%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO253+1 : TPTP v8.1.0. Bugfixed v6.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n026.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 03:49:13 EDT 2022 % Result : Theorem 8.16s 2.55s % Output : Proof 14.67s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.11 % Problem : GEO253+1 : TPTP v8.1.0. Bugfixed v6.4.0. % 0.10/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n026.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 : Fri Jun 17 20:45:39 EDT 2022 % 0.12/0.33 % CPUTime : % 0.18/0.57 ____ _ % 0.18/0.57 ___ / __ \_____(_)___ ________ __________ % 0.18/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.18/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.18/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.18/0.57 % 0.18/0.57 A Theorem Prover for First-Order Logic % 0.18/0.58 (ePrincess v.1.0) % 0.18/0.58 % 0.18/0.58 (c) Philipp Rümmer, 2009-2015 % 0.18/0.58 (c) Peter Backeman, 2014-2015 % 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.18/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.18/0.58 Bug reports to peter@backeman.se % 0.18/0.58 % 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.18/0.58 % 0.60/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.69/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.73/0.98 Prover 0: Preprocessing ... % 2.55/1.24 Prover 0: Warning: ignoring some quantifiers % 2.55/1.27 Prover 0: Constructing countermodel ... % 3.14/1.38 Prover 0: gave up % 3.14/1.38 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.14/1.43 Prover 1: Preprocessing ... % 4.18/1.60 Prover 1: Constructing countermodel ... % 4.18/1.67 Prover 1: gave up % 4.18/1.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.59/1.73 Prover 2: Preprocessing ... % 5.90/2.07 Prover 2: Warning: ignoring some quantifiers % 6.35/2.09 Prover 2: Constructing countermodel ... % 8.16/2.55 Prover 2: proved (878ms) % 8.16/2.55 % 8.16/2.55 No countermodel exists, formula is valid % 8.16/2.55 % SZS status Theorem for theBenchmark % 8.16/2.55 % 8.16/2.55 Generating proof ... Warning: ignoring some quantifiers % 13.69/3.83 found it (size 11) % 13.69/3.83 % 13.69/3.83 % SZS output start Proof for theBenchmark % 13.69/3.83 Assumed formulas after preprocessing and simplification: % 13.69/3.83 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v4 = 0) & parallel_through_point(v2, v0) = v3 & apart_point_and_line(v1, v3) = v4 & apart_point_and_line(v1, v2) = v5 & apart_point_and_line(v0, v2) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v11 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (reverse_line(v9) = v12) | ~ (reverse_line(v8) = v10) | ~ (left_apart_point(v7, v12) = v13) | ~ (left_apart_point(v7, v10) = v11) | ? [v14] : ((v14 = 0 & left_apart_point(v7, v9) = 0) | (v14 = 0 & left_apart_point(v7, v8) = 0) | (v14 = 0 & left_apart_point(v6, v12) = 0) | (v14 = 0 & left_apart_point(v6, v10) = 0) | (v14 = 0 & left_apart_point(v6, v9) = 0) | (v14 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v14 = 0) & distinct_lines(v8, v9) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v11 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (reverse_line(v9) = v12) | ~ (reverse_line(v8) = v10) | ~ (left_apart_point(v6, v12) = v13) | ~ (left_apart_point(v6, v10) = v11) | ? [v14] : ((v14 = 0 & left_apart_point(v7, v12) = 0) | (v14 = 0 & left_apart_point(v7, v10) = 0) | (v14 = 0 & left_apart_point(v7, v9) = 0) | (v14 = 0 & left_apart_point(v7, v8) = 0) | (v14 = 0 & left_apart_point(v6, v9) = 0) | (v14 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v14 = 0) & distinct_lines(v8, v9) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v11 = 0 | ~ (reverse_line(v9) = v12) | ~ (reverse_line(v8) = v10) | ~ (left_apart_point(v7, v12) = v13) | ~ (left_apart_point(v6, v10) = v11) | ? [v14] : ((v14 = 0 & left_apart_point(v7, v10) = 0) | (v14 = 0 & left_apart_point(v7, v9) = 0) | (v14 = 0 & left_apart_point(v7, v8) = 0) | (v14 = 0 & left_apart_point(v6, v12) = 0) | (v14 = 0 & left_apart_point(v6, v9) = 0) | (v14 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v14 = 0) & distinct_lines(v8, v9) = v14) | ( ~ (v14 = 0) & distinct_points(v6, v7) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v11 = 0 | ~ (reverse_line(v9) = v12) | ~ (reverse_line(v8) = v10) | ~ (left_apart_point(v7, v10) = v11) | ~ (left_apart_point(v6, v12) = v13) | ? [v14] : ((v14 = 0 & left_apart_point(v7, v12) = 0) | (v14 = 0 & left_apart_point(v7, v9) = 0) | (v14 = 0 & left_apart_point(v7, v8) = 0) | (v14 = 0 & left_apart_point(v6, v10) = 0) | (v14 = 0 & left_apart_point(v6, v9) = 0) | (v14 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v14 = 0) & distinct_lines(v8, v9) = v14) | ( ~ (v14 = 0) & distinct_points(v6, v7) = v14))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (reverse_line(v9) = v10) | ~ (left_apart_point(v7, v10) = v12) | ~ (left_apart_point(v6, v10) = v11) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (reverse_line(v8) = v10) | ~ (left_apart_point(v7, v10) = v12) | ~ (left_apart_point(v6, v10) = v11) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (reverse_line(v9) = v11) | ~ (left_apart_point(v7, v11) = v12) | ~ (left_apart_point(v6, v9) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (reverse_line(v9) = v11) | ~ (left_apart_point(v7, v9) = v10) | ~ (left_apart_point(v6, v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v11) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (reverse_line(v8) = v11) | ~ (left_apart_point(v7, v11) = v12) | ~ (left_apart_point(v6, v8) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (reverse_line(v8) = v11) | ~ (left_apart_point(v7, v8) = v10) | ~ (left_apart_point(v6, v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v11) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (reverse_line(v9) = v11) | ~ (left_apart_point(v7, v11) = v12) | ~ (left_apart_point(v7, v8) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (reverse_line(v9) = v11) | ~ (left_apart_point(v6, v11) = v12) | ~ (left_apart_point(v6, v8) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v11) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (reverse_line(v8) = v11) | ~ (left_apart_point(v7, v11) = v12) | ~ (left_apart_point(v7, v9) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (reverse_line(v8) = v11) | ~ (left_apart_point(v6, v11) = v12) | ~ (left_apart_point(v6, v9) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v11) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (reverse_line(v9) = v11) | ~ (left_apart_point(v7, v11) = v12) | ~ (left_apart_point(v6, v8) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (reverse_line(v9) = v11) | ~ (left_apart_point(v7, v8) = v10) | ~ (left_apart_point(v6, v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v8) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v11) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (reverse_line(v8) = v11) | ~ (left_apart_point(v7, v11) = v12) | ~ (left_apart_point(v6, v9) = v10) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v9) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (reverse_line(v8) = v11) | ~ (left_apart_point(v7, v9) = v10) | ~ (left_apart_point(v6, v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v7, v13) = 0) | (v14 = 0 & reverse_line(v9) = v13 & left_apart_point(v6, v13) = 0) | (v13 = 0 & left_apart_point(v7, v11) = 0) | (v13 = 0 & left_apart_point(v7, v8) = 0) | (v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v13 = 0) & distinct_lines(v8, v9) = v13) | ( ~ (v13 = 0) & distinct_points(v6, v7) = v13))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (left_apart_point(v7, v9) = v11) | ~ (left_apart_point(v6, v9) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v6, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v6, v12) = 0) | (v12 = 0 & left_apart_point(v7, v8) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v8, v9) = 0) | ~ (left_apart_point(v7, v8) = v11) | ~ (left_apart_point(v6, v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v6, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v6, v12) = 0) | (v12 = 0 & left_apart_point(v7, v9) = 0) | (v12 = 0 & left_apart_point(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (left_apart_point(v7, v9) = v11) | ~ (left_apart_point(v7, v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v6, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v6, v12) = 0) | (v12 = 0 & left_apart_point(v6, v9) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_points(v6, v7) = 0) | ~ (left_apart_point(v6, v9) = v11) | ~ (left_apart_point(v6, v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v6, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v6, v12) = 0) | (v12 = 0 & left_apart_point(v7, v9) = 0) | (v12 = 0 & left_apart_point(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (left_apart_point(v7, v9) = v11) | ~ (left_apart_point(v6, v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v6, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v6, v12) = 0) | (v12 = 0 & left_apart_point(v7, v8) = 0) | (v12 = 0 & left_apart_point(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (left_apart_point(v7, v8) = v10) | ~ (left_apart_point(v6, v9) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v9) = v12 & left_apart_point(v6, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v7, v12) = 0) | (v13 = 0 & reverse_line(v8) = v12 & left_apart_point(v6, v12) = 0) | (v12 = 0 & left_apart_point(v7, v9) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (reverse_line(v8) = v10) | ~ (left_apart_point(v6, v10) = v11) | ? [v12] : (( ~ (v12 = 0) & unequally_directed_lines(v7, v8) = v12) | ( ~ (v12 = 0) & left_apart_point(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (between_on_line(v11, v10, v9, v8) = v7) | ~ (between_on_line(v11, v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unequally_directed_lines(v7, v10) = v11) | ~ (unequally_directed_lines(v6, v9) = 0) | ~ (reverse_line(v8) = v10) | ~ (reverse_line(v7) = v9) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unequally_directed_lines(v6, v10) = 0 & unequally_directed_lines(v6, v8) = 0) | (v12 = 0 & v11 = 0 & unequally_directed_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unequally_directed_lines(v7, v10) = v11) | ~ (unequally_directed_lines(v6, v8) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v7, v8) = 0) | (v12 = 0 & v9 = 0 & unequally_directed_lines(v6, v10) = 0) | ( ~ (v13 = 0) & unequally_directed_lines(v6, v12) = v13 & reverse_line(v7) = v12) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unequally_directed_lines(v7, v9) = v11) | ~ (unequally_directed_lines(v6, v9) = v10) | ~ (reverse_line(v8) = v9) | ? [v12] : ? [v13] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v7, v8) = 0) | (v12 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0) | ( ~ (v13 = 0) & unequally_directed_lines(v6, v12) = v13 & reverse_line(v7) = v12) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unequally_directed_lines(v7, v8) = v11) | ~ (unequally_directed_lines(v6, v9) = v10) | ~ (reverse_line(v8) = v9) | ? [v12] : ? [v13] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v7, v9) = 0) | (v12 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0) | ( ~ (v13 = 0) & unequally_directed_lines(v6, v12) = v13 & reverse_line(v7) = v12) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (unequally_directed_lines(v6, v10) = v11) | ~ (unequally_directed_lines(v6, v9) = 0) | ~ (reverse_line(v8) = v10) | ~ (reverse_line(v7) = v9) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unequally_directed_lines(v7, v10) = 0 & unequally_directed_lines(v7, v8) = 0) | (v12 = 0 & v11 = 0 & unequally_directed_lines(v6, v8) = 0) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (left_convergent_lines(v6, v8) = v10) | ~ (unequally_directed_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & left_convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (left_apart_point(v7, v8) = v10) | ? [v11] : ( ~ (v11 = 0) & left_apart_point(v6, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unequally_directed_lines(v7, v8) = v10) | ~ (unequally_directed_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (left_convergent_lines(v9, v8) = v10) | ~ (line_connecting(v6, v7) = v9) | ? [v11] : ((v11 = 0 & left_apart_point(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v6, v7) = v11) | ( ~ (v11 = 0) & left_apart_point(v6, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (between_on_line(v6, v7, v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & before_on_line(v6, v9, v8) = v11) | ( ~ (v11 = 0) & before_on_line(v6, v8, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (between_on_line(v6, v7, v8, v9) = v10) | ? [v11] : (( ~ (v11 = 0) & before_on_line(v6, v8, v9) = v11) | ( ~ (v11 = 0) & before_on_line(v6, v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (line_connecting(v7, v8) = v9) | ~ (unequally_directed_lines(v6, v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & reverse_line(v6) = v11 & left_apart_point(v8, v11) = 0) | (v12 = 0 & reverse_line(v6) = v11 & left_apart_point(v7, v11) = 0) | (v11 = 0 & before_on_line(v6, v7, v8) = 0) | (v11 = 0 & left_apart_point(v8, v6) = 0) | (v11 = 0 & left_apart_point(v7, v6) = 0) | ( ~ (v11 = 0) & distinct_points(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (unequally_directed_lines(v7, v8) = 0) | ~ (reverse_line(v8) = v9) | ~ (left_apart_point(v6, v9) = v10) | ? [v11] : ((v11 = 0 & distinct_lines(v7, v8) = 0) | ( ~ (v11 = 0) & left_apart_point(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (reverse_line(v8) = v9) | ~ (left_apart_point(v6, v9) = v10) | ~ (left_apart_point(v6, v7) = 0) | ? [v11] : ((v11 = 0 & distinct_lines(v7, v8) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (before_on_line(v10, v9, v8) = v7) | ~ (before_on_line(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (divides_points(v10, v9, v8) = v7) | ~ (divides_points(v10, v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (line_connecting(v7, v8) = v9) | ~ (unequally_directed_lines(v6, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v11 