%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO266+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n013.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 03:49:21 EDT 2022 % Result : Theorem 10.89s 3.20s % Output : Proof 27.40s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : GEO266+3 : TPTP v8.1.0. Released v4.0.0. % 0.12/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.34 % Computer : n013.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jun 18 05:21:59 EDT 2022 % 0.12/0.34 % CPUTime : % 0.60/0.60 ____ _ % 0.60/0.60 ___ / __ \_____(_)___ ________ __________ % 0.60/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.60/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.60/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.60/0.60 % 0.60/0.60 A Theorem Prover for First-Order Logic % 0.60/0.60 (ePrincess v.1.0) % 0.60/0.60 % 0.60/0.60 (c) Philipp Rümmer, 2009-2015 % 0.60/0.60 (c) Peter Backeman, 2014-2015 % 0.60/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.60/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.60/0.60 Bug reports to peter@backeman.se % 0.60/0.60 % 0.60/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.60/0.60 % 0.60/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.73/0.98 Prover 0: Preprocessing ... % 2.65/1.25 Prover 0: Warning: ignoring some quantifiers % 2.65/1.28 Prover 0: Constructing countermodel ... % 3.29/1.45 Prover 0: gave up % 3.29/1.46 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.69/1.50 Prover 1: Preprocessing ... % 4.37/1.67 Prover 1: Constructing countermodel ... % 4.75/1.70 Prover 1: gave up % 4.75/1.70 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 4.75/1.74 Prover 2: Preprocessing ... % 6.04/2.01 Prover 2: Warning: ignoring some quantifiers % 6.04/2.03 Prover 2: Constructing countermodel ... % 10.89/3.20 Prover 2: proved (1497ms) % 10.89/3.20 % 10.89/3.20 No countermodel exists, formula is valid % 10.89/3.20 % SZS status Theorem for theBenchmark % 10.89/3.20 % 10.89/3.20 Generating proof ... Warning: ignoring some quantifiers % 26.25/7.87 found it (size 187) % 26.25/7.87 % 26.25/7.87 % SZS output start Proof for theBenchmark % 26.25/7.87 Assumed formulas after preprocessing and simplification: % 26.25/7.87 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : (unequally_directed_opposite_lines(v1, v0) = v3 & unequally_directed_opposite_lines(v0, v1) = v2 & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v5, v10) = v11) | ~ (left_apart_point(v5, v8) = v9) | ~ (reverse_line(v7) = v10) | ~ (reverse_line(v6) = v8) | ? [v12] : ((v12 = 0 & left_apart_point(v5, v7) = 0) | (v12 = 0 & left_apart_point(v5, v6) = 0) | (v12 = 0 & left_apart_point(v4, v10) = 0) | (v12 = 0 & left_apart_point(v4, v8) = 0) | (v12 = 0 & left_apart_point(v4, v7) = 0) | (v12 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v12 = 0) & distinct_lines(v6, v7) = v12))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v4, v10) = v11) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v7) = v10) | ~ (reverse_line(v6) = v8) | ? [v12] : ((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 & left_apart_point(v5, v6) = 0) | (v12 = 0 & left_apart_point(v4, v7) = 0) | (v12 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v12 = 0) & distinct_lines(v6, v7) = v12))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v5, v10) = v11) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v7) = v10) | ~ (reverse_line(v6) = v8) | ? [v12] : ((v12 = 0 & left_apart_point(v5, v8) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | (v12 = 0 & left_apart_point(v5, v6) = 0) | (v12 = 0 & left_apart_point(v4, v10) = 0) | (v12 = 0 & left_apart_point(v4, v7) = 0) | (v12 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v12 = 0) & distinct_lines(v6, v7) = v12) | ( ~ (v12 = 0) & distinct_points(v4, v5) = v12))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v9 = 0 | ~ (left_apart_point(v5, v8) = v9) | ~ (left_apart_point(v4, v10) = v11) | ~ (reverse_line(v7) = v10) | ~ (reverse_line(v6) = v8) | ? [v12] : ((v12 = 0 & left_apart_point(v5, v10) = 0) | (v12 = 0 & left_apart_point(v5, v7) = 0) | (v12 = 0 & left_apart_point(v5, v6) = 0) | (v12 = 0 & left_apart_point(v4, v8) = 0) | (v12 = 0 & left_apart_point(v4, v7) = 0) | (v12 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v12 = 0) & distinct_lines(v6, v7) = v12) | ( ~ (v12 = 