TSTP Solution File: GEO187+3 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 03:48:24 EDT 2022
% Result : Theorem 16.74s 4.51s
% Output : Proof 40.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 05:19:28 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.58 ____ _
% 0.19/0.58 ___ / __ \_____(_)___ ________ __________
% 0.19/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.19/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.19/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.19/0.58
% 0.19/0.58 A Theorem Prover for First-Order Logic
% 0.19/0.58 (ePrincess v.1.0)
% 0.19/0.58
% 0.19/0.58 (c) Philipp Rümmer, 2009-2015
% 0.19/0.58 (c) Peter Backeman, 2014-2015
% 0.19/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.19/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.19/0.58 Bug reports to peter@backeman.se
% 0.19/0.58
% 0.19/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.19/0.58
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.75/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.79/0.96 Prover 0: Preprocessing ...
% 2.22/1.17 Prover 0: Warning: ignoring some quantifiers
% 2.52/1.20 Prover 0: Constructing countermodel ...
% 13.91/3.88 Prover 0: gave up
% 13.91/3.88 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 14.06/3.92 Prover 1: Preprocessing ...
% 14.52/4.04 Prover 1: Constructing countermodel ...
% 14.85/4.08 Prover 1: gave up
% 14.85/4.08 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 14.85/4.12 Prover 2: Preprocessing ...
% 15.57/4.30 Prover 2: Warning: ignoring some quantifiers
% 15.57/4.31 Prover 2: Constructing countermodel ...
% 16.74/4.51 Prover 2: proved (428ms)
% 16.74/4.51
% 16.74/4.51 No countermodel exists, formula is valid
% 16.74/4.51 % SZS status Theorem for theBenchmark
% 16.74/4.51
% 16.74/4.51 Generating proof ... Warning: ignoring some quantifiers
% 39.36/12.40 found it (size 1126)
% 39.36/12.40
% 39.36/12.40 % SZS output start Proof for theBenchmark
% 39.36/12.40 Assumed formulas after preprocessing and simplification:
% 39.36/12.40 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (incident_point_and_line(v1, v4) = 0 & incident_point_and_line(v0, v4) = 0 & line_connecting(v2, v3) = v4 & line_connecting(v0, v1) = v5 & distinct_points(v2, v3) = 0 & distinct_points(v0, v1) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (unorthogonal_lines(v10, v11) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ~ (distinct_lines(v9, v10) = 0) | ? [v14] : ((v14 = 0 & unorthogonal_lines(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v9) = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (unorthogonal_lines(v10, v11) = v13) | ~ (apart_point_and_line(v8, v9) = v12) | ? [v14] : ((v14 = 0 & unorthogonal_lines(v9, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v14 = 0) & distinct_lines(v9, v10) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (unorthogonal_lines(v9, v11) = v13) | ~ (apart_point_and_line(v8, v10) = v12) | ? [v14] : ((v14 = 0 & unorthogonal_lines(v10, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v9) = 0) | ( ~ (v14 = 0) & distinct_lines(v9, v10) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = 0 | ~ (unorthogonal_lines(v9, v11) = v13) | ~ (apart_point_and_line(v8, v9) = v12) | ~ (distinct_lines(v9, v10) = 0) | ? [v14] : ((v14 = 0 & unorthogonal_lines(v10, v11) = 0) | (v14 = 0 & apart_point_and_line(v8, v10) = 0))) & ! [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 | ~ (unorthogonal_lines(v8, v10) = v12) | ~ (unorthogonal_lines(v8, v9) = v11) | ? [v13] : ( ~ (v13 = 0) & convergent_lines(v9, v10) = v13)) & ! [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) | ~ (apart_point_and_line(v8, v9) = v11) | ? [v13] : ((v13 = 0 & convergent_lines(v9, v10) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = 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 | ~ (apart_point_and_line(v8, v10) = v11) | ~ (convergent_lines(v9, v10) = v12) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (apart_point_and_line(v8, v9) = v11) | ~ (convergent_lines(v9, v10) = v12) | ? [v13] : ((v13 = 0 & apart_point_and_line(v8, v10) = 0) | ( ~ (v13 = 0) & distinct_lines(v9, v10) = 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] : ! [v12] : ( ~ (unorthogonal_lines(v9, v10) = v12) | ~ (unorthogonal_lines(v8, v10) = v11) | ? [v13] : ((v13 = 0 & v12 = 0 & convergent_lines(v9, v10) = 0) | (v13 = 0 & v11 = 0 & convergent_lines(v8, v10) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v8, v9) = v13) | ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unorthogonal_lines(v9, v10) = v12) | ~ (convergent_lines(v8, v10) = v11) | ? [v13] : ((v13 = 0 & v12 = 0 & convergent_lines(v9, v10) = 0) | (v13 = 0 & v11 = 0 & unorthogonal_lines(v8, v10) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v8, v9) = v13) | ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unorthogonal_lines(v8, v10) = v12) | ~ (unorthogonal_lines(v8, v9) = v11) | ? [v13] : ((v13 = 0 & v12 = 0 & convergent_lines(v8, v10) = 0) | (v13 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v9, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v9, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unorthogonal_lines(v8, v10) = v12) | ~ (convergent_lines(v8, v9) = v11) | ? [v13] : ((v13 = 0 & v12 = 0 & convergent_lines(v8, v10) = 0) | (v13 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v9, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v9, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unorthogonal_lines(v8, v10) = v11) | ~ (convergent_lines(v9, v10) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & v11 = 0 & convergent_lines(v8, v10) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v8, v9) = v13) | ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (unorthogonal_lines(v8, v9) = v11) | ~ (convergent_lines(v8, v10) = v12) | ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v9, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v9, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (convergent_lines(v9, v10) = v12) | ~ (convergent_lines(v8, v10) = v11) | ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v9, v10) = 0) | (v13 = 0 & v11 = 0 & unorthogonal_lines(v8, v10) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v8, v9) = v13) | ( ~ (v13 = 0) & convergent_lines(v8, v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (convergent_lines(v8, v10) = v12) | ~ (convergent_lines(v8, v9) = v11) | ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0) | (v13 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v13 = 0) & unorthogonal_lines(v9, v10) = v13) | ( ~ (v13 = 0) & convergent_lines(v9, v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unorthogonal_lines(v8, v10) = v11) | ~ (convergent_lines(v9, v10) = 0) | unorthogonal_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (convergent_lines(v9, v10) = 0) | unorthogonal_lines(v8, v10) = 0) & ! [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, v10) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v8, v9) = 0) | (v12 = 0 & convergent_lines(v9, v10) = 0))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (apart_point_and_line(v8, v9) = v11) | ~ (distinct_lines(v9, v10) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v8, v10) = 0) | (v12 = 0 & convergent_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 | ~ (orthogonal_lines(v11, v10) = v9) | ~ (orthogonal_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (incident_point_and_line(v11, v10) = v9) | ~ (incident_point_and_line(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (parallel_lines(v11, v10) = v9) | ~ (parallel_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_lines(v11, v10) = v9) | ~ (equal_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (equal_points(v11, v10) = v9) | ~ (equal_points(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (orthogonal_through_point(v11, v10) = v9) | ~ (orthogonal_through_point(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (unorthogonal_lines(v11, v10) = v9) | ~ (unorthogonal_lines(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (parallel_through_point(v11, v10) = v9) | ~ (parallel_through_point(v11, v10) = v8)) & ! [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] : ( ~ (unorthogonal_lines(v9, v10) = v11) | ~ (unorthogonal_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v9, v10) = 0) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v9, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v9, v10) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v9, v10) = 0) | ~ (unorthogonal_lines(v8, v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v8, v10) = 0) | ( ~ (v12 = 0) & convergent_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v9, v10) = 0) | ~ (unorthogonal_lines(v8, v9) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v12 = 0) & convergent_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v9, v10) = 0) | ~ (convergent_lines(v8, v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v10) = 0) | ( ~ (v12 = 0) & convergent_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v9, v10) = 0) | ~ (convergent_lines(v8, v9) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v12 = 0) & convergent_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v10) = v11) | ~ (unorthogonal_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v9, v10) = 0 & convergent_lines(v9, v10) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v8, v10) = 0) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v10) = v11) | ~ (convergent_lines(v9, v10) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v8, v10) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v9, v10) = 0 & convergent_lines(v9, v10) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v8, v10) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = v11) | ~ (convergent_lines(v9, v10) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & convergent_lines(v8, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ~ (convergent_lines(v9, v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v9, v10) = 0) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ~ (convergent_lines(v8, v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v9, v10) = 0 & convergent_lines(v9, v10) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v10) = 0) | ( ~ (v12 = 0) & convergent_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (convergent_lines(v9, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v9, v10) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (convergent_lines(v9, v10) = 0) | ~ (convergent_lines(v8, v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v9) = 0 & convergent_lines(v8, v9) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v10) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (convergent_lines(v9, v10) = 0) | ~ (convergent_lines(v8, v9) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v8, v10) = 0 & convergent_lines(v8, v10) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v9) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v9, v10) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (convergent_lines(v8, v10) = v11) | ~ (convergent_lines(v8, v9) = 0) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unorthogonal_lines(v9, v10) = 0 & convergent_lines(v9, v10) = 0) | (v12 = 0 & v11 = 0 & unorthogonal_lines(v8, v10) = 0) | ( ~ (v12 = 0) & unorthogonal_lines(v8, v9) = v12))) & ! [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] : (v10 = 0 | ~ (orthogonal_lines(v8, v9) = v10) | unorthogonal_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (incident_point_and_line(v8, v9) = v10) | apart_point_and_line(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (parallel_lines(v8, v9) = v10) | convergent_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_lines(v8, v9) = v10) | distinct_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (equal_points(v8, v9) = v10) | distinct_points(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v10) | orthogonal_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v10) | convergent_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (apart_point_and_line(v8, v9) = v10) | incident_point_and_line(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v8, v9) = v10) | parallel_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v8, v9) = v10) | unorthogonal_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (convergent_lines(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v8, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_lines(v8, v9) = v10) | equal_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (distinct_points(v8, v9) = v10) | equal_points(v8, v9) = 0) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (point(v10) = v9) | ~ (point(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (line(v10) = v9) | ~ (line(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (orthogonal_through_point(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & unorthogonal_lines(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (orthogonal_through_point(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (orthogonal_through_point(v8, v9) = v10) | ? [v11] : ((v11 = 0 & line(v10) = 0) | ( ~ (v11 = 0) & point(v9) = v11) | ( ~ (v11 = 0) & line(v8) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v8, v10) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v9, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v10, v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (parallel_through_point(v8, v9) = v10) | ? [v11] : ((v11 = 0 & line(v10) = 0) | ( ~ (v11 = 0) & point(v9) = v11) | ( ~ (v11 = 0) & line(v8) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (intersection_point(v8, v9) = v10) | ? [v11] : ((v11 = 0 & point(v10) = 0) | ( ~ (v11 = 0) & line(v9) = v11) | ( ~ (v11 = 0) & line(v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v8, v9) = v11))) & ! [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 & line(v10) = 0) | ( ~ (v11 = 0) & point(v9) = v11) | ( ~ (v11 = 0) & point(v8) = v11) | ( ~ (v11 = 0) & distinct_points(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] : ( ~ (orthogonal_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & unorthogonal_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (incident_point_and_line(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (parallel_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (equal_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (equal_points(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & orthogonal_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (apart_point_and_line(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & incident_point_and_line(v8, v9) = v10)) & ! [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] : ( ~ (convergent_lines(v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & point(v10) = 0 & intersection_point(v8, v9) = v10) | ( ~ (v10 = 0) & line(v9) = v10) | ( ~ (v10 = 0) & line(v8) = v10))) & ! [v8] : ! [v9] : ( ~ (convergent_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & parallel_lines(v8, v9) = v10)) & ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | convergent_lines(v8, v9) = 0) & ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & equal_lines(v8, v9) = v10)) & ! [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] : ! [v9] : ( ~ (distinct_points(v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & line(v10) = 0 & line_connecting(v8, v9) = v10) | ( ~ (v10 = 0) & point(v9) = v10) | ( ~ (v10 = 0) & point(v8) = v10))) & ! [v8] : ! [v9] : ( ~ (distinct_points(v8, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & equal_points(v8, v9) = v10)) & ! [v8] : ~ (convergent_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_lines(v8, v8) = 0) & ! [v8] : ~ (distinct_points(v8, v8) = 0) & ? [v8] : ? [v9] : ? [v10] : orthogonal_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : incident_point_and_line(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : parallel_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : equal_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : equal_points(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : orthogonal_through_point(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : unorthogonal_lines(v9, v8) = v10 & ? [v8] : ? [v9] : ? [v10] : parallel_through_point(v9, v8) = v10 & ? [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 & ? [v8] : ? [v9] : point(v8) = v9 & ? [v8] : ? [v9] : line(v8) = v9 & (( ~ (v7 = 0) & incident_point_and_line(v3, v5) = v7) | ( ~ (v6 = 0) & incident_point_and_line(v2, v5) = v6)))
% 39.52/12.49 | 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:
% 39.52/12.49 | (1) incident_point_and_line(all_0_6_6, all_0_3_3) = 0 & incident_point_and_line(all_0_7_7, all_0_3_3) = 0 & line_connecting(all_0_5_5, all_0_4_4) = all_0_3_3 & line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2 & distinct_points(all_0_5_5, all_0_4_4) = 0 & distinct_points(all_0_7_7, all_0_6_6) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [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) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = 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 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = 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] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [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, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_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 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [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] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [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] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [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 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(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] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [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] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [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] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [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 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 & (( ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_4_4, all_0_2_2) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & incident_point_and_line(all_0_5_5, all_0_2_2) = all_0_1_1))
% 39.96/12.52 |
% 39.96/12.52 | Applying alpha-rule on (1) yields:
% 39.96/12.52 | (2) ? [v0] : ? [v1] : line(v0) = v1
% 39.96/12.52 | (3) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0)
% 39.96/12.52 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0))
% 39.96/12.52 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 39.96/12.52 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3))
% 39.96/12.52 | (7) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0)
% 39.96/12.52 | (8) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0)
% 39.96/12.52 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0))
% 39.96/12.52 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 39.96/12.53 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0))
% 39.96/12.53 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 39.96/12.53 | (13) ! [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))
% 39.96/12.53 | (14) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2)))
% 39.96/12.53 | (15) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2
% 39.96/12.53 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0))
% 39.96/12.53 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 39.96/12.53 | (18) line_connecting(all_0_5_5, all_0_4_4) = all_0_3_3
% 39.96/12.53 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0))
% 39.96/12.53 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 39.96/12.53 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 39.96/12.53 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 39.96/12.53 | (23) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3))
% 39.96/12.53 | (24) ! [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)))
% 39.96/12.53 | (25) ! [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))
% 39.96/12.53 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0)))
% 39.96/12.53 | (27) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3)))
% 39.96/12.53 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3))
% 39.96/12.53 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 39.96/12.53 | (30) ! [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)))
% 39.96/12.53 | (31) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2
% 39.96/12.53 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0))
% 39.96/12.53 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 39.96/12.53 | (34) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3))
% 39.96/12.53 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 39.96/12.53 | (36) ! [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)
% 39.96/12.53 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0)
% 39.96/12.54 | (38) distinct_points(all_0_7_7, all_0_6_6) = 0
% 39.96/12.54 | (39) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2
% 39.96/12.54 | (40) ! [v0] : ~ (distinct_lines(v0, v0) = 0)
% 39.96/12.54 | (41) ? [v0] : ? [v1] : point(v0) = v1
% 39.96/12.54 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0)
% 39.96/12.54 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 39.96/12.54 | (44) line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2
% 39.96/12.54 | (45) ! [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)))
% 39.96/12.54 | (46) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2))
% 39.96/12.54 | (47) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2))
% 39.96/12.54 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 39.96/12.54 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 39.96/12.54 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 39.96/12.54 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 39.96/12.54 | (52) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3))
% 39.96/12.54 | (53) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2
% 39.96/12.54 | (54) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2
% 39.96/12.54 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0)
% 39.96/12.54 | (56) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2
% 39.96/12.54 | (57) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2
% 39.96/12.54 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 39.96/12.54 | (59) ! [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)))
% 39.96/12.54 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3))
% 39.96/12.54 | (61) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2))
% 39.96/12.54 | (62) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2))
% 39.96/12.54 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0))
% 39.96/12.54 | (64) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0)
% 39.96/12.54 | (65) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0)
% 39.96/12.54 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 39.96/12.55 | (67) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 39.96/12.55 | (68) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 39.96/12.55 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6)))
% 39.96/12.55 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0)
% 39.96/12.55 | (71) incident_point_and_line(all_0_7_7, all_0_3_3) = 0
% 39.96/12.55 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0))
% 39.96/12.55 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 39.96/12.55 | (74) ! [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)))
% 39.96/12.55 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0))
% 39.96/12.55 | (76) ! [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))
% 39.96/12.55 | (77) ! [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))
% 39.96/12.55 | (78) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2
% 39.96/12.55 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 39.96/12.55 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0)
% 39.96/12.55 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3)))
% 39.96/12.55 | (82) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2))
% 39.96/12.55 | (83) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2))
% 39.96/12.55 | (84) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3))
% 39.96/12.55 | (85) ! [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)))
% 39.96/12.55 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4)))
% 39.96/12.55 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 39.96/12.55 | (88) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2
% 39.96/12.55 | (89) ! [v0] : ~ (distinct_points(v0, v0) = 0)
% 39.96/12.55 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0))
% 39.96/12.55 | (91) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2
% 39.96/12.55 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0)
% 39.96/12.55 | (93) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 39.96/12.55 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0)))
% 39.96/12.55 | (95) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2)))
% 39.96/12.55 | (96) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2
% 39.96/12.55 | (97) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2
% 39.96/12.55 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5)))
% 39.96/12.55 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 39.96/12.55 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)))
% 39.96/12.56 | (101) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2))
% 39.96/12.56 | (102) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2))
% 39.96/12.56 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 39.96/12.56 | (104) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0)
% 39.96/12.56 | (105) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0)
% 39.96/12.56 | (106) incident_point_and_line(all_0_6_6, all_0_3_3) = 0
% 39.96/12.56 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 39.96/12.56 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4)))
% 39.96/12.56 | (109) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3))
% 39.96/12.56 | (110) ! [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)))
% 39.96/12.56 | (111) ! [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)))
% 39.96/12.56 | (112) ! [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)
% 39.96/12.56 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 39.96/12.56 | (114) ! [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)
% 39.96/12.56 | (115) ! [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))
% 39.96/12.56 | (116) ! [v0] : ~ (convergent_lines(v0, v0) = 0)
% 39.96/12.56 | (117) ! [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)))
% 39.96/12.56 | (118) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2
% 39.96/12.56 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0))
% 39.96/12.56 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0))
% 39.96/12.56 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0))
% 39.96/12.56 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)))
% 39.96/12.56 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0))
% 39.96/12.56 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0)
% 39.96/12.56 | (125) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0)
% 39.96/12.56 | (126) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0)
% 39.96/12.56 | (127) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0)
% 39.96/12.56 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0))
% 39.96/12.56 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0)
% 39.96/12.56 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)))
% 39.96/12.56 | (131) distinct_points(all_0_5_5, all_0_4_4) = 0
% 39.96/12.56 | (132) ( ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_4_4, all_0_2_2) = all_0_0_0) | ( ~ (all_0_1_1 = 0) & incident_point_and_line(all_0_5_5, all_0_2_2) = all_0_1_1)
% 39.96/12.56 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4)))
% 39.96/12.56 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0)))
% 39.96/12.56 | (135) ! [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)))
% 39.96/12.56 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4)))
% 39.96/12.57 | (137) ! [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))
% 39.96/12.57 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0)
% 39.96/12.57 | (139) ! [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)))
% 39.96/12.57 | (140) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2
% 39.96/12.57 | (141) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0))
% 39.96/12.57 | (142) ! [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)
% 39.96/12.57 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))
% 39.96/12.57 | (144) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2))
% 39.96/12.57 | (145) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2))
% 39.96/12.57 | (146) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (102) with all_0_3_3, all_0_6_6 and discharging atoms incident_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 39.96/12.57 | (147) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_3_3) = v0)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (102) with all_0_3_3, all_0_7_7 and discharging atoms incident_point_and_line(all_0_7_7, all_0_3_3) = 0, yields:
% 39.96/12.57 | (148) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_3_3) = v0)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (45) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 39.96/12.57 | (149) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (24) with all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 39.96/12.57 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_4_4) = v0))
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (45) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 39.96/12.57 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (24) with all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 39.96/12.57 | (152) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_7_7, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (84) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 39.96/12.57 | (153) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_4_4, v0) = v1)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (23) with all_0_4_4, all_0_5_5 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 39.96/12.57 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(all_0_5_5, v0) = v1)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (84) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 39.96/12.57 | (155) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_6_6, v0) = v1)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating formula (23) with all_0_6_6, all_0_7_7 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 39.96/12.57 | (156) ? [v0] : ? [v1] : ( ~ (v1 = 0) & line_connecting(all_0_7_7, all_0_6_6) = v0 & apart_point_and_line(all_0_7_7, v0) = v1)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (156) with all_43_0_57, all_43_1_58 yields:
% 39.96/12.57 | (157) ~ (all_43_0_57 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_43_1_58 & apart_point_and_line(all_0_7_7, all_43_1_58) = all_43_0_57
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (157) yields:
% 39.96/12.57 | (158) ~ (all_43_0_57 = 0)
% 39.96/12.57 | (159) line_connecting(all_0_7_7, all_0_6_6) = all_43_1_58
% 39.96/12.57 | (160) apart_point_and_line(all_0_7_7, all_43_1_58) = all_43_0_57
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (153) with all_46_0_61, all_46_1_62 yields:
% 39.96/12.57 | (161) ~ (all_46_0_61 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_46_1_62 & apart_point_and_line(all_0_4_4, all_46_1_62) = all_46_0_61
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (161) yields:
% 39.96/12.57 | (162) ~ (all_46_0_61 = 0)
% 39.96/12.57 | (163) line_connecting(all_0_5_5, all_0_4_4) = all_46_1_62
% 39.96/12.57 | (164) apart_point_and_line(all_0_4_4, all_46_1_62) = all_46_0_61
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (152) with all_48_0_63 yields:
% 39.96/12.57 | (165) ( ~ (all_48_0_63 = 0) & apart_point_and_line(all_0_7_7, all_0_2_2) = all_48_0_63) | ( ~ (all_48_0_63 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_48_0_63)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (154) with all_49_0_64, all_49_1_65 yields:
% 39.96/12.57 | (166) ~ (all_49_0_64 = 0) & line_connecting(all_0_5_5, all_0_4_4) = all_49_1_65 & apart_point_and_line(all_0_5_5, all_49_1_65) = all_49_0_64
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (166) yields:
% 39.96/12.57 | (167) ~ (all_49_0_64 = 0)
% 39.96/12.57 | (168) line_connecting(all_0_5_5, all_0_4_4) = all_49_1_65
% 39.96/12.57 | (169) apart_point_and_line(all_0_5_5, all_49_1_65) = all_49_0_64
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (155) with all_51_0_66, all_51_1_67 yields:
% 39.96/12.57 | (170) ~ (all_51_0_66 = 0) & line_connecting(all_0_7_7, all_0_6_6) = all_51_1_67 & apart_point_and_line(all_0_6_6, all_51_1_67) = all_51_0_66
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (170) yields:
% 39.96/12.57 | (171) ~ (all_51_0_66 = 0)
% 39.96/12.57 | (172) line_connecting(all_0_7_7, all_0_6_6) = all_51_1_67
% 39.96/12.57 | (173) apart_point_and_line(all_0_6_6, all_51_1_67) = all_51_0_66
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (151) with all_55_0_69 yields:
% 39.96/12.57 | (174) ( ~ (all_55_0_69 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = all_55_0_69) | ( ~ (all_55_0_69 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_55_0_69)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (148) with all_58_0_72 yields:
% 39.96/12.57 | (175) ~ (all_58_0_72 = 0) & apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (175) yields:
% 39.96/12.57 | (176) ~ (all_58_0_72 = 0)
% 39.96/12.57 | (177) apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (147) with all_60_0_73 yields:
% 39.96/12.57 | (178) ~ (all_60_0_73 = 0) & apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (178) yields:
% 39.96/12.57 | (179) ~ (all_60_0_73 = 0)
% 39.96/12.57 | (180) apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (150) with all_62_0_74 yields:
% 39.96/12.57 | (181) ( ~ (all_62_0_74 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_62_0_74) | ( ~ (all_62_0_74 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_62_0_74)
% 39.96/12.57 |
% 39.96/12.57 | Instantiating (149) with all_63_0_75 yields:
% 39.96/12.57 | (182) ( ~ (all_63_0_75 = 0) & apart_point_and_line(all_0_4_4, all_0_3_3) = all_63_0_75) | ( ~ (all_63_0_75 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_63_0_75)
% 39.96/12.57 |
% 39.96/12.57 +-Applying beta-rule and splitting (165), into two cases.
