TSTP Solution File: GEO205+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n028.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 03:48:40 EDT 2022

% Result   : Theorem 5.21s 1.83s
% Output   : Proof 23.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : GEO205+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12  % Command  : ePrincess-casc -timeout=%d %s
% 0.12/0.32  % Computer : n028.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 600
% 0.12/0.32  % DateTime : Sat Jun 18 16:29:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.56/0.58          ____       _                          
% 0.56/0.58    ___  / __ \_____(_)___  ________  __________
% 0.56/0.58   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.56/0.58  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.56/0.58  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.56/0.58  
% 0.56/0.58  A Theorem Prover for First-Order Logic
% 0.61/0.58  (ePrincess v.1.0)
% 0.61/0.58  
% 0.61/0.58  (c) Philipp Rümmer, 2009-2015
% 0.61/0.58  (c) Peter Backeman, 2014-2015
% 0.61/0.58  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.58  Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.58  Bug reports to peter@backeman.se
% 0.61/0.58  
% 0.61/0.58  For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.58  
% 0.61/0.58  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.61/0.63  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.52/0.89  Prover 0: Preprocessing ...
% 1.86/1.01  Prover 0: Warning: ignoring some quantifiers
% 1.86/1.03  Prover 0: Constructing countermodel ...
% 2.38/1.19  Prover 0: gave up
% 2.38/1.19  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 2.49/1.21  Prover 1: Preprocessing ...
% 2.91/1.31  Prover 1: Constructing countermodel ...
% 3.11/1.37  Prover 1: gave up
% 3.11/1.37  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 3.11/1.39  Prover 2: Preprocessing ...
% 3.70/1.52  Prover 2: Warning: ignoring some quantifiers
% 3.70/1.53  Prover 2: Constructing countermodel ...
% 5.21/1.83  Prover 2: proved (454ms)
% 5.21/1.83  
% 5.21/1.83  No countermodel exists, formula is valid
% 5.21/1.83  % SZS status Theorem for theBenchmark
% 5.21/1.83  
% 5.21/1.83  Generating proof ... Warning: ignoring some quantifiers
% 22.33/6.85  found it (size 461)
% 22.33/6.85  
% 22.33/6.85  % SZS output start Proof for theBenchmark
% 22.33/6.85  Assumed formulas after preprocessing and simplification: 
% 22.33/6.85  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] :  ? [v4] :  ? [v5] :  ? [v6] :  ? [v7] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = 0 & distinct_lines(v1, v2) = v3 &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = 0 |  ~ (apart_point_and_line(v9, v11) = v13) |  ~ (apart_point_and_line(v9, v10) = v12) |  ~ (distinct_points(v8, v9) = 0) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v8, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = 0 |  ~ (apart_point_and_line(v9, v11) = v13) |  ~ (apart_point_and_line(v8, v11) = v12) |  ~ (distinct_lines(v10, v11) = 0) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v10) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = 0 |  ~ (apart_point_and_line(v9, v11) = v13) |  ~ (apart_point_and_line(v8, v10) = v12) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v10) = 0) | (v14 = 0 & apart_point_and_line(v8, v11) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = 0 |  ~ (apart_point_and_line(v9, v10) = v13) |  ~ (apart_point_and_line(v8, v11) = v12) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = 0 |  ~ (apart_point_and_line(v9, v10) = v13) |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (distinct_lines(v10, v11) = 0) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v11) = 0) | ( ~ (v14 = 0) & distinct_points(v8, v9) = v14))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] :  ! [v13] : (v13 = 0 | v12 = 0 |  ~ (apart_point_and_line(v8, v11) = v13) |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (distinct_points(v8, v9) = 0) |  ? [v14] : ((v14 = 0 & apart_point_and_line(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v9, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v10, v11) = v14))) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v10, v9) = v12) |  ~ (distinct_points(v8, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v12) |  ~ (distinct_lines(v9, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & apart_point_and_line(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (convergent_lines(v9, v10) = v12) |  ~ (convergent_lines(v8, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (convergent_lines(v8, v10) = v12) |  ~ (distinct_lines(v9, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (distinct_lines(v9, v10) = v12) |  ~ (distinct_lines(v8, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] :  ! [v12] : (v12 = 0 | v11 = 0 |  ~ (distinct_points(v9, v10) = v12) |  ~ (distinct_points(v8, v10) = v11) |  ? [v13] : ( ~ (v13 = 0) & distinct_points(v8, v9) = v13)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (apart_point_and_line(v10, v9) = v11) |  ~ (apart_point_and_line(v8, v9) = 0) | distinct_points(v8, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (apart_point_and_line(v8, v10) = v11) |  ~ (apart_point_and_line(v8, v9) = 0) | distinct_lines(v9, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (apart_point_and_line(v8, v9) = 0) |  ~ (distinct_lines(v9, v10) = v11) | apart_point_and_line(v8, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (apart_point_and_line(v8, v9) = 0) |  ~ (distinct_points(v8, v10) = v11) | apart_point_and_line(v10, v9) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (convergent_lines(v9, v10) = v11) |  ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v8, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (convergent_lines(v8, v10) = v11) |  ~ (convergent_lines(v8, v9) = 0) | convergent_lines(v9, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (convergent_lines(v8, v10) = v11) |  ~ (convergent_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (convergent_lines(v8, v9) = 0) |  ~ (distinct_lines(v9, v10) = v11) | convergent_lines(v8, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (distinct_lines(v9, v10) = v11) |  ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v8, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (distinct_lines(v8, v10) = v11) |  ~ (distinct_lines(v8, v9) = 0) | distinct_lines(v9, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (distinct_points(v9, v10) = v11) |  ~ (distinct_points(v8, v9) = 0) | distinct_points(v8, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v11 = 0 |  ~ (distinct_points(v8, v10) = v11) |  ~ (distinct_points(v8, v9) = 0) | distinct_points(v9, v10) = 0) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (intersection_point(v11, v10) = v9) |  ~ (intersection_point(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (line_connecting(v11, v10) = v9) |  ~ (line_connecting(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (apart_point_and_line(v11, v10) = v9) |  ~ (apart_point_and_line(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (convergent_lines(v11, v10) = v9) |  ~ (convergent_lines(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (distinct_lines(v11, v10) = v9) |  ~ (distinct_lines(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : (v9 = v8 |  ~ (distinct_points(v11, v10) = v9) |  ~ (distinct_points(v11, v10) = v8)) &  ! [v8] :  ! [v9] :  ! [v10] :  ! [v11] : ( ~ (distinct_lines(v10, v11) = 0) |  ~ (distinct_points(v8, v9) = 0) |  ? [v12] : ((v12 = 0 & apart_point_and_line(v9, v11) = 0) | (v12 = 0 & apart_point_and_line(v9, v10) = 0) | (v12 = 0 & apart_point_and_line(v8, v11) = 0) | (v12 = 0 & apart_point_and_line(v8, v10) = 0))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (intersection_point(v8, v9) = v10) |  ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v10, v9) = v11) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (intersection_point(v8, v9) = v10) |  ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v10, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (line_connecting(v8, v9) = v10) |  ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v9, v10) = v11) | ( ~ (v11 = 0) & distinct_points(v8, v9) = v11))) &  ! [v8] :  ! [v9] :  ! [v10] : ( ~ (line_connecting(v8, v9) = v10) |  ? [v11] : (( ~ (v11 = 0) & apart_point_and_line(v8, v10) = v11) | ( ~ (v11 = 0) & distinct_points(v8, v9) = v11))) &  ! [v8] :  ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & intersection_point(v8, v9) = v10 & apart_point_and_line(v10, v9) = v11)) &  ! [v8] :  ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & intersection_point(v8, v9) = v10 & apart_point_and_line(v10, v8) = v11)) &  ! [v8] :  ! [v9] : ( ~ (distinct_points(v8, v9) = 0) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & line_connecting(v8, v9) = v10 & apart_point_and_line(v9, v10) = v11)) &  ! [v8] :  ! [v9] : ( ~ (distinct_points(v8, v9) = 0) |  ? [v10] :  ? [v11] : ( ~ (v11 = 0) & line_connecting(v8, v9) = v10 & apart_point_and_line(v8, v10) = v11)) &  ! [v8] :  ~ (convergent_lines(v8, v8) = 0) &  ! [v8] :  ~ (distinct_lines(v8, v8) = 0) &  ! [v8] :  ~ (distinct_points(v8, v8) = 0) &  ? [v8] :  ? [v9] :  ? [v10] : intersection_point(v9, v8) = v10 &  ? [v8] :  ? [v9] :  ? [v10] : line_connecting(v9, v8) = v10 &  ? [v8] :  ? [v9] :  ? [v10] : apart_point_and_line(v9, v8) = v10 &  ? [v8] :  ? [v9] :  ? [v10] : convergent_lines(v9, v8) = v10 &  ? [v8] :  ? [v9] :  ? [v10] : distinct_lines(v9, v8) = v10 &  ? [v8] :  ? [v9] :  ? [v10] : distinct_points(v9, v8) = v10 & ((v7 = 0 & intersection_point(v0, v2) = v6 & intersection_point(v0, v1) = v5 & distinct_points(v5, v6) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v2) = v4)))
% 22.55/6.91  | 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 yields:
% 22.55/6.91  | (1)  ~ (all_0_4_4 = 0) & convergent_lines(all_0_7_7, all_0_6_6) = 0 & distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4 &  ! [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 & intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_0_3_3 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3))
% 22.55/6.92  |
% 22.55/6.92  | Applying alpha-rule on (1) yields:
% 22.55/6.92  | (2)  ! [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)))
% 22.55/6.92  | (3)  ! [v0] :  ~ (convergent_lines(v0, v0) = 0)
% 22.55/6.92  | (4)  ? [v0] :  ? [v1] :  ? [v2] : intersection_point(v1, v0) = v2
% 22.55/6.92  | (5)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v1) = 0) |  ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 22.55/6.92  | (6) distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4
% 22.55/6.92  | (7)  ? [v0] :  ? [v1] :  ? [v2] : line_connecting(v1, v0) = v2
% 22.55/6.92  | (8)  ! [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)))
% 22.55/6.92  | (9)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 22.55/6.93  | (10)  ! [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)))
% 22.55/6.93  | (11)  ! [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))
% 22.55/6.93  | (12) convergent_lines(all_0_7_7, all_0_6_6) = 0
% 22.55/6.93  | (13)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 22.55/6.93  | (14)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_points(v3, v2) = v1) |  ~ (distinct_points(v3, v2) = v0))
% 22.55/6.93  | (15)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v1, v2) = v4) |  ~ (distinct_points(v0, v1) = 0) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6)))
% 22.55/6.93  | (16)  ! [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))
% 22.55/6.93  | (17)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (distinct_lines(v3, v2) = v1) |  ~ (distinct_lines(v3, v2) = v0))
% 22.55/6.93  | (18)  ! [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)
% 22.55/6.93  | (19)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (convergent_lines(v3, v2) = v1) |  ~ (convergent_lines(v3, v2) = v0))
% 22.55/6.93  | (20)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 22.55/6.93  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v0, v1) = 0) |  ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0)
% 22.55/6.93  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (line_connecting(v3, v2) = v1) |  ~ (line_connecting(v3, v2) = v0))
% 22.55/6.93  | (23)  ? [v0] :  ? [v1] :  ? [v2] : convergent_lines(v1, v0) = v2
% 22.55/6.93  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v1, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 22.55/6.93  | (25)  ! [v0] :  ! [v1] : ( ~ (distinct_points(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 22.55/6.93  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v0, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 22.55/6.93  | (27)  ! [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)
% 22.55/6.93  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_lines(v0, v2) = v3) |  ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.55/6.93  | (29)  ! [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)))
% 22.55/6.93  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (distinct_points(v1, v2) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5))
% 22.55/6.93  | (31)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v3) |  ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 22.55/6.93  | (32)  ! [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)))
% 22.55/6.93  | (33)  ! [v0] :  ~ (distinct_points(v0, v0) = 0)
% 22.55/6.93  | (34)  ! [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)))
% 22.55/6.93  | (35)  ? [v0] :  ? [v1] :  ? [v2] : apart_point_and_line(v1, v0) = v2
% 22.55/6.93  | (36)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v1, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 22.55/6.94  | (37)  ! [v0] :  ~ (distinct_lines(v0, v0) = 0)
% 22.55/6.94  | (38)  ! [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))
% 22.55/6.94  | (39)  ? [v0] :  ? [v1] :  ? [v2] : distinct_points(v1, v0) = v2
% 22.55/6.94  | (40)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (intersection_point(v3, v2) = v1) |  ~ (intersection_point(v3, v2) = v0))
% 22.55/6.94  | (41)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : (v5 = 0 | v4 = 0 |  ~ (apart_point_and_line(v1, v3) = v5) |  ~ (apart_point_and_line(v0, v2) = v4) |  ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6)))
% 22.55/6.94  | (42)  ! [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))
% 22.55/6.94  | (43)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (apart_point_and_line(v3, v2) = v1) |  ~ (apart_point_and_line(v3, v2) = v0))
% 22.55/6.94  | (44)  ! [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)))
% 22.55/6.94  | (45)  ~ (all_0_4_4 = 0)
% 22.55/6.94  | (46)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (distinct_points(v1, v2) = v3) |  ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 22.55/6.94  | (47)  ? [v0] :  ? [v1] :  ? [v2] : distinct_lines(v1, v0) = v2
% 22.55/6.94  | (48)  ! [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)))
% 22.55/6.94  | (49)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v3 = 0 |  ~ (convergent_lines(v0, v2) = v3) |  ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 22.55/6.94  | (50) (all_0_0_0 = 0 & intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_2_2, all_0_1_1) = 0) | ( ~ (all_0_3_3 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3)
% 22.55/6.94  | (51)  ! [v0] :  ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) |  ? [v2] :  ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 22.55/6.94  | (52)  ! [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)))
% 22.55/6.94  | (53)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = 0 | v3 = 0 |  ~ (apart_point_and_line(v2, v1) = v4) |  ~ (distinct_points(v0, v2) = v3) |  ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5))
% 22.55/6.94  |
% 22.55/6.94  | Instantiating formula (9) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 22.55/6.94  | (54)  ? [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)
% 22.55/6.94  |
% 22.55/6.94  | Instantiating formula (51) with all_0_6_6, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_6_6) = 0, yields:
% 22.55/6.94  | (55)  ? [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)
% 22.86/6.94  |
% 22.86/6.94  | Instantiating formula (5) with all_0_4_4, all_0_5_5, 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_5_5) = all_0_4_4, yields:
% 22.86/6.94  | (56) all_0_4_4 = 0 | convergent_lines(all_0_7_7, all_0_5_5) = 0
% 22.86/6.94  |
% 22.86/6.94  | Instantiating formula (16) with all_0_4_4, all_0_4_4, all_0_5_5, all_0_6_6, all_0_6_6 and discharging atoms distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 22.86/6.94  | (57) all_0_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0)
% 22.86/6.94  |
% 22.86/6.94  | Instantiating (55) with all_20_0_26, all_20_1_27 yields:
% 22.86/6.94  | (58)  ~ (all_20_0_26 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_20_1_27 & apart_point_and_line(all_20_1_27, all_0_7_7) = all_20_0_26
% 22.86/6.94  |
% 22.86/6.94  | Applying alpha-rule on (58) yields:
% 22.86/6.94  | (59)  ~ (all_20_0_26 = 0)
% 22.86/6.94  | (60) intersection_point(all_0_7_7, all_0_6_6) = all_20_1_27
% 22.86/6.94  | (61) apart_point_and_line(all_20_1_27, all_0_7_7) = all_20_0_26
% 22.86/6.94  |
% 22.86/6.94  | Instantiating (54) with all_22_0_28, all_22_1_29 yields:
% 22.86/6.94  | (62)  ~ (all_22_0_28 = 0) & intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29 & apart_point_and_line(all_22_1_29, all_0_6_6) = all_22_0_28
% 22.86/6.95  |
% 22.86/6.95  | Applying alpha-rule on (62) yields:
% 22.86/6.95  | (63)  ~ (all_22_0_28 = 0)
% 22.86/6.95  | (64) intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29
% 22.86/6.95  | (65) apart_point_and_line(all_22_1_29, all_0_6_6) = all_22_0_28
% 22.86/6.95  |
% 22.86/6.95  +-Applying beta-rule and splitting (56), into two cases.
