%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO253+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.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 9.55s 2.90s % Output : Proof 17.99s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : GEO253+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n008.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.35 % DateTime : Sat Jun 18 09:49:07 EDT 2022 % 0.13/0.35 % CPUTime : % 0.52/0.60 ____ _ % 0.52/0.60 ___ / __ \_____(_)___ ________ __________ % 0.52/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.52/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.52/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.52/0.60 % 0.52/0.60 A Theorem Prover for First-Order Logic % 0.52/0.60 (ePrincess v.1.0) % 0.52/0.60 % 0.52/0.60 (c) Philipp Rümmer, 2009-2015 % 0.52/0.60 (c) Peter Backeman, 2014-2015 % 0.52/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.52/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.52/0.60 Bug reports to peter@backeman.se % 0.52/0.60 % 0.52/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.52/0.60 % 0.52/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.77/1.01 Prover 0: Preprocessing ... % 2.63/1.30 Prover 0: Warning: ignoring some quantifiers % 2.89/1.34 Prover 0: Constructing countermodel ... % 3.75/1.60 Prover 0: gave up % 3.75/1.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.08/1.66 Prover 1: Preprocessing ... % 5.05/1.86 Prover 1: Constructing countermodel ... % 5.44/1.92 Prover 1: gave up % 5.44/1.92 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.44/1.95 Prover 2: Preprocessing ... % 6.84/2.25 Prover 2: Warning: ignoring some quantifiers % 6.84/2.26 Prover 2: Constructing countermodel ... % 9.55/2.90 Prover 2: proved (981ms) % 9.55/2.90 % 9.55/2.90 No countermodel exists, formula is valid % 9.55/2.90 % SZS status Theorem for theBenchmark % 9.55/2.90 % 9.55/2.90 Generating proof ... Warning: ignoring some quantifiers % 17.01/4.65 found it (size 14) % 17.01/4.65 % 17.01/4.65 % SZS output start Proof for theBenchmark % 17.01/4.65 Assumed formulas after preprocessing and simplification: % 17.01/4.65 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & parallel_through_point(v2, v0) = v3 & incident_point_and_line(v1, v3) = 0 & apart_point_and_line(v1, v2) = v4 & apart_point_and_line(v0, v2) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v11) = v12) | ~ (left_apart_point(v6, v9) = v10) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v11) = 0) | (v13 = 0 & left_apart_point(v5, v9) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v11) = v12) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((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 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (left_apart_point(v6, v11) = v12) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v9) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v11) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13) | ( ~ (v13 = 0) & distinct_points(v5, v6) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v10 = 0 | ~ (left_apart_point(v6, v9) = v10) | ~ (left_apart_point(v5, v11) = v12) | ~ (reverse_line(v8) = v11) | ~ (reverse_line(v7) = v9) | ? [v13] : ((v13 = 0 & left_apart_point(v6, v11) = 0) | (v13 = 0 & left_apart_point(v6, v8) = 0) | (v13 = 0 & left_apart_point(v6, v7) = 0) | (v13 = 0 & left_apart_point(v5, v9) = 0) | (v13 = 0 & left_apart_point(v5, v8) = 0) | (v13 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v13 = 0) & distinct_lines(v7, v8) = v13) | ( ~ (v13 = 0) & distinct_points(v5, v6) = v13))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v9) = v11) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v8) = v9) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v9) = v11) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v7) = v9) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v7) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v8) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v7) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v6, v8) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v6, v7) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v10) = v11) | ~ (left_apart_point(v5, v7) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v10) = v11) | ~ (left_apart_point(v5, v7) = v9) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v8) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v7) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v8) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v8) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v7) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v6, v7) = v9) | ~ (left_apart_point(v5, v10) = v11) | ~ (reverse_line(v8) = v10) | ? [v12] : ? [v13] : ((v13 = 0 & left_apart_point(v6, v12) = 0 & reverse_line(v7) = v12) | (v13 = 0 & left_apart_point(v5, v12) = 0 & reverse_line(v7) = v12) | (v12 = 0 & left_apart_point(v6, v10) = 0) | (v12 = 0 & left_apart_point(v6, v8) = 0) | (v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12) | ( ~ (v12 = 0) & distinct_points(v5, v6) = v12))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v8) = v10) | ~ (left_apart_point(v5, v8) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v7) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = 0) | ~ (left_apart_point(v6, v7) = v10) | ~ (left_apart_point(v5, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v6, v8) = v10) | ~ (left_apart_point(v6, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v8) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v5, v6) = 0) | ~ (left_apart_point(v5, v8) = v10) | ~ (left_apart_point(v5, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (left_apart_point(v6, v8) = v10) | ~ (left_apart_point(v5, v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v7) = 0) | (v11 = 0 & left_apart_point(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (left_apart_point(v6, v7) = v9) | ~ (left_apart_point(v5, v8) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v6, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v8) = v11) | (v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v6, v8) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (left_apart_point(v5, v9) = v10) | ~ (reverse_line(v7) = v9) | ? [v11] : (( ~ (v11 = 0) & left_apart_point(v5, v6) = v11) | ( ~ (v11 = 0) & unequally_directed_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (between_on_line(v10, v9, v8, v7) = v6) | ~ (between_on_line(v10, v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v9) | ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v6, v9) = v10) | ~ (unequally_directed_lines(v5, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v5, v9) = 0 & unequally_directed_lines(v5, v7) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v9) | ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v5, v9) = v10) | ~ (unequally_directed_lines(v5, v8) = 0) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v9) | ~ (unequally_directed_lines(v6, v9) = v10) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v8 = 0 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v8) = v10) | ~ (unequally_directed_lines(v5, v8) = v9) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v7) = v10) | ~ (unequally_directed_lines(v5, v8) = v9) | ? [v11] : ? [v12] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v12 = 0) & reverse_line(v6) = v11 & unequally_directed_lines(v5, v11) = v12) | ( ~ (v11 = 0) & unequally_directed_lines(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (left_apart_point(v6, v7) = v9) | ? [v10] : ( ~ (v10 = 0) & left_apart_point(v5, v7) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (left_convergent_lines(v5, v7) = v9) | ~ (unequally_directed_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & left_convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (unequally_directed_lines(v6, v7) = v9) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (between_on_line(v5, v6, v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & before_on_line(v5, v8, v7) = v10) | ( ~ (v10 = 0) & before_on_line(v5, v7, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (between_on_line(v5, v6, v7, v8) = v9) | ? [v10] : (( ~ (v10 = 0) & before_on_line(v5, v7, v8) = v10) | ( ~ (v10 = 0) & before_on_line(v5, v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (line_connecting(v5, v6) = v8) | ~ (left_convergent_lines(v8, v7) = v9) | ? [v10] : ((v10 = 0 & left_apart_point(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v5, v6) = v10) | ( ~ (v10 = 0) & left_apart_point(v5, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_apart_point(v5, v8) = v9) | ~ (left_apart_point(v5, v6) = 0) | ~ (reverse_line(v7) = v8) | ? [v10] : ((v10 = 0 & distinct_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v7) = 0) | ? [v10] : ((v10 = 0 & distinct_lines(v6, v7) = 0) | ( ~ (v10 = 0) & left_apart_point(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (before_on_line(v9, v8, v7) = v6) | ~ (before_on_line(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (divides_points(v9, v8, v7) = v6) | ~ (divides_points(v9, v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (line_connecting(v6, v7) = v8) | ~ (equally_directed_lines(v5, v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & v10 = 0 & v9 = 0 & distinct_points(v6, v7) = 0 & incident_point_and_line(v7, v5) = 0 & incident_point_and_line(v6, v5) = 0) | ( ~ (v10 = 0) & before_on_line(v5, v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v6, v8) = v9) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v8) = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v6, v7) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v7) = v8) | ~ (unequally_directed_lines(v5, v8) = v9) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v6, v8) = 0 & unequally_directed_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v6, v7) = v9) | ~ (unequally_directed_lines(v5, v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v10 = 0 & reverse_line(v7) = v11 & unequally_directed_lines(v5, v11) = 0 & unequally_directed_lines(v5, v7) = 0) | (v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v5, v8) = 0) | ~ (unequally_directed_lines(v5, v7) = v9) | ? [v10] : ? [v11] : ? [v12] : ((v12 = 0 & v11 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0 & unequally_directed_lines(v6, v7) = 0) | (v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unequally_directed_lines(v6, v7) = v9) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v6, v10) = 0) | (v11 = 0 & v8 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0) | ( ~ (v11 = 0) & reverse_line(v6) = v10 & unequally_directed_lines(v5, v10) = v11) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (left_apart_point(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (before_on_line(v5, v6, v7) = v8) | ? [v9] : ? [v10] : (( ~ (v10 = 0) & line_connecting(v6, v7) = v9 & equally_directed_lines(v5, v9) = v10) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v7, v5) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v6, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (left_apart_point(v5, v7) = 0) | left_apart_point(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (divides_points(v7, v5, v6) = v8) | ? [v9] : (( ~ (v9 = 0) & left_apart_point(v6, v7) = v9) | ( ~ (v9 = 0) & right_apart_point(v5, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (divides_points(v7, v5, v6) = v8) | ? [v9] : (( ~ (v9 = 0) & left_apart_point(v5, v7) = v9) | ( ~ (v9 = 0) & right_apart_point(v6, v7) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v7) = v8) | ~ (left_convergent_lines(v5, v6) = 0) | unequally_directed_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v9] : ( ~ (v9 = 0) & right_convergent_lines(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v9] : ((v9 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v7) = v9) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_convergent_lines(v5, v6) = 0) | ~ (unequally_directed_lines(v6, v7) = v8) | left_convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v6, v7) = v8) | ~ (left_apart_point(v5, v7) = 0) | distinct_points(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v5, v7) = v8) | ~ (reverse_line(v6) = v7) | ? [v9] : ( ~ (v9 = 0) & right_apart_point(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = v8) | unequally_directed_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & unequally_directed_opposite_lines(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unequally_directed_lines(v6, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | unequally_directed_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unequally_directed_lines(v5, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | unequally_directed_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (incident_point_and_line(v8, v7) = v6) | ~ (incident_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equally_directed_opposite_lines(v8, v7) = v6) | ~ (equally_directed_opposite_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (equally_directed_lines(v8, v7) = v6) | ~ (equally_directed_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (left_convergent_lines(v8, v7) = v6) | ~ (left_convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (right_convergent_lines(v8, v7) = v6) | ~ (right_convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (left_apart_point(v8, v7) = v6) | ~ (left_apart_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (right_apart_point(v8, v7) = v6) | ~ (right_apart_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unequally_directed_lines(v8, v7) = v6) | ~ (unequally_directed_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unequally_directed_opposite_lines(v8, v7) = v6) | ~ (unequally_directed_opposite_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & left_apart_point(v6, v9) = 0 & reverse_line(v8) = v9) | (v10 = 0 & left_apart_point(v6, v9) = 0 & reverse_line(v7) = v9) | (v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v8) = v9) | (v10 = 0 & left_apart_point(v5, v9) = 0 & reverse_line(v7) = v9) | (v9 = 0 & left_apart_point(v6, v8) = 0) | (v9 = 0 & left_apart_point(v6, v7) = 0) | (v9 = 0 & left_apart_point(v5, v8) = 0) | (v9 = 0 & left_apart_point(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (between_on_line(v5, v6, v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & before_on_line(v5, v8, v7) = 0 & before_on_line(v5, v7, v6) = 0) | (v10 = 0 & v9 = 0 & before_on_line(v5, v7, v8) = 0 & before_on_line(v5, v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ~ (equally_directed_lines(v5, v8) = 0) | ? [v9] : ((v9 = 0 & before_on_line(v5, v6, v7) = 0) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v7, v5) = v9) | ( ~ (v9 = 0) & incident_point_and_line(v6, v5) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v6, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v7) = v10 & unequally_directed_lines(v5, v10) = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v6, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v5, v7) = v8) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v6, v9) = 0 & unequally_directed_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v7) = v9 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = v10))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8) | ( ~ (v8 = 0) & unequally_directed_opposite_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (apart_point_and_line(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & left_apart_point(v5, v6) = v8 & right_apart_point(v5, v6) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equally_directed_opposite_lines(v5, v6) = v7) | unequally_directed_opposite_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (equally_directed_lines(v5, v6) = v7) | unequally_directed_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ((v9 = 0 & left_convergent_lines(v5, v8) = 0 & reverse_line(v6) = v8) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (right_convergent_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & left_convergent_lines(v5, v8) = v9 & reverse_line(v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & right_apart_point(v5, v6) = 0) | ( ~ (v8 = 0) & apart_point_and_line(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (right_apart_point(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & left_apart_point(v5, v8) = v9 & reverse_line(v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (right_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & left_apart_point(v5, v6) = 0) | ( ~ (v8 = 0) & apart_point_and_line(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v5, v6) = v7) | equally_directed_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v5, v6) = v7) | ? [v8] : (reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_opposite_lines(v5, v6) = v7) | equally_directed_opposite_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_opposite_lines(v5, v6) = v7) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (point(v7) = v6) | ~ (point(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (line(v7) = v6) | ~ (line(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (reverse_line(v7) = v6) | ~ (reverse_line(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | equally_directed_lines(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : ? [v9] : ((v8 = 0 & point(v7) = 0) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & apart_point_and_line(v7, v6) = v9 & apart_point_and_line(v7, v5) = v8) | ( ~ (v9 = 0) & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v6, v5) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & line_connecting(v5, v6) = v8 & equally_directed_lines(v8, v9) = 0 & reverse_line(v7) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & line_connecting(v6, v5) = v8 & equally_directed_lines(v7, v9) = 0 & reverse_line(v8) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & apart_point_and_line(v6, v7) = v9 & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : ((v8 = 0 & line(v7) = 0) | ( ~ (v8 = 0) & point(v6) = v8) | ( ~ (v8 = 0) & point(v5) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (before_on_line(v5, v6, v7) = 0) | ? [v8] : (line_connecting(v6, v7) = v8 & distinct_points(v6, v7) = 0 & incident_point_and_line(v7, v5) = 0 & incident_point_and_line(v6, v5) = 0 & equally_directed_lines(v5, v8) = 0)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (divides_points(v7, v5, v6) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & left_apart_point(v6, v7) = 0 & right_apart_point(v5, v7) = 0) | (v9 = 0 & v8 = 0 & left_apart_point(v5, v7) = 0 & right_apart_point(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_convergent_lines(v5, v7) = 0) | ~ (reverse_line(v6) = v7) | right_convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_convergent_lines(v5, v7) = 0) | ~ (reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v7) = 0) | ~ (reverse_line(v6) = v7) | right_apart_point(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v7) = 0) | ~ (reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v8 = 0) & ~ (v7 = 0) & right_apart_point(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (left_apart_point(v5, v6) = 0) | ~ (unequally_directed_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v5, v8) = 0 & reverse_line(v7) = v8) | (v8 = 0 & distinct_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (right_apart_point(v5, v6) = v7) | ? [v8] : ((v8 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v8 = 0) & ~ (v7 = 0) & left_apart_point(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | unequally_directed_opposite_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | ? [v8] : ? [v9] : ? [v10] : (( ~ (v10 = 0) & ~ (v9 = 0) & intersection_point(v5, v6) = v8 & apart_point_and_line(v8, v6) = v10 & apart_point_and_line(v8, v5) = v9) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & intersection_point(v5, v6) = v8 & point(v8) = 0) | ( ~ (v8 = 0) & line(v6) = v8) | ( ~ (v8 = 0) & line(v5) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = 0) | ? [v8] : ((v8 = 0 & left_convergent_lines(v5, v7) = 0) | (v8 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_opposite_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_opposite_lines(v5, v6) = v7) | ? [v8] : ((v8 = 0 & v7 = 0 & unequally_directed_lines(v5, v6) = 0) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : (v6 = 0 | ~ (equally_directed_lines(v5, v5) = v6)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = 0) & ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v9 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (line_connecting(v6, v5) = v8 & line_connecting(v5, v6) = v7 & equally_directed_lines(v7, v9) = 0 & reverse_line(v8) = v9)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & line(v7) = 0 & line_connecting(v5, v6) = v7) | ( ~ (v7 = 0) & point(v6) = v7) | ( ~ (v7 = 0) & point(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | (unequally_directed_lines(v5, v6) = 0 & unequally_directed_opposite_lines(v5, v6) = 0)) & ! [v5] : ! [v6] : ( ~ (apart_point_and_line(v5, v6) = 0) | ? [v7] : ((v7 = 0 & left_apart_point(v5, v6) = 0) | (v7 = 0 & right_apart_point(v5, v6) = 0))) & ! [v5] : ! [v6] : ( ~ (equally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & unequally_directed_opposite_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (equally_directed_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & unequally_directed_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ~ (left_convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ( ~ (right_convergent_lines(v5, v6) = 0) | ? [v7] : (left_convergent_lines(v5, v7) = 0 & reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ~ (left_apart_point(v5, v6) = 0) & ! [v5] : ! [v6] : ( ~ (right_apart_point(v5, v6) = 0) | ? [v7] : (left_apart_point(v5, v7) = 0 & reverse_line(v6) = v7)) & ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ? [v7] : ( ~ (v7 = 0) & distinct_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & line(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v9 & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & intersection_point(v5, v6) = v7 & point(v7) = 0) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8) | ( ~ (v7 = 0) & line(v6) = v7) | ( ~ (v7 = 0) & line(v5) = v7))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & left_convergent_lines(v5, v7) = 0 & reverse_line(v6) = v7) | (v7 = 0 & left_convergent_lines(v5, v6) = 0) | ( ~ (v8 = 0) & reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = v8))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & equally_directed_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ((v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v7 = 0) & unequally_directed_opposite_lines(v5, v6) = v7))) & ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : ( ~ (v7 = 0) & equally_directed_opposite_lines(v5, v6) = v7)) & ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : (reverse_line(v6) = v7 & unequally_directed_lines(v5, v7) = 0)) & ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v5, v6) = 0) | ? [v7] : ((v7 = 0 & convergent_lines(v5, v6) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v5, v6) = v7))) & ! [v5] : ( ~ (line(v5) = 0) | ? [v6] : (line(v6) = 0 & reverse_line(v5) = v6)) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : between_on_line(v8, v7, v6, v5) = v9 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : before_on_line(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : ? [v8] : divides_points(v7, v6, v5) = v8 & ? [v5] : ? [v6] : ? [v7] : parallel_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : incident_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equally_directed_opposite_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : equally_directed_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : left_convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : right_convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : left_apart_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : right_apart_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unequally_directed_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unequally_directed_opposite_lines(v6, v5) = v7 & ? [v5] : ? [v6] : point(v5) = v6 & ? [v5] : ? [v6] : line(v5) = v6 & ? [v5] : ? [v6] : reverse_line(v5) = v6) % 17.51/4.76 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 17.51/4.76 | (1) ~ (all_0_0_0 = 0) & parallel_through_point(all_0_2_2, all_0_4_4) = all_0_1_1 & incident_point_and_line(all_0_3_3, all_0_1_1) = 0 & apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_0_0 & apart_point_and_line(all_0_4_4, all_0_2_2) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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 | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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] : (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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = 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] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [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] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [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] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) & ! [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 | ~ (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 | ~ (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 | ~ (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(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [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 | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = 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) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [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) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [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) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (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 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) & ! [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 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (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 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = 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] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4))) & ! [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) & right_convergent_lines(v0, v1) = v4)) & ! [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 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4)) & ! [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] : (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 | ~ (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 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(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 