0) & distinct_points(v4, v5) = v12))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v8) = v10) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v7) = v8) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v8) = v10) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v6) = v8) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v9) = v10) | ~ (left_apart_point(v4, v7) = v8) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v9) = v10) | ~ (left_apart_point(v4, v6) = v8) | ~ (reverse_line(v6) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v7) = v8) | ~ (left_apart_point(v4, v9) = v10) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v9) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v6) = v8) | ~ (left_apart_point(v4, v9) = v10) | ~ (reverse_line(v6) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v9) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v5, v9) = v10) | ~ (left_apart_point(v5, v7) = v8) | ~ (reverse_line(v6) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v5, v9) = v10) | ~ (left_apart_point(v5, v6) = v8) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v4, v9) = v10) | ~ (left_apart_point(v4, v7) = v8) | ~ (reverse_line(v6) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v9) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v4, v9) = v10) | ~ (left_apart_point(v4, v6) = v8) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v9) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (left_apart_point(v5, v9) = v10) | ~ (left_apart_point(v4, v7) = v8) | ~ (reverse_line(v6) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (left_apart_point(v5, v9) = v10) | ~ (left_apart_point(v4, v6) = v8) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v9) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (left_apart_point(v5, v7) = v8) | ~ (left_apart_point(v4, v9) = v10) | ~ (reverse_line(v6) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v7) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v7) = v11) | (v11 = 0 & left_apart_point(v5, v9) = 0) | (v11 = 0 & left_apart_point(v5, v6) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v8 = 0 | ~ (left_apart_point(v5, v6) = v8) | ~ (left_apart_point(v4, v9) = v10) | ~ (reverse_line(v7) = v9) | ? [v11] : ? [v12] : ((v12 = 0 & left_apart_point(v5, v11) = 0 & reverse_line(v6) = v11) | (v12 = 0 & left_apart_point(v4, v11) = 0 & reverse_line(v6) = v11) | (v11 = 0 & left_apart_point(v5, v9) = 0) | (v11 = 0 & left_apart_point(v5, v7) = 0) | (v11 = 0 & left_apart_point(v4, v7) = 0) | (v11 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11) | ( ~ (v11 = 0) & distinct_points(v4, v5) = v11))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v7) = v9) | ~ (left_apart_point(v4, v7) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v5, v6) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = 0) | ~ (left_apart_point(v5, v6) = v9) | ~ (left_apart_point(v4, v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v5, v7) = 0) | (v10 = 0 & left_apart_point(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v5, v7) = v9) | ~ (left_apart_point(v5, v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v4, v7) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v4, v5) = 0) | ~ (left_apart_point(v4, v7) = v9) | ~ (left_apart_point(v4, v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v5, v7) = 0) | (v10 = 0 & left_apart_point(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (left_apart_point(v5, v7) = v9) | ~ (left_apart_point(v4, v6) = v8) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v5, v6) = 0) | (v10 = 0 & left_apart_point(v4, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (left_apart_point(v5, v6) = v8) | ~ (left_apart_point(v4, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v5, v10) = 0 & reverse_line(v6) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v7) = v10) | (v11 = 0 & left_apart_point(v4, v10) = 0 & reverse_line(v6) = v10) | (v10 = 0 & left_apart_point(v5, v7) = 0) | (v10 = 0 & left_apart_point(v4, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10) | ( ~ (v10 = 0) & distinct_points(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ~ (left_apart_point(v4, v8) = v9) | ~ (reverse_line(v6) = v8) | ? [v10] : (( ~ (v10 = 0) & left_apart_point(v4, v5) = v10) | ( ~ (v10 = 0) & unequally_directed_lines(v5, v6) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (between_on_line(v9, v8, v7, v6) = v5) | ~ (between_on_line(v9, v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ (unequally_directed_lines(v5, v8) = v9) | ~ (unequally_directed_lines(v4, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v4, v8) = 0 & unequally_directed_lines(v4, v6) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v6) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (reverse_line(v5) = v7) | ~ (unequally_directed_lines(v4, v8) = v9) | ~ (unequally_directed_lines(v4, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unequally_directed_lines(v5, v8) = 0 & unequally_directed_lines(v5, v6) = 0) | (v10 = 0 & v9 = 0 & unequally_directed_lines(v4, v6) = 0) | ( ~ (v10 = 0) & unequally_directed_lines(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v8) | ~ (unequally_directed_lines(v5, v8) = v9) | ~ (unequally_directed_lines(v4, v6) = v7) | ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v6) = 0) | (v10 = 0 & v7 = 0 & unequally_directed_lines(v4, v8) = 0) | ( ~ (v11 = 0) & reverse_line(v5) = v10 & unequally_directed_lines(v4, v10) = v11) | ( ~ (v10 = 0) & unequally_directed_lines(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = v9) | ~ (unequally_directed_lines(v4, v7) = v8) | ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v6) = 0) | (v10 = 0 & v8 = 0 & unequally_directed_lines(v4, v6) = 0) | ( ~ (v11 = 0) & reverse_line(v5) = v10 & unequally_directed_lines(v4, v10) = v11) | ( ~ (v10 = 0) & unequally_directed_lines(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v6) = v9) | ~ (unequally_directed_lines(v4, v7) = v8) | ? [v10] : ? [v11] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0) | (v10 = 0 & v8 = 0 & unequally_directed_lines(v4, v6) = 0) | ( ~ (v11 = 0) & reverse_line(v5) = v10 & unequally_directed_lines(v4, v10) = v11) | ( ~ (v10 = 0) & unequally_directed_lines(v4, v5) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_lines(v5, v6) = v8) | ~ (distinct_lines(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_points(v5, v6) = v8) | ~ (distinct_points(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & distinct_points(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (distinct_points(v4, v5) = v7) | ~ (left_apart_point(v5, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & left_apart_point(v4, v6) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (left_convergent_lines(v4, v6) = v8) | ~ (unequally_directed_lines(v5, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & left_convergent_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | v7 = 0 | ~ (unequally_directed_lines(v5, v6) = v8) | ~ (unequally_directed_lines(v4, v6) = v7) | ? [v9] : ( ~ (v9 = 0) & unequally_directed_lines(v4, v5) = v9)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (between_on_line(v4, v5, v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & before_on_line(v4, v7, v6) = v9) | ( ~ (v9 = 0) & before_on_line(v4, v6, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (between_on_line(v4, v5, v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & before_on_line(v4, v6, v7) = v9) | ( ~ (v9 = 0) & before_on_line(v4, v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (line_connecting(v4, v5) = v7) | ~ (left_convergent_lines(v7, v6) = v8) | ? [v9] : ((v9 = 0 & left_apart_point(v5, v6) = 0) | ( ~ (v9 = 0) & distinct_points(v4, v5) = v9) | ( ~ (v9 = 0) & left_apart_point(v4, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v4, v7) = v8) | ~ (left_apart_point(v4, v5) = 0) | ~ (reverse_line(v6) = v7) | ? [v9] : ((v9 = 0 & distinct_lines(v5, v6) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (left_apart_point(v4, v7) = v8) | ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v9] : ((v9 = 0 & distinct_lines(v5, v6) = 0) | ( ~ (v9 = 0) & left_apart_point(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (before_on_line(v8, v7, v6) = v5) | ~ (before_on_line(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (divides_points(v8, v7, v6) = v5) | ~ (divides_points(v8, v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v5, v6) = v7) | ~ (equally_directed_lines(v4, v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & v9 = 0 & v8 = 0 & distinct_points(v5, v6) = 0 & incident_point_and_line(v6, v4) = 0 & incident_point_and_line(v5, v4) = 0) | ( ~ (v9 = 0) & before_on_line(v4, v5, v6) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v5, v7) = v8) | ~ (unequally_directed_lines(v4, v5) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v4, v7) = 