																								|
% 27.04/8.68  																																																																																									| Applying alpha-rule on (1013) yields:
% 27.04/8.68  																																																																																									| (930)  ~ (all_272_0_417 = 0)
% 27.04/8.68  																																																																																									| (1015) distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417
% 27.04/8.68  																																																																																									|
% 27.04/8.68  																																																																																									| Instantiating formula (35) with all_0_2_2, all_0_5_5, 0, all_272_0_417 and discharging atoms distinct_points(all_0_2_2, all_0_5_5) = all_272_0_417, distinct_points(all_0_2_2, all_0_5_5) = 0, yields:
% 27.04/8.68  																																																																																									| (920) all_272_0_417 = 0
% 27.04/8.68  																																																																																									|
% 27.04/8.68  																																																																																									| Equations (920) can reduce 930 to:
% 27.04/8.68  																																																																																									| (101) $false
% 27.04/8.68  																																																																																									|
% 27.04/8.68  																																																																																									|-The branch is then unsatisfiable
% 27.04/8.68  																																																																																							|-Branch two:
% 27.04/8.68  																																																																																							| (601)  ~ (distinct_points(all_0_2_2, all_0_5_5) = 0)
% 27.04/8.68  																																																																																							| (210) all_20_0_28 = 0
% 27.04/8.68  																																																																																							|
% 27.04/8.68  																																																																																								| Equations (210) can reduce 72 to:
% 27.04/8.68  																																																																																								| (101) $false
% 27.04/8.68  																																																																																								|
% 27.04/8.68  																																																																																								|-The branch is then unsatisfiable
% 27.04/8.68  				|-Branch two:
% 27.04/8.68  				| (1021)  ~ (all_25_0_33 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33
% 27.04/8.68  				|
% 27.04/8.68  					| Applying alpha-rule on (1021) yields:
% 27.04/8.68  					| (105)  ~ (all_25_0_33 = 0)
% 27.04/8.68  					| (1023) convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33
% 27.04/8.68  					|
% 27.04/8.68  					| Instantiating formula (5) with all_0_7_7, all_0_6_6, all_25_0_33, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = all_25_0_33, convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 27.04/8.68  					| (198) all_25_0_33 = 0
% 27.04/8.68  					|
% 27.04/8.68  					| Equations (198) can reduce 105 to:
% 27.04/8.68  					| (101) $false
% 27.04/8.68  					|
% 27.04/8.68  					|-The branch is then unsatisfiable
% 27.04/8.68  		|-Branch two:
% 27.04/8.68  		| (1026)  ~ (all_24_0_32 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32
% 27.04/8.68  		|
% 27.04/8.68  			| Applying alpha-rule on (1026) yields:
% 27.04/8.68  			| (98)  ~ (all_24_0_32 = 0)
% 27.04/8.68  			| (1028) convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32
% 27.04/8.68  			|
% 27.04/8.68  			| Instantiating formula (5) with all_0_7_7, all_0_6_6, all_24_0_32, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = all_24_0_32, convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 27.04/8.68  			| (202) all_24_0_32 = 0
% 27.04/8.68  			|
% 27.04/8.68  			| Equations (202) can reduce 98 to:
% 27.04/8.68  			| (101) $false
% 27.04/8.68  			|
% 27.04/8.68  			|-The branch is then unsatisfiable
% 27.04/8.68  	|-Branch two:
% 27.04/8.68  	| (1031)  ~ (all_23_0_31 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31
% 27.04/8.68  	|
% 27.04/8.68  		| Applying alpha-rule on (1031) yields:
% 27.04/8.68  		| (95)  ~ (all_23_0_31 = 0)
% 27.04/8.68  		| (1033) convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31
% 27.04/8.68  		|
% 27.04/8.68  		| Instantiating formula (5) with all_0_9_9, all_0_8_8, all_23_0_31, 0 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = all_23_0_31, convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 27.04/8.68  		| (206) all_23_0_31 = 0
% 27.04/8.68  		|
% 27.04/8.68  		| Equations (206) can reduce 95 to:
% 27.04/8.68  		| (101) $false
% 27.04/8.68  		|
% 27.04/8.68  		|-The branch is then unsatisfiable
% 27.04/8.68  |-Branch two:
% 27.04/8.68  | (1036)  ~ (all_22_0_30 = 0) & convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30
% 27.04/8.68  |
% 27.04/8.68  	| Applying alpha-rule on (1036) yields:
% 27.04/8.68  	| (92)  ~ (all_22_0_30 = 0)
% 27.04/8.68  	| (1038) convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30
% 27.04/8.68  	|
% 27.04/8.68  	| Instantiating formula (5) with all_0_9_9, all_0_8_8, all_22_0_30, 0 and discharging atoms convergent_lines(all_0_9_9, all_0_8_8) = all_22_0_30, convergent_lines(all_0_9_9, all_0_8_8) = 0, yields:
% 27.04/8.68  	| (1039) all_22_0_30 = 0
% 27.04/8.68  	|
% 27.04/8.68  	| Equations (1039) can reduce 92 to:
% 27.04/8.68  	| (101) $false
% 27.04/8.68  	|
% 27.04/8.68  	|-The branch is then unsatisfiable
% 27.04/8.68  % SZS output end Proof for theBenchmark
% 27.04/8.68  
% 27.04/8.68  8077ms
%------------------------------------------------------------------------------