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(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] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(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 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (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] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) & ! [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) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4)) & ! [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) | equally_directed_lines(v2, v1) = 0) & ! [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) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (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) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [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] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & right_apart_point(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [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] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [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] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [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, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) & ! [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] : ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4)) & ! [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) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0))) & ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2)) & ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2)) & ! [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] : ( ~ (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) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (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) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0)) & ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))) & ! [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] : ? [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] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 & ? [v0] : ? [v1] : reverse_line(v0) = v1 % 17.70/4.81 | % 17.70/4.81 | Applying alpha-rule on (1) yields: % 17.70/4.81 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 17.70/4.81 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.70/4.81 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) % 17.70/4.81 | (5) ! [v0] : ! [v1] : ! [v2] : ( ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & left_apart_point(v0, v1) = v3))) % 17.70/4.81 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v3 = 0) & ~ (v2 = 0) & right_apart_point(v0, v1) = v3))) % 17.70/4.81 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.70/4.81 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [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) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) % 17.70/4.81 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 17.70/4.81 | (10) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) % 17.70/4.81 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.70/4.81 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v1, v4) = 0 & reverse_line(v2) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v3) = v4) | (v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | (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))) % 17.70/4.81 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) % 17.70/4.81 | (14) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3) | ( ~ (v3 = 0) & unequally_directed_opposite_lines(v0, v1) = v3))) % 17.70/4.81 | (15) ! [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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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))) % 17.70/4.81 | (16) apart_point_and_line(all_0_3_3, all_0_2_2) = all_0_0_0 % 17.70/4.81 | (17) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) % 17.70/4.81 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v3) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 17.70/4.81 | (19) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 % 17.70/4.81 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) % 17.70/4.81 | (21) ! [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))) % 17.70/4.81 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.70/4.82 | (23) ! [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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 17.70/4.82 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) % 17.70/4.82 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v1, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v0, v2) = v4))) % 17.70/4.82 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [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))) % 17.70/4.82 | (27) ! [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) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) % 17.70/4.82 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) % 17.70/4.82 | (29) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0) % 17.70/4.82 | (30) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) % 17.70/4.82 | (31) ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2 % 17.70/4.82 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.82 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0) % 17.70/4.82 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (left_apart_point(v0, v1) = 0) | ~ (reverse_line(v2) = v3) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v1, v2) = v5))) % 17.70/4.82 | (35) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 17.70/4.82 | (36) ! [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)) % 17.70/4.82 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v4) = v5) | ~ (left_apart_point(v0, v6) = v7) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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))) % 17.70/4.82 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 17.70/4.82 | (39) ! [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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v0, v3) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 17.70/4.82 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.82 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (divides_points(v2, v0, v1) = v3) | ? [v4] : (( ~ (v4 = 0) & left_apart_point(v0, v2) = v4) | ( ~ (v4 = 0) & right_apart_point(v1, v2) = v4))) % 17.70/4.82 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 17.70/4.82 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (left_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & right_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) % 17.70/4.82 | (44) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 % 17.70/4.82 