0 & unequally_directed_lines(v4, v6) = 0) | (v9 = 0 & v8 = 0 & unequally_directed_lines(v5, v6) = 0) | ( ~ (v10 = 0) & reverse_line(v5) = v9 & unequally_directed_lines(v4, v9) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v6) = v7) | ~ (unequally_directed_lines(v4, v7) = v8) | ~ (unequally_directed_lines(v4, v5) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unequally_directed_lines(v5, v7) = 0 & unequally_directed_lines(v5, v6) = 0) | (v9 = 0 & v8 = 0 & unequally_directed_lines(v4, v6) = 0) | ( ~ (v10 = 0) & reverse_line(v5) = v9 & unequally_directed_lines(v4, v9) = v10))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v7) | ~ (unequally_directed_lines(v5, v6) = v8) | ~ (unequally_directed_lines(v4, v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v9 = 0 & reverse_line(v6) = v10 & unequally_directed_lines(v4, v10) = 0 & unequally_directed_lines(v4, v6) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (reverse_line(v5) = v7) | ~ (unequally_directed_lines(v4, v7) = 0) | ~ (unequally_directed_lines(v4, v6) = v8) | ? [v9] : ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = 0 & unequally_directed_lines(v5, v6) = 0) | (v10 = 0 & v8 = 0 & reverse_line(v6) = v9 & unequally_directed_lines(v4, v9) = 0) | ( ~ (v9 = 0) & unequally_directed_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unequally_directed_lines(v5, v6) = v8) | ~ (unequally_directed_lines(v4, v6) = v7) | ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & reverse_line(v6) = v9 & unequally_directed_lines(v5, v9) = 0) | (v10 = 0 & v7 = 0 & reverse_line(v6) = v9 & unequally_directed_lines(v4, v9) = 0) | ( ~ (v10 = 0) & reverse_line(v5) = v9 & unequally_directed_lines(v4, v9) = v10) | ( ~ (v9 = 0) & unequally_directed_lines(v4, v5) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ~ (left_apart_point(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v4, v8) = 0 & reverse_line(v6) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_lines(v4, v6) = v7) | ~ (distinct_lines(v4, v5) = 0) | distinct_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (before_on_line(v4, v5, v6) = v7) | ? [v8] : ? [v9] : (( ~ (v9 = 0) & line_connecting(v5, v6) = v8 & equally_directed_lines(v4, v8) = v9) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8) | ( ~ (v8 = 0) & incident_point_and_line(v6, v4) = v8) | ( ~ (v8 = 0) & incident_point_and_line(v5, v4) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v5, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v6) = v7) | ~ (distinct_points(v4, v5) = 0) | distinct_points(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (distinct_points(v4, v5) = v7) | ~ (left_apart_point(v4, v6) = 0) | left_apart_point(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (divides_points(v6, v4, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & left_apart_point(v5, v6) = v8) | ( ~ (v8 = 0) & right_apart_point(v4, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (divides_points(v6, v4, v5) = v7) | ? [v8] : (( ~ (v8 = 0) & left_apart_point(v4, v6) = v8) | ( ~ (v8 = 0) & right_apart_point(v5, v6) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v6) = v7) | ~ (left_convergent_lines(v4, v5) = 0) | unequally_directed_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v8] : ( ~ (v8 = 0) & right_convergent_lines(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v8] : ((v8 = 0 & left_convergent_lines(v4, v5) = 0) | ( ~ (v8 = 0) & unequally_directed_lines(v4, v6) = v8) | ( ~ (v8 = 0) & unequally_directed_lines(v4, v5) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_convergent_lines(v4, v5) = 0) | ~ (unequally_directed_lines(v5, v6) = v7) | left_convergent_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v5, v6) = v7) | ~ (left_apart_point(v4, v6) = 0) | distinct_points(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (left_apart_point(v4, v6) = v7) | ~ (reverse_line(v5) = v6) | ? [v8] : ( ~ (v8 = 0) & right_apart_point(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = v7) | unequally_directed_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & unequally_directed_opposite_lines(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v5, v6) = v7) | ~ (unequally_directed_lines(v4, v5) = 0) | unequally_directed_lines(v4, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unequally_directed_lines(v4, v6) = v7) | ~ (unequally_directed_lines(v4, v5) = 