% 22.86/6.95  |-Branch one:
% 22.86/6.95  | (66) convergent_lines(all_0_7_7, all_0_5_5) = 0
% 22.86/6.95  |
% 22.86/6.95  	+-Applying beta-rule and splitting (50), into two cases.
% 22.86/6.95  	|-Branch one:
% 22.86/6.95  	| (67) all_0_0_0 = 0 & intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1 & intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_2_2, all_0_1_1) = 0
% 22.86/6.95  	|
% 22.86/6.95  		| Applying alpha-rule on (67) yields:
% 22.86/6.95  		| (68) all_0_0_0 = 0
% 22.86/6.95  		| (69) intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1
% 22.86/6.95  		| (70) intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2
% 22.86/6.95  		| (71) distinct_points(all_0_2_2, all_0_1_1) = 0
% 22.86/6.95  		|
% 22.86/6.95  		+-Applying beta-rule and splitting (57), into two cases.
% 22.86/6.95  		|-Branch one:
% 22.86/6.95  		| (72) all_0_4_4 = 0
% 22.86/6.95  		|
% 22.86/6.95  			| Equations (72) can reduce 45 to:
% 22.86/6.95  			| (73) $false
% 22.86/6.95  			|
% 22.86/6.95  			|-The branch is then unsatisfiable
% 22.86/6.95  		|-Branch two:
% 22.86/6.95  		| (45)  ~ (all_0_4_4 = 0)
% 22.86/6.95  		| (75)  ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0)
% 22.86/6.95  		|
% 22.86/6.95  			| Instantiating formula (40) with all_0_7_7, all_0_6_6, all_20_1_27, all_22_1_29 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29, intersection_point(all_0_7_7, all_0_6_6) = all_20_1_27, yields:
% 22.86/6.95  			| (76) all_22_1_29 = all_20_1_27
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (40) with all_0_7_7, all_0_6_6, all_0_2_2, all_22_1_29 and discharging atoms intersection_point(all_0_7_7, all_0_6_6) = all_22_1_29, intersection_point(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 22.86/6.95  			| (77) all_22_1_29 = all_0_2_2
% 22.86/6.95  			|
% 22.86/6.95  			| Combining equations (77,76) yields a new equation:
% 22.86/6.95  			| (78) all_20_1_27 = all_0_2_2
% 22.86/6.95  			|
% 22.86/6.95  			| Combining equations (78,76) yields a new equation:
% 22.86/6.95  			| (77) all_22_1_29 = all_0_2_2
% 22.86/6.95  			|
% 22.86/6.95  			| From (77) and (65) follows:
% 22.86/6.95  			| (80) apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28
% 22.86/6.95  			|
% 22.86/6.95  			| From (78) and (61) follows:
% 22.86/6.95  			| (81) apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (34) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 22.86/6.95  			| (82)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = v0))
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (44) with all_0_1_1, all_0_5_5, all_0_7_7 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 22.86/6.95  			| (83)  ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_7_7) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = v0))
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (41) with all_22_0_28, all_22_0_28, 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_22_0_28, yields:
% 22.86/6.95  			| (84) all_22_0_28 = 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))
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (41) with all_20_0_26, all_22_0_28, 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_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.86/6.95  			| (85) all_22_0_28 = 0 | all_20_0_26 = 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))
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (41) with all_22_0_28, all_20_0_26, 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_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.86/6.95  			| (86) all_22_0_28 = 0 | all_20_0_26 = 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))
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (41) with all_20_0_26, all_20_0_26, 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_20_0_26, yields:
% 22.86/6.95  			| (87) all_20_0_26 = 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))
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (9) with all_0_5_5, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 22.86/6.95  			| (88)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_5_5) = v0 & apart_point_and_line(v0, all_0_5_5) = v1)
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (51) with all_0_5_5, all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 22.86/6.95  			| (89)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_7_7, all_0_5_5) = v0 & apart_point_and_line(v0, all_0_7_7) = v1)
% 22.86/6.95  			|
% 22.86/6.95  			| Instantiating formula (8) with all_22_0_28, all_22_0_28, all_0_6_6, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.95  			| (90) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating formula (8) with all_22_0_28, all_20_0_26, all_0_6_6, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96  			| (91) all_22_0_28 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0))
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating formula (8) with all_20_0_26, all_22_0_28, all_0_7_7, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96  			| (92) all_22_0_28 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0))
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating formula (8) with all_20_0_26, all_20_0_26, all_0_7_7, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96  			| (93) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0))
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating formula (13) with all_0_1_1, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96  			| (94)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(all_0_1_1, v0) = v1)
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating formula (25) with all_0_1_1, all_0_2_2 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.86/6.96  			| (95)  ? [v0] :  ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_2_2, all_0_1_1) = v0 & apart_point_and_line(all_0_2_2, v0) = v1)
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating (95) with all_47_0_31, all_47_1_32 yields:
% 22.86/6.96  			| (96)  ~ (all_47_0_31 = 0) & line_connecting(all_0_2_2, all_0_1_1) = all_47_1_32 & apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31
% 22.86/6.96  			|
% 22.86/6.96  			| Applying alpha-rule on (96) yields:
% 22.86/6.96  			| (97)  ~ (all_47_0_31 = 0)
% 22.86/6.96  			| (98) line_connecting(all_0_2_2, all_0_1_1) = all_47_1_32
% 22.86/6.96  			| (99) apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating (94) with all_49_0_33, all_49_1_34 yields:
% 22.86/6.96  			| (100)  ~ (all_49_0_33 = 0) & line_connecting(all_0_2_2, all_0_1_1) = all_49_1_34 & apart_point_and_line(all_0_1_1, all_49_1_34) = all_49_0_33
% 22.86/6.96  			|
% 22.86/6.96  			| Applying alpha-rule on (100) yields:
% 22.86/6.96  			| (101)  ~ (all_49_0_33 = 0)
% 22.86/6.96  			| (102) line_connecting(all_0_2_2, all_0_1_1) = all_49_1_34
% 22.86/6.96  			| (103) apart_point_and_line(all_0_1_1, all_49_1_34) = all_49_0_33
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating (89) with all_51_0_35, all_51_1_36 yields:
% 22.86/6.96  			| (104)  ~ (all_51_0_35 = 0) & intersection_point(all_0_7_7, all_0_5_5) = all_51_1_36 & apart_point_and_line(all_51_1_36, all_0_7_7) = all_51_0_35
% 22.86/6.96  			|
% 22.86/6.96  			| Applying alpha-rule on (104) yields:
% 22.86/6.96  			| (105)  ~ (all_51_0_35 = 0)
% 22.86/6.96  			| (106) intersection_point(all_0_7_7, all_0_5_5) = all_51_1_36
% 22.86/6.96  			| (107) apart_point_and_line(all_51_1_36, all_0_7_7) = all_51_0_35
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating (88) with all_53_0_37, all_53_1_38 yields:
% 22.86/6.96  			| (108)  ~ (all_53_0_37 = 0) & intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38 & apart_point_and_line(all_53_1_38, all_0_5_5) = all_53_0_37
% 22.86/6.96  			|
% 22.86/6.96  			| Applying alpha-rule on (108) yields:
% 22.86/6.96  			| (109)  ~ (all_53_0_37 = 0)
% 22.86/6.96  			| (110) intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38
% 22.86/6.96  			| (111) apart_point_and_line(all_53_1_38, all_0_5_5) = all_53_0_37
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating (83) with all_55_0_39 yields:
% 22.86/6.96  			| (112) ( ~ (all_55_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39) | ( ~ (all_55_0_39 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39)
% 22.86/6.96  			|
% 22.86/6.96  			| Instantiating (82) with all_56_0_40 yields:
% 22.86/6.96  			| (113) ( ~ (all_56_0_40 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40) | ( ~ (all_56_0_40 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40)
% 22.86/6.96  			|
% 22.86/6.96  			+-Applying beta-rule and splitting (112), into two cases.
% 22.86/6.96  			|-Branch one:
% 22.86/6.96  			| (114)  ~ (all_55_0_39 = 0) & apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39
% 22.86/6.96  			|
% 22.86/6.96  				| Applying alpha-rule on (114) yields:
% 22.86/6.96  				| (115)  ~ (all_55_0_39 = 0)
% 22.86/6.96  				| (116) apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39
% 22.86/6.96  				|
% 22.86/6.96  				+-Applying beta-rule and splitting (113), into two cases.
% 22.86/6.96  				|-Branch one:
% 22.86/6.96  				| (117)  ~ (all_56_0_40 = 0) & apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40
% 22.86/6.96  				|
% 22.86/6.96  					| Applying alpha-rule on (117) yields:
% 22.86/6.96  					| (118)  ~ (all_56_0_40 = 0)
% 22.86/6.96  					| (119) apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40
% 22.86/6.96  					|
% 22.86/6.96  					+-Applying beta-rule and splitting (90), into two cases.
% 22.86/6.96  					|-Branch one:
% 22.86/6.96  					| (120) all_22_0_28 = 0
% 22.86/6.96  					|
% 22.86/6.96  						| Equations (120) can reduce 63 to:
% 22.86/6.96  						| (73) $false
% 22.86/6.96  						|
% 22.86/6.96  						|-The branch is then unsatisfiable
% 22.86/6.96  					|-Branch two:
% 22.86/6.96  					| (63)  ~ (all_22_0_28 = 0)
% 22.86/6.96  					| (123)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_6_6) = v0))
% 22.86/6.96  					|
% 22.86/6.96  						+-Applying beta-rule and splitting (93), into two cases.
% 22.86/6.96  						|-Branch one:
% 22.86/6.96  						| (124) all_20_0_26 = 0
% 22.86/6.96  						|
% 22.86/6.96  							| Equations (124) can reduce 59 to:
% 22.86/6.96  							| (73) $false
% 22.86/6.96  							|
% 22.86/6.96  							|-The branch is then unsatisfiable
% 22.86/6.96  						|-Branch two:
% 22.86/6.96  						| (59)  ~ (all_20_0_26 = 0)
% 22.86/6.96  						| (127)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0))
% 22.86/6.96  						|
% 22.86/6.96  							+-Applying beta-rule and splitting (84), into two cases.
% 22.86/6.96  							|-Branch one:
% 22.86/6.96  							| (120) all_22_0_28 = 0
% 22.86/6.96  							|
% 22.86/6.96  								| Equations (120) can reduce 63 to:
% 22.86/6.96  								| (73) $false
% 22.86/6.96  								|
% 22.86/6.96  								|-The branch is then unsatisfiable
% 22.86/6.96  							|-Branch two:
% 22.86/6.96  							| (63)  ~ (all_22_0_28 = 0)
% 22.86/6.96  							| (131)  ? [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))
% 22.86/6.97  							|
% 22.86/6.97  								+-Applying beta-rule and splitting (87), into two cases.