% 39.96/12.57 |-Branch one:
% 39.96/12.57 | (183) ~ (all_48_0_63 = 0) & apart_point_and_line(all_0_7_7, all_0_2_2) = all_48_0_63
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (183) yields:
% 39.96/12.57 | (184) ~ (all_48_0_63 = 0)
% 39.96/12.57 | (185) apart_point_and_line(all_0_7_7, all_0_2_2) = all_48_0_63
% 39.96/12.57 |
% 39.96/12.57 +-Applying beta-rule and splitting (181), into two cases.
% 39.96/12.57 |-Branch one:
% 39.96/12.57 | (186) ~ (all_62_0_74 = 0) & apart_point_and_line(all_0_5_5, all_0_3_3) = all_62_0_74
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (186) yields:
% 39.96/12.57 | (187) ~ (all_62_0_74 = 0)
% 39.96/12.57 | (188) apart_point_and_line(all_0_5_5, all_0_3_3) = all_62_0_74
% 39.96/12.57 |
% 39.96/12.57 +-Applying beta-rule and splitting (174), into two cases.
% 39.96/12.57 |-Branch one:
% 39.96/12.57 | (189) ~ (all_55_0_69 = 0) & apart_point_and_line(all_0_6_6, all_0_2_2) = all_55_0_69
% 39.96/12.57 |
% 39.96/12.57 | Applying alpha-rule on (189) yields:
% 39.96/12.57 | (190) ~ (all_55_0_69 = 0)
% 39.96/12.57 | (191) apart_point_and_line(all_0_6_6, all_0_2_2) = all_55_0_69
% 39.96/12.58 |
% 39.96/12.58 +-Applying beta-rule and splitting (182), into two cases.
% 39.96/12.58 |-Branch one:
% 39.96/12.58 | (192) ~ (all_63_0_75 = 0) & apart_point_and_line(all_0_4_4, all_0_3_3) = all_63_0_75
% 39.96/12.58 |
% 39.96/12.58 | Applying alpha-rule on (192) yields:
% 39.96/12.58 | (193) ~ (all_63_0_75 = 0)
% 39.96/12.58 | (194) apart_point_and_line(all_0_4_4, all_0_3_3) = all_63_0_75
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (63) with all_0_5_5, all_0_4_4, all_49_1_65, all_0_3_3 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_49_1_65, line_connecting(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 39.96/12.58 | (195) all_49_1_65 = all_0_3_3
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (63) with all_0_5_5, all_0_4_4, all_46_1_62, all_49_1_65 and discharging atoms line_connecting(all_0_5_5, all_0_4_4) = all_49_1_65, line_connecting(all_0_5_5, all_0_4_4) = all_46_1_62, yields:
% 39.96/12.58 | (196) all_49_1_65 = all_46_1_62
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (63) with all_0_7_7, all_0_6_6, all_51_1_67, all_0_2_2 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_51_1_67, line_connecting(all_0_7_7, all_0_6_6) = all_0_2_2, yields:
% 39.96/12.58 | (197) all_51_1_67 = all_0_2_2
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (63) with all_0_7_7, all_0_6_6, all_43_1_58, all_51_1_67 and discharging atoms line_connecting(all_0_7_7, all_0_6_6) = all_51_1_67, line_connecting(all_0_7_7, all_0_6_6) = all_43_1_58, yields:
% 39.96/12.58 | (198) all_51_1_67 = all_43_1_58
% 39.96/12.58 |
% 39.96/12.58 | Combining equations (197,198) yields a new equation:
% 39.96/12.58 | (199) all_43_1_58 = all_0_2_2
% 39.96/12.58 |
% 39.96/12.58 | Combining equations (196,195) yields a new equation:
% 39.96/12.58 | (200) all_46_1_62 = all_0_3_3
% 39.96/12.58 |
% 39.96/12.58 | Simplifying 200 yields:
% 39.96/12.58 | (201) all_46_1_62 = all_0_3_3
% 39.96/12.58 |
% 39.96/12.58 | Combining equations (199,198) yields a new equation:
% 39.96/12.58 | (197) all_51_1_67 = all_0_2_2
% 39.96/12.58 |
% 39.96/12.58 | From (201) and (164) follows:
% 39.96/12.58 | (203) apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61
% 39.96/12.58 |
% 39.96/12.58 | From (195) and (169) follows:
% 39.96/12.58 | (204) apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64
% 39.96/12.58 |
% 39.96/12.58 | From (197) and (173) follows:
% 39.96/12.58 | (205) apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66
% 39.96/12.58 |
% 39.96/12.58 | From (199) and (160) follows:
% 39.96/12.58 | (206) apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (19) with all_0_4_4, all_0_3_3, all_46_0_61, all_63_0_75 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_63_0_75, apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, yields:
% 39.96/12.58 | (207) all_63_0_75 = all_46_0_61
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (19) with all_0_5_5, all_0_3_3, all_49_0_64, all_62_0_74 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_62_0_74, apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, yields:
% 39.96/12.58 | (208) all_62_0_74 = all_49_0_64
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (19) with all_0_6_6, all_0_2_2, all_51_0_66, all_55_0_69 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_55_0_69, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (209) all_55_0_69 = all_51_0_66
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (19) with all_0_7_7, all_0_2_2, all_43_0_57, all_48_0_63 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_48_0_63, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 39.96/12.58 | (210) all_48_0_63 = all_43_0_57
% 39.96/12.58 |
% 39.96/12.58 | Equations (207) can reduce 193 to:
% 39.96/12.58 | (162) ~ (all_46_0_61 = 0)
% 39.96/12.58 |
% 39.96/12.58 | Equations (208) can reduce 187 to:
% 39.96/12.58 | (167) ~ (all_49_0_64 = 0)
% 39.96/12.58 |
% 39.96/12.58 | Equations (209) can reduce 190 to:
% 39.96/12.58 | (171) ~ (all_51_0_66 = 0)
% 39.96/12.58 |
% 39.96/12.58 | Equations (210) can reduce 184 to:
% 39.96/12.58 | (158) ~ (all_43_0_57 = 0)
% 39.96/12.58 |
% 39.96/12.58 | From (207) and (194) follows:
% 39.96/12.58 | (203) apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61
% 39.96/12.58 |
% 39.96/12.58 | From (208) and (188) follows:
% 39.96/12.58 | (204) apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64
% 39.96/12.58 |
% 39.96/12.58 | From (209) and (191) follows:
% 39.96/12.58 | (205) apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66
% 39.96/12.58 |
% 39.96/12.58 | From (210) and (185) follows:
% 39.96/12.58 | (206) apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (135) with all_46_0_61, all_46_0_61, all_0_3_3, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 39.96/12.58 | (219) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (29) with all_46_0_61, all_46_0_61, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, yields:
% 39.96/12.58 | (220) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_46_0_61, all_46_0_61, all_0_3_3, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, yields:
% 39.96/12.58 | (221) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_49_0_64, all_46_0_61, all_0_3_3, all_0_3_3, all_0_5_5, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, yields:
% 39.96/12.58 | (222) all_49_0_64 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (59) with all_49_0_64, all_49_0_64, all_0_3_3, all_0_3_3, all_0_4_4, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 39.96/12.58 | (223) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (29) with all_49_0_64, all_49_0_64, all_0_3_3, all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, yields:
% 39.96/12.58 | (224) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_49_0_64, all_49_0_64, all_0_3_3, all_0_3_3, all_0_5_5, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, yields:
% 39.96/12.58 | (225) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_51_0_66, all_46_0_61, all_0_2_2, all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (226) all_51_0_66 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_46_0_61, all_51_0_66, all_0_3_3, all_0_2_2, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (227) all_51_0_66 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (117) with all_51_0_66, all_46_0_61, all_0_3_3, all_0_2_2, all_0_6_6, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (228) all_51_0_66 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (117) with all_46_0_61, all_51_0_66, all_0_2_2, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (229) all_51_0_66 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_51_0_66, all_49_0_64, all_0_2_2, all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (230) all_51_0_66 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 39.96/12.58 |
% 39.96/12.58 | Instantiating formula (111) with all_49_0_64, all_51_0_66, all_0_3_3, all_0_2_2, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.58 | (231) all_51_0_66 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (117) with all_51_0_66, all_49_0_64, all_0_3_3, all_0_2_2, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.59 | (232) all_51_0_66 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (117) with all_49_0_64, all_51_0_66, all_0_2_2, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.59 | (233) all_51_0_66 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (29) with all_51_0_66, all_51_0_66, all_0_2_2, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.59 | (234) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_51_0_66, all_51_0_66, all_0_2_2, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, yields:
% 39.96/12.59 | (235) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_60_0_73, all_46_0_61, all_0_3_3, all_0_3_3, all_0_6_6, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (236) all_60_0_73 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_46_0_61, all_60_0_73, all_0_3_3, all_0_3_3, all_0_4_4, all_0_6_6 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (237) all_60_0_73 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_60_0_73, all_49_0_64, all_0_3_3, all_0_3_3, all_0_6_6, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (238) all_60_0_73 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_49_0_64, all_60_0_73, all_0_3_3, all_0_3_3, all_0_5_5, all_0_6_6 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (239) all_60_0_73 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (135) with all_60_0_73, all_51_0_66, all_0_3_3, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 39.96/12.59 | (240) all_60_0_73 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (135) with all_51_0_66, all_60_0_73, all_0_2_2, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 39.96/12.59 | (241) all_60_0_73 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (29) with all_60_0_73, all_51_0_66, all_0_3_3, all_0_2_2, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (242) all_60_0_73 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (29) with all_51_0_66, all_60_0_73, all_0_2_2, all_0_3_3, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (243) all_60_0_73 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_60_0_73, all_51_0_66, all_0_3_3, all_0_2_2, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (244) all_60_0_73 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_51_0_66, all_60_0_73, all_0_2_2, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (245) all_60_0_73 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (29) with all_60_0_73, all_60_0_73, all_0_3_3, all_0_3_3, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (246) all_60_0_73 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_60_0_73, all_60_0_73, all_0_3_3, all_0_3_3, all_0_6_6, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, yields:
% 39.96/12.59 | (247) all_60_0_73 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_43_0_57, all_46_0_61, all_0_2_2, all_0_3_3, all_0_7_7, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 39.96/12.59 | (248) all_46_0_61 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (111) with all_46_0_61, all_43_0_57, all_0_3_3, all_0_2_2, all_0_4_4, all_0_7_7 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 39.96/12.59 | (249) all_46_0_61 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 39.96/12.59 |
% 39.96/12.59 | Instantiating formula (117) with all_43_0_57, all_46_0_61, all_0_3_3, all_0_2_2, all_0_7_7, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 39.96/12.59 | (250) all_46_0_61 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.42/12.59 |
% 40.42/12.59 | Instantiating formula (117) with all_46_0_61, all_43_0_57, all_0_2_2, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.59 | (251) all_46_0_61 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.42/12.59 |
% 40.42/12.59 | Instantiating formula (111) with all_43_0_57, all_49_0_64, all_0_2_2, all_0_3_3, all_0_7_7, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.59 | (252) all_49_0_64 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.42/12.59 |
% 40.42/12.59 | Instantiating formula (111) with all_49_0_64, all_43_0_57, all_0_3_3, all_0_2_2, all_0_5_5, all_0_7_7 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.59 | (253) all_49_0_64 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.42/12.59 |
% 40.42/12.59 | Instantiating formula (117) with all_43_0_57, all_49_0_64, all_0_3_3, all_0_2_2, all_0_7_7, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.59 | (254) all_49_0_64 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.42/12.59 |
% 40.42/12.59 | Instantiating formula (117) with all_49_0_64, all_43_0_57, all_0_2_2, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.59 | (255) all_49_0_64 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.42/12.59 |
% 40.42/12.59 | Instantiating formula (111) with all_43_0_57, all_51_0_66, all_0_2_2, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.59 | (256) all_51_0_66 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_51_0_66, all_43_0_57, all_0_2_2, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (257) all_51_0_66 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_43_0_57, all_60_0_73, all_0_2_2, all_0_3_3, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (258) all_60_0_73 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_60_0_73, all_43_0_57, all_0_3_3, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (259) all_60_0_73 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (117) with all_43_0_57, all_60_0_73, all_0_3_3, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (260) all_60_0_73 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (117) with all_60_0_73, all_43_0_57, all_0_2_2, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (261) all_60_0_73 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (59) with all_43_0_57, all_43_0_57, all_0_2_2, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.42/12.60 | (262) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (29) with all_43_0_57, all_43_0_57, all_0_2_2, all_0_2_2, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (263) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_43_0_57, all_43_0_57, all_0_2_2, all_0_2_2, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, yields:
% 40.42/12.60 | (264) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_58_0_72, all_46_0_61, all_0_3_3, all_0_3_3, all_0_7_7, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (265) all_58_0_72 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_46_0_61, all_58_0_72, all_0_3_3, all_0_3_3, all_0_4_4, all_0_7_7 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (266) all_58_0_72 = 0 | all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_58_0_72, all_49_0_64, all_0_3_3, all_0_3_3, all_0_7_7, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (267) all_58_0_72 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_49_0_64, all_58_0_72, all_0_3_3, all_0_3_3, all_0_5_5, all_0_7_7 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (268) all_58_0_72 = 0 | all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_58_0_72, all_51_0_66, all_0_3_3, all_0_2_2, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (269) all_58_0_72 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_51_0_66, all_58_0_72, all_0_2_2, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (270) all_58_0_72 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (117) with all_58_0_72, all_51_0_66, all_0_2_2, all_0_3_3, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (271) all_58_0_72 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (117) with all_51_0_66, all_58_0_72, all_0_3_3, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (272) all_58_0_72 = 0 | all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_58_0_72, all_60_0_73, all_0_3_3, all_0_3_3, all_0_7_7, all_0_6_6 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (273) all_60_0_73 = 0 | all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_60_0_73, all_58_0_72, all_0_3_3, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (274) all_60_0_73 = 0 | all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (59) with all_58_0_72, all_43_0_57, all_0_3_3, all_0_2_2, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.42/12.60 | (275) all_58_0_72 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (59) with all_43_0_57, all_58_0_72, all_0_2_2, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.42/12.60 | (276) all_58_0_72 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (29) with all_58_0_72, all_43_0_57, all_0_3_3, all_0_2_2, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (277) all_58_0_72 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (29) with all_43_0_57, all_58_0_72, all_0_2_2, all_0_3_3, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (278) all_58_0_72 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_58_0_72, all_43_0_57, all_0_3_3, all_0_2_2, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (279) all_58_0_72 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (111) with all_43_0_57, all_58_0_72, all_0_2_2, all_0_3_3, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.60 | (280) all_58_0_72 = 0 | all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.42/12.60 |
% 40.42/12.60 | Instantiating formula (59) with all_58_0_72, all_58_0_72, all_0_3_3, all_0_3_3, all_0_6_6, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.42/12.61 | (281) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.42/12.61 |
% 40.42/12.61 | Instantiating formula (29) with all_58_0_72, all_58_0_72, all_0_3_3, all_0_3_3, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.61 | (282) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.42/12.61 |
% 40.42/12.61 | Instantiating formula (111) with all_58_0_72, all_58_0_72, all_0_3_3, all_0_3_3, all_0_7_7, all_0_7_7 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, yields:
% 40.42/12.61 | (283) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (132), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (284) ~ (all_0_0_0 = 0) & incident_point_and_line(all_0_4_4, all_0_2_2) = all_0_0_0
% 40.42/12.61 |
% 40.42/12.61 | Applying alpha-rule on (284) yields:
% 40.42/12.61 | (285) ~ (all_0_0_0 = 0)
% 40.42/12.61 | (286) incident_point_and_line(all_0_4_4, all_0_2_2) = all_0_0_0
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (246), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (287) all_60_0_73 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (287) can reduce 179 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.42/12.61 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (263), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (291) all_43_0_57 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (291) can reduce 158 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (158) ~ (all_43_0_57 = 0)
% 40.42/12.61 | (294) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (282), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (295) all_58_0_72 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (295) can reduce 176 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (176) ~ (all_58_0_72 = 0)
% 40.42/12.61 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (262), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (291) all_43_0_57 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (291) can reduce 158 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (158) ~ (all_43_0_57 = 0)
% 40.42/12.61 | (302) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (247), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (287) all_60_0_73 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (287) can reduce 179 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.42/12.61 | (306) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (281), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (295) all_58_0_72 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (295) can reduce 176 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (176) ~ (all_58_0_72 = 0)
% 40.42/12.61 | (310) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (283), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (295) all_58_0_72 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (295) can reduce 176 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (176) ~ (all_58_0_72 = 0)
% 40.42/12.61 | (314) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (277), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (295) all_58_0_72 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (295) can reduce 176 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (176) ~ (all_58_0_72 = 0)
% 40.42/12.61 | (318) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.42/12.61 |
% 40.42/12.61 +-Applying beta-rule and splitting (243), into two cases.
% 40.42/12.61 |-Branch one:
% 40.42/12.61 | (287) all_60_0_73 = 0
% 40.42/12.61 |
% 40.42/12.61 | Equations (287) can reduce 179 to:
% 40.42/12.61 | (288) $false
% 40.42/12.61 |
% 40.42/12.61 |-The branch is then unsatisfiable
% 40.42/12.61 |-Branch two:
% 40.42/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.42/12.61 | (322) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (242), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (287) all_60_0_73 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (287) can reduce 179 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.51/12.61 | (326) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (278), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (295) all_58_0_72 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (295) can reduce 176 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (176) ~ (all_58_0_72 = 0)
% 40.51/12.61 | (330) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (239), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (287) all_60_0_73 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (287) can reduce 179 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.51/12.61 | (334) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (254), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (335) all_49_0_64 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (335) can reduce 167 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (167) ~ (all_49_0_64 = 0)
% 40.51/12.61 | (338) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (256), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (339) all_51_0_66 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (339) can reduce 171 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (171) ~ (all_51_0_66 = 0)
% 40.51/12.61 | (342) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (245), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (287) all_60_0_73 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (287) can reduce 179 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.51/12.61 | (346) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (248), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (347) all_46_0_61 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (347) can reduce 162 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (162) ~ (all_46_0_61 = 0)
% 40.51/12.61 | (350) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (241), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.61 | (287) all_60_0_73 = 0
% 40.51/12.61 |
% 40.51/12.61 | Equations (287) can reduce 179 to:
% 40.51/12.61 | (288) $false
% 40.51/12.61 |
% 40.51/12.61 |-The branch is then unsatisfiable
% 40.51/12.61 |-Branch two:
% 40.51/12.61 | (179) ~ (all_60_0_73 = 0)
% 40.51/12.61 | (354) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.51/12.61 |
% 40.51/12.61 +-Applying beta-rule and splitting (279), into two cases.
% 40.51/12.61 |-Branch one:
% 40.51/12.62 | (295) all_58_0_72 = 0
% 40.51/12.62 |
% 40.51/12.62 | Equations (295) can reduce 176 to:
% 40.51/12.62 | (288) $false
% 40.51/12.62 |
% 40.51/12.62 |-The branch is then unsatisfiable
% 40.51/12.62 |-Branch two:
% 40.51/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (358) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (253), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (335) all_49_0_64 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (335) can reduce 167 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.62 | (362) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (255), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (335) all_49_0_64 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (335) can reduce 167 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.62 | (366) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (268), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (370) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (257), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (339) all_51_0_66 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (339) can reduce 171 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.62 | (374) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (270), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (378) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (274), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (382) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (273), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (386) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (280), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (390) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (269), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (394) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (240), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (398) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (271), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (402) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (272), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (406) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (260), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (410) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (275), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (414) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (276), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (295) all_58_0_72 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (295) can reduce 176 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.62 | (418) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (259), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (422) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (258), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (426) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.62 |
% 40.53/12.62 +-Applying beta-rule and splitting (261), into two cases.
% 40.53/12.62 |-Branch one:
% 40.53/12.62 | (287) all_60_0_73 = 0
% 40.53/12.62 |
% 40.53/12.62 | Equations (287) can reduce 179 to:
% 40.53/12.62 | (288) $false
% 40.53/12.62 |
% 40.53/12.62 |-The branch is then unsatisfiable
% 40.53/12.62 |-Branch two:
% 40.53/12.62 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.62 | (430) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (238), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (287) all_60_0_73 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (287) can reduce 179 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.63 | (434) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (244), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (287) all_60_0_73 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (287) can reduce 179 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.63 | (438) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (234), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (294) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (326), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (446) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (338), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (450) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (342), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (454) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (354), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (458) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (362), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (462) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (366), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (466) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (386), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (295) all_58_0_72 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (295) can reduce 176 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.63 | (470) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (390), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (474) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (394), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (398), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.63 |
% 40.53/12.63 | Instantiating (482) with all_271_0_299 yields:
% 40.53/12.63 | (483) (all_271_0_299 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_271_0_299 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (all_271_0_299 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_299)
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (402), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (487) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (406), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (339) all_51_0_66 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (339) can reduce 171 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.63 | (491) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.63 |
% 40.53/12.63 | Instantiating (491) with all_279_0_301 yields:
% 40.53/12.63 | (492) (all_279_0_301 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (all_279_0_301 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_279_0_301 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_301) | ( ~ (all_279_0_301 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_279_0_301)
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (414), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.63 |
% 40.53/12.63 | Instantiating (496) with all_283_0_302 yields:
% 40.53/12.63 | (497) (all_283_0_302 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_283_0_302 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (all_283_0_302 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_302)
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (418), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (501) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.63 |
% 40.53/12.63 +-Applying beta-rule and splitting (422), into two cases.