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v1, v0) = v3 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 17.70/4.82 | (46) ! [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)) % 17.70/4.82 | (47) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0) % 17.70/4.82 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 17.70/4.82 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_convergent_lines(v0, v1) = v4)) % 17.70/4.82 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 17.70/4.82 | (51) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_opposite_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 17.70/4.82 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) % 17.70/4.82 | (53) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v1, v0) = v2) | ? [v3] : ? [v4] : ? [v5] : ((v5 = 0 & line_connecting(v0, v1) = v3 & equally_directed_lines(v3, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 17.70/4.82 | (54) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [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))) % 17.70/4.82 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & v5 = 0 & v4 = 0 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0) | ( ~ (v5 = 0) & before_on_line(v0, v1, v2) = v5))) % 17.70/4.82 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v1, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.83 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v0, v3) = v4) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [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) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6))) % 17.70/4.83 | (58) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 17.70/4.83 | (59) ! [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))) % 17.70/4.83 | (60) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 17.70/4.83 | (61) ? [v0] : ? [v1] : reverse_line(v0) = v1 % 17.70/4.83 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) % 17.70/4.83 | (63) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2)) % 17.70/4.83 | (64) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) % 17.70/4.83 | (65) ! [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))) % 17.70/4.83 | (66) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 % 17.70/4.83 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & left_apart_point(v0, v4) = 0 & reverse_line(v2) = v4) | ( ~ (v4 = 0) & unequally_directed_lines(v1, v2) = v4))) % 17.70/4.83 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) % 17.70/4.83 | (69) ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2 % 17.70/4.83 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.83 | (71) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) % 17.70/4.83 | (72) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) % 17.70/4.83 | (73) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 17.70/4.83 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0)) % 17.70/4.83 | (75) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_apart_point(v0, v3) = v4 & reverse_line(v1) = v3)) % 17.70/4.83 | (76) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & intersection_point(v0, v1) = v2 & point(v2) = 0) | ( ~ (v3 = 0) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) % 17.70/4.83 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0)) % 17.70/4.83 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (unequally_directed_lines(v1, v4) = v5) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v3 = 0 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 17.70/4.83 | (79) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4 % 17.70/4.83 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 17.70/4.83 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (before_on_line(v0, v1, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v5 = 0) & line_connecting(v1, v2) = v4 & equally_directed_lines(v0, v4) = v5) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) % 17.70/4.83 | (82) ? [v0] : ? [v1] : point(v0) = v1 % 17.70/4.83 | (83) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4)) % 17.70/4.83 | (84) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & left_apart_point(v0, v1) = v3 & right_apart_point(v0, v1) = v4)) % 17.70/4.83 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [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))) % 17.70/4.83 | (86) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3 % 17.70/4.83 | (87) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0)) % 17.70/4.83 | (88) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 17.70/4.83 | (89) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0)) % 17.70/4.83 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 17.70/4.83 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) % 17.70/4.83 | (92) ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2 % 17.70/4.83 | (93) ! [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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (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))) % 17.70/4.83 | (94) ! [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) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 17.70/4.83 | (95) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2)) % 17.70/4.83 | (96) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 17.70/4.83 | (97) ! [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))) % 17.70/4.83 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 17.70/4.83 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v1, v2) = v3) | ~ (equally_directed_lines(v0, v3) = 0) | ? [v4] : ((v4 = 0 & before_on_line(v0, v1, v2) = 0) | ( ~ (v4 = 0) & distinct_points(v1, v2) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v2, v0) = v4) | ( ~ (v4 = 0) & incident_point_and_line(v1, v0) = v4))) % 17.70/4.84 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (line_connecting(v0, v1) = v3) | ~ (left_convergent_lines(v3, v2) = v4) | ? [v5] : ((v5 = 0 & left_apart_point(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_points(v0, v1) = v5) | ( ~ (v5 = 0) & left_apart_point(v0, v2) = v5))) % 17.70/4.84 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 17.70/4.84 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v4) | ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v4) = v5) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [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))) % 17.70/4.84 | (103) ? [v0] : ? [v1] : line(v0) = v1 % 17.70/4.84 | (104) incident_point_and_line(all_0_3_3, all_0_1_1) = 0 % 17.70/4.84 | (105) ! [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))) % 17.70/4.84 | (106) ~ (all_0_0_0 = 0) % 17.70/4.84 | (107) ! [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) & reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = v3))) % 