% 22.86/6.97  								|-Branch one:
% 22.86/6.97  								| (124) all_20_0_26 = 0
% 22.86/6.97  								|
% 22.86/6.97  									| Equations (124) can reduce 59 to:
% 22.86/6.97  									| (73) $false
% 22.86/6.97  									|
% 22.86/6.97  									|-The branch is then unsatisfiable
% 22.86/6.97  								|-Branch two:
% 22.86/6.97  								| (59)  ~ (all_20_0_26 = 0)
% 22.86/6.97  								| (135)  ? [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))
% 22.86/6.97  								|
% 22.86/6.97  									+-Applying beta-rule and splitting (86), into two cases.
% 22.86/6.97  									|-Branch one:
% 22.86/6.97  									| (120) all_22_0_28 = 0
% 22.86/6.97  									|
% 22.86/6.97  										| Equations (120) can reduce 63 to:
% 22.86/6.97  										| (73) $false
% 22.86/6.97  										|
% 22.86/6.97  										|-The branch is then unsatisfiable
% 22.86/6.97  									|-Branch two:
% 22.86/6.97  									| (63)  ~ (all_22_0_28 = 0)
% 22.86/6.97  									| (139) all_20_0_26 = 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))
% 22.86/6.97  									|
% 22.86/6.97  										+-Applying beta-rule and splitting (92), into two cases.
% 22.86/6.97  										|-Branch one:
% 22.86/6.97  										| (120) all_22_0_28 = 0
% 22.86/6.97  										|
% 22.86/6.97  											| Equations (120) can reduce 63 to:
% 22.86/6.97  											| (73) $false
% 22.86/6.97  											|
% 22.86/6.97  											|-The branch is then unsatisfiable
% 22.86/6.97  										|-Branch two:
% 22.86/6.97  										| (63)  ~ (all_22_0_28 = 0)
% 22.86/6.97  										| (143) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0))
% 22.86/6.97  										|
% 22.86/6.97  											+-Applying beta-rule and splitting (91), into two cases.
% 22.86/6.97  											|-Branch one:
% 22.86/6.97  											| (120) all_22_0_28 = 0
% 22.86/6.97  											|
% 22.86/6.97  												| Equations (120) can reduce 63 to:
% 22.86/6.97  												| (73) $false
% 22.86/6.97  												|
% 22.86/6.97  												|-The branch is then unsatisfiable
% 22.86/6.97  											|-Branch two:
% 22.86/6.97  											| (63)  ~ (all_22_0_28 = 0)
% 22.86/6.97  											| (147) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0))
% 22.98/6.97  											|
% 22.98/6.97  												+-Applying beta-rule and splitting (85), into two cases.
% 22.98/6.97  												|-Branch one:
% 22.98/6.97  												| (120) all_22_0_28 = 0
% 22.98/6.97  												|
% 22.98/6.97  													| Equations (120) can reduce 63 to:
% 22.98/6.97  													| (73) $false
% 22.98/6.97  													|
% 22.98/6.97  													|-The branch is then unsatisfiable
% 22.98/6.97  												|-Branch two:
% 22.98/6.97  												| (63)  ~ (all_22_0_28 = 0)
% 22.98/6.97  												| (151) all_20_0_26 = 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))
% 22.98/6.97  												|
% 22.98/6.97  													+-Applying beta-rule and splitting (139), into two cases.
% 22.98/6.97  													|-Branch one:
% 22.98/6.97  													| (124) all_20_0_26 = 0
% 22.98/6.97  													|
% 22.98/6.97  														| Equations (124) can reduce 59 to:
% 22.98/6.97  														| (73) $false
% 22.98/6.97  														|
% 22.98/6.97  														|-The branch is then unsatisfiable
% 22.98/6.97  													|-Branch two:
% 22.98/6.97  													| (59)  ~ (all_20_0_26 = 0)
% 22.98/6.97  													| (155)  ? [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))
% 22.98/6.97  													|
% 22.98/6.97  														+-Applying beta-rule and splitting (147), into two cases.
% 22.98/6.97  														|-Branch one:
% 22.98/6.97  														| (124) all_20_0_26 = 0
% 22.98/6.97  														|
% 22.98/6.97  															| Equations (124) can reduce 59 to:
% 22.98/6.97  															| (73) $false
% 22.98/6.97  															|
% 22.98/6.97  															|-The branch is then unsatisfiable
% 22.98/6.97  														|-Branch two:
% 22.98/6.97  														| (59)  ~ (all_20_0_26 = 0)
% 22.98/6.97  														| (159)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_6_6) = v0))
% 22.98/6.97  														|
% 22.98/6.97  															+-Applying beta-rule and splitting (143), into two cases.
% 22.98/6.97  															|-Branch one:
% 22.98/6.97  															| (124) all_20_0_26 = 0
% 22.98/6.97  															|
% 22.98/6.97  																| Equations (124) can reduce 59 to:
% 22.98/6.97  																| (73) $false
% 22.98/6.97  																|
% 22.98/6.97  																|-The branch is then unsatisfiable
% 22.98/6.97  															|-Branch two:
% 22.98/6.97  															| (59)  ~ (all_20_0_26 = 0)
% 22.98/6.97  															| (163)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = v0))
% 22.98/6.97  															|
% 22.98/6.97  																| Instantiating (163) with all_110_0_51 yields:
% 22.98/6.97  																| (164) (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (all_110_0_51 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51)
% 22.98/6.97  																|
% 22.98/6.97  																+-Applying beta-rule and splitting (151), into two cases.
% 22.98/6.97  																|-Branch one:
% 22.98/6.97  																| (124) all_20_0_26 = 0
% 22.98/6.97  																|
% 22.98/6.97  																	| Equations (124) can reduce 59 to:
% 22.98/6.97  																	| (73) $false
% 22.98/6.97  																	|
% 22.98/6.97  																	|-The branch is then unsatisfiable
% 22.98/6.97  																|-Branch two:
% 22.98/6.97  																| (59)  ~ (all_20_0_26 = 0)
% 22.98/6.97  																| (168)  ? [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))
% 22.98/6.97  																|
% 22.98/6.97  																	| Instantiating formula (40) with all_0_7_7, all_0_5_5, all_53_1_38, all_0_1_1 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38, intersection_point(all_0_7_7, all_0_5_5) = all_0_1_1, yields:
% 22.98/6.97  																	| (169) all_53_1_38 = all_0_1_1
% 22.98/6.97  																	|
% 22.98/6.97  																	| Instantiating formula (40) with all_0_7_7, all_0_5_5, all_51_1_36, all_53_1_38 and discharging atoms intersection_point(all_0_7_7, all_0_5_5) = all_53_1_38, intersection_point(all_0_7_7, all_0_5_5) = all_51_1_36, yields:
% 22.98/6.97  																	| (170) all_53_1_38 = all_51_1_36
% 22.98/6.97  																	|
% 22.98/6.97  																	| Instantiating formula (22) with all_0_2_2, all_0_1_1, all_47_1_32, all_49_1_34 and discharging atoms line_connecting(all_0_2_2, all_0_1_1) = all_49_1_34, line_connecting(all_0_2_2, all_0_1_1) = all_47_1_32, yields:
% 22.98/6.97  																	| (171) all_49_1_34 = all_47_1_32
% 22.98/6.97  																	|
% 22.98/6.97  																	| Combining equations (169,170) yields a new equation:
% 22.98/6.97  																	| (172) all_51_1_36 = all_0_1_1
% 22.98/6.97  																	|
% 22.98/6.97  																	| Combining equations (172,170) yields a new equation:
% 22.98/6.97  																	| (169) all_53_1_38 = all_0_1_1
% 22.98/6.97  																	|
% 22.98/6.97  																	| From (169) and (111) follows:
% 22.98/6.98  																	| (174) apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37
% 22.98/6.98  																	|
% 22.98/6.98  																	| From (172) and (107) follows:
% 22.98/6.98  																	| (175) apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35
% 22.98/6.98  																	|
% 22.98/6.98  																	| From (171) and (103) follows:
% 22.98/6.98  																	| (176) apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (43) with all_0_1_1, all_0_5_5, all_53_0_37, all_56_0_40 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_56_0_40, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/6.98  																	| (177) all_56_0_40 = all_53_0_37
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (43) with all_0_1_1, all_0_7_7, all_51_0_35, all_55_0_39 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_55_0_39, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/6.98  																	| (178) all_55_0_39 = all_51_0_35
% 22.98/6.98  																	|
% 22.98/6.98  																	| Equations (177) can reduce 118 to:
% 22.98/6.98  																	| (109)  ~ (all_53_0_37 = 0)
% 22.98/6.98  																	|
% 22.98/6.98  																	| Equations (178) can reduce 115 to:
% 22.98/6.98  																	| (105)  ~ (all_51_0_35 = 0)
% 22.98/6.98  																	|
% 22.98/6.98  																	| From (177) and (119) follows:
% 22.98/6.98  																	| (174) apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37
% 22.98/6.98  																	|
% 22.98/6.98  																	| From (178) and (116) follows:
% 22.98/6.98  																	| (175) apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (41) with all_49_0_33, all_22_0_28, all_47_1_32, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98  																	| (183) all_49_0_33 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (41) with all_22_0_28, all_49_0_33, all_0_6_6, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98  																	| (184) all_49_0_33 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (52) with all_49_0_33, all_22_0_28, all_0_6_6, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98  																	| (185) all_49_0_33 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (52) with all_22_0_28, all_49_0_33, all_47_1_32, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.98  																	| (186) all_49_0_33 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (41) with all_49_0_33, all_20_0_26, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98  																	| (187) all_49_0_33 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (41) with all_20_0_26, all_49_0_33, all_0_7_7, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98  																	| (188) all_49_0_33 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (52) with all_49_0_33, all_20_0_26, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98  																	| (189) all_49_0_33 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.98  																	|
% 22.98/6.98  																	| Instantiating formula (52) with all_20_0_26, all_49_0_33, all_47_1_32, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.98  																	| (190) all_49_0_33 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (15) with all_49_0_33, all_49_0_33, all_47_1_32, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/6.99  																	| (191) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (41) with all_49_0_33, all_49_0_33, all_47_1_32, all_47_1_32, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, yields:
% 22.98/6.99  																	| (192) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (41) with all_53_0_37, all_22_0_28, all_0_5_5, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99  																	| (193) all_53_0_37 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (41) with all_22_0_28, all_53_0_37, all_0_6_6, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99  																	| (194) all_53_0_37 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (52) with all_53_0_37, all_22_0_28, all_0_6_6, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99  																	| (195) all_53_0_37 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (52) with all_22_0_28, all_53_0_37, all_0_5_5, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/6.99  																	| (196) all_53_0_37 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (41) with all_53_0_37, all_20_0_26, all_0_5_5, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99  																	| (197) all_53_0_37 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (41) with all_20_0_26, all_53_0_37, all_0_7_7, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99  																	| (198) all_53_0_37 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (52) with all_53_0_37, all_20_0_26, all_0_7_7, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99  																	| (199) all_53_0_37 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (52) with all_20_0_26, all_53_0_37, all_0_5_5, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/6.99  																	| (200) all_53_0_37 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (15) with all_53_0_37, all_49_0_33, all_0_5_5, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/6.99  																	| (201) all_53_0_37 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (15) with all_49_0_33, all_53_0_37, all_47_1_32, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/6.99  																	| (202) all_53_0_37 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0))
% 22.98/6.99  																	|
% 22.98/6.99  																	| Instantiating formula (41) with all_53_0_37, all_49_0_33, all_0_5_5, all_47_1_32, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/7.00  																	| (203) all_53_0_37 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (41) with all_49_0_33, all_53_0_37, all_47_1_32, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/7.00  																	| (204) all_53_0_37 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (15) with all_53_0_37, all_53_0_37, all_0_5_5, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.00  																	| (205) all_53_0_37 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (41) with all_53_0_37, all_53_0_37, all_0_5_5, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, yields:
% 22.98/7.00  																	| (206) all_53_0_37 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (11) with all_53_0_37, all_0_4_4, all_0_5_5, all_0_6_6, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, distinct_lines(all_0_6_6, all_0_5_5) = all_0_4_4, yields:
% 22.98/7.00  																	| (207) all_53_0_37 = 0 | all_0_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0)
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (41) with all_51_0_35, all_22_0_28, all_0_7_7, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00  																	| (208) all_51_0_35 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (41) with all_22_0_28, all_51_0_35, all_0_6_6, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00  																	| (209) all_51_0_35 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (52) with all_51_0_35, all_22_0_28, all_0_6_6, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00  																	| (210) all_51_0_35 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (52) with all_22_0_28, all_51_0_35, all_0_7_7, all_0_6_6, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.00  																	| (211) all_51_0_35 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (41) with all_20_0_26, all_51_0_35, all_0_7_7, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/7.00  																	| (212) all_51_0_35 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 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_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (15) with all_51_0_35, all_49_0_33, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.00  																	| (213) all_51_0_35 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 22.98/7.00  																	|
% 22.98/7.00  																	| Instantiating formula (15) with all_49_0_33, all_51_0_35, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.01  																	| (214) all_51_0_35 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 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_47_1_32) = v0))
% 22.98/7.01  																	|
% 22.98/7.01  																	| Instantiating formula (41) with all_51_0_35, all_49_0_33, all_0_7_7, all_47_1_32, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.01  																	| (215) all_51_0_35 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.01  																	|
% 22.98/7.01  																	| Instantiating formula (41) with all_49_0_33, all_51_0_35, all_47_1_32, all_0_7_7, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.01  																	| (216) all_51_0_35 = 0 | all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.01  																	|
% 22.98/7.01  																	| Instantiating formula (15) with all_51_0_35, all_53_0_37, all_0_7_7, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.01  																	| (217) all_53_0_37 = 0 | all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0))
% 22.98/7.01  																	|
% 22.98/7.01  																	| Instantiating formula (15) with all_53_0_37, all_51_0_35, all_0_5_5, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.01  																	| (218) all_53_0_37 = 0 | all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 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_5_5) = v0))
% 22.98/7.01  																	|
% 22.98/7.01  																	| Instantiating formula (41) with all_51_0_35, all_53_0_37, all_0_7_7, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.01  																	| (219) all_53_0_37 = 0 | all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_53_0_37, all_51_0_35, all_0_5_5, all_0_7_7, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.02  																	| (220) all_53_0_37 = 0 | all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_51_0_35, all_51_0_35, all_0_7_7, all_0_7_7, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, yields:
% 22.98/7.02  																	| (221) all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (8) with all_47_0_31, all_22_0_28, all_47_1_32, all_0_6_6, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02  																	| (222) all_47_0_31 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (8) with all_22_0_28, all_47_0_31, all_0_6_6, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02  																	| (223) all_47_0_31 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_47_0_31, all_22_0_28, all_47_1_32, all_0_6_6, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.02  																	| (224) all_47_0_31 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_22_0_28, all_47_0_31, all_0_6_6, all_47_1_32, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_6_6) = all_22_0_28, yields:
% 22.98/7.02  																	| (225) all_47_0_31 = 0 | all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (8) with all_47_0_31, all_20_0_26, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02  																	| (226) all_47_0_31 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (8) with all_20_0_26, all_47_0_31, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 22.98/7.02  																	| (227) all_47_0_31 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_47_0_31, all_20_0_26, all_47_1_32, all_0_7_7, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/7.02  																	| (228) all_47_0_31 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_20_0_26, all_47_0_31, all_0_7_7, all_47_1_32, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, yields:
% 22.98/7.02  																	| (229) all_47_0_31 = 0 | all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 22.98/7.02  																	|
% 22.98/7.02  																	| Instantiating formula (41) with all_49_0_33, all_47_0_31, all_47_1_32, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_47_1_32) = all_49_0_33, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 22.98/7.02  																	| (230) all_49_0_33 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.02  																	|
% 23.24/7.02  																	| Instantiating formula (41) with all_47_0_31, all_53_0_37, all_47_1_32, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02  																	| (231) all_53_0_37 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.02  																	|
% 23.24/7.02  																	| Instantiating formula (41) with all_53_0_37, all_47_0_31, all_0_5_5, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02  																	| (232) all_53_0_37 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.02  																	|
% 23.24/7.02  																	| Instantiating formula (52) with all_47_0_31, all_53_0_37, all_0_5_5, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02  																	| (233) all_53_0_37 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.02  																	|
% 23.24/7.02  																	| Instantiating formula (52) with all_53_0_37, all_47_0_31, all_47_1_32, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_53_0_37, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.02  																	| (234) all_53_0_37 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.02  																	|
% 23.24/7.02  																	| Instantiating formula (41) with all_47_0_31, all_51_0_35, all_47_1_32, all_0_7_7, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03  																	| (235) all_51_0_35 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																	| Instantiating formula (41) with all_51_0_35, all_47_0_31, all_0_7_7, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03  																	| (236) all_51_0_35 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																	| Instantiating formula (52) with all_47_0_31, all_51_0_35, all_0_7_7, all_47_1_32, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03  																	| (237) all_51_0_35 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																	| Instantiating formula (52) with all_51_0_35, all_47_0_31, all_47_1_32, all_0_7_7, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03  																	| (238) all_51_0_35 = 0 | all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																	| Instantiating formula (8) with all_47_0_31, all_47_0_31, all_47_1_32, all_47_1_32, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 23.24/7.03  																	| (239) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																	| Instantiating formula (41) with all_47_0_31, all_47_0_31, all_47_1_32, all_47_1_32, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_47_1_32) = all_47_0_31, yields:
% 23.24/7.03  																	| (240) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																	+-Applying beta-rule and splitting (191), into two cases.