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & ~ (v14 = 0) & ~ (v12 = 0) & ~ (v10 = 0) & distinct_points(v7, v8) = 0 & reverse_line(v6) = v13 & left_apart_point(v8, v13) = v16 & left_apart_point(v8, v6) = v15 & left_apart_point(v7, v13) = v14 & left_apart_point(v7, v6) = v12) | ( ~ (v11 = 0) & before_on_line(v6, v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unequally_directed_lines(v7, v9) = v10) | ~ (unequally_directed_lines(v6, v7) = 0) | ~ (reverse_line(v8) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v8) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v7, v8) = 0) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v11) = v12 & reverse_line(v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unequally_directed_lines(v7, v8) = v10) | ~ (unequally_directed_lines(v6, v9) = 0) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v11 = 0 & unequally_directed_lines(v6, v12) = 0 & unequally_directed_lines(v6, v8) = 0 & reverse_line(v8) = v12) | (v12 = 0 & v10 = 0 & unequally_directed_lines(v7, v11) = 0 & reverse_line(v8) = v11) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unequally_directed_lines(v7, v8) = v10) | ~ (unequally_directed_lines(v6, v8) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & v10 = 0 & unequally_directed_lines(v7, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & v9 = 0 & unequally_directed_lines(v6, v11) = 0 & reverse_line(v8) = v11) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v11) = v12 & reverse_line(v7) = v11) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unequally_directed_lines(v6, v9) = v10) | ~ (unequally_directed_lines(v6, v7) = 0) | ~ (reverse_line(v8) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v7, v9) = 0 & unequally_directed_lines(v7, v8) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0) | ( ~ (v12 = 0) & unequally_directed_lines(v6, v11) = v12 & reverse_line(v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unequally_directed_lines(v6, v9) = 0) | ~ (unequally_directed_lines(v6, v8) = v10) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ? [v13] : ((v13 = 0 & v12 = 0 & unequally_directed_lines(v7, v11) = 0 & unequally_directed_lines(v7, v8) = 0 & reverse_line(v8) = v11) | (v12 = 0 & v10 = 0 & unequally_directed_lines(v6, v11) = 0 & reverse_line(v8) = v11) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_convergent_lines(v6, v8) = v9) | ~ (left_convergent_lines(v6, v7) = 0) | unequally_directed_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_convergent_lines(v6, v8) = v9) | ~ (reverse_line(v7) = v8) | ? [v10] : ((v10 = 0 & left_convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v8) = v10) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_convergent_lines(v6, v7) = 0) | ~ (unequally_directed_lines(v7, v8) = v9) | left_convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (left_apart_point(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & reverse_line(v8) = v10 & left_apart_point(v6, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (before_on_line(v6, v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & line_connecting(v7, v8) = v10 & unequally_directed_lines(v6, v10) = 0) | (v11 = 0 & reverse_line(v6) = v10 & left_apart_point(v8, v10) = 0) | (v11 = 0 & reverse_line(v6) = v10 & left_apart_point(v7, v10) = 0) | (v10 = 0 & left_apart_point(v8, v6) = 0) | (v10 = 0 & left_apart_point(v7, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (left_apart_point(v6, v8) = 0) | left_apart_point(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (divides_points(v8, v6, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ((( ~ (v13 = 0) & reverse_line(v8) = v11 & left_apart_point(v7, v11) = v13) | ( ~ (v10 = 0) & left_apart_point(v6, v8) = v10)) & (( ~ (v12 = 0) & reverse_line(v8) = v11 & left_apart_point(v6, v11) = v12) | ( ~ (v12 = 0) & left_apart_point(v7, v8) = v12)))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unequally_directed_lines(v7, v8) = v9) | ~ (unequally_directed_lines(v6, v7) = 0) | unequally_directed_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unequally_directed_lines(v6, v8) = v9) | ~ (unequally_directed_lines(v6, v7) = 0) | unequally_directed_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unequally_directed_lines(v6, v8) = v9) | ~ (reverse_line(v7) = v8) | ? [v10] : ((v10 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v10 = 0) & line(v7) = v10) | ( ~ (v10 = 0) & line(v6) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (reverse_line(v7) = v8) | ~ (left_apart_point(v6, v8) = v9) | ? [v10] : ((v10 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v10 = 0) & apart_point_and_line(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_apart_point(v7, v8) = v9) | ~ (left_apart_point(v6, v8) = 0) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (left_convergent_lines(v9, v8) = v7) | ~ (left_convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unequally_directed_lines(v9, v8) = v7) | ~ (unequally_directed_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (left_apart_point(v9, v8) = v7) | ~ (left_apart_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & reverse_line(v9) = v10 & left_apart_point(v7, v10) = 0) | (v11 = 0 & reverse_line(v9) = v10 & left_apart_point(v6, v10) = 0) | (v11 = 0 & reverse_line(v8) = v10 & left_apart_point(v7, v10) = 0) | (v11 = 0 & reverse_line(v8) = v10 & left_apart_point(v6, v10) = 0) | (v10 = 0 & left_apart_point(v7, v9) = 0) | (v10 = 0 & left_apart_point(v7, v8) = 0) | (v10 = 0 & left_apart_point(v6, v9) = 0) | (v10 = 0 & left_apart_point(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (between_on_line(v6, v7, v8, v9) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & before_on_line(v6, v9, v8) = 0 & before_on_line(v6, v8, v7) = 0) | (v11 = 0 & v10 = 0 & before_on_line(v6, v8, v9) = 0 & before_on_line(v6, v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unequally_directed_lines(v7, v8) = v9) | ~ (unequally_directed_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v10 = 0 & unequally_directed_lines(v6, v11) = 0 & unequally_directed_lines(v6, v8) = 0 & reverse_line(v8) = v11) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v7, v10) = 0 & reverse_line(v8) = v10) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v10) = v11 & reverse_line(v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unequally_directed_lines(v6, v8) = v9) | ~ (unequally_directed_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v7, v10) = 0 & unequally_directed_lines(v7, v8) = 0 & reverse_line(v8) = v10) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v6, v10) = 0 & reverse_line(v8) = v10) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v10) = v11 & reverse_line(v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unequally_directed_lines(v6, v8) = v9) | ~ (reverse_line(v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v7) = v8) | ~ (left_apart_point(v6, v8) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v10 = 0) & ~ (v9 = 0) & left_apart_point(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & left_convergent_lines(v6, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v9) = v10 