17.70/4.84 | (108) ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2 % 17.70/4.84 | (109) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ? [v4] : (line_connecting(v1, v0) = v3 & line_connecting(v0, v1) = v2 & equally_directed_lines(v2, v4) = 0 & reverse_line(v3) = v4)) % 17.70/4.84 | (110) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 17.70/4.84 | (111) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 17.70/4.84 | (112) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) % 17.70/4.84 | (113) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 17.70/4.84 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v5 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0 & unequally_directed_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v0, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) % 17.70/4.84 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | (v6 = 0 & v3 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v6 = 0) & reverse_line(v1) = v5 & unequally_directed_lines(v0, v5) = v6) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) % 17.70/4.84 | (116) ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2 % 17.70/4.84 | (117) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_apart_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & left_apart_point(v0, v1) = 0) | ( ~ (v3 = 0) & apart_point_and_line(v0, v1) = v3))) % 17.70/4.84 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.84 | (119) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3 % 17.70/4.84 | (120) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2))) % 17.70/4.84 | (121) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ((v2 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2))) % 17.70/4.84 | (122) ! [v0] : ! [v1] : ! [v2] : ( ~ (divides_points(v2, v0, v1) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & v3 = 0 & left_apart_point(v1, v2) = 0 & right_apart_point(v0, v2) = 0) | (v4 = 0 & v3 = 0 & left_apart_point(v0, v2) = 0 & right_apart_point(v1, v2) = 0))) % 17.70/4.84 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0)) % 17.70/4.84 | (124) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (right_convergent_lines(v0, v1) = v2) | ? [v3] : ? [v4] : ( ~ (v4 = 0) & left_convergent_lines(v0, v3) = v4 & reverse_line(v1) = v3)) % 17.70/4.84 | (125) ! [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)) % 17.70/4.84 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) % 17.70/4.84 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | ? [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))) % 17.70/4.84 | (128) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) % 17.70/4.84 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v2) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.84 | (130) ! [v0] : ! [v1] : ! [v2] : ( ~ (unequally_directed_opposite_lines(v0, v1) = v2) | ? [v3] : ((v3 = 0 & v2 = 0 & unequally_directed_lines(v0, v1) = 0) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 17.70/4.84 | (131) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0) % 17.70/4.84 | (132) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) % 17.70/4.84 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) % 17.70/4.84 | (134) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) % 17.70/4.84 | (135) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 17.70/4.84 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0)) % 17.70/4.84 | (137) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 17.70/4.84 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v5) = v6) | ~ (left_apart_point(v0, v2) = v4) | ~ (reverse_line(v3) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v2) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v2) = v7) | (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))) % 17.70/4.84 | (139) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 % 17.70/4.84 | (140) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 17.70/4.84 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 17.70/4.84 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v5) = v6) | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.70/4.84 | (143) ! [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)) % 17.70/4.85 | (144) ! [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)) % 17.70/4.85 | (145) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 17.70/4.85 | (146) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ((v2 = 0 & left_apart_point(v0, v1) = 0) | (v2 = 0 & right_apart_point(v0, v1) = 0))) % 17.70/4.85 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v0, v2) = v3) | ~ (reverse_line(v1) = v2) | ? [v4] : ( ~ (v4 = 0) & right_apart_point(v0, v1) = v4)) % 17.70/4.85 | (148) ! [v0] : ! [v1] : ! [v2] : ( ~ (before_on_line(v0, v1, v2) = 0) | ? [v3] : (line_connecting(v1, v2) = v3 & distinct_points(v1, v2) = 0 & incident_point_and_line(v2, v0) = 0 & incident_point_and_line(v1, v0) = 0 & equally_directed_lines(v0, v3) = 0)) % 17.70/4.85 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v3) = v5) | ~ (unequally_directed_lines(v0, v3) = v4) | ? [v6] : ? [v7] : ((v6 = 0 & v5 = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & unequally_directed_lines(v0, v2) = 0) | ( ~ (v7 = 0) & reverse_line(v1) = v6 & unequally_directed_lines(v0, v6) = v7) | ( ~ (v6 = 0) & unequally_directed_lines(v0, v1) = v6))) % 17.70/4.85 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v0, v3) = 0) | ~ (unequally_directed_lines(v0, v2) = v4) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v6 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0 & unequally_directed_lines(v1, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) % 17.70/4.85 | (151) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 17.70/4.85 | (152) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) % 17.99/4.85 | (153) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) % 17.99/4.85 | (154) ! [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))) % 17.99/4.85 | (155) ! [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))) % 17.99/4.85 | (156) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v0, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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))) % 17.99/4.85 | (157) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) % 17.99/4.85 | (158) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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))) % 17.99/4.85 | (159) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v3] : ? [v4] : ((v4 = 0 & left_apart_point(v0, v3) = 0 & reverse_line(v2) = v3) | (v3 = 0 & distinct_lines(v1, v2) = 0))) % 17.99/4.85 | (160) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0)) % 