% 23.24/7.03  																	|-Branch one:
% 23.24/7.03  																	| (241) all_49_0_33 = 0
% 23.24/7.03  																	|
% 23.24/7.03  																		| Equations (241) can reduce 101 to:
% 23.24/7.03  																		| (73) $false
% 23.24/7.03  																		|
% 23.24/7.03  																		|-The branch is then unsatisfiable
% 23.24/7.03  																	|-Branch two:
% 23.24/7.03  																	| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.03  																	| (244)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 23.24/7.03  																	|
% 23.24/7.03  																		+-Applying beta-rule and splitting (192), into two cases.
% 23.24/7.03  																		|-Branch one:
% 23.24/7.03  																		| (241) all_49_0_33 = 0
% 23.24/7.03  																		|
% 23.24/7.03  																			| Equations (241) can reduce 101 to:
% 23.24/7.03  																			| (73) $false
% 23.24/7.03  																			|
% 23.24/7.03  																			|-The branch is then unsatisfiable
% 23.24/7.03  																		|-Branch two:
% 23.24/7.03  																		| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.03  																		| (248)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.03  																		|
% 23.24/7.03  																			+-Applying beta-rule and splitting (205), into two cases.
% 23.24/7.03  																			|-Branch one:
% 23.24/7.03  																			| (249) all_53_0_37 = 0
% 23.24/7.03  																			|
% 23.24/7.03  																				| Equations (249) can reduce 109 to:
% 23.24/7.03  																				| (73) $false
% 23.24/7.03  																				|
% 23.24/7.03  																				|-The branch is then unsatisfiable
% 23.24/7.03  																			|-Branch two:
% 23.24/7.03  																			| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.03  																			| (252)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0))
% 23.24/7.03  																			|
% 23.24/7.03  																				+-Applying beta-rule and splitting (206), into two cases.
% 23.24/7.03  																				|-Branch one:
% 23.24/7.03  																				| (249) all_53_0_37 = 0
% 23.24/7.03  																				|
% 23.24/7.03  																					| Equations (249) can reduce 109 to:
% 23.24/7.03  																					| (73) $false
% 23.24/7.03  																					|
% 23.24/7.03  																					|-The branch is then unsatisfiable
% 23.24/7.03  																				|-Branch two:
% 23.24/7.03  																				| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.03  																				| (256)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.03  																				|
% 23.24/7.03  																					+-Applying beta-rule and splitting (221), into two cases.
% 23.24/7.03  																					|-Branch one:
% 23.24/7.03  																					| (257) all_51_0_35 = 0
% 23.24/7.03  																					|
% 23.24/7.03  																						| Equations (257) can reduce 105 to:
% 23.24/7.03  																						| (73) $false
% 23.24/7.03  																						|
% 23.24/7.03  																						|-The branch is then unsatisfiable
% 23.24/7.03  																					|-Branch two:
% 23.24/7.03  																					| (105)  ~ (all_51_0_35 = 0)
% 23.24/7.03  																					| (260)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.03  																					|
% 23.24/7.03  																						+-Applying beta-rule and splitting (239), into two cases.
% 23.24/7.03  																						|-Branch one:
% 23.24/7.03  																						| (261) all_47_0_31 = 0
% 23.24/7.03  																						|
% 23.24/7.03  																							| Equations (261) can reduce 97 to:
% 23.24/7.03  																							| (73) $false
% 23.24/7.03  																							|
% 23.24/7.03  																							|-The branch is then unsatisfiable
% 23.24/7.03  																						|-Branch two:
% 23.24/7.03  																						| (97)  ~ (all_47_0_31 = 0)
% 23.24/7.03  																						| (264)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0))
% 23.24/7.03  																						|
% 23.24/7.03  																							+-Applying beta-rule and splitting (240), into two cases.
% 23.24/7.03  																							|-Branch one:
% 23.24/7.03  																							| (261) all_47_0_31 = 0
% 23.24/7.03  																							|
% 23.24/7.03  																								| Equations (261) can reduce 97 to:
% 23.24/7.03  																								| (73) $false
% 23.24/7.03  																								|
% 23.24/7.03  																								|-The branch is then unsatisfiable
% 23.24/7.03  																							|-Branch two:
% 23.24/7.03  																							| (97)  ~ (all_47_0_31 = 0)
% 23.24/7.03  																							| (268)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.24/7.03  																							|
% 23.24/7.03  																								+-Applying beta-rule and splitting (183), into two cases.
% 23.24/7.03  																								|-Branch one:
% 23.24/7.03  																								| (241) all_49_0_33 = 0
% 23.24/7.03  																								|
% 23.24/7.03  																									| Equations (241) can reduce 101 to:
% 23.24/7.03  																									| (73) $false
% 23.24/7.03  																									|
% 23.24/7.03  																									|-The branch is then unsatisfiable
% 23.24/7.03  																								|-Branch two:
% 23.24/7.03  																								| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.03  																								| (272) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.03  																								|
% 23.24/7.03  																									+-Applying beta-rule and splitting (184), into two cases.
% 23.24/7.03  																									|-Branch one:
% 23.24/7.03  																									| (241) all_49_0_33 = 0
% 23.24/7.03  																									|
% 23.24/7.03  																										| Equations (241) can reduce 101 to:
% 23.24/7.03  																										| (73) $false
% 23.24/7.03  																										|
% 23.24/7.03  																										|-The branch is then unsatisfiable
% 23.24/7.03  																									|-Branch two:
% 23.24/7.03  																									| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.03  																									| (276) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.03  																									|
% 23.24/7.03  																										+-Applying beta-rule and splitting (185), into two cases.
% 23.24/7.03  																										|-Branch one:
% 23.24/7.03  																										| (241) all_49_0_33 = 0
% 23.24/7.03  																										|
% 23.24/7.03  																											| Equations (241) can reduce 101 to:
% 23.24/7.03  																											| (73) $false
% 23.24/7.03  																											|
% 23.24/7.03  																											|-The branch is then unsatisfiable
% 23.24/7.03  																										|-Branch two:
% 23.24/7.03  																										| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.03  																										| (280) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																										|
% 23.24/7.04  																											+-Applying beta-rule and splitting (230), into two cases.
% 23.24/7.04  																											|-Branch one:
% 23.24/7.04  																											| (241) all_49_0_33 = 0
% 23.24/7.04  																											|
% 23.24/7.04  																												| Equations (241) can reduce 101 to:
% 23.24/7.04  																												| (73) $false
% 23.24/7.04  																												|
% 23.24/7.04  																												|-The branch is then unsatisfiable
% 23.24/7.04  																											|-Branch two:
% 23.24/7.04  																											| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.04  																											| (284) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																											|
% 23.24/7.04  																												+-Applying beta-rule and splitting (231), into two cases.
% 23.24/7.04  																												|-Branch one:
% 23.24/7.04  																												| (249) all_53_0_37 = 0
% 23.24/7.04  																												|
% 23.24/7.04  																													| Equations (249) can reduce 109 to:
% 23.24/7.04  																													| (73) $false
% 23.24/7.04  																													|
% 23.24/7.04  																													|-The branch is then unsatisfiable
% 23.24/7.04  																												|-Branch two:
% 23.24/7.04  																												| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																												| (288) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04  																												|
% 23.24/7.04  																													+-Applying beta-rule and splitting (201), into two cases.
% 23.24/7.04  																													|-Branch one:
% 23.24/7.04  																													| (249) all_53_0_37 = 0
% 23.24/7.04  																													|
% 23.24/7.04  																														| Equations (249) can reduce 109 to:
% 23.24/7.04  																														| (73) $false
% 23.24/7.04  																														|
% 23.24/7.04  																														|-The branch is then unsatisfiable
% 23.24/7.04  																													|-Branch two:
% 23.24/7.04  																													| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																													| (292) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0))
% 23.24/7.04  																													|
% 23.24/7.04  																														+-Applying beta-rule and splitting (197), into two cases.
% 23.24/7.04  																														|-Branch one:
% 23.24/7.04  																														| (249) all_53_0_37 = 0
% 23.24/7.04  																														|
% 23.24/7.04  																															| Equations (249) can reduce 109 to:
% 23.24/7.04  																															| (73) $false
% 23.24/7.04  																															|
% 23.24/7.04  																															|-The branch is then unsatisfiable
% 23.24/7.04  																														|-Branch two:
% 23.24/7.04  																														| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																														| (296) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																														|
% 23.24/7.04  																															+-Applying beta-rule and splitting (193), into two cases.
% 23.24/7.04  																															|-Branch one:
% 23.24/7.04  																															| (249) all_53_0_37 = 0
% 23.24/7.04  																															|
% 23.24/7.04  																																| Equations (249) can reduce 109 to:
% 23.24/7.04  																																| (73) $false
% 23.24/7.04  																																|
% 23.24/7.04  																																|-The branch is then unsatisfiable
% 23.24/7.04  																															|-Branch two:
% 23.24/7.04  																															| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																															| (300) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																															|
% 23.24/7.04  																																+-Applying beta-rule and splitting (194), into two cases.
% 23.24/7.04  																																|-Branch one:
% 23.24/7.04  																																| (249) all_53_0_37 = 0
% 23.24/7.04  																																|
% 23.24/7.04  																																	| Equations (249) can reduce 109 to:
% 23.24/7.04  																																	| (73) $false
% 23.24/7.04  																																	|
% 23.24/7.04  																																	|-The branch is then unsatisfiable
% 23.24/7.04  																																|-Branch two:
% 23.24/7.04  																																| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																| (304) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04  																																|
% 23.24/7.04  																																	+-Applying beta-rule and splitting (203), into two cases.
% 23.24/7.04  																																	|-Branch one:
% 23.24/7.04  																																	| (249) all_53_0_37 = 0
% 23.24/7.04  																																	|
% 23.24/7.04  																																		| Equations (249) can reduce 109 to:
% 23.24/7.04  																																		| (73) $false
% 23.24/7.04  																																		|
% 23.24/7.04  																																		|-The branch is then unsatisfiable
% 23.24/7.04  																																	|-Branch two:
% 23.24/7.04  																																	| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																	| (308) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.04  																																	|
% 23.24/7.04  																																		+-Applying beta-rule and splitting (232), into two cases.