% 40.53/12.63 |-Branch one:
% 40.53/12.63 | (291) all_43_0_57 = 0
% 40.53/12.63 |
% 40.53/12.63 | Equations (291) can reduce 158 to:
% 40.53/12.63 | (288) $false
% 40.53/12.63 |
% 40.53/12.63 |-The branch is then unsatisfiable
% 40.53/12.63 |-Branch two:
% 40.53/12.63 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.63 | (505) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.63 |
% 40.53/12.63 | Instantiating (505) with all_291_0_304 yields:
% 40.53/12.63 | (506) (all_291_0_304 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_291_0_304 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (all_291_0_304 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304) | ( ~ (all_291_0_304 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_291_0_304)
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (430), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (291) all_43_0_57 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (291) can reduce 158 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.64 | (510) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (434), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (335) all_49_0_64 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (335) can reduce 167 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.64 | (514) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (438), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (518) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (220), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (347) all_46_0_61 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (347) can reduce 162 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.64 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (224), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (335) all_49_0_64 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (335) can reduce 167 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.64 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (219), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (347) all_46_0_61 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (347) can reduce 162 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.64 | (530) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (223), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (335) all_49_0_64 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (335) can reduce 167 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.64 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (221), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (347) all_46_0_61 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (347) can reduce 162 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.64 | (538) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (497), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (539) (all_283_0_302 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_283_0_302 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0)
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (539), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (540) all_283_0_302 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.53/12.64 |
% 40.53/12.64 | Applying alpha-rule on (540) yields:
% 40.53/12.64 | (541) all_283_0_302 = 0
% 40.53/12.64 | (542) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (235), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (546) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (232), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (550) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (226), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (554) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (227), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (558) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (233), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (562) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (322), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (346), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (378), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.64 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.64 |
% 40.53/12.64 +-Applying beta-rule and splitting (230), into two cases.
% 40.53/12.64 |-Branch one:
% 40.53/12.64 | (339) all_51_0_66 = 0
% 40.53/12.64 |
% 40.53/12.64 | Equations (339) can reduce 171 to:
% 40.53/12.64 | (288) $false
% 40.53/12.64 |
% 40.53/12.64 |-The branch is then unsatisfiable
% 40.53/12.64 |-Branch two:
% 40.53/12.64 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.65 | (578) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (228), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (339) all_51_0_66 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (339) can reduce 171 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.65 | (582) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (229), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (339) all_51_0_66 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (339) can reduce 171 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.65 | (586) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (231), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (339) all_51_0_66 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (339) can reduce 171 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.65 | (590) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.53/12.65 |
% 40.53/12.65 | Instantiating formula (19) with all_0_6_6, all_0_2_2, 0, all_51_0_66 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 40.53/12.65 | (339) all_51_0_66 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (339) can reduce 171 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (593) all_283_0_302 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.53/12.65 |
% 40.53/12.65 | Applying alpha-rule on (593) yields:
% 40.53/12.65 | (541) all_283_0_302 = 0
% 40.53/12.65 | (595) apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (236), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (287) all_60_0_73 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (287) can reduce 179 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.65 | (599) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (237), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (287) all_60_0_73 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (287) can reduce 179 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.65 | (603) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.65 |
% 40.53/12.65 | Instantiating formula (19) with all_0_6_6, all_0_3_3, 0, all_60_0_73 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 40.53/12.65 | (287) all_60_0_73 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (287) can reduce 179 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (606) ~ (all_283_0_302 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_302
% 40.53/12.65 |
% 40.53/12.65 | Applying alpha-rule on (606) yields:
% 40.53/12.65 | (607) ~ (all_283_0_302 = 0)
% 40.53/12.65 | (608) distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_302
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (264), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (291) all_43_0_57 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (291) can reduce 158 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.65 | (612) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (266), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (295) all_58_0_72 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (295) can reduce 176 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.65 | (616) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (267), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (295) all_58_0_72 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (295) can reduce 176 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.65 | (620) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (249), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (347) all_46_0_61 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (347) can reduce 162 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.65 | (624) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (250), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (347) all_46_0_61 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (347) can reduce 162 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.65 | (628) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (251), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (347) all_46_0_61 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (347) can reduce 162 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.65 | (632) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (252), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (335) all_49_0_64 = 0
% 40.53/12.65 |
% 40.53/12.65 | Equations (335) can reduce 167 to:
% 40.53/12.65 | (288) $false
% 40.53/12.65 |
% 40.53/12.65 |-The branch is then unsatisfiable
% 40.53/12.65 |-Branch two:
% 40.53/12.65 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.65 | (636) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.53/12.65 |
% 40.53/12.65 +-Applying beta-rule and splitting (483), into two cases.
% 40.53/12.65 |-Branch one:
% 40.53/12.65 | (637) (all_271_0_299 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_271_0_299 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0)
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (637), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (638) all_271_0_299 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.53/12.66 |
% 40.53/12.66 | Applying alpha-rule on (638) yields:
% 40.53/12.66 | (639) all_271_0_299 = 0
% 40.53/12.66 | (640) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (318), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (446) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (426), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (648) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (628), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (652) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (632), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (656) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (330), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (350), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (664) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (358), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (668) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (374), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (672) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (410), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (676) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (624), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (680) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (636), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.66 | (684) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_43_0_57 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 40.53/12.66 | (291) all_43_0_57 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (291) can reduce 158 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (687) all_271_0_299 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.53/12.66 |
% 40.53/12.66 | Applying alpha-rule on (687) yields:
% 40.53/12.66 | (639) all_271_0_299 = 0
% 40.53/12.66 | (689) apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (265), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (295) all_58_0_72 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (295) can reduce 176 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.66 | (693) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.66 |
% 40.53/12.66 | Instantiating formula (19) with all_0_7_7, all_0_3_3, 0, all_58_0_72 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, apart_point_and_line(all_0_7_7, all_0_3_3) = 0, yields:
% 40.53/12.66 | (295) all_58_0_72 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (295) can reduce 176 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (696) ~ (all_271_0_299 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_299
% 40.53/12.66 |
% 40.53/12.66 | Applying alpha-rule on (696) yields:
% 40.53/12.66 | (697) ~ (all_271_0_299 = 0)
% 40.53/12.66 | (698) distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_299
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (235), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (339) all_51_0_66 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (339) can reduce 171 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.66 | (546) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (232), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (339) all_51_0_66 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (339) can reduce 171 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.66 | (550) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (236), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (287) all_60_0_73 = 0
% 40.53/12.66 |
% 40.53/12.66 | Equations (287) can reduce 179 to:
% 40.53/12.66 | (288) $false
% 40.53/12.66 |
% 40.53/12.66 |-The branch is then unsatisfiable
% 40.53/12.66 |-Branch two:
% 40.53/12.66 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.66 | (599) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.66 |
% 40.53/12.66 +-Applying beta-rule and splitting (237), into two cases.
% 40.53/12.66 |-Branch one:
% 40.53/12.66 | (287) all_60_0_73 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (287) can reduce 179 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.67 | (603) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (226), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (554) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (227), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (558) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (233), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (562) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (318), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (291) all_43_0_57 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (291) can reduce 158 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.67 | (446) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (426), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (291) all_43_0_57 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (291) can reduce 158 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.67 | (648) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (616), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (347) all_46_0_61 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (347) can reduce 162 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.67 | (738) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (628), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (291) all_43_0_57 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (291) can reduce 158 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.67 | (652) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (632), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (291) all_43_0_57 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (291) can reduce 158 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.67 | (656) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (506), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (747) (all_291_0_304 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_291_0_304 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (all_291_0_304 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304)
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (747), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (748) (all_291_0_304 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_291_0_304 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0)
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (748), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (749) all_291_0_304 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.53/12.67 |
% 40.53/12.67 | Applying alpha-rule on (749) yields:
% 40.53/12.67 | (750) all_291_0_304 = 0
% 40.53/12.67 | (542) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (322), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (346), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (378), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (229), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (586) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (230), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (578) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (231), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (590) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (228), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.67 | (582) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.67 |
% 40.53/12.67 | Instantiating formula (19) with all_0_6_6, all_0_2_2, 0, all_51_0_66 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (339) can reduce 171 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (782) all_291_0_304 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.53/12.67 |
% 40.53/12.67 | Applying alpha-rule on (782) yields:
% 40.53/12.67 | (750) all_291_0_304 = 0
% 40.53/12.67 | (689) apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (265), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (295) all_58_0_72 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (295) can reduce 176 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.67 | (693) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.67 |
% 40.53/12.67 | Instantiating formula (19) with all_0_7_7, all_0_3_3, 0, all_58_0_72 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, apart_point_and_line(all_0_7_7, all_0_3_3) = 0, yields:
% 40.53/12.67 | (295) all_58_0_72 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (295) can reduce 176 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (791) ~ (all_291_0_304 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304
% 40.53/12.67 |
% 40.53/12.67 | Applying alpha-rule on (791) yields:
% 40.53/12.67 | (792) ~ (all_291_0_304 = 0)
% 40.53/12.67 | (793) distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (222), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (335) all_49_0_64 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (335) can reduce 167 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.67 | (797) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (265), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (295) all_58_0_72 = 0
% 40.53/12.67 |
% 40.53/12.67 | Equations (295) can reduce 176 to:
% 40.53/12.67 | (288) $false
% 40.53/12.67 |
% 40.53/12.67 |-The branch is then unsatisfiable
% 40.53/12.67 |-Branch two:
% 40.53/12.67 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.67 | (693) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.67 |
% 40.53/12.67 +-Applying beta-rule and splitting (322), into two cases.
% 40.53/12.67 |-Branch one:
% 40.53/12.67 | (339) all_51_0_66 = 0
% 40.53/12.67 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (330), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (291) all_43_0_57 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (291) can reduce 158 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.68 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (346), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (339) all_51_0_66 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (350), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (291) all_43_0_57 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (291) can reduce 158 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.68 | (664) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (358), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (291) all_43_0_57 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (291) can reduce 158 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.68 | (668) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (378), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (339) all_51_0_66 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (554), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (829) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (410), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (291) all_43_0_57 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (291) can reduce 158 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.68 | (676) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (624), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (291) all_43_0_57 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (291) can reduce 158 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.68 | (680) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (636), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (291) all_43_0_57 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (291) can reduce 158 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.68 | (684) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (603), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (845) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (558), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (849) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (797), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (853) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (693), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (857) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (230), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (339) all_51_0_66 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (578) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (231), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (339) all_51_0_66 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (590) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (228), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (339) all_51_0_66 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (582) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (229), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (339) all_51_0_66 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (339) can reduce 171 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.68 | (586) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (582), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (877) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (586), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (347) all_46_0_61 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (347) can reduce 162 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.68 | (881) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (492), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (882) (all_279_0_301 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (all_279_0_301 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_279_0_301 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_301)
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (882), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (883) (all_279_0_301 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (all_279_0_301 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0)
% 40.53/12.68 |
% 40.53/12.68 +-Applying beta-rule and splitting (883), into two cases.