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & unequally_directed_lines(v6, v9) = v10 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unequally_directed_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & unequally_directed_lines(v6, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & ~ (v9 = 0) & reverse_line(v7) = v10 & left_apart_point(v6, v10) = v11 & left_apart_point(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & reverse_line(v7) = v9 & left_apart_point(v6, v9) = 0) | ( ~ (v9 = 0) & apart_point_and_line(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (reverse_line(v8) = v7) | ~ (reverse_line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unequally_directed_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ? [v10] : ((v9 = 0 & point(v8) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v9) = v10 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ~ (v9 = 0) & apart_point_and_line(v8, v7) = v10 & apart_point_and_line(v8, v6) = v9) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v9) = v10 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (left_convergent_lines(v6, v8) = 0) | ~ (reverse_line(v7) = v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v7, v6) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & line_connecting(v6, v7) = v9 & unequally_directed_lines(v9, v10) = v11 & reverse_line(v8) = v10)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ( ~ (v11 = 0) & line_connecting(v7, v6) = v9 & unequally_directed_lines(v8, v10) = v11 & reverse_line(v9) = v10)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & ~ (v9 = 0) & apart_point_and_line(v7, v8) = v10 & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (before_on_line(v6, v7, v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ( ~ (v15 = 0) & ~ (v13 = 0) & ~ (v12 = 0) & ~ (v11 = 0) & ~ (v9 = 0) & line_connecting(v7, v8) = v14 & distinct_points(v7, v8) = 0 & unequally_directed_lines(v6, v14) = v15 & reverse_line(v6) = v10 & left_apart_point(v8, v10) = v13 & left_apart_point(v8, v6) = v12 & left_apart_point(v7, v10) = v11 & left_apart_point(v7, v6) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (divides_points(v8, v6, v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : (reverse_line(v8) = v10 & ((v12 = 0 & v11 = 0 & left_apart_point(v7, v8) = 0 & left_apart_point(v6, v10) = 0) | (v11 = 0 & v9 = 0 & left_apart_point(v7, v10) = 0 & left_apart_point(v6, v8) = 0)))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v7) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & reverse_line(v8) = v9 & left_apart_point(v6, v9) = 0) | (v9 = 0 & distinct_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v8) = 0) | ~ (reverse_line(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : (( ~ (v11 = 0) & ~ (v10 = 0) & intersection_point(v6, v7) = v9 & apart_point_and_line(v9, v7) = v11 & apart_point_and_line(v9, v6) = v10) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v8) = 0) | ~ (reverse_line(v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & intersection_point(v6, v7) = v9 & point(v9) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v8) = 0) | ~ (reverse_line(v7) = v8) | ? [v9] : ((v9 = 0 & left_convergent_lines(v6, v8) = 0) | (v9 = 0 & left_convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v8) = 0) | ~ (reverse_line(v7) = v8) | ? [v9] : ((v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & unequally_directed_lines(v6, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v7) = v8) | ~ (left_apart_point(v6, v8) = 0)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (left_apart_point(v6, v7) = v8) | ? [v9] : ? [v10] : ((v9 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v10 = 0) & ~ (v8 = 0) & reverse_line(v7) = v9 & left_apart_point(v6, v9) = v10))) & ! [v6] : ! [v7] : ~ (left_convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = 0) & ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v10 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : (unequally_directed_lines(v6, v8) = 0 & unequally_directed_lines(v6, v7) = 0 & reverse_line(v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v10 = 0) & ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v10 & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v8) = v9 & reverse_line(v7) = v8))) & ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & intersection_point(v6, v7) = v8 & point(v8) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v8) = v9 & reverse_line(v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & left_convergent_lines(v6, v8) = 0 & reverse_line(v7) = v8) | (v8 = 0 & left_convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v8) = v9 & reverse_line(v7) = v8))) & ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v8) = v9 & reverse_line(v7) = v8))) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & reverse_line(v7) = v8 & left_apart_point(v6, v8) = 0) | (v8 = 0 & left_apart_point(v6, v7) = 0))) & ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ~ (left_apart_point(v6, v7) = 0) & ! [v6] : ( ~ (line(v6) = 0) | ? [v7] : (line(v7) = 0 & reverse_line(v6) = v7)) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ! [v6] : ~ (unequally_directed_lines(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : between_on_line(v9, v8, v7, v6) = v10 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : before_on_line(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : ? [v9] : divides_points(v8, v7, v6) = v9 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : left_convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unequally_directed_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : left_apart_point(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7 & ? [v6] : ? [v7] : reverse_line(v6) = v7) % 14.22/3.93 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 14.22/3.93 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & parallel_through_point(all_0_3_3, all_0_5_5) = all_0_2_2 & apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1 & apart_point_and_line(all_0_4_4, all_0_3_3) = all_0_0_0 & apart_point_and_line(all_0_5_5, all_0_3_3) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v3) = v4) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(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 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(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 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v0, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6) | ( ~ (v6 = 0) & left_apart_point(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v0, v6) = v7 & reverse_line(v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v0, v6) = v7 & reverse_line(v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v0, v6) = v7 & reverse_line(v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (left_convergent_lines(v0, v2) = v4) | ~ (unequally_directed_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & left_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] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v1, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_convergent_lines(v3, v2) = v4) | ~ (line_connecting(v0, v1) = v3) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & reverse_line(v0) = v5 & left_apart_point(v2, v5) = 0) | (v6 = 0 & reverse_line(v0) = v5 & left_apart_point(v1, v5) = 0) | (v5 = 0 & before_on_line(v0, v1, v2) = 0) | (v5 = 0 & left_apart_point(v2, v0) = 0) | (v5 = 0 & left_apart_point(v1, v0) = 0) | ( ~ (v5 = 0) & distinct_points(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unequally_directed_lines(v1, v2) = 0) | ~ (reverse_line(v2) = v3) | ~ (left_apart_point(v0, v3) = v4) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (reverse_line(v2) = v3) | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v5 = 0 & ~ (v10 = 0) & ~ (v9 = 0) & ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = 0) & distinct_points(v1, v2) = 0 & reverse_line(v0) = v7 & left_apart_point(v2, v7) = v10 & left_apart_point(v2, v0) = v9 & left_apart_point(v1, v7) = v8 & left_apart_point(v1, v0) = v6) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v5) = v6 & reverse_line(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0 & reverse_line(v2) = v6) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v1, v5) = 0 & reverse_line(v2) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & unequally_directed_lines(v1, v5) = 0 & reverse_line(v2) = v5) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v5) = 0 & reverse_line(v2) = v5) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v5) = v6 & reverse_line(v1) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v5) = v6 & reverse_line(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ~ (reverse_line(v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0 & reverse_line(v2) = v5) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v5) = 0 & reverse_line(v2) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_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(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & reverse_line(v2) = v4 & left_apart_point(v0, v4) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4))) & ! [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 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v2) = v4 & unequally_directed_lines(v0, v4) = 0) | (v5 = 0 & reverse_line(v0) = v4 & left_apart_point(v2, v4) = 0) | (v5 = 0 & reverse_line(v0) = v4 & left_apart_point(v1, v4) = 0) | (v4 = 0 & left_apart_point(v2, v0) = 0) | (v4 = 0 & left_apart_point(v1, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4))) & ! [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] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((( ~ (v7 = 0) & reverse_line(v2) = v5 & left_apart_point(v1, v5) = v7) | ( ~ (v4 = 0) & left_apart_point(v0, v2) = v4)) & (( ~ (v6 = 0) & reverse_line(v2) = v5 & left_apart_point(v0, v5) = v6) | ( ~ (v6 = 0) & left_apart_point(v1, v2) = v6)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v4 = 0) & line(v1) = v4) | ( ~ (v4 = 0) & line(v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = v3) | ? [v4] : ((v4 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v4 = 0) & apart_point_and_line(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) & ! [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 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_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 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(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 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(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 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & reverse_line(v3) = v4 & left_apart_point(v1, v4) = 0) | (v5 = 0 & reverse_line(v3) = v4 & left_apart_point(v0, v4) = 0) | (v5 = 0 & reverse_line(v2) = v4 & left_apart_point(v1, v4) = 0) | (v5 = 0 & reverse_line(v2) = v4 & left_apart_point(v0, v4) = 0) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0 & reverse_line(v2) = v5) | (v5 = 0 & v3 = 0 & unequally_directed_lines(v1, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0 & reverse_line(v2) = v4) | (v5 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & v3 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = v3) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & unequally_directed_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v3 = 0) & reverse_line(v1) = v4 & left_apart_point(v0, v4) = v5 & left_apart_point(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & reverse_line(v1) = v3 & left_apart_point(v0, v3) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [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] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unequally_directed_lines(v2, v1) = 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(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] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v0, v1) = v3 & unequally_directed_lines(v3, v4) = v5 & reverse_line(v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v3 & unequally_directed_lines(v2, v4) = v5 & reverse_line(v3) = v4)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(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] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v6 = 0) & ~ (v5 = 0) & ~ (v3 = 0) & line_connecting(v1, v2) = v8 & distinct_points(v1, v2) = 0 & unequally_directed_lines(v0, v8) = v9 & reverse_line(v0) = v4 & left_apart_point(v2, v4) = v7 & left_apart_point(v2, v0) = v6 & left_apart_point(v1, v4) = v5 & left_apart_point(v1, v0) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (reverse_line(v2) = v4 & ((v6 = 0 & v5 = 0 & left_apart_point(v1, v2) = 0 & left_apart_point(v0, v4) = 0) | (v5 = 0 & v3 = 0 & left_apart_point(v1, v4) = 0 & left_apart_point(v0, v2) = 0)))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v1, v2) = 0) | ~ (left_apart_point(v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & reverse_line(v2) = v3 & left_apart_point(v0, v3) = 0) | (v3 = 0 & distinct_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & unequally_directed_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ (v2 = 0) & reverse_line(v1) = v3 & left_apart_point(v0, v3) = v4))) & ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & 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] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : (unequally_directed_lines(v0, v2) = 0 & unequally_directed_lines(v0, v1) = 0 & reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & reverse_line(v1) = v2 & left_apart_point(v0, v2) = 0) | (v2 = 0 & left_apart_point(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) & ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ! [v0] : ~ (unequally_directed_lines(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 & ? [v0] : ? [v1] : reverse_line(v0) = v1 % 14.22/3.97 | % 14.22/3.97 | Applying alpha-rule on (1) yields: % 14.22/3.97 | (2) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3)) % 14.22/3.97 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v1) = v4))) % 