0) | unequally_directed_lines(v5, v6) = 0) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (parallel_through_point(v7, v6) = v5) | ~ (parallel_through_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (intersection_point(v7, v6) = v5) | ~ (intersection_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_lines(v7, v6) = v5) | ~ (distinct_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (line_connecting(v7, v6) = v5) | ~ (line_connecting(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (distinct_points(v7, v6) = v5) | ~ (distinct_points(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (incident_point_and_line(v7, v6) = v5) | ~ (incident_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (convergent_lines(v7, v6) = v5) | ~ (convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (apart_point_and_line(v7, v6) = v5) | ~ (apart_point_and_line(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equally_directed_opposite_lines(v7, v6) = v5) | ~ (equally_directed_opposite_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (equally_directed_lines(v7, v6) = v5) | ~ (equally_directed_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (left_convergent_lines(v7, v6) = v5) | ~ (left_convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (right_convergent_lines(v7, v6) = v5) | ~ (right_convergent_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (left_apart_point(v7, v6) = v5) | ~ (left_apart_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (right_apart_point(v7, v6) = v5) | ~ (right_apart_point(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unequally_directed_lines(v7, v6) = v5) | ~ (unequally_directed_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (unequally_directed_opposite_lines(v7, v6) = v5) | ~ (unequally_directed_opposite_lines(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ~ (distinct_points(v4, v5) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & left_apart_point(v5, v8) = 0 & reverse_line(v7) = v8) | (v9 = 0 & left_apart_point(v5, v8) = 0 & reverse_line(v6) = v8) | (v9 = 0 & left_apart_point(v4, v8) = 0 & reverse_line(v7) = v8) | (v9 = 0 & left_apart_point(v4, v8) = 0 & reverse_line(v6) = v8) | (v8 = 0 & left_apart_point(v5, v7) = 0) | (v8 = 0 & left_apart_point(v5, v6) = 0) | (v8 = 0 & left_apart_point(v4, v7) = 0) | (v8 = 0 & left_apart_point(v4, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (between_on_line(v4, v5, v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & v8 = 0 & before_on_line(v4, v7, v6) = 0 & before_on_line(v4, v6, v5) = 0) | (v9 = 0 & v8 = 0 & before_on_line(v4, v6, v7) = 0 & before_on_line(v4, v5, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ~ (equally_directed_lines(v4, v7) = 0) | ? [v8] : ((v8 = 0 & before_on_line(v4, v5, v6) = 0) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8) | ( ~ (v8 = 0) & incident_point_and_line(v6, v4) = v8) | ( ~ (v8 = 0) & incident_point_and_line(v5, v4) = v8))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v5, v6) = v7) | ~ (unequally_directed_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v8 = 0 & reverse_line(v6) = v9 & unequally_directed_lines(v4, v9) = 0 & unequally_directed_lines(v4, v6) = 0) | (v9 = 0 & v7 = 0 & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = 0) | ( ~ (v9 = 0) & reverse_line(v5) = v8 & unequally_directed_lines(v4, v8) = v9))) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (unequally_directed_lines(v4, v6) = v7) | ~ (unequally_directed_lines(v4, v5) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & reverse_line(v6) = v8 & unequally_directed_lines(v5, v8) = 0 & unequally_directed_lines(v5, v6) = 0) | (v9 = 0 & v7 = 0 & reverse_line(v6) = v8 & unequally_directed_lines(v4, v8) = 0) | ( ~ (v9 = 0) & reverse_line(v5) = v8 & unequally_directed_lines(v4, v8) = v9))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (convergent_lines(v4, v5) = v6) | ? [v7] : (( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7) | ( ~ (v7 = 0) & unequally_directed_opposite_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (apart_point_and_line(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & left_apart_point(v4, v5) = v7 & right_apart_point(v4, v5) = v8)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equally_directed_opposite_lines(v4, v5) = v6) | unequally_directed_opposite_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (equally_directed_lines(v4, v5) = v6) | unequally_directed_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_convergent_lines(v4, v5) = v6) | ? [v7] : ? [v8] : ((v8 = 0 & left_convergent_lines(v4, v7) = 0 & reverse_line(v5) = v7) | ( ~ (v8 = 0) & reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = v8) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (right_convergent_lines(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & left_convergent_lines(v4, v7) = v8 & reverse_line(v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (left_apart_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & right_apart_point(v4, v5) = 0) | ( ~ (v7 = 0) & apart_point_and_line(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (right_apart_point(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & left_apart_point(v4, v7) = v8 & reverse_line(v5) = v7)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (right_apart_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & left_apart_point(v4, v5) = 0) | ( ~ (v7 = 0) & apart_point_and_line(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unequally_directed_lines(v4, v5) = v6) | equally_directed_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unequally_directed_lines(v4, v5) = v6) | ? [v7] : (reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unequally_directed_opposite_lines(v4, v5) = v6) | equally_directed_opposite_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (unequally_directed_opposite_lines(v4, v5) = v6) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = v8)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (point(v6) = v5) | ~ (point(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (line(v6) = v5) | ~ (line(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (reverse_line(v6) = v5) | ~ (reverse_line(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | equally_directed_lines(v6, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v5, v4) = v6) | ? [v7] : ( ~ (v7 = 0) & apart_point_and_line(v4, v6) = v7)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (parallel_through_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & point(v5) = v7) | ( ~ (v7 = 0) & line(v4) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : ? [v8] : ((v7 = 0 & point(v6) = 0) | ( ~ (v8 = 0) & reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = v8) | ( ~ (v7 = 0) & line(v5) = v7) | ( ~ (v7 = 0) & line(v4) = v7) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (intersection_point(v4, v5) = v6) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & ~ (v7 = 0) & apart_point_and_line(v6, v5) = v8 & apart_point_and_line(v6, v4) = v7) | ( ~ (v8 = 0) & reverse_line(v5) = v7 & unequally_directed_lines(v4, v7) = v8) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v5, v4) = v6) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & line_connecting(v4, v5) = v7 & equally_directed_lines(v7, v8) = 0 & reverse_line(v6) = v8) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : ? [v8] : ? [v9] : ((v9 = 0 & line_connecting(v5, v4) = v7 & equally_directed_lines(v6, v8) = 0 & reverse_line(v7) = v8) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : ? [v8] : (( ~ (v8 = 0) & ~ (v7 = 0) & apart_point_and_line(v5, v6) = v8 & apart_point_and_line(v4, v6) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (line_connecting(v4, v5) = v6) | ? [v7] : ((v7 = 0 & line(v6) = 0) | ( ~ (v7 = 0) & point(v5) = v7) | ( ~ (v7 = 0) & point(v4) = v7) | ( ~ (v7 = 0) & distinct_points(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (before_on_line(v4, v5, v6) = 0) | ? [v7] : (line_connecting(v5, v6) = v7 & distinct_points(v5, v6) = 0 & incident_point_and_line(v6, v4) = 0 & incident_point_and_line(v5, v4) = 0 & equally_directed_lines(v4, v7) = 0)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (divides_points(v6, v4, v5) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & v7 = 0 & left_apart_point(v5, v6) = 0 & right_apart_point(v4, v6) = 0) | (v8 = 0 & v7 = 0 & left_apart_point(v4, v6) = 0 & right_apart_point(v5, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_convergent_lines(v4, v6) = 0) | ~ (reverse_line(v5) = v6) | right_convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_convergent_lines(v4, v6) = 0) | ~ (reverse_line(v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_apart_point(v4, v6) = 0) | ~ (reverse_line(v5) = v6) | right_apart_point(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_apart_point(v4, v6) = 