% 23.24/7.04  																																		|-Branch one:
% 23.24/7.04  																																		| (249) all_53_0_37 = 0
% 23.24/7.04  																																		|
% 23.24/7.04  																																			| Equations (249) can reduce 109 to:
% 23.24/7.04  																																			| (73) $false
% 23.24/7.04  																																			|
% 23.24/7.04  																																			|-The branch is then unsatisfiable
% 23.24/7.04  																																		|-Branch two:
% 23.24/7.04  																																		| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																		| (312) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																																		|
% 23.24/7.04  																																			+-Applying beta-rule and splitting (233), into two cases.
% 23.24/7.04  																																			|-Branch one:
% 23.24/7.04  																																			| (249) all_53_0_37 = 0
% 23.24/7.04  																																			|
% 23.24/7.04  																																				| Equations (249) can reduce 109 to:
% 23.24/7.04  																																				| (73) $false
% 23.24/7.04  																																				|
% 23.24/7.04  																																				|-The branch is then unsatisfiable
% 23.24/7.04  																																			|-Branch two:
% 23.24/7.04  																																			| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																			| (316) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04  																																			|
% 23.24/7.04  																																				+-Applying beta-rule and splitting (186), into two cases.
% 23.24/7.04  																																				|-Branch one:
% 23.24/7.04  																																				| (241) all_49_0_33 = 0
% 23.24/7.04  																																				|
% 23.24/7.04  																																					| Equations (241) can reduce 101 to:
% 23.24/7.04  																																					| (73) $false
% 23.24/7.04  																																					|
% 23.24/7.04  																																					|-The branch is then unsatisfiable
% 23.24/7.04  																																				|-Branch two:
% 23.24/7.04  																																				| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.04  																																				| (320) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04  																																				|
% 23.24/7.04  																																					+-Applying beta-rule and splitting (189), into two cases.
% 23.24/7.04  																																					|-Branch one:
% 23.24/7.04  																																					| (241) all_49_0_33 = 0
% 23.24/7.04  																																					|
% 23.24/7.04  																																						| Equations (241) can reduce 101 to:
% 23.24/7.04  																																						| (73) $false
% 23.24/7.04  																																						|
% 23.24/7.04  																																						|-The branch is then unsatisfiable
% 23.24/7.04  																																					|-Branch two:
% 23.24/7.04  																																					| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.04  																																					| (324) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																																					|
% 23.24/7.04  																																						+-Applying beta-rule and splitting (215), into two cases.
% 23.24/7.04  																																						|-Branch one:
% 23.24/7.04  																																						| (257) all_51_0_35 = 0
% 23.24/7.04  																																						|
% 23.24/7.04  																																							| Equations (257) can reduce 105 to:
% 23.24/7.04  																																							| (73) $false
% 23.24/7.04  																																							|
% 23.24/7.04  																																							|-The branch is then unsatisfiable
% 23.24/7.04  																																						|-Branch two:
% 23.24/7.04  																																						| (105)  ~ (all_51_0_35 = 0)
% 23.24/7.04  																																						| (328) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.04  																																						|
% 23.24/7.04  																																							+-Applying beta-rule and splitting (204), into two cases.
% 23.24/7.04  																																							|-Branch one:
% 23.24/7.04  																																							| (249) all_53_0_37 = 0
% 23.24/7.04  																																							|
% 23.24/7.04  																																								| Equations (249) can reduce 109 to:
% 23.24/7.04  																																								| (73) $false
% 23.24/7.04  																																								|
% 23.24/7.04  																																								|-The branch is then unsatisfiable
% 23.24/7.04  																																							|-Branch two:
% 23.24/7.04  																																							| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																							| (332) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.04  																																							|
% 23.24/7.04  																																								+-Applying beta-rule and splitting (195), into two cases.
% 23.24/7.04  																																								|-Branch one:
% 23.24/7.04  																																								| (249) all_53_0_37 = 0
% 23.24/7.04  																																								|
% 23.24/7.04  																																									| Equations (249) can reduce 109 to:
% 23.24/7.04  																																									| (73) $false
% 23.24/7.04  																																									|
% 23.24/7.04  																																									|-The branch is then unsatisfiable
% 23.24/7.04  																																								|-Branch two:
% 23.24/7.04  																																								| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																								| (336) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.04  																																								|
% 23.24/7.04  																																									+-Applying beta-rule and splitting (196), into two cases.
% 23.24/7.04  																																									|-Branch one:
% 23.24/7.04  																																									| (249) all_53_0_37 = 0
% 23.24/7.04  																																									|
% 23.24/7.04  																																										| Equations (249) can reduce 109 to:
% 23.24/7.04  																																										| (73) $false
% 23.24/7.04  																																										|
% 23.24/7.04  																																										|-The branch is then unsatisfiable
% 23.24/7.04  																																									|-Branch two:
% 23.24/7.04  																																									| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.04  																																									| (340) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.04  																																									|
% 23.24/7.04  																																										+-Applying beta-rule and splitting (216), into two cases.
% 23.24/7.04  																																										|-Branch one:
% 23.24/7.04  																																										| (257) all_51_0_35 = 0
% 23.24/7.04  																																										|
% 23.24/7.04  																																											| Equations (257) can reduce 105 to:
% 23.24/7.04  																																											| (73) $false
% 23.24/7.04  																																											|
% 23.24/7.04  																																											|-The branch is then unsatisfiable
% 23.24/7.04  																																										|-Branch two:
% 23.24/7.04  																																										| (105)  ~ (all_51_0_35 = 0)
% 23.24/7.04  																																										| (344) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.24/7.05  																																										|
% 23.24/7.05  																																											+-Applying beta-rule and splitting (217), into two cases.
% 23.24/7.05  																																											|-Branch one:
% 23.24/7.05  																																											| (249) all_53_0_37 = 0
% 23.24/7.05  																																											|
% 23.24/7.05  																																												| Equations (249) can reduce 109 to:
% 23.24/7.05  																																												| (73) $false
% 23.24/7.05  																																												|
% 23.24/7.05  																																												|-The branch is then unsatisfiable
% 23.24/7.05  																																											|-Branch two:
% 23.24/7.05  																																											| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.05  																																											| (348) all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0))
% 23.24/7.05  																																											|
% 23.24/7.05  																																												+-Applying beta-rule and splitting (218), into two cases.
% 23.24/7.05  																																												|-Branch one:
% 23.24/7.05  																																												| (249) all_53_0_37 = 0
% 23.24/7.05  																																												|
% 23.24/7.05  																																													| Equations (249) can reduce 109 to:
% 23.24/7.05  																																													| (73) $false
% 23.24/7.05  																																													|
% 23.24/7.05  																																													|-The branch is then unsatisfiable
% 23.24/7.05  																																												|-Branch two:
% 23.24/7.05  																																												| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.05  																																												| (352) all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 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_5_5) = v0))
% 23.24/7.05  																																												|
% 23.24/7.05  																																													+-Applying beta-rule and splitting (198), into two cases.
% 23.24/7.05  																																													|-Branch one:
% 23.24/7.05  																																													| (249) all_53_0_37 = 0
% 23.24/7.05  																																													|
% 23.24/7.05  																																														| Equations (249) can reduce 109 to:
% 23.24/7.05  																																														| (73) $false
% 23.24/7.05  																																														|
% 23.24/7.05  																																														|-The branch is then unsatisfiable
% 23.24/7.05  																																													|-Branch two:
% 23.24/7.05  																																													| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.05  																																													| (356) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.05  																																													|
% 23.24/7.05  																																														+-Applying beta-rule and splitting (199), into two cases.
% 23.24/7.05  																																														|-Branch one:
% 23.24/7.05  																																														| (249) all_53_0_37 = 0
% 23.24/7.05  																																														|
% 23.24/7.05  																																															| Equations (249) can reduce 109 to:
% 23.24/7.05  																																															| (73) $false
% 23.24/7.05  																																															|
% 23.24/7.05  																																															|-The branch is then unsatisfiable
% 23.24/7.05  																																														|-Branch two:
% 23.24/7.05  																																														| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.05  																																														| (360) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.05  																																														|
% 23.24/7.05  																																															+-Applying beta-rule and splitting (200), into two cases.
% 23.24/7.05  																																															|-Branch one:
% 23.24/7.05  																																															| (249) all_53_0_37 = 0
% 23.24/7.05  																																															|
% 23.24/7.05  																																																| Equations (249) can reduce 109 to:
% 23.24/7.05  																																																| (73) $false
% 23.24/7.05  																																																|
% 23.24/7.05  																																																|-The branch is then unsatisfiable
% 23.24/7.05  																																															|-Branch two:
% 23.24/7.05  																																															| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.05  																																															| (364) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.24/7.05  																																															|
% 23.24/7.05  																																																+-Applying beta-rule and splitting (222), into two cases.
% 23.24/7.05  																																																|-Branch one:
% 23.24/7.05  																																																| (261) all_47_0_31 = 0
% 23.24/7.05  																																																|
% 23.24/7.05  																																																	| Equations (261) can reduce 97 to:
% 23.24/7.05  																																																	| (73) $false
% 23.24/7.05  																																																	|
% 23.24/7.05  																																																	|-The branch is then unsatisfiable
% 23.24/7.05  																																																|-Branch two:
% 23.24/7.05  																																																| (97)  ~ (all_47_0_31 = 0)
% 23.24/7.05  																																																| (368) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0))
% 23.24/7.05  																																																|
% 23.24/7.05  																																																	+-Applying beta-rule and splitting (202), into two cases.
% 23.24/7.05  																																																	|-Branch one:
% 23.24/7.05  																																																	| (249) all_53_0_37 = 0
% 23.24/7.05  																																																	|
% 23.24/7.05  																																																		| Equations (249) can reduce 109 to:
% 23.24/7.05  																																																		| (73) $false
% 23.24/7.05  																																																		|
% 23.24/7.05  																																																		|-The branch is then unsatisfiable
% 23.24/7.05  																																																	|-Branch two:
% 23.24/7.05  																																																	| (109)  ~ (all_53_0_37 = 0)
% 23.24/7.05  																																																	| (372) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0))
% 23.24/7.05  																																																	|
% 23.24/7.05  																																																		+-Applying beta-rule and splitting (236), into two cases.
% 23.24/7.05  																																																		|-Branch one:
% 23.24/7.05  																																																		| (257) all_51_0_35 = 0
% 23.24/7.05  																																																		|
% 23.24/7.05  																																																			| Equations (257) can reduce 105 to:
% 23.24/7.05  																																																			| (73) $false
% 23.24/7.05  																																																			|
% 23.24/7.05  																																																			|-The branch is then unsatisfiable
% 23.24/7.05  																																																		|-Branch two:
% 23.24/7.05  																																																		| (105)  ~ (all_51_0_35 = 0)
% 23.24/7.05  																																																		| (376) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.05  																																																		|
% 23.24/7.05  																																																			+-Applying beta-rule and splitting (187), into two cases.
% 23.24/7.05  																																																			|-Branch one:
% 23.24/7.05  																																																			| (241) all_49_0_33 = 0
% 23.24/7.05  																																																			|
% 23.24/7.05  																																																				| Equations (241) can reduce 101 to:
% 23.24/7.05  																																																				| (73) $false
% 23.24/7.05  																																																				|
% 23.24/7.05  																																																				|-The branch is then unsatisfiable
% 23.24/7.05  																																																			|-Branch two:
% 23.24/7.05  																																																			| (101)  ~ (all_49_0_33 = 0)
% 23.24/7.05  																																																			| (380) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.24/7.05  																																																			|
% 23.24/7.05  																																																				+-Applying beta-rule and splitting (223), into two cases.
% 23.24/7.05  																																																				|-Branch one:
% 23.24/7.05  																																																				| (261) all_47_0_31 = 0
% 23.24/7.05  																																																				|
% 23.24/7.05  																																																					| Equations (261) can reduce 97 to:
% 23.24/7.05  																																																					| (73) $false
% 23.24/7.05  																																																					|
% 23.24/7.05  																																																					|-The branch is then unsatisfiable
% 23.24/7.05  																																																				|-Branch two:
% 23.24/7.05  																																																				| (97)  ~ (all_47_0_31 = 0)
% 23.24/7.05  																																																				| (384) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0))
% 23.38/7.05  																																																				|
% 23.38/7.05  																																																					+-Applying beta-rule and splitting (188), into two cases.
% 23.38/7.05  																																																					|-Branch one:
% 23.38/7.05  																																																					| (241) all_49_0_33 = 0
% 23.38/7.05  																																																					|
% 23.38/7.05  																																																						| Equations (241) can reduce 101 to:
% 23.38/7.05  																																																						| (73) $false
% 23.38/7.05  																																																						|
% 23.38/7.05  																																																						|-The branch is then unsatisfiable
% 23.38/7.05  																																																					|-Branch two:
% 23.38/7.05  																																																					| (101)  ~ (all_49_0_33 = 0)
% 23.38/7.05  																																																					| (388) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.05  																																																					|
% 23.38/7.05  																																																						+-Applying beta-rule and splitting (224), into two cases.
% 23.38/7.05  																																																						|-Branch one:
% 23.38/7.05  																																																						| (261) all_47_0_31 = 0
% 23.38/7.05  																																																						|
% 23.38/7.05  																																																							| Equations (261) can reduce 97 to:
% 23.38/7.05  																																																							| (73) $false
% 23.38/7.05  																																																							|
% 23.38/7.05  																																																							|-The branch is then unsatisfiable
% 23.38/7.05  																																																						|-Branch two:
% 23.38/7.05  																																																						| (97)  ~ (all_47_0_31 = 0)
% 23.38/7.05  																																																						| (392) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.05  																																																						|
% 23.38/7.05  																																																							+-Applying beta-rule and splitting (190), into two cases.