14.22/3.97 | (4) ! [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)) % 14.22/3.97 | (5) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) % 14.22/3.97 | (6) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 14.22/3.97 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & v2 = 0 & unequally_directed_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 14.22/3.97 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) % 14.22/3.97 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 14.22/3.97 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) % 14.22/3.97 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/3.97 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) % 14.22/3.97 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 14.22/3.97 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/3.98 | (15) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) % 14.22/3.98 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/3.98 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 14.22/3.98 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0)) % 14.22/3.98 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v3) = v4) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/3.98 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 14.22/3.98 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0 & reverse_line(v2) = v4) | (v5 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) = v4))) % 14.22/3.98 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5)) % 14.22/3.98 | (23) apart_point_and_line(all_0_4_4, all_0_2_2) = all_0_1_1 % 14.22/3.98 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0) % 14.22/3.98 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & reverse_line(v2) = v4 & left_apart_point(v0, v4) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4))) % 14.22/3.98 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (unequally_directed_lines(v1, v2) = 0) | ~ (reverse_line(v2) = v3) | ~ (left_apart_point(v0, v3) = v4) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5))) % 14.22/3.98 | (27) ~ (all_0_0_0 = 0) % 14.22/3.98 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (between_on_line(v0, v1, v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & before_on_line(v0, v3, v2) = 0 & before_on_line(v0, v2, v1) = 0) | (v5 = 0 & v4 = 0 & before_on_line(v0, v2, v3) = 0 & before_on_line(v0, v1, v2) = 0))) % 14.22/3.98 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 14.22/3.98 | (30) ! [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))) % 14.22/3.98 | (31) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & unequally_directed_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 14.22/3.98 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 14.22/3.98 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = v3) | ? [v4] : ((v4 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v4 = 0) & apart_point_and_line(v0, v1) = v4))) % 14.22/3.98 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 14.22/3.98 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v0, v6) = v7 & reverse_line(v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 14.22/3.98 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 14.22/3.98 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ((v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.22/3.98 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : (reverse_line(v2) = v4 & ((v6 = 0 & v5 = 0 & left_apart_point(v1, v2) = 0 & left_apart_point(v0, v4) = 0) | (v5 = 0 & v3 = 0 & left_apart_point(v1, v4) = 0 & left_apart_point(v0, v2) = 0)))) % 14.22/3.98 | (39) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & reverse_line(v1) = v2 & left_apart_point(v0, v2) = 0) | (v2 = 0 & left_apart_point(v0, v1) = 0))) % 14.22/3.98 | (40) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3 % 14.22/3.98 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v3) = v5) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 14.22/3.98 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) % 14.22/3.98 | (43) ? [v0] : ? [v1] : point(v0) = v1 % 14.22/3.98 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_convergent_lines(v3, v2) = v4) | ~ (line_connecting(v0, v1) = v3) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))) % 14.22/3.99 | (45) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 14.22/3.99 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.22/3.99 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 14.22/3.99 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) % 14.22/3.99 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ (v2 = 0) & reverse_line(v1) = v3 & left_apart_point(v0, v3) = v4))) % 14.22/3.99 | (50) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & left_convergent_lines(v0, v3) = 0 & reverse_line(v1) = v3) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.22/3.99 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) % 14.22/3.99 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) % 14.22/3.99 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) % 14.22/3.99 | (54) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 14.22/3.99 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 14.22/3.99 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ~ (reverse_line(v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0 & reverse_line(v2) = v5) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v5) = 0 & reverse_line(v2) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) % 14.22/3.99 | (57) ? [v0] : ? [v1] : line(v0) = v1 % 14.22/3.99 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v2) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v0, v6) = v7 & reverse_line(v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 14.22/3.99 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v3, v2) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v2, v1) = v5))) % 14.22/3.99 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v2) = v4 & unequally_directed_lines(v0, v4) = 0) | (v5 = 0 & reverse_line(v0) = v4 & left_apart_point(v2, v4) = 0) | (v5 = 0 & reverse_line(v0) = v4 & left_apart_point(v1, v4) = 0) | (v4 = 0 & left_apart_point(v2, v0) = 0) | (v4 = 0 & left_apart_point(v1, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4))) % 14.22/3.99 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 14.22/3.99 | (62) apart_point_and_line(all_0_4_4, all_0_3_3) = all_0_0_0 % 14.22/3.99 | (63) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & reverse_line(v1) = v3 & left_apart_point(v0, v3) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) % 14.22/3.99 | (64) ! [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))) % 14.22/3.99 | (65) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) % 14.22/3.99 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) % 14.22/3.99 | (67) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2))) % 14.22/3.99 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ? [v4] : ? [v5] : (( ~ (v5 = 0) & ~ (v4 = 0) & intersection_point(v0, v1) = v3 & apart_point_and_line(v3, v1) = v5 & apart_point_and_line(v3, v0) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.22/3.99 | (69) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : (unequally_directed_lines(v0, v2) = 0 & unequally_directed_lines(v0, v1) = 0 & reverse_line(v1) = v2)) % 14.22/3.99 | (70) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 % 14.22/3.99 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & reverse_line(v3) = v4 & left_apart_point(v1, v4) = 0) | (v5 = 0 & reverse_line(v3) = v4 & left_apart_point(v0, v4) = 0) | (v5 = 0 & reverse_line(v2) = v4 & left_apart_point(v1, v4) = 0) | (v5 = 0 & reverse_line(v2) = v4 & left_apart_point(v0, v4) = 0) | (v4 = 0 & left_apart_point(v1, v3) = 0) | (v4 = 0 & left_apart_point(v1, v2) = 0) | (v4 = 0 & left_apart_point(v0, v3) = 0) | (v4 = 0 & left_apart_point(v0, v2) = 0))) % 14.22/3.99 | (72) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 14.22/3.99 | (73) ? [v0] : ? [v1] : reverse_line(v0) = v1 % 14.22/3.99 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/3.99 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 14.22/3.99 | (76) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 14.22/3.99 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unequally_directed_lines(v2, v1) = v3)) % 14.22/4.00 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/4.00 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & v3 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 14.22/4.00 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) % 14.22/4.00 | (81) parallel_through_point(all_0_3_3, all_0_5_5) = all_0_2_2 % 14.22/4.00 | (82) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4 % 14.22/4.00 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) % 14.22/4.00 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ((v4 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v4 = 0) & line(v1) = v4) | ( ~ (v4 = 0) & line(v0) = v4))) % 14.22/4.00 | (85) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2) | (v2 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2))) % 14.22/4.00 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/4.00 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (left_convergent_lines(v0, v2) = v4) | ~ (unequally_directed_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & left_convergent_lines(v0, v1) = v5)) % 14.22/4.00 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v2) = v5) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v3) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/4.00 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0)) % 14.22/4.00 | (90) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 % 14.22/4.00 | (91) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2))) % 14.22/4.00 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ((v5 = 0 & ~ (v10 = 0) & ~ (v9 = 0) & ~ (v8 = 0) & ~ (v6 = 0) & ~ (v4 = 0) & distinct_points(v1, v2) = 0 & reverse_line(v0) = v7 & left_apart_point(v2, v7) = v10 & left_apart_point(v2, v0) = v9 & left_apart_point(v1, v7) = v8 & left_apart_point(v1, v0) = v6) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) % 14.22/4.00 | (93) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 14.22/4.00 | (94) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v2) = v3 & reverse_line(v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) % 14.22/4.00 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v2, v1) = v4 & apart_point_and_line(v2, v0) = v3) | ( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.22/4.00 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v5) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.22/4.00 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3 % 14.22/4.00 | (98) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 % 14.22/4.00 | (99) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ? [v4] : ((v4 = 0 & intersection_point(v0, v1) = v3 & point(v3) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.22/4.00 | (100) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 14.22/4.00 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 14.22/4.00 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v1) = v3) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0 & reverse_line(v2) = v6) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v1, v5) = 0 & reverse_line(v2) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) % 14.22/4.00 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ((v6 = 0 & reverse_line(v0) = v5 & left_apart_point(v2, v5) = 0) | (v6 = 0 & reverse_line(v0) = v5 & left_apart_point(v1, v5) = 0) | (v5 = 0 & before_on_line(v0, v1, v2) = 0) | (v5 = 0 & left_apart_point(v2, v0) = 0) | (v5 = 0 & left_apart_point(v1, v0) = 0) | ( ~ (v5 = 0) & distinct_points(v1, v2) = v5))) % 14.22/4.00 | (104) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 14.22/4.00 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v1, v0) = v3 & unequally_directed_lines(v2, v4) = v5 & reverse_line(v3) = v4)) % 14.22/4.01 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v0, v4) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 14.67/4.01 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v7 = 0) & ~ (v6 = 0) & ~ (v5 = 0) & ~ (v3 = 0) & line_connecting(v1, v2) = v8 & distinct_points(v1, v2) = 0 & unequally_directed_lines(v0, v8) = v9 & reverse_line(v0) = v4 & left_apart_point(v2, v4) = v7 & left_apart_point(v2, v0) = v6 & left_apart_point(v1, v4) = v5 & left_apart_point(v1, v0) = v3)) % 14.67/4.01 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0 & reverse_line(v2) = v5) | (v5 = 0 & v3 = 0 & unequally_directed_lines(v1, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v4) = v5 & reverse_line(v1) = v4))) % 14.67/4.01 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) % 14.67/4.01 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v6) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) % 14.67/4.01 | (111) apart_point_and_line(all_0_5_5, all_0_3_3) = 0 % 14.67/4.01 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((( ~ (v7 = 0) & reverse_line(v2) = v5 & left_apart_point(v1, v5) = v7) | ( ~ (v4 = 0) & left_apart_point(v0, v2) = v4)) & (( ~ (v6 = 0) & reverse_line(v2) = v5 & left_apart_point(v0, v5) = v6) | ( ~ (v6 = 0) & left_apart_point(v1, v2) = v6)))) % 14.67/4.01 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v5) | ~ (left_apart_point(v0, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 14.67/4.01 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & ~ (v3 = 0) & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 14.67/4.01 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & line_connecting(v0, v1) = v3 & unequally_directed_lines(v3, v4) = v5 & reverse_line(v2) = v4)) % 14.67/4.01 | (116) ! [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)) % 14.67/4.01 | (117) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 14.67/4.01 | (118) ! [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))) % 14.67/4.01 | (119) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v0, v3) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 14.67/4.01 | (120) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v1, v2) = 0) | ~ (left_apart_point(v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & reverse_line(v2) = v3 & left_apart_point(v0, v3) = 0) | (v3 = 0 & distinct_lines(v1, v2) = 0))) % 14.67/4.01 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v5) = v6 & reverse_line(v1) = v5))) % 14.67/4.01 | (122) ! [v0] : ~ (unequally_directed_lines(v0, v0) = 0) % 14.67/4.01 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 14.67/4.01 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & unequally_directed_lines(v1, v5) = 0 & reverse_line(v2) = v5) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v5) = 0 & reverse_line(v2) = v5) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v5) = v6 & reverse_line(v1) = v5) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) % 14.67/4.01 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | ? [v3] : ((v3 = 0 & left_convergent_lines(v0, v2) = 0) | (v3 = 0 & left_convergent_lines(v0, v1) = 0) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.67/4.01 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 14.67/4.01 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 14.67/4.01 | (128) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : (( ~ (v4 = 0) & unequally_directed_lines(v0, v3) = v4 & reverse_line(v1) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 14.67/4.01 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v4) = 0) | (v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8) | ( ~ (v8 = 0) & distinct_points(v0, v1) = v8))) % 14.67/4.01 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ? [v8] : ((v8 = 0 & left_apart_point(v1, v3) = 0) | (v8 = 0 & left_apart_point(v1, v2) = 0) | (v8 = 0 & left_apart_point(v0, v6) = 0) | (v8 = 0 & left_apart_point(v0, v4) = 0) | (v8 = 0 & left_apart_point(v0, v3) = 0) | (v8 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v8 = 0) & distinct_lines(v2, v3) = v8))) % 14.67/4.01 | (131) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 14.67/4.01 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) % 14.67/4.02 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v1, v2) = v4) | ? [v5] : ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5)) % 14.67/4.02 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (between_on_line(v0, v1, v2, v3) = v4) | ? [v5] : (( ~ (v5 = 0) & before_on_line(v0, v2, v3) = v5) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) % 14.67/4.02 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) % 14.67/4.02 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (reverse_line(v2) = v3) | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) % 14.67/4.02 | (137) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & ~ (v3 = 0) & reverse_line(v1) = v4 & left_apart_point(v0, v4) = v5 & left_apart_point(v0, v1) = v3)) % 14.67/4.02 | (138) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) % 14.67/4.02 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v0, v3) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v4 = 0 & unequally_directed_lines(v1, v2) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v5) = v6 & reverse_line(v1) = v5))) % 14.67/4.02 | (140) ~ (all_0_1_1 = 0) % 14.67/4.02 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v1, v2) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7) | ( ~ (v7 = 0) & distinct_points(v0, v1) = v7))) % 14.67/4.02 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (reverse_line(v3) = v5) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v1, v7) = 0) | (v8 = 0 & reverse_line(v2) = v7 & left_apart_point(v0, v7) = 0) | (v7 = 0 & left_apart_point(v1, v3) = 0) | (v7 = 0 & left_apart_point(v0, v5) = 0) | (v7 = 0 & left_apart_point(v0, v3) = 0) | (v7 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v7 = 0) & distinct_lines(v2, v3) = v7))) % 14.67/4.02 | (143) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 14.67/4.02 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v3) = v5) | ~ (left_apart_point(v1, v2) = v4) | ? [v6] : ? [v7] : ((v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v3) = v6 & left_apart_point(v0, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v1, v6) = 0) | (v7 = 0 & reverse_line(v2) = v6 & left_apart_point(v0, v6) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 14.67/4.02 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (reverse_line(v2) = v4) | ~ (left_apart_point(v0, v4) = v5) | ? [v6] : (( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6) | ( ~ (v6 = 0) & left_apart_point(v0, v1) = v6))) % 14.67/4.02 | (146) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 14.67/4.02 | (147) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = 0)) % 14.67/4.02 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v0, v6) = v7 & reverse_line(v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 14.67/4.02 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (reverse_line(v1) = v2) | ~ (left_apart_point(v0, v2) = v3) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v4))) % 14.67/4.02 | % 14.67/4.02 | Instantiating formula (39) with all_0_3_3, all_0_5_5 and discharging atoms apart_point_and_line(all_0_5_5, all_0_3_3) = 0, yields: % 14.67/4.02 | (150) ? [v0] : ? [v1] : ((v1 = 0 & reverse_line(all_0_3_3) = v0 & left_apart_point(all_0_5_5, v0) = 0) | (v0 = 0 & left_apart_point(all_0_5_5, all_0_3_3) = 0)) % 14.67/4.02 | % 14.67/4.02 | Instantiating (150) with all_40_0_55, all_40_1_56 yields: % 14.67/4.02 | (151) (all_40_0_55 = 0 & reverse_line(all_0_3_3) = all_40_1_56 & left_apart_point(all_0_5_5, all_40_1_56) = 0) | (all_40_1_56 = 0 & left_apart_point(all_0_5_5, all_0_3_3) = 0) % 14.67/4.02 | % 14.67/4.02 +-Applying beta-rule and splitting (151), into two cases. % 14.67/4.02 |-Branch one: % 14.67/4.02 | (152) all_40_0_55 = 0 & reverse_line(all_0_3_3) = all_40_1_56 & left_apart_point(all_0_5_5, all_40_1_56) = 0 % 14.67/4.02 | % 14.67/4.02 | Applying alpha-rule on (152) yields: % 14.67/4.02 | (153) all_40_0_55 = 0 % 14.67/4.02 | (154) reverse_line(all_0_3_3) = all_40_1_56 % 14.67/4.02 | (155) left_apart_point(all_0_5_5, all_40_1_56) = 0 % 14.67/4.02 | % 14.67/4.02 | Instantiating formula (15) with all_40_1_56, all_0_5_5 and discharging atoms left_apart_point(all_0_5_5, all_40_1_56) = 0, yields: % 14.67/4.02 | (156) $false % 14.67/4.02 | % 14.67/4.02 |-The branch is then unsatisfiable % 14.67/4.02 |-Branch two: % 14.67/4.02 | (157) all_40_1_56 = 0 & left_apart_point(all_0_5_5, all_0_3_3) = 0 % 14.67/4.02 | % 14.67/4.02 | Applying alpha-rule on (157) yields: % 14.67/4.02 | (158) all_40_1_56 = 0 % 14.67/4.02 | (159) left_apart_point(all_0_5_5, all_0_3_3) = 0 % 14.67/4.02 | % 14.67/4.02 | Instantiating formula (15) with all_0_3_3, all_0_5_5 and discharging atoms left_apart_point(all_0_5_5, all_0_3_3) = 0, yields: % 14.67/4.02 | (156) $false % 14.67/4.02 | % 14.67/4.02 |-The branch is then unsatisfiable % 14.67/4.02 % SZS output end Proof for theBenchmark % 14.67/4.02 % 14.67/4.02 3427ms %------------------------------------------------------------------------------