% 40.53/12.68 |-Branch one:
% 40.53/12.68 | (884) all_279_0_301 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.53/12.68 |
% 40.53/12.68 | Applying alpha-rule on (884) yields:
% 40.53/12.68 | (885) all_279_0_301 = 0
% 40.53/12.68 | (595) apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.53/12.68 |
% 40.53/12.68 | Instantiating formula (19) with all_0_6_6, all_0_3_3, 0, all_60_0_73 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 40.53/12.68 | (287) all_60_0_73 = 0
% 40.53/12.68 |
% 40.53/12.68 | Equations (287) can reduce 179 to:
% 40.53/12.68 | (288) $false
% 40.53/12.68 |
% 40.53/12.68 |-The branch is then unsatisfiable
% 40.53/12.68 |-Branch two:
% 40.53/12.68 | (889) all_279_0_301 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.53/12.68 |
% 40.53/12.69 | Applying alpha-rule on (889) yields:
% 40.53/12.69 | (885) all_279_0_301 = 0
% 40.53/12.69 | (640) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_43_0_57 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 40.53/12.69 | (291) all_43_0_57 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (291) can reduce 158 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (894) ~ (all_279_0_301 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_301
% 40.53/12.69 |
% 40.53/12.69 | Applying alpha-rule on (894) yields:
% 40.53/12.69 | (895) ~ (all_279_0_301 = 0)
% 40.53/12.69 | (896) distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_301
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (599), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (347) all_46_0_61 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (347) can reduce 162 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.69 | (900) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (16) with all_0_2_2, all_0_3_3, all_283_0_302, all_291_0_304 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304, distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_302, yields:
% 40.53/12.69 | (901) all_291_0_304 = all_283_0_302
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (16) with all_0_2_2, all_0_3_3, all_279_0_301, all_291_0_304 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304, distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_301, yields:
% 40.53/12.69 | (902) all_291_0_304 = all_279_0_301
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (16) with all_0_2_2, all_0_3_3, all_271_0_299, all_291_0_304 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_304, distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_299, yields:
% 40.53/12.69 | (903) all_291_0_304 = all_271_0_299
% 40.53/12.69 |
% 40.53/12.69 | Combining equations (902,901) yields a new equation:
% 40.53/12.69 | (904) all_283_0_302 = all_279_0_301
% 40.53/12.69 |
% 40.53/12.69 | Combining equations (903,901) yields a new equation:
% 40.53/12.69 | (905) all_283_0_302 = all_271_0_299
% 40.53/12.69 |
% 40.53/12.69 | Combining equations (904,905) yields a new equation:
% 40.53/12.69 | (906) all_279_0_301 = all_271_0_299
% 40.53/12.69 |
% 40.53/12.69 | Simplifying 906 yields:
% 40.53/12.69 | (907) all_279_0_301 = all_271_0_299
% 40.53/12.69 |
% 40.53/12.69 | Equations (907) can reduce 895 to:
% 40.53/12.69 | (697) ~ (all_271_0_299 = 0)
% 40.53/12.69 |
% 40.53/12.69 | From (907) and (896) follows:
% 40.53/12.69 | (698) distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_299
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (8) with all_0_0_0, all_0_2_2, all_0_4_4 and discharging atoms incident_point_and_line(all_0_4_4, all_0_2_2) = all_0_0_0, yields:
% 40.53/12.69 | (910) all_0_0_0 = 0 | apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (115) with all_46_0_61, all_271_0_299, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_3_3) = all_46_0_61, distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_299, yields:
% 40.53/12.69 | (911) all_271_0_299 = 0 | all_46_0_61 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0)
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (910), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (912) apart_point_and_line(all_0_4_4, all_0_2_2) = 0
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (911), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (639) all_271_0_299 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (639) can reduce 697 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (697) ~ (all_271_0_299 = 0)
% 40.53/12.69 | (916) all_46_0_61 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0)
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (916), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (347) all_46_0_61 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (347) can reduce 162 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.69 | (920) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = v0)
% 40.53/12.69 |
% 40.53/12.69 | Instantiating (920) with all_600_0_1911 yields:
% 40.53/12.69 | (921) ~ (all_600_0_1911 = 0) & apart_point_and_line(all_0_4_4, all_0_2_2) = all_600_0_1911
% 40.53/12.69 |
% 40.53/12.69 | Applying alpha-rule on (921) yields:
% 40.53/12.69 | (922) ~ (all_600_0_1911 = 0)
% 40.53/12.69 | (923) apart_point_and_line(all_0_4_4, all_0_2_2) = all_600_0_1911
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (19) with all_0_4_4, all_0_2_2, 0, all_600_0_1911 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = all_600_0_1911, apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields:
% 40.53/12.69 | (924) all_600_0_1911 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (924) can reduce 922 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (926) ~ (apart_point_and_line(all_0_4_4, all_0_2_2) = 0)
% 40.53/12.69 | (927) all_0_0_0 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (927) can reduce 285 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (929) ~ (all_279_0_301 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_279_0_301
% 40.53/12.69 |
% 40.53/12.69 | Applying alpha-rule on (929) yields:
% 40.53/12.69 | (895) ~ (all_279_0_301 = 0)
% 40.53/12.69 | (931) distinct_points(all_0_7_7, all_0_6_6) = all_279_0_301
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (32) with all_0_7_7, all_0_6_6, all_279_0_301, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_279_0_301, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.53/12.69 | (885) all_279_0_301 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (885) can reduce 895 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (934) ~ (all_291_0_304 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_291_0_304
% 40.53/12.69 |
% 40.53/12.69 | Applying alpha-rule on (934) yields:
% 40.53/12.69 | (792) ~ (all_291_0_304 = 0)
% 40.53/12.69 | (936) distinct_points(all_0_7_7, all_0_6_6) = all_291_0_304
% 40.53/12.69 |
% 40.53/12.69 | Instantiating formula (32) with all_0_7_7, all_0_6_6, all_291_0_304, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_291_0_304, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.53/12.69 | (750) all_291_0_304 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (750) can reduce 792 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (939) ~ (all_0_1_1 = 0) & incident_point_and_line(all_0_5_5, all_0_2_2) = all_0_1_1
% 40.53/12.69 |
% 40.53/12.69 | Applying alpha-rule on (939) yields:
% 40.53/12.69 | (940) ~ (all_0_1_1 = 0)
% 40.53/12.69 | (941) incident_point_and_line(all_0_5_5, all_0_2_2) = all_0_1_1
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (246), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (287) all_60_0_73 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (287) can reduce 179 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.69 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (263), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (291) all_43_0_57 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (291) can reduce 158 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.69 | (294) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (282), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (295) all_58_0_72 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (295) can reduce 176 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.69 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (262), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (291) all_43_0_57 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (291) can reduce 158 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (158) ~ (all_43_0_57 = 0)
% 40.53/12.69 | (302) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (247), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (287) all_60_0_73 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (287) can reduce 179 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.69 | (306) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (281), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (295) all_58_0_72 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (295) can reduce 176 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.69 | (310) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (283), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (295) all_58_0_72 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (295) can reduce 176 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.69 | (314) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (277), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (295) all_58_0_72 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (295) can reduce 176 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.69 | (318) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.69 |
% 40.53/12.69 +-Applying beta-rule and splitting (243), into two cases.
% 40.53/12.69 |-Branch one:
% 40.53/12.69 | (287) all_60_0_73 = 0
% 40.53/12.69 |
% 40.53/12.69 | Equations (287) can reduce 179 to:
% 40.53/12.69 | (288) $false
% 40.53/12.69 |
% 40.53/12.69 |-The branch is then unsatisfiable
% 40.53/12.69 |-Branch two:
% 40.53/12.69 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (322) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (242), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (287) all_60_0_73 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (287) can reduce 179 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (326) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (278), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (295) all_58_0_72 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (295) can reduce 176 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.70 | (330) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (239), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (287) all_60_0_73 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (287) can reduce 179 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (334) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (254), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (335) all_49_0_64 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (335) can reduce 167 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.70 | (338) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (256), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (339) all_51_0_66 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (339) can reduce 171 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.70 | (342) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (245), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (287) all_60_0_73 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (287) can reduce 179 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (346) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (248), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (347) all_46_0_61 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (347) can reduce 162 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (162) ~ (all_46_0_61 = 0)
% 40.53/12.70 | (350) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (241), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (287) all_60_0_73 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (287) can reduce 179 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (354) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (279), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (295) all_58_0_72 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (295) can reduce 176 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.70 | (358) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (253), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (335) all_49_0_64 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (335) can reduce 167 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.70 | (362) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (255), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (335) all_49_0_64 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (335) can reduce 167 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (167) ~ (all_49_0_64 = 0)
% 40.53/12.70 | (366) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (268), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (295) all_58_0_72 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (295) can reduce 176 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.70 | (370) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (257), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (339) all_51_0_66 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (339) can reduce 171 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (171) ~ (all_51_0_66 = 0)
% 40.53/12.70 | (374) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (270), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (295) all_58_0_72 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (295) can reduce 176 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.53/12.70 | (378) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (274), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (287) all_60_0_73 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (287) can reduce 179 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (382) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.53/12.70 |
% 40.53/12.70 +-Applying beta-rule and splitting (273), into two cases.
% 40.53/12.70 |-Branch one:
% 40.53/12.70 | (287) all_60_0_73 = 0
% 40.53/12.70 |
% 40.53/12.70 | Equations (287) can reduce 179 to:
% 40.53/12.70 | (288) $false
% 40.53/12.70 |
% 40.53/12.70 |-The branch is then unsatisfiable
% 40.53/12.70 |-Branch two:
% 40.53/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.53/12.70 | (386) all_58_0_72 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (280), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (295) all_58_0_72 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (295) can reduce 176 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.70 | (390) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (269), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (295) all_58_0_72 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (295) can reduce 176 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.70 | (394) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (240), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (287) all_60_0_73 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (287) can reduce 179 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.70 | (398) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (271), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (295) all_58_0_72 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (295) can reduce 176 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.70 | (402) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (272), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (295) all_58_0_72 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (295) can reduce 176 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.70 | (406) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (260), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (287) all_60_0_73 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (287) can reduce 179 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.70 | (410) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (275), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (295) all_58_0_72 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (295) can reduce 176 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.70 | (414) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (276), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (295) all_58_0_72 = 0
% 40.89/12.70 |
% 40.89/12.70 | Equations (295) can reduce 176 to:
% 40.89/12.70 | (288) $false
% 40.89/12.70 |
% 40.89/12.70 |-The branch is then unsatisfiable
% 40.89/12.70 |-Branch two:
% 40.89/12.70 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.70 | (418) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.70 |
% 40.89/12.70 +-Applying beta-rule and splitting (259), into two cases.