% 23.38/7.05  																																																							|-Branch one:
% 23.38/7.05  																																																							| (241) all_49_0_33 = 0
% 23.38/7.05  																																																							|
% 23.38/7.05  																																																								| Equations (241) can reduce 101 to:
% 23.38/7.05  																																																								| (73) $false
% 23.38/7.05  																																																								|
% 23.38/7.05  																																																								|-The branch is then unsatisfiable
% 23.38/7.05  																																																							|-Branch two:
% 23.38/7.05  																																																							| (101)  ~ (all_49_0_33 = 0)
% 23.38/7.05  																																																							| (396) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.05  																																																							|
% 23.38/7.05  																																																								+-Applying beta-rule and splitting (238), into two cases.
% 23.38/7.05  																																																								|-Branch one:
% 23.38/7.05  																																																								| (257) all_51_0_35 = 0
% 23.38/7.05  																																																								|
% 23.38/7.05  																																																									| Equations (257) can reduce 105 to:
% 23.38/7.05  																																																									| (73) $false
% 23.38/7.05  																																																									|
% 23.38/7.05  																																																									|-The branch is then unsatisfiable
% 23.38/7.05  																																																								|-Branch two:
% 23.38/7.05  																																																								| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.05  																																																								| (400) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.05  																																																								|
% 23.38/7.05  																																																									+-Applying beta-rule and splitting (225), into two cases.
% 23.38/7.05  																																																									|-Branch one:
% 23.38/7.05  																																																									| (261) all_47_0_31 = 0
% 23.38/7.05  																																																									|
% 23.38/7.05  																																																										| Equations (261) can reduce 97 to:
% 23.38/7.05  																																																										| (73) $false
% 23.38/7.05  																																																										|
% 23.38/7.05  																																																										|-The branch is then unsatisfiable
% 23.38/7.05  																																																									|-Branch two:
% 23.38/7.05  																																																									| (97)  ~ (all_47_0_31 = 0)
% 23.38/7.05  																																																									| (404) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.05  																																																									|
% 23.38/7.05  																																																										+-Applying beta-rule and splitting (226), into two cases.
% 23.38/7.05  																																																										|-Branch one:
% 23.38/7.05  																																																										| (261) all_47_0_31 = 0
% 23.38/7.05  																																																										|
% 23.38/7.05  																																																											| Equations (261) can reduce 97 to:
% 23.38/7.05  																																																											| (73) $false
% 23.38/7.05  																																																											|
% 23.38/7.05  																																																											|-The branch is then unsatisfiable
% 23.38/7.05  																																																										|-Branch two:
% 23.38/7.05  																																																										| (97)  ~ (all_47_0_31 = 0)
% 23.38/7.05  																																																										| (408) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 23.38/7.05  																																																										|
% 23.38/7.05  																																																											+-Applying beta-rule and splitting (229), into two cases.
% 23.38/7.05  																																																											|-Branch one:
% 23.38/7.05  																																																											| (261) all_47_0_31 = 0
% 23.38/7.05  																																																											|
% 23.38/7.05  																																																												| Equations (261) can reduce 97 to:
% 23.38/7.05  																																																												| (73) $false
% 23.38/7.05  																																																												|
% 23.38/7.05  																																																												|-The branch is then unsatisfiable
% 23.38/7.05  																																																											|-Branch two:
% 23.38/7.05  																																																											| (97)  ~ (all_47_0_31 = 0)
% 23.38/7.05  																																																											| (412) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.05  																																																											|
% 23.38/7.05  																																																												+-Applying beta-rule and splitting (227), into two cases.
% 23.38/7.05  																																																												|-Branch one:
% 23.38/7.05  																																																												| (261) all_47_0_31 = 0
% 23.38/7.05  																																																												|
% 23.38/7.05  																																																													| Equations (261) can reduce 97 to:
% 23.38/7.05  																																																													| (73) $false
% 23.38/7.05  																																																													|
% 23.38/7.05  																																																													|-The branch is then unsatisfiable
% 23.38/7.05  																																																												|-Branch two:
% 23.38/7.05  																																																												| (97)  ~ (all_47_0_31 = 0)
% 23.38/7.05  																																																												| (416) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 23.38/7.06  																																																												|
% 23.38/7.06  																																																													+-Applying beta-rule and splitting (228), into two cases.
% 23.38/7.06  																																																													|-Branch one:
% 23.38/7.06  																																																													| (261) all_47_0_31 = 0
% 23.38/7.06  																																																													|
% 23.38/7.06  																																																														| Equations (261) can reduce 97 to:
% 23.38/7.06  																																																														| (73) $false
% 23.38/7.06  																																																														|
% 23.38/7.06  																																																														|-The branch is then unsatisfiable
% 23.38/7.06  																																																													|-Branch two:
% 23.38/7.06  																																																													| (97)  ~ (all_47_0_31 = 0)
% 23.38/7.06  																																																													| (420) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.06  																																																													|
% 23.38/7.06  																																																														+-Applying beta-rule and splitting (234), into two cases.
% 23.38/7.06  																																																														|-Branch one:
% 23.38/7.06  																																																														| (249) all_53_0_37 = 0
% 23.38/7.06  																																																														|
% 23.38/7.06  																																																															| Equations (249) can reduce 109 to:
% 23.38/7.06  																																																															| (73) $false
% 23.38/7.06  																																																															|
% 23.38/7.06  																																																															|-The branch is then unsatisfiable
% 23.38/7.06  																																																														|-Branch two:
% 23.38/7.06  																																																														| (109)  ~ (all_53_0_37 = 0)
% 23.38/7.06  																																																														| (424) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.06  																																																														|
% 23.38/7.06  																																																															+-Applying beta-rule and splitting (235), into two cases.
% 23.38/7.06  																																																															|-Branch one:
% 23.38/7.06  																																																															| (257) all_51_0_35 = 0
% 23.38/7.06  																																																															|
% 23.38/7.06  																																																																| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																| (73) $false
% 23.38/7.06  																																																																|
% 23.38/7.06  																																																																|-The branch is then unsatisfiable
% 23.38/7.06  																																																															|-Branch two:
% 23.38/7.06  																																																															| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																															| (428) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06  																																																															|
% 23.38/7.06  																																																																+-Applying beta-rule and splitting (237), into two cases.
% 23.38/7.06  																																																																|-Branch one:
% 23.38/7.06  																																																																| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																|
% 23.38/7.06  																																																																	| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																	| (73) $false
% 23.38/7.06  																																																																	|
% 23.38/7.06  																																																																	|-The branch is then unsatisfiable
% 23.38/7.06  																																																																|-Branch two:
% 23.38/7.06  																																																																| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																| (432) all_47_0_31 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06  																																																																|
% 23.38/7.06  																																																																	+-Applying beta-rule and splitting (207), into two cases.
% 23.38/7.06  																																																																	|-Branch one:
% 23.38/7.06  																																																																	| (249) all_53_0_37 = 0
% 23.38/7.06  																																																																	|
% 23.38/7.06  																																																																		| Equations (249) can reduce 109 to:
% 23.38/7.06  																																																																		| (73) $false
% 23.38/7.06  																																																																		|
% 23.38/7.06  																																																																		|-The branch is then unsatisfiable
% 23.38/7.06  																																																																	|-Branch two:
% 23.38/7.06  																																																																	| (109)  ~ (all_53_0_37 = 0)
% 23.38/7.06  																																																																	| (436) all_0_4_4 = 0 |  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0)
% 23.38/7.06  																																																																	|
% 23.38/7.06  																																																																		+-Applying beta-rule and splitting (208), into two cases.
% 23.38/7.06  																																																																		|-Branch one:
% 23.38/7.06  																																																																		| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																		|
% 23.38/7.06  																																																																			| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																			| (73) $false
% 23.38/7.06  																																																																			|
% 23.38/7.06  																																																																			|-The branch is then unsatisfiable
% 23.38/7.06  																																																																		|-Branch two:
% 23.38/7.06  																																																																		| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																		| (440) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0))
% 23.38/7.06  																																																																		|
% 23.38/7.06  																																																																			+-Applying beta-rule and splitting (209), into two cases.
% 23.38/7.06  																																																																			|-Branch one:
% 23.38/7.06  																																																																			| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																			|
% 23.38/7.06  																																																																				| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																				| (73) $false
% 23.38/7.06  																																																																				|
% 23.38/7.06  																																																																				|-The branch is then unsatisfiable
% 23.38/7.06  																																																																			|-Branch two:
% 23.38/7.06  																																																																			| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																			| (444) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0))
% 23.38/7.06  																																																																			|
% 23.38/7.06  																																																																				+-Applying beta-rule and splitting (210), into two cases.
% 23.38/7.06  																																																																				|-Branch one:
% 23.38/7.06  																																																																				| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																				|
% 23.38/7.06  																																																																					| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																					| (73) $false
% 23.38/7.06  																																																																					|
% 23.38/7.06  																																																																					|-The branch is then unsatisfiable
% 23.38/7.06  																																																																				|-Branch two:
% 23.38/7.06  																																																																				| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																				| (448) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0))
% 23.38/7.06  																																																																				|
% 23.38/7.06  																																																																					+-Applying beta-rule and splitting (213), into two cases.
% 23.38/7.06  																																																																					|-Branch one:
% 23.38/7.06  																																																																					| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																					|
% 23.38/7.06  																																																																						| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																						| (73) $false
% 23.38/7.06  																																																																						|
% 23.38/7.06  																																																																						|-The branch is then unsatisfiable
% 23.38/7.06  																																																																					|-Branch two:
% 23.38/7.06  																																																																					| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																					| (452) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 23.38/7.06  																																																																					|
% 23.38/7.06  																																																																						+-Applying beta-rule and splitting (211), into two cases.
% 23.38/7.06  																																																																						|-Branch one:
% 23.38/7.06  																																																																						| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																						|
% 23.38/7.06  																																																																							| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																							| (73) $false
% 23.38/7.06  																																																																							|
% 23.38/7.06  																																																																							|-The branch is then unsatisfiable
% 23.38/7.06  																																																																						|-Branch two:
% 23.38/7.06  																																																																						| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																						| (456) all_22_0_28 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1, all_0_2_2) = v0))
% 23.38/7.06  																																																																						|
% 23.38/7.06  																																																																							+-Applying beta-rule and splitting (212), into two cases.
% 23.38/7.06  																																																																							|-Branch one:
% 23.38/7.06  																																																																							| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																							|
% 23.38/7.06  																																																																								| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																								| (73) $false
% 23.38/7.06  																																																																								|
% 23.38/7.06  																																																																								|-The branch is then unsatisfiable
% 23.38/7.06  																																																																							|-Branch two:
% 23.38/7.06  																																																																							| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																							| (460) all_20_0_26 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 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_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06  																																																																							|
% 23.38/7.06  																																																																								+-Applying beta-rule and splitting (214), into two cases.
% 23.38/7.06  																																																																								|-Branch one:
% 23.38/7.06  																																																																								| (257) all_51_0_35 = 0
% 23.38/7.06  																																																																								|
% 23.38/7.06  																																																																									| Equations (257) can reduce 105 to:
% 23.38/7.06  																																																																									| (73) $false
% 23.38/7.06  																																																																									|
% 23.38/7.06  																																																																									|-The branch is then unsatisfiable
% 23.38/7.06  																																																																								|-Branch two:
% 23.38/7.06  																																																																								| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.06  																																																																								| (464) all_49_0_33 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 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_47_1_32) = v0))
% 23.38/7.06  																																																																								|
% 23.38/7.06  																																																																									+-Applying beta-rule and splitting (219), into two cases.
% 23.38/7.06  																																																																									|-Branch one:
% 23.38/7.06  																																																																									| (249) all_53_0_37 = 0
% 23.38/7.06  																																																																									|
% 23.38/7.06  																																																																										| Equations (249) can reduce 109 to:
% 23.38/7.06  																																																																										| (73) $false
% 23.38/7.06  																																																																										|
% 23.38/7.06  																																																																										|-The branch is then unsatisfiable
% 23.38/7.06  																																																																									|-Branch two:
% 23.38/7.06  																																																																									| (109)  ~ (all_53_0_37 = 0)
% 23.38/7.06  																																																																									| (468) all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.06  																																																																									|
% 23.38/7.06  																																																																										+-Applying beta-rule and splitting (220), into two cases.
% 23.38/7.06  																																																																										|-Branch one:
% 23.38/7.06  																																																																										| (249) all_53_0_37 = 0
% 23.38/7.06  																																																																										|
% 23.38/7.06  																																																																											| Equations (249) can reduce 109 to:
% 23.38/7.06  																																																																											| (73) $false
% 23.38/7.06  																																																																											|
% 23.38/7.06  																																																																											|-The branch is then unsatisfiable
% 23.38/7.06  																																																																										|-Branch two:
% 23.38/7.06  																																																																										| (109)  ~ (all_53_0_37 = 0)
% 23.38/7.06  																																																																										| (472) all_51_0_35 = 0 |  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.06  																																																																										|
% 23.38/7.06  																																																																											+-Applying beta-rule and splitting (272), into two cases.
% 23.38/7.06  																																																																											|-Branch one:
% 23.38/7.06  																																																																											| (120) all_22_0_28 = 0
% 23.38/7.06  																																																																											|
% 23.38/7.06  																																																																												| Equations (120) can reduce 63 to:
% 23.38/7.06  																																																																												| (73) $false
% 23.38/7.06  																																																																												|
% 23.38/7.06  																																																																												|-The branch is then unsatisfiable
% 23.38/7.06  																																																																											|-Branch two:
% 23.38/7.06  																																																																											| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.06  																																																																											| (476)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.06  																																																																											|
% 23.38/7.06  																																																																												+-Applying beta-rule and splitting (276), into two cases.