17.99/4.85 | (161) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ? [v6] : ((v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v0, v5) = 0 & unequally_directed_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & reverse_line(v2) = v4 & unequally_directed_lines(v1, v4) = 0) | ( ~ (v5 = 0) & reverse_line(v1) = v4 & unequally_directed_lines(v0, v4) = v5))) % 17.99/4.85 | (162) ! [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))) % 17.99/4.85 | (163) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v5 = 0 | ~ (distinct_lines(v2, v3) = 0) | ~ (left_apart_point(v1, v4) = v6) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.99/4.85 | (164) ! [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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v3) = 0) | (v6 = 0 & left_apart_point(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 17.99/4.85 | (165) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) % 17.99/4.85 | (166) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (left_apart_point(v0, v4) = v5) | ~ (reverse_line(v2) = v4) | ? [v6] : (( ~ (v6 = 0) & left_apart_point(v0, v1) = v6) | ( ~ (v6 = 0) & unequally_directed_lines(v1, v2) = v6))) % 17.99/4.85 | (167) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0)) % 17.99/4.85 | (168) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (reverse_line(v1) = v3) | ~ (unequally_directed_lines(v1, v2) = v4) | ~ (unequally_directed_lines(v0, v3) = 0) | ? [v5] : ? [v6] : ? [v7] : ((v7 = 0 & v5 = 0 & reverse_line(v2) = v6 & unequally_directed_lines(v0, v6) = 0 & unequally_directed_lines(v0, v2) = 0) | (v6 = 0 & v4 = 0 & reverse_line(v2) = v5 & unequally_directed_lines(v1, v5) = 0) | ( ~ (v5 = 0) & unequally_directed_lines(v0, v1) = v5))) % 17.99/4.85 | (169) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2)) % 17.99/4.85 | (170) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | v4 = 0 | ~ (left_apart_point(v1, v3) = v4) | ~ (left_apart_point(v0, v5) = v6) | ~ (reverse_line(v2) = v5) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v1, v7) = 0 & reverse_line(v3) = v7) | (v8 = 0 & left_apart_point(v0, v7) = 0 & reverse_line(v3) = v7) | (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))) % 17.99/4.85 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 17.99/4.85 | (172) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) % 17.99/4.85 | (173) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) % 17.99/4.85 | (174) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | v5 = 0 | ~ (distinct_points(v0, v1) = 0) | ~ (left_apart_point(v1, v6) = v7) | ~ (left_apart_point(v1, v4) = v5) | ~ (reverse_line(v3) = v6) | ~ (reverse_line(v2) = v4) | ? [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))) % 17.99/4.85 | (175) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ? [v4] : ((v3 = 0 & point(v2) = 0) | ( ~ (v4 = 0) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 17.99/4.85 | (176) apart_point_and_line(all_0_4_4, all_0_2_2) = 0 % 17.99/4.85 | (177) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & unequally_directed_opposite_lines(v0, v1) = v4)) % 17.99/4.85 | (178) parallel_through_point(all_0_2_2, all_0_4_4) = all_0_1_1 % 17.99/4.85 | (179) ! [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 & left_apart_point(v1, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v1, v6) = 0 & reverse_line(v2) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v3) = v6) | (v7 = 0 & left_apart_point(v0, v6) = 0 & reverse_line(v2) = v6) | (v6 = 0 & left_apart_point(v1, v2) = 0) | (v6 = 0 & left_apart_point(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 17.99/4.86 | (180) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (left_apart_point(v0, v3) = v4) | ~ (reverse_line(v2) = v3) | ~ (unequally_directed_lines(v1, v2) = 0) | ? [v5] : ((v5 = 0 & distinct_lines(v1, v2) = 0) | ( ~ (v5 = 0) & left_apart_point(v0, v1) = v5))) % 17.99/4.86 | (181) ! [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) & reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = v4) | ( ~ (v3 = 0) & unequally_directed_lines(v0, v1) = v3))) % 17.99/4.86 | (182) ! [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)) % 17.99/4.86 | % 17.99/4.86 | Instantiating formula (146) with all_0_2_2, all_0_4_4 and discharging atoms apart_point_and_line(all_0_4_4, all_0_2_2) = 0, yields: % 17.99/4.86 | (183) ? [v0] : ((v0 = 0 & left_apart_point(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & right_apart_point(all_0_4_4, all_0_2_2) = 0)) % 17.99/4.86 | % 17.99/4.86 | Instantiating (183) with all_53_0_72 yields: % 17.99/4.86 | (184) (all_53_0_72 = 0 & left_apart_point(all_0_4_4, all_0_2_2) = 0) | (all_53_0_72 = 0 & right_apart_point(all_0_4_4, all_0_2_2) = 0) % 17.99/4.86 | % 17.99/4.86 +-Applying beta-rule and splitting (184), into two cases. % 17.99/4.86 |-Branch one: % 17.99/4.86 | (185) all_53_0_72 = 0 & left_apart_point(all_0_4_4, all_0_2_2) = 0 % 17.99/4.86 | % 17.99/4.86 | Applying alpha-rule on (185) yields: % 17.99/4.86 | (186) all_53_0_72 = 0 % 17.99/4.86 | (187) left_apart_point(all_0_4_4, all_0_2_2) = 0 % 17.99/4.86 | % 17.99/4.86 | Instantiating formula (134) with all_0_2_2, all_0_4_4 and discharging atoms left_apart_point(all_0_4_4, all_0_2_2) = 0, yields: % 17.99/4.86 | (188) $false % 17.99/4.86 | % 17.99/4.86 |-The branch is then unsatisfiable % 17.99/4.86 |-Branch two: % 17.99/4.86 | (189) all_53_0_72 = 0 & right_apart_point(all_0_4_4, all_0_2_2) = 0 % 17.99/4.86 | % 17.99/4.86 | Applying alpha-rule on (189) yields: % 17.99/4.86 | (186) all_53_0_72 = 0 % 17.99/4.86 | (191) right_apart_point(all_0_4_4, all_0_2_2) = 0 % 17.99/4.86 | % 17.99/4.86 | Instantiating formula (169) with all_0_2_2, all_0_4_4 and discharging atoms right_apart_point(all_0_4_4, all_0_2_2) = 0, yields: % 17.99/4.86 | (192) ? [v0] : (left_apart_point(all_0_4_4, v0) = 0 & reverse_line(all_0_2_2) = v0) % 17.99/4.86 | % 17.99/4.86 | Instantiating (192) with all_680_0_347 yields: % 17.99/4.86 | (193) left_apart_point(all_0_4_4, all_680_0_347) = 0 & reverse_line(all_0_2_2) = all_680_0_347 % 17.99/4.86 | % 17.99/4.86 | Applying alpha-rule on (193) yields: % 17.99/4.86 | (194) left_apart_point(all_0_4_4, all_680_0_347) = 0 % 17.99/4.86 | (195) reverse_line(all_0_2_2) = all_680_0_347 % 17.99/4.86 | % 17.99/4.86 | Instantiating formula (28) with all_680_0_347, all_0_2_2, all_0_4_4 and discharging atoms left_apart_point(all_0_4_4, all_680_0_347) = 0, reverse_line(all_0_2_2) = all_680_0_347, yields: % 17.99/4.86 | (188) $false % 17.99/4.86 | % 17.99/4.86 |-The branch is then unsatisfiable % 17.99/4.86 % SZS output end Proof for theBenchmark % 17.99/4.86 % 17.99/4.86 4250ms %------------------------------------------------------------------------------