% 40.89/12.70 |-Branch one:
% 40.89/12.70 | (287) all_60_0_73 = 0
% 40.89/12.70 |
% 40.89/12.71 | Equations (287) can reduce 179 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.71 | (422) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (258), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (287) all_60_0_73 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (287) can reduce 179 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.71 | (426) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (261), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (287) all_60_0_73 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (287) can reduce 179 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.71 | (430) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (238), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (287) all_60_0_73 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (287) can reduce 179 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.71 | (434) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (244), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (287) all_60_0_73 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (287) can reduce 179 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.71 | (438) all_51_0_66 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (234), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (294) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (326), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (446) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (338), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (450) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (342), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (454) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (354), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (458) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (362), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (462) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (366), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (466) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (386), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (295) all_58_0_72 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (295) can reduce 176 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.71 | (470) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (390), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (474) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (394), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (478) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (398), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (482) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.71 |
% 40.89/12.71 | Instantiating (482) with all_271_0_2382 yields:
% 40.89/12.71 | (1138) (all_271_0_2382 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_271_0_2382 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (all_271_0_2382 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_2382)
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (402), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (487) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (406), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (339) all_51_0_66 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (339) can reduce 171 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.71 | (491) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 | Instantiating (491) with all_279_0_2384 yields:
% 40.89/12.71 | (1147) (all_279_0_2384 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (all_279_0_2384 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_279_0_2384 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_2384) | ( ~ (all_279_0_2384 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_279_0_2384)
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (414), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.71 |
% 40.89/12.71 | Instantiating (496) with all_283_0_2385 yields:
% 40.89/12.71 | (1152) (all_283_0_2385 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_283_0_2385 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (all_283_0_2385 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_2385)
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (418), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (501) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (422), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (505) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 | Instantiating (505) with all_291_0_2387 yields:
% 40.89/12.71 | (1161) (all_291_0_2387 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_291_0_2387 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (all_291_0_2387 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387) | ( ~ (all_291_0_2387 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_291_0_2387)
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (430), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (291) all_43_0_57 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (291) can reduce 158 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.71 | (510) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.71 |
% 40.89/12.71 +-Applying beta-rule and splitting (434), into two cases.
% 40.89/12.71 |-Branch one:
% 40.89/12.71 | (335) all_49_0_64 = 0
% 40.89/12.71 |
% 40.89/12.71 | Equations (335) can reduce 167 to:
% 40.89/12.71 | (288) $false
% 40.89/12.71 |
% 40.89/12.71 |-The branch is then unsatisfiable
% 40.89/12.71 |-Branch two:
% 40.89/12.71 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.71 | (514) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (438), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (518) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (220), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (347) all_46_0_61 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (347) can reduce 162 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (162) ~ (all_46_0_61 = 0)
% 40.89/12.72 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (224), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (335) all_49_0_64 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (335) can reduce 167 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.72 | (290) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (219), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (347) all_46_0_61 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (347) can reduce 162 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (162) ~ (all_46_0_61 = 0)
% 40.89/12.72 | (530) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (223), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (335) all_49_0_64 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (335) can reduce 167 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.72 | (534) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (221), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (347) all_46_0_61 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (347) can reduce 162 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (162) ~ (all_46_0_61 = 0)
% 40.89/12.72 | (538) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_4_4) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (1152), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (1194) (all_283_0_2385 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_283_0_2385 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0)
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (1194), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (1195) all_283_0_2385 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.89/12.72 |
% 40.89/12.72 | Applying alpha-rule on (1195) yields:
% 40.89/12.72 | (1196) all_283_0_2385 = 0
% 40.89/12.72 | (542) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (235), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (546) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (232), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (550) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (226), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (554) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (227), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (558) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (233), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (562) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (322), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (346), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (378), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (230), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (578) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (228), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (582) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (229), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (586) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (231), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.72 | (590) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.72 |
% 40.89/12.72 | Instantiating formula (19) with all_0_6_6, all_0_2_2, 0, all_51_0_66 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 40.89/12.72 | (339) all_51_0_66 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (339) can reduce 171 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (1248) all_283_0_2385 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.89/12.72 |
% 40.89/12.72 | Applying alpha-rule on (1248) yields:
% 40.89/12.72 | (1196) all_283_0_2385 = 0
% 40.89/12.72 | (595) apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (236), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (287) all_60_0_73 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (287) can reduce 179 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.72 | (599) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (237), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (287) all_60_0_73 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (287) can reduce 179 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.72 | (603) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.89/12.72 |
% 40.89/12.72 | Instantiating formula (19) with all_0_6_6, all_0_3_3, 0, all_60_0_73 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 40.89/12.72 | (287) all_60_0_73 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (287) can reduce 179 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (1261) ~ (all_283_0_2385 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_2385
% 40.89/12.72 |
% 40.89/12.72 | Applying alpha-rule on (1261) yields:
% 40.89/12.72 | (1262) ~ (all_283_0_2385 = 0)
% 40.89/12.72 | (1263) distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_2385
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (264), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (291) all_43_0_57 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (291) can reduce 158 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.72 | (612) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (266), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (295) all_58_0_72 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (295) can reduce 176 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.72 | (616) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.72 |
% 40.89/12.72 +-Applying beta-rule and splitting (267), into two cases.
% 40.89/12.72 |-Branch one:
% 40.89/12.72 | (295) all_58_0_72 = 0
% 40.89/12.72 |
% 40.89/12.72 | Equations (295) can reduce 176 to:
% 40.89/12.72 | (288) $false
% 40.89/12.72 |
% 40.89/12.72 |-The branch is then unsatisfiable
% 40.89/12.72 |-Branch two:
% 40.89/12.72 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.72 | (620) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (249), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (347) all_46_0_61 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (347) can reduce 162 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (162) ~ (all_46_0_61 = 0)
% 40.89/12.73 | (624) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (250), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (347) all_46_0_61 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (347) can reduce 162 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (162) ~ (all_46_0_61 = 0)
% 40.89/12.73 | (628) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (251), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (347) all_46_0_61 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (347) can reduce 162 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (162) ~ (all_46_0_61 = 0)
% 40.89/12.73 | (632) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (252), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (335) all_49_0_64 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (335) can reduce 167 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.73 | (636) all_43_0_57 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (1138), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (1292) (all_271_0_2382 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (all_271_0_2382 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0)
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (1292), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (1293) all_271_0_2382 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.89/12.73 |
% 40.89/12.73 | Applying alpha-rule on (1293) yields:
% 40.89/12.73 | (1294) all_271_0_2382 = 0
% 40.89/12.73 | (640) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (318), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (446) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (426), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (648) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (628), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (652) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (632), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (656) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (330), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (350), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (664) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (358), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (668) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (374), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (672) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (410), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (676) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (624), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (680) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (636), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.73 | (684) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_43_0_57 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 40.89/12.73 | (291) all_43_0_57 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (291) can reduce 158 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (1342) all_271_0_2382 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.89/12.73 |
% 40.89/12.73 | Applying alpha-rule on (1342) yields:
% 40.89/12.73 | (1294) all_271_0_2382 = 0
% 40.89/12.73 | (689) apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (265), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (295) all_58_0_72 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (295) can reduce 176 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.73 | (693) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.73 |
% 40.89/12.73 | Instantiating formula (19) with all_0_7_7, all_0_3_3, 0, all_58_0_72 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, apart_point_and_line(all_0_7_7, all_0_3_3) = 0, yields:
% 40.89/12.73 | (295) all_58_0_72 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (295) can reduce 176 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (1351) ~ (all_271_0_2382 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_2382
% 40.89/12.73 |
% 40.89/12.73 | Applying alpha-rule on (1351) yields:
% 40.89/12.73 | (1352) ~ (all_271_0_2382 = 0)
% 40.89/12.73 | (1353) distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_2382
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (235), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (339) all_51_0_66 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (339) can reduce 171 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.73 | (546) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (232), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (339) all_51_0_66 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (339) can reduce 171 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.73 | (550) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (236), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (287) all_60_0_73 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (287) can reduce 179 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.73 | (599) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (237), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (287) all_60_0_73 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (287) can reduce 179 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (179) ~ (all_60_0_73 = 0)
% 40.89/12.73 | (603) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.89/12.73 |
% 40.89/12.73 +-Applying beta-rule and splitting (226), into two cases.
% 40.89/12.73 |-Branch one:
% 40.89/12.73 | (339) all_51_0_66 = 0
% 40.89/12.73 |
% 40.89/12.73 | Equations (339) can reduce 171 to:
% 40.89/12.73 | (288) $false
% 40.89/12.73 |
% 40.89/12.73 |-The branch is then unsatisfiable
% 40.89/12.73 |-Branch two:
% 40.89/12.73 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.73 | (554) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (227), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (558) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (233), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (562) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (318), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (446) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (426), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (648) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (628), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (652) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (632), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (656) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (1161), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (1398) (all_291_0_2387 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_291_0_2387 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (all_291_0_2387 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387)
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (1398), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (1399) (all_291_0_2387 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (all_291_0_2387 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0)
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (1399), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (1400) all_291_0_2387 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.89/12.74 |
% 40.89/12.74 | Applying alpha-rule on (1400) yields:
% 40.89/12.74 | (1401) all_291_0_2387 = 0
% 40.89/12.74 | (542) apart_point_and_line(all_0_6_6, all_0_2_2) = 0
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (322), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (346), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (378), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (229), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (586) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_4_4) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (230), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (578) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (231), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (590) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (228), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (582) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 | Instantiating formula (19) with all_0_6_6, all_0_2_2, 0, all_51_0_66 and discharging atoms apart_point_and_line(all_0_6_6, all_0_2_2) = all_51_0_66, apart_point_and_line(all_0_6_6, all_0_2_2) = 0, yields:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (1433) all_291_0_2387 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.89/12.74 |
% 40.89/12.74 | Applying alpha-rule on (1433) yields:
% 40.89/12.74 | (1401) all_291_0_2387 = 0
% 40.89/12.74 | (689) apart_point_and_line(all_0_7_7, all_0_3_3) = 0
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (265), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (295) all_58_0_72 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (295) can reduce 176 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (176) ~ (all_58_0_72 = 0)
% 40.89/12.74 | (693) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.74 |
% 40.89/12.74 | Instantiating formula (19) with all_0_7_7, all_0_3_3, 0, all_58_0_72 and discharging atoms apart_point_and_line(all_0_7_7, all_0_3_3) = all_58_0_72, apart_point_and_line(all_0_7_7, all_0_3_3) = 0, yields:
% 40.89/12.74 | (295) all_58_0_72 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (295) can reduce 176 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (1442) ~ (all_291_0_2387 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387
% 40.89/12.74 |
% 40.89/12.74 | Applying alpha-rule on (1442) yields:
% 40.89/12.74 | (1443) ~ (all_291_0_2387 = 0)
% 40.89/12.74 | (1444) distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (222), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (335) all_49_0_64 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (335) can reduce 167 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.74 | (797) all_46_0_61 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_5_5) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (322), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (330), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (566) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (334), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (335) all_49_0_64 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (335) can reduce 167 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.74 | (1460) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (346), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (570) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (350), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (664) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_4_4, all_0_7_7) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (358), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (291) all_43_0_57 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (291) can reduce 158 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.74 | (668) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_7_7) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (378), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (339) all_51_0_66 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (339) can reduce 171 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.74 | (574) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_6_6) = v0))
% 40.89/12.74 |
% 40.89/12.74 +-Applying beta-rule and splitting (550), into two cases.