% 23.38/7.06  																																																																												|-Branch one:
% 23.38/7.06  																																																																												| (120) all_22_0_28 = 0
% 23.38/7.06  																																																																												|
% 23.38/7.06  																																																																													| Equations (120) can reduce 63 to:
% 23.38/7.06  																																																																													| (73) $false
% 23.38/7.06  																																																																													|
% 23.38/7.06  																																																																													|-The branch is then unsatisfiable
% 23.38/7.06  																																																																												|-Branch two:
% 23.38/7.06  																																																																												| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.06  																																																																												| (480)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.06  																																																																												|
% 23.38/7.06  																																																																													+-Applying beta-rule and splitting (300), into two cases.
% 23.38/7.06  																																																																													|-Branch one:
% 23.38/7.06  																																																																													| (120) all_22_0_28 = 0
% 23.38/7.06  																																																																													|
% 23.38/7.06  																																																																														| Equations (120) can reduce 63 to:
% 23.38/7.06  																																																																														| (73) $false
% 23.38/7.06  																																																																														|
% 23.38/7.06  																																																																														|-The branch is then unsatisfiable
% 23.38/7.06  																																																																													|-Branch two:
% 23.38/7.06  																																																																													| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.06  																																																																													| (484)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07  																																																																													|
% 23.38/7.07  																																																																														+-Applying beta-rule and splitting (304), into two cases.
% 23.38/7.07  																																																																														|-Branch one:
% 23.38/7.07  																																																																														| (120) all_22_0_28 = 0
% 23.38/7.07  																																																																														|
% 23.38/7.07  																																																																															| Equations (120) can reduce 63 to:
% 23.38/7.07  																																																																															| (73) $false
% 23.38/7.07  																																																																															|
% 23.38/7.07  																																																																															|-The branch is then unsatisfiable
% 23.38/7.07  																																																																														|-Branch two:
% 23.38/7.07  																																																																														| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.07  																																																																														| (488)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07  																																																																														|
% 23.38/7.07  																																																																															+-Applying beta-rule and splitting (324), into two cases.
% 23.38/7.07  																																																																															|-Branch one:
% 23.38/7.07  																																																																															| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																															|
% 23.38/7.07  																																																																																| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																| (73) $false
% 23.38/7.07  																																																																																|
% 23.38/7.07  																																																																																|-The branch is then unsatisfiable
% 23.38/7.07  																																																																															|-Branch two:
% 23.38/7.07  																																																																															| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																															| (492)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07  																																																																															|
% 23.38/7.07  																																																																																+-Applying beta-rule and splitting (348), into two cases.
% 23.38/7.07  																																																																																|-Branch one:
% 23.38/7.07  																																																																																| (257) all_51_0_35 = 0
% 23.38/7.07  																																																																																|
% 23.38/7.07  																																																																																	| Equations (257) can reduce 105 to:
% 23.38/7.07  																																																																																	| (73) $false
% 23.38/7.07  																																																																																	|
% 23.38/7.07  																																																																																	|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																|-Branch two:
% 23.38/7.07  																																																																																| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.07  																																																																																| (496)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0))
% 23.38/7.07  																																																																																|
% 23.38/7.07  																																																																																	+-Applying beta-rule and splitting (360), into two cases.
% 23.38/7.07  																																																																																	|-Branch one:
% 23.38/7.07  																																																																																	| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																	|
% 23.38/7.07  																																																																																		| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																		| (73) $false
% 23.38/7.07  																																																																																		|
% 23.38/7.07  																																																																																		|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																	|-Branch two:
% 23.38/7.07  																																																																																	| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																	| (500)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07  																																																																																	|
% 23.38/7.07  																																																																																		+-Applying beta-rule and splitting (364), into two cases.
% 23.38/7.07  																																																																																		|-Branch one:
% 23.38/7.07  																																																																																		| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																		|
% 23.38/7.07  																																																																																			| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																			| (73) $false
% 23.38/7.07  																																																																																			|
% 23.38/7.07  																																																																																			|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																		|-Branch two:
% 23.38/7.07  																																																																																		| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																		| (504)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07  																																																																																		|
% 23.38/7.07  																																																																																			+-Applying beta-rule and splitting (368), into two cases.
% 23.38/7.07  																																																																																			|-Branch one:
% 23.38/7.07  																																																																																			| (120) all_22_0_28 = 0
% 23.38/7.07  																																																																																			|
% 23.38/7.07  																																																																																				| Equations (120) can reduce 63 to:
% 23.38/7.07  																																																																																				| (73) $false
% 23.38/7.07  																																																																																				|
% 23.38/7.07  																																																																																				|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																			|-Branch two:
% 23.38/7.07  																																																																																			| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.07  																																																																																			| (508)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_6_6, all_47_1_32) = v0))
% 23.38/7.07  																																																																																			|
% 23.38/7.07  																																																																																				+-Applying beta-rule and splitting (380), into two cases.
% 23.38/7.07  																																																																																				|-Branch one:
% 23.38/7.07  																																																																																				| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																				|
% 23.38/7.07  																																																																																					| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																					| (73) $false
% 23.38/7.07  																																																																																					|
% 23.38/7.07  																																																																																					|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																				|-Branch two:
% 23.38/7.07  																																																																																				| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																				| (512)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.07  																																																																																				|
% 23.38/7.07  																																																																																					+-Applying beta-rule and splitting (388), into two cases.
% 23.38/7.07  																																																																																					|-Branch one:
% 23.38/7.07  																																																																																					| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																					|
% 23.38/7.07  																																																																																						| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																						| (73) $false
% 23.38/7.07  																																																																																						|
% 23.38/7.07  																																																																																						|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																					|-Branch two:
% 23.38/7.07  																																																																																					| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																					| (516)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07  																																																																																					|
% 23.38/7.07  																																																																																						+-Applying beta-rule and splitting (404), into two cases.
% 23.38/7.07  																																																																																						|-Branch one:
% 23.38/7.07  																																																																																						| (120) all_22_0_28 = 0
% 23.38/7.07  																																																																																						|
% 23.38/7.07  																																																																																							| Equations (120) can reduce 63 to:
% 23.38/7.07  																																																																																							| (73) $false
% 23.38/7.07  																																																																																							|
% 23.38/7.07  																																																																																							|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																						|-Branch two:
% 23.38/7.07  																																																																																						| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.07  																																																																																						| (520)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_6_6) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_6_6) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.07  																																																																																						|
% 23.38/7.07  																																																																																							+-Applying beta-rule and splitting (408), into two cases.
% 23.38/7.07  																																																																																							|-Branch one:
% 23.38/7.07  																																																																																							| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																							|
% 23.38/7.07  																																																																																								| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																								| (73) $false
% 23.38/7.07  																																																																																								|
% 23.38/7.07  																																																																																								|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																							|-Branch two:
% 23.38/7.07  																																																																																							| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																							| (524)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0))
% 23.38/7.07  																																																																																							|
% 23.38/7.07  																																																																																								+-Applying beta-rule and splitting (416), into two cases.
% 23.38/7.07  																																																																																								|-Branch one:
% 23.38/7.07  																																																																																								| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																								|
% 23.38/7.07  																																																																																									| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																									| (73) $false
% 23.38/7.07  																																																																																									|
% 23.38/7.07  																																																																																									|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																								|-Branch two:
% 23.38/7.07  																																																																																								| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																								| (528)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0))
% 23.38/7.07  																																																																																								|
% 23.38/7.07  																																																																																									+-Applying beta-rule and splitting (436), into two cases.
% 23.38/7.07  																																																																																									|-Branch one:
% 23.38/7.07  																																																																																									| (72) all_0_4_4 = 0
% 23.38/7.07  																																																																																									|
% 23.38/7.07  																																																																																										| Equations (72) can reduce 45 to:
% 23.38/7.07  																																																																																										| (73) $false
% 23.38/7.07  																																																																																										|
% 23.38/7.07  																																																																																										|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																									|-Branch two:
% 23.38/7.07  																																																																																									| (45)  ~ (all_0_4_4 = 0)
% 23.38/7.07  																																																																																									| (532)  ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = v0)
% 23.38/7.07  																																																																																									|
% 23.38/7.07  																																																																																										| Instantiating (532) with all_418_0_790 yields:
% 23.38/7.07  																																																																																										| (533)  ~ (all_418_0_790 = 0) & apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790
% 23.38/7.07  																																																																																										|
% 23.38/7.07  																																																																																										| Applying alpha-rule on (533) yields:
% 23.38/7.07  																																																																																										| (534)  ~ (all_418_0_790 = 0)
% 23.38/7.07  																																																																																										| (535) apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790
% 23.38/7.07  																																																																																										|
% 23.38/7.07  																																																																																										+-Applying beta-rule and splitting (440), into two cases.
% 23.38/7.07  																																																																																										|-Branch one:
% 23.38/7.07  																																																																																										| (120) all_22_0_28 = 0
% 23.38/7.07  																																																																																										|
% 23.38/7.07  																																																																																											| Equations (120) can reduce 63 to:
% 23.38/7.07  																																																																																											| (73) $false
% 23.38/7.07  																																																																																											|
% 23.38/7.07  																																																																																											|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																										|-Branch two:
% 23.38/7.07  																																																																																										| (63)  ~ (all_22_0_28 = 0)
% 23.38/7.07  																																																																																										| (539)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, 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_1_1) = v0))
% 23.38/7.07  																																																																																										|
% 23.38/7.07  																																																																																											| Instantiating (539) with all_423_0_791 yields:
% 23.38/7.07  																																																																																											| (540) (all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (all_423_0_791 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791) | ( ~ (all_423_0_791 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791)
% 23.38/7.07  																																																																																											|
% 23.38/7.07  																																																																																											+-Applying beta-rule and splitting (460), into two cases.
% 23.38/7.07  																																																																																											|-Branch one:
% 23.38/7.07  																																																																																											| (124) all_20_0_26 = 0
% 23.38/7.07  																																																																																											|
% 23.38/7.07  																																																																																												| Equations (124) can reduce 59 to:
% 23.38/7.07  																																																																																												| (73) $false
% 23.38/7.07  																																																																																												|
% 23.38/7.07  																																																																																												|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																											|-Branch two:
% 23.38/7.07  																																																																																											| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.07  																																																																																											| (544)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 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_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.07  																																																																																											|
% 23.38/7.07  																																																																																												+-Applying beta-rule and splitting (468), into two cases.
% 23.38/7.07  																																																																																												|-Branch one:
% 23.38/7.07  																																																																																												| (257) all_51_0_35 = 0
% 23.38/7.07  																																																																																												|
% 23.38/7.07  																																																																																													| Equations (257) can reduce 105 to:
% 23.38/7.07  																																																																																													| (73) $false
% 23.38/7.07  																																																																																													|
% 23.38/7.07  																																																																																													|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																												|-Branch two:
% 23.38/7.07  																																																																																												| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.07  																																																																																												| (548)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.07  																																																																																												|
% 23.38/7.07  																																																																																													+-Applying beta-rule and splitting (472), into two cases.
% 23.38/7.07  																																																																																													|-Branch one:
% 23.38/7.07  																																																																																													| (257) all_51_0_35 = 0
% 23.38/7.07  																																																																																													|
% 23.38/7.07  																																																																																														| Equations (257) can reduce 105 to:
% 23.38/7.07  																																																																																														| (73) $false
% 23.38/7.07  																																																																																														|
% 23.38/7.07  																																																																																														|-The branch is then unsatisfiable
% 23.38/7.07  																																																																																													|-Branch two:
% 23.38/7.07  																																																																																													| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.08  																																																																																													| (552)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0))
% 23.38/7.08  																																																																																													|
% 23.38/7.08  																																																																																														+-Applying beta-rule and splitting (164), into two cases.
% 23.38/7.08  																																																																																														|-Branch one:
% 23.38/7.08  																																																																																														| (553) (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0)
% 23.38/7.08  																																																																																														|
% 23.38/7.08  																																																																																															+-Applying beta-rule and splitting (553), into two cases.
% 23.38/7.08  																																																																																															|-Branch one:
% 23.38/7.08  																																																																																															| (554) all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08  																																																																																															|
% 23.38/7.08  																																																																																																| Applying alpha-rule on (554) yields:
% 23.38/7.08  																																																																																																| (555) all_110_0_51 = 0
% 23.38/7.08  																																																																																																| (556) apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																| Instantiating formula (43) with all_0_1_1, all_0_6_6, 0, all_418_0_790 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790, apart_point_and_line(all_0_1_1, all_0_6_6) = 0, yields:
% 23.38/7.08  																																																																																																| (557) all_418_0_790 = 0
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																| Equations (557) can reduce 534 to:
% 23.38/7.08  																																																																																																| (73) $false
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																															|-Branch two:
% 23.38/7.08  																																																																																															| (559) all_110_0_51 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0
% 23.38/7.08  																																																																																															|
% 23.38/7.08  																																																																																																| Applying alpha-rule on (559) yields:
% 23.38/7.08  																																																																																																| (555) all_110_0_51 = 0
% 23.38/7.08  																																																																																																| (561) apart_point_and_line(all_0_1_1, all_0_7_7) = 0
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																+-Applying beta-rule and splitting (352), into two cases.