0) | ~ (reverse_line(v5) = v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_apart_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & right_apart_point(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (left_apart_point(v4, v5) = 0) | ~ (unequally_directed_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & left_apart_point(v4, v7) = 0 & reverse_line(v6) = v7) | (v7 = 0 & distinct_lines(v5, v6) = 0))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (right_apart_point(v4, v5) = v6) | ? [v7] : ((v7 = 0 & apart_point_and_line(v4, v5) = 0) | ( ~ (v7 = 0) & ~ (v6 = 0) & left_apart_point(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = 0) | unequally_directed_opposite_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = 0) | ? [v7] : ? [v8] : ? [v9] : (( ~ (v9 = 0) & ~ (v8 = 0) & intersection_point(v4, v5) = v7 & apart_point_and_line(v7, v5) = v9 & apart_point_and_line(v7, v4) = v8) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = 0) | ? [v7] : ? [v8] : ((v8 = 0 & intersection_point(v4, v5) = v7 & point(v7) = 0) | ( ~ (v7 = 0) & line(v5) = v7) | ( ~ (v7 = 0) & line(v4) = v7) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (reverse_line(v5) = v6) | ~ (unequally_directed_lines(v4, v6) = 0) | ? [v7] : ((v7 = 0 & left_convergent_lines(v4, v6) = 0) | (v7 = 0 & left_convergent_lines(v4, v5) = 0) | ( ~ (v7 = 0) & unequally_directed_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (unequally_directed_lines(v4, v5) = v6) | ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_opposite_lines(v4, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (unequally_directed_opposite_lines(v4, v5) = v6) | ? [v7] : ((v7 = 0 & v6 = 0 & unequally_directed_lines(v4, v5) = 0) | ( ~ (v7 = 0) & convergent_lines(v4, v5) = v7))) & ! [v4] : ! [v5] : (v5 = 0 | ~ (equally_directed_lines(v4, v4) = v5)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = 0) & ~ (v7 = 0) & line_connecting(v4, v5) = v6 & apart_point_and_line(v5, v6) = v8 & apart_point_and_line(v4, v6) = v7)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (line_connecting(v5, v4) = v7 & line_connecting(v4, v5) = v6 & equally_directed_lines(v6, v8) = 0 & reverse_line(v7) = v8)) & ! [v4] : ! [v5] : ( ~ (distinct_points(v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & line(v6) = 0 & line_connecting(v4, v5) = v6) | ( ~ (v6 = 0) & point(v5) = v6) | ( ~ (v6 = 0) & point(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (convergent_lines(v4, v5) = 0) | (unequally_directed_lines(v4, v5) = 0 & unequally_directed_opposite_lines(v4, v5) = 0)) & ! [v4] : ! [v5] : ( ~ (apart_point_and_line(v4, v5) = 0) | ? [v6] : ((v6 = 0 & left_apart_point(v4, v5) = 0) | (v6 = 0 & right_apart_point(v4, v5) = 0))) & ! [v4] : ! [v5] : ( ~ (equally_directed_opposite_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unequally_directed_opposite_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (equally_directed_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & unequally_directed_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ~ (left_convergent_lines(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (right_convergent_lines(v4, v5) = 0) | ? [v6] : (left_convergent_lines(v4, v6) = 0 & reverse_line(v5) = v6)) & ! [v4] : ! [v5] : ~ (left_apart_point(v4, v5) = 0) & ! [v4] : ! [v5] : ( ~ (right_apart_point(v4, v5) = 0) | ? [v6] : (left_apart_point(v4, v6) = 0 & reverse_line(v5) = v6)) & ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ? [v6] : ( ~ (v6 = 0) & distinct_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (reverse_line(v4) = v5) | ? [v6] : ((v6 = 0 & line(v5) = 0) | ( ~ (v6 = 0) & line(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ? [v8] : (( ~ (v8 = 0) & ~ (v7 = 0) & intersection_point(v4, v5) = v6 & apart_point_and_line(v6, v5) = v8 & apart_point_and_line(v6, v4) = v7) | ( ~ (v7 = 0) & reverse_line(v5) = v6 & unequally_directed_lines(v4, v6) = v7))) & ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & intersection_point(v4, v5) = v6 & point(v6) = 0) | ( ~ (v7 = 0) & reverse_line(v5) = v6 & unequally_directed_lines(v4, v6) = v7) | ( ~ (v6 = 0) & line(v5) = v6) | ( ~ (v6 = 0) & line(v4) = v6))) & ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v4, v5) = 0) | ? [v6] : ? [v7] : ((v7 = 0 & left_convergent_lines(v4, v6) = 0 & reverse_line(v5) = v6) | (v6 = 0 & left_convergent_lines(v4, v5) = 0) | ( ~ (v7 = 0) & reverse_