% 40.89/12.74 |-Branch one:
% 40.89/12.74 | (335) all_49_0_64 = 0
% 40.89/12.74 |
% 40.89/12.74 | Equations (335) can reduce 167 to:
% 40.89/12.74 | (288) $false
% 40.89/12.74 |
% 40.89/12.74 |-The branch is then unsatisfiable
% 40.89/12.74 |-Branch two:
% 40.89/12.74 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.74 | (1480) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (410), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (291) all_43_0_57 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (291) can reduce 158 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.75 | (676) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_6_6, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_7_7) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (225), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1488) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_5_5) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (370), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1492) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_5_5) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (620), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1496) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (624), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (291) all_43_0_57 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (291) can reduce 158 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.75 | (680) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_7_7, all_0_4_4) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (636), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (291) all_43_0_57 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (291) can reduce 158 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (158) ~ (all_43_0_57 = 0)
% 40.89/12.75 | (684) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_7_7, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_7_7) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (230), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (339) all_51_0_66 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (339) can reduce 171 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.75 | (578) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (231), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (339) all_51_0_66 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (339) can reduce 171 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (171) ~ (all_51_0_66 = 0)
% 40.89/12.75 | (590) all_49_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (578), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1516) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_5_5, all_0_6_6) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (1147), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (1517) (all_279_0_2384 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (all_279_0_2384 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0) | ( ~ (all_279_0_2384 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_2384)
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (1517), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (1518) (all_279_0_2384 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | (all_279_0_2384 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0)
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (1518), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (1519) all_279_0_2384 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.89/12.75 |
% 40.89/12.75 | Applying alpha-rule on (1519) yields:
% 40.89/12.75 | (1520) all_279_0_2384 = 0
% 40.89/12.75 | (595) apart_point_and_line(all_0_6_6, all_0_3_3) = 0
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (19) with all_0_6_6, all_0_3_3, 0, all_60_0_73 and discharging atoms apart_point_and_line(all_0_6_6, all_0_3_3) = all_60_0_73, apart_point_and_line(all_0_6_6, all_0_3_3) = 0, yields:
% 40.89/12.75 | (287) all_60_0_73 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (287) can reduce 179 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (1524) all_279_0_2384 = 0 & apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.89/12.75 |
% 40.89/12.75 | Applying alpha-rule on (1524) yields:
% 40.89/12.75 | (1520) all_279_0_2384 = 0
% 40.89/12.75 | (640) apart_point_and_line(all_0_7_7, all_0_2_2) = 0
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (19) with all_0_7_7, all_0_2_2, 0, all_43_0_57 and discharging atoms apart_point_and_line(all_0_7_7, all_0_2_2) = all_43_0_57, apart_point_and_line(all_0_7_7, all_0_2_2) = 0, yields:
% 40.89/12.75 | (291) all_43_0_57 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (291) can reduce 158 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (1529) ~ (all_279_0_2384 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_2384
% 40.89/12.75 |
% 40.89/12.75 | Applying alpha-rule on (1529) yields:
% 40.89/12.75 | (1530) ~ (all_279_0_2384 = 0)
% 40.89/12.75 | (1531) distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_2384
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (562), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1535) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_2_2) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (590), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1539) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_5_5, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_0_6_6, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_6_6, all_0_5_5) = v0))
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (16) with all_0_2_2, all_0_3_3, all_283_0_2385, all_291_0_2387 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387, distinct_lines(all_0_2_2, all_0_3_3) = all_283_0_2385, yields:
% 40.89/12.75 | (1540) all_291_0_2387 = all_283_0_2385
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (16) with all_0_2_2, all_0_3_3, all_279_0_2384, all_291_0_2387 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387, distinct_lines(all_0_2_2, all_0_3_3) = all_279_0_2384, yields:
% 40.89/12.75 | (1541) all_291_0_2387 = all_279_0_2384
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (16) with all_0_2_2, all_0_3_3, all_271_0_2382, all_291_0_2387 and discharging atoms distinct_lines(all_0_2_2, all_0_3_3) = all_291_0_2387, distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_2382, yields:
% 40.89/12.75 | (1542) all_291_0_2387 = all_271_0_2382
% 40.89/12.75 |
% 40.89/12.75 | Combining equations (1541,1540) yields a new equation:
% 40.89/12.75 | (1543) all_283_0_2385 = all_279_0_2384
% 40.89/12.75 |
% 40.89/12.75 | Combining equations (1542,1540) yields a new equation:
% 40.89/12.75 | (1544) all_283_0_2385 = all_271_0_2382
% 40.89/12.75 |
% 40.89/12.75 | Combining equations (1543,1544) yields a new equation:
% 40.89/12.75 | (1545) all_279_0_2384 = all_271_0_2382
% 40.89/12.75 |
% 40.89/12.75 | Simplifying 1545 yields:
% 40.89/12.75 | (1546) all_279_0_2384 = all_271_0_2382
% 40.89/12.75 |
% 40.89/12.75 | Equations (1546) can reduce 1530 to:
% 40.89/12.75 | (1352) ~ (all_271_0_2382 = 0)
% 40.89/12.75 |
% 40.89/12.75 | From (1546) and (1531) follows:
% 40.89/12.75 | (1353) distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_2382
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (8) with all_0_1_1, all_0_2_2, all_0_5_5 and discharging atoms incident_point_and_line(all_0_5_5, all_0_2_2) = all_0_1_1, yields:
% 40.89/12.75 | (1549) all_0_1_1 = 0 | apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (115) with all_49_0_64, all_271_0_2382, all_0_3_3, all_0_2_2, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = all_49_0_64, distinct_lines(all_0_2_2, all_0_3_3) = all_271_0_2382, yields:
% 40.89/12.75 | (1550) all_271_0_2382 = 0 | all_49_0_64 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0)
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (1549), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (1551) apart_point_and_line(all_0_5_5, all_0_2_2) = 0
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (1550), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (1294) all_271_0_2382 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (1294) can reduce 1352 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (1352) ~ (all_271_0_2382 = 0)
% 40.89/12.75 | (1555) all_49_0_64 = 0 | ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0)
% 40.89/12.75 |
% 40.89/12.75 +-Applying beta-rule and splitting (1555), into two cases.
% 40.89/12.75 |-Branch one:
% 40.89/12.75 | (335) all_49_0_64 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (335) can reduce 167 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.75 |-Branch two:
% 40.89/12.75 | (167) ~ (all_49_0_64 = 0)
% 40.89/12.75 | (1559) ? [v0] : ( ~ (v0 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = v0)
% 40.89/12.75 |
% 40.89/12.75 | Instantiating (1559) with all_597_0_3994 yields:
% 40.89/12.75 | (1560) ~ (all_597_0_3994 = 0) & apart_point_and_line(all_0_5_5, all_0_2_2) = all_597_0_3994
% 40.89/12.75 |
% 40.89/12.75 | Applying alpha-rule on (1560) yields:
% 40.89/12.75 | (1561) ~ (all_597_0_3994 = 0)
% 40.89/12.75 | (1562) apart_point_and_line(all_0_5_5, all_0_2_2) = all_597_0_3994
% 40.89/12.75 |
% 40.89/12.75 | Instantiating formula (19) with all_0_5_5, all_0_2_2, 0, all_597_0_3994 and discharging atoms apart_point_and_line(all_0_5_5, all_0_2_2) = all_597_0_3994, apart_point_and_line(all_0_5_5, all_0_2_2) = 0, yields:
% 40.89/12.75 | (1563) all_597_0_3994 = 0
% 40.89/12.75 |
% 40.89/12.75 | Equations (1563) can reduce 1561 to:
% 40.89/12.75 | (288) $false
% 40.89/12.75 |
% 40.89/12.75 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1565) ~ (apart_point_and_line(all_0_5_5, all_0_2_2) = 0)
% 40.89/12.76 | (1566) all_0_1_1 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1566) can reduce 940 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1568) ~ (all_279_0_2384 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_279_0_2384
% 40.89/12.76 |
% 40.89/12.76 | Applying alpha-rule on (1568) yields:
% 40.89/12.76 | (1530) ~ (all_279_0_2384 = 0)
% 40.89/12.76 | (1570) distinct_points(all_0_7_7, all_0_6_6) = all_279_0_2384
% 40.89/12.76 |
% 40.89/12.76 | Instantiating formula (32) with all_0_7_7, all_0_6_6, all_279_0_2384, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_279_0_2384, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.89/12.76 | (1520) all_279_0_2384 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1520) can reduce 1530 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1573) ~ (all_291_0_2387 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_291_0_2387
% 40.89/12.76 |
% 40.89/12.76 | Applying alpha-rule on (1573) yields:
% 40.89/12.76 | (1443) ~ (all_291_0_2387 = 0)
% 40.89/12.76 | (1575) distinct_points(all_0_7_7, all_0_6_6) = all_291_0_2387
% 40.89/12.76 |
% 40.89/12.76 | Instantiating formula (32) with all_0_7_7, all_0_6_6, all_291_0_2387, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_291_0_2387, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.89/12.76 | (1401) all_291_0_2387 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1401) can reduce 1443 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1578) ~ (all_63_0_75 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_63_0_75
% 40.89/12.76 |
% 40.89/12.76 | Applying alpha-rule on (1578) yields:
% 40.89/12.76 | (193) ~ (all_63_0_75 = 0)
% 40.89/12.76 | (1580) distinct_points(all_0_5_5, all_0_4_4) = all_63_0_75
% 40.89/12.76 |
% 40.89/12.76 | Instantiating formula (32) with all_0_5_5, all_0_4_4, all_63_0_75, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_63_0_75, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 40.89/12.76 | (1581) all_63_0_75 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1581) can reduce 193 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1583) ~ (all_55_0_69 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_55_0_69
% 40.89/12.76 |
% 40.89/12.76 | Applying alpha-rule on (1583) yields:
% 40.89/12.76 | (190) ~ (all_55_0_69 = 0)
% 40.89/12.76 | (1585) distinct_points(all_0_7_7, all_0_6_6) = all_55_0_69
% 40.89/12.76 |
% 40.89/12.76 | Instantiating formula (32) with all_0_7_7, all_0_6_6, all_55_0_69, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_55_0_69, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.89/12.76 | (1586) all_55_0_69 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1586) can reduce 190 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1588) ~ (all_62_0_74 = 0) & distinct_points(all_0_5_5, all_0_4_4) = all_62_0_74
% 40.89/12.76 |
% 40.89/12.76 | Applying alpha-rule on (1588) yields:
% 40.89/12.76 | (187) ~ (all_62_0_74 = 0)
% 40.89/12.76 | (1590) distinct_points(all_0_5_5, all_0_4_4) = all_62_0_74
% 40.89/12.76 |
% 40.89/12.76 | Instantiating formula (32) with all_0_5_5, all_0_4_4, all_62_0_74, 0 and discharging atoms distinct_points(all_0_5_5, all_0_4_4) = all_62_0_74, distinct_points(all_0_5_5, all_0_4_4) = 0, yields:
% 40.89/12.76 | (1591) all_62_0_74 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1591) can reduce 187 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 |-Branch two:
% 40.89/12.76 | (1593) ~ (all_48_0_63 = 0) & distinct_points(all_0_7_7, all_0_6_6) = all_48_0_63
% 40.89/12.76 |
% 40.89/12.76 | Applying alpha-rule on (1593) yields:
% 40.89/12.76 | (184) ~ (all_48_0_63 = 0)
% 40.89/12.76 | (1595) distinct_points(all_0_7_7, all_0_6_6) = all_48_0_63
% 40.89/12.76 |
% 40.89/12.76 | Instantiating formula (32) with all_0_7_7, all_0_6_6, all_48_0_63, 0 and discharging atoms distinct_points(all_0_7_7, all_0_6_6) = all_48_0_63, distinct_points(all_0_7_7, all_0_6_6) = 0, yields:
% 40.89/12.76 | (1596) all_48_0_63 = 0
% 40.89/12.76 |
% 40.89/12.76 | Equations (1596) can reduce 184 to:
% 40.89/12.76 | (288) $false
% 40.89/12.76 |
% 40.89/12.76 |-The branch is then unsatisfiable
% 40.89/12.76 % SZS output end Proof for theBenchmark
% 40.89/12.76
% 40.89/12.76 12167ms
%------------------------------------------------------------------------------