% 23.38/7.08  																																																																																																|-Branch one:
% 23.38/7.08  																																																																																																| (257) all_51_0_35 = 0
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																	| Equations (257) can reduce 105 to:
% 23.38/7.08  																																																																																																	| (73) $false
% 23.38/7.08  																																																																																																	|
% 23.38/7.08  																																																																																																	|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																|-Branch two:
% 23.38/7.08  																																																																																																| (105)  ~ (all_51_0_35 = 0)
% 23.38/7.08  																																																																																																| (565)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 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_5_5) = v0))
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																	| Instantiating formula (43) with all_0_1_1, all_0_7_7, 0, all_51_0_35 and discharging atoms apart_point_and_line(all_0_1_1, all_0_7_7) = all_51_0_35, apart_point_and_line(all_0_1_1, all_0_7_7) = 0, yields:
% 23.38/7.08  																																																																																																	| (257) all_51_0_35 = 0
% 23.38/7.08  																																																																																																	|
% 23.38/7.08  																																																																																																	| Equations (257) can reduce 105 to:
% 23.38/7.08  																																																																																																	| (73) $false
% 23.38/7.08  																																																																																																	|
% 23.38/7.08  																																																																																																	|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																														|-Branch two:
% 23.38/7.08  																																																																																														| (568)  ~ (all_110_0_51 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51
% 23.38/7.08  																																																																																														|
% 23.38/7.08  																																																																																															| Applying alpha-rule on (568) yields:
% 23.38/7.08  																																																																																															| (569)  ~ (all_110_0_51 = 0)
% 23.38/7.08  																																																																																															| (570) distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51
% 23.38/7.08  																																																																																															|
% 23.38/7.08  																																																																																															+-Applying beta-rule and splitting (296), into two cases.
% 23.38/7.08  																																																																																															|-Branch one:
% 23.38/7.08  																																																																																															| (124) all_20_0_26 = 0
% 23.38/7.08  																																																																																															|
% 23.38/7.08  																																																																																																| Equations (124) can reduce 59 to:
% 23.38/7.08  																																																																																																| (73) $false
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																															|-Branch two:
% 23.38/7.08  																																																																																															| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.08  																																																																																															| (574)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0))
% 23.38/7.08  																																																																																															|
% 23.38/7.08  																																																																																																+-Applying beta-rule and splitting (356), into two cases.
% 23.38/7.08  																																																																																																|-Branch one:
% 23.38/7.08  																																																																																																| (124) all_20_0_26 = 0
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																	| Equations (124) can reduce 59 to:
% 23.38/7.08  																																																																																																	| (73) $false
% 23.38/7.08  																																																																																																	|
% 23.38/7.08  																																																																																																	|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																|-Branch two:
% 23.38/7.08  																																																																																																| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.08  																																																																																																| (578)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.08  																																																																																																|
% 23.38/7.08  																																																																																																	+-Applying beta-rule and splitting (396), into two cases.
% 23.38/7.08  																																																																																																	|-Branch one:
% 23.38/7.08  																																																																																																	| (124) all_20_0_26 = 0
% 23.38/7.08  																																																																																																	|
% 23.38/7.08  																																																																																																		| Equations (124) can reduce 59 to:
% 23.38/7.08  																																																																																																		| (73) $false
% 23.38/7.08  																																																																																																		|
% 23.38/7.08  																																																																																																		|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																	|-Branch two:
% 23.38/7.08  																																																																																																	| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.08  																																																																																																	| (582)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_7_7) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_7_7, all_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0))
% 23.38/7.08  																																																																																																	|
% 23.38/7.08  																																																																																																		+-Applying beta-rule and splitting (412), into two cases.
% 23.38/7.08  																																																																																																		|-Branch one:
% 23.38/7.08  																																																																																																		| (124) all_20_0_26 = 0
% 23.38/7.08  																																																																																																		|
% 23.38/7.08  																																																																																																			| Equations (124) can reduce 59 to:
% 23.38/7.08  																																																																																																			| (73) $false
% 23.38/7.08  																																																																																																			|
% 23.38/7.08  																																																																																																			|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																		|-Branch two:
% 23.38/7.08  																																																																																																		| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.08  																																																																																																		| (586)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (v0 = 0) & distinct_lines(all_47_1_32, all_0_7_7) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.08  																																																																																																		|
% 23.38/7.08  																																																																																																			+-Applying beta-rule and splitting (420), into two cases.
% 23.38/7.08  																																																																																																			|-Branch one:
% 23.38/7.08  																																																																																																			| (124) all_20_0_26 = 0
% 23.38/7.08  																																																																																																			|
% 23.38/7.08  																																																																																																				| Equations (124) can reduce 59 to:
% 23.38/7.08  																																																																																																				| (73) $false
% 23.38/7.08  																																																																																																				|
% 23.38/7.08  																																																																																																				|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																			|-Branch two:
% 23.38/7.08  																																																																																																			| (59)  ~ (all_20_0_26 = 0)
% 23.38/7.08  																																																																																																			| (590)  ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_47_1_32) = 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_47_1_32) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0))
% 23.38/7.08  																																																																																																			|
% 23.38/7.08  																																																																																																				+-Applying beta-rule and splitting (540), into two cases.
% 23.38/7.08  																																																																																																				|-Branch one:
% 23.38/7.08  																																																																																																				| (591) (all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0) | ( ~ (all_423_0_791 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791)
% 23.38/7.08  																																																																																																				|
% 23.38/7.08  																																																																																																					+-Applying beta-rule and splitting (591), into two cases.
% 23.38/7.08  																																																																																																					|-Branch one:
% 23.38/7.08  																																																																																																					| (592) (all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0) | (all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0)
% 23.38/7.08  																																																																																																					|
% 23.38/7.08  																																																																																																						+-Applying beta-rule and splitting (592), into two cases.
% 23.38/7.08  																																																																																																						|-Branch one:
% 23.38/7.08  																																																																																																						| (593) all_423_0_791 = 0 & apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																							| Applying alpha-rule on (593) yields:
% 23.38/7.08  																																																																																																							| (594) all_423_0_791 = 0
% 23.38/7.08  																																																																																																							| (556) apart_point_and_line(all_0_1_1, all_0_6_6) = 0
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							| Instantiating formula (43) with all_0_1_1, all_0_6_6, 0, all_418_0_790 and discharging atoms apart_point_and_line(all_0_1_1, all_0_6_6) = all_418_0_790, apart_point_and_line(all_0_1_1, all_0_6_6) = 0, yields:
% 23.38/7.08  																																																																																																							| (557) all_418_0_790 = 0
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							| Equations (557) can reduce 534 to:
% 23.38/7.08  																																																																																																							| (73) $false
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																						|-Branch two:
% 23.38/7.08  																																																																																																						| (598) all_423_0_791 = 0 & apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																							| Applying alpha-rule on (598) yields:
% 23.38/7.08  																																																																																																							| (594) all_423_0_791 = 0
% 23.38/7.08  																																																																																																							| (600) apart_point_and_line(all_0_2_2, all_0_7_7) = 0
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							| Instantiating formula (43) with all_0_2_2, all_0_7_7, 0, all_20_0_26 and discharging atoms apart_point_and_line(all_0_2_2, all_0_7_7) = all_20_0_26, apart_point_and_line(all_0_2_2, all_0_7_7) = 0, yields:
% 23.38/7.08  																																																																																																							| (124) all_20_0_26 = 0
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							| Equations (124) can reduce 59 to:
% 23.38/7.08  																																																																																																							| (73) $false
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																					|-Branch two:
% 23.38/7.08  																																																																																																					| (603)  ~ (all_423_0_791 = 0) & distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791
% 23.38/7.08  																																																																																																					|
% 23.38/7.08  																																																																																																						| Applying alpha-rule on (603) yields:
% 23.38/7.08  																																																																																																						| (604)  ~ (all_423_0_791 = 0)
% 23.38/7.08  																																																																																																						| (605) distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																						| Instantiating formula (17) with all_0_6_6, all_0_7_7, all_110_0_51, all_423_0_791 and discharging atoms distinct_lines(all_0_6_6, all_0_7_7) = all_423_0_791, distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51, yields:
% 23.38/7.08  																																																																																																						| (606) all_423_0_791 = all_110_0_51
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																						| Equations (606) can reduce 604 to:
% 23.38/7.08  																																																																																																						| (569)  ~ (all_110_0_51 = 0)
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																						| From (606) and (605) follows:
% 23.38/7.08  																																																																																																						| (570) distinct_lines(all_0_6_6, all_0_7_7) = all_110_0_51
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																						| Instantiating formula (5) with all_110_0_51, 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_110_0_51, yields:
% 23.38/7.08  																																																																																																						| (609) all_110_0_51 = 0 | convergent_lines(all_0_7_7, all_0_7_7) = 0
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																						+-Applying beta-rule and splitting (609), into two cases.
% 23.38/7.08  																																																																																																						|-Branch one:
% 23.38/7.08  																																																																																																						| (610) convergent_lines(all_0_7_7, all_0_7_7) = 0
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																							| Instantiating formula (3) with all_0_7_7 and discharging atoms convergent_lines(all_0_7_7, all_0_7_7) = 0, yields:
% 23.38/7.08  																																																																																																							| (611) $false
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																						|-Branch two:
% 23.38/7.08  																																																																																																						| (612)  ~ (convergent_lines(all_0_7_7, all_0_7_7) = 0)
% 23.38/7.08  																																																																																																						| (555) all_110_0_51 = 0
% 23.38/7.08  																																																																																																						|
% 23.38/7.08  																																																																																																							| Equations (555) can reduce 569 to:
% 23.38/7.08  																																																																																																							| (73) $false
% 23.38/7.08  																																																																																																							|
% 23.38/7.08  																																																																																																							|-The branch is then unsatisfiable
% 23.38/7.08  																																																																																																				|-Branch two:
% 23.38/7.08  																																																																																																				| (615)  ~ (all_423_0_791 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791
% 23.38/7.08  																																																																																																				|
% 23.38/7.08  																																																																																																					| Applying alpha-rule on (615) yields:
% 23.38/7.08  																																																																																																					| (604)  ~ (all_423_0_791 = 0)
% 23.38/7.08  																																																																																																					| (617) distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791
% 23.38/7.08  																																																																																																					|
% 23.38/7.08  																																																																																																					| Instantiating formula (14) with all_0_2_2, all_0_1_1, all_423_0_791, 0 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_423_0_791, distinct_points(all_0_2_2, all_0_1_1) = 0, yields:
% 23.38/7.08  																																																																																																					| (594) all_423_0_791 = 0
% 23.38/7.08  																																																																																																					|
% 23.38/7.08  																																																																																																					| Equations (594) can reduce 604 to:
% 23.38/7.08  																																																																																																					| (73) $false
% 23.38/7.08  																																																																																																					|
% 23.38/7.08  																																																																																																					|-The branch is then unsatisfiable
% 23.38/7.09  				|-Branch two:
% 23.38/7.09  				| (620)  ~ (all_56_0_40 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40
% 23.38/7.09  				|
% 23.38/7.09  					| Applying alpha-rule on (620) yields:
% 23.38/7.09  					| (118)  ~ (all_56_0_40 = 0)
% 23.38/7.09  					| (622) convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40
% 23.38/7.09  					|
% 23.38/7.09  					| Instantiating formula (19) with all_0_7_7, all_0_5_5, all_56_0_40, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = all_56_0_40, convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 23.38/7.09  					| (623) all_56_0_40 = 0
% 23.38/7.09  					|
% 23.38/7.09  					| Equations (623) can reduce 118 to:
% 23.38/7.09  					| (73) $false
% 23.38/7.09  					|
% 23.38/7.09  					|-The branch is then unsatisfiable
% 23.38/7.09  			|-Branch two:
% 23.38/7.09  			| (625)  ~ (all_55_0_39 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39
% 23.38/7.09  			|
% 23.38/7.09  				| Applying alpha-rule on (625) yields:
% 23.38/7.09  				| (115)  ~ (all_55_0_39 = 0)
% 23.38/7.09  				| (627) convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39
% 23.38/7.09  				|
% 23.38/7.09  				| Instantiating formula (19) with all_0_7_7, all_0_5_5, all_55_0_39, 0 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = all_55_0_39, convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 23.38/7.09  				| (628) all_55_0_39 = 0
% 23.38/7.09  				|
% 23.38/7.09  				| Equations (628) can reduce 115 to:
% 23.38/7.09  				| (73) $false
% 23.38/7.09  				|
% 23.38/7.09  				|-The branch is then unsatisfiable
% 23.38/7.09  	|-Branch two:
% 23.38/7.09  	| (630)  ~ (all_0_3_3 = 0) & convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3
% 23.38/7.09  	|
% 23.38/7.09  		| Applying alpha-rule on (630) yields:
% 23.38/7.09  		| (631)  ~ (all_0_3_3 = 0)
% 23.38/7.09  		| (632) convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3
% 23.38/7.09  		|
% 23.38/7.09  		| Instantiating formula (19) with all_0_7_7, all_0_5_5, 0, all_0_3_3 and discharging atoms convergent_lines(all_0_7_7, all_0_5_5) = all_0_3_3, convergent_lines(all_0_7_7, all_0_5_5) = 0, yields:
% 23.38/7.09  		| (633) all_0_3_3 = 0
% 23.38/7.09  		|
% 23.38/7.09  		| Equations (633) can reduce 631 to:
% 23.38/7.09  		| (73) $false
% 23.38/7.09  		|
% 23.38/7.09  		|-The branch is then unsatisfiable
% 23.38/7.09  |-Branch two:
% 23.38/7.09  | (635)  ~ (convergent_lines(all_0_7_7, all_0_5_5) = 0)
% 23.38/7.09  | (72) all_0_4_4 = 0
% 23.38/7.09  |
% 23.38/7.09  	| Equations (72) can reduce 45 to:
% 23.38/7.09  	| (73) $false
% 23.38/7.09  	|
% 23.38/7.09  	|-The branch is then unsatisfiable
% 23.38/7.09  % SZS output end Proof for theBenchmark
% 23.38/7.09  
% 23.38/7.09  6497ms
%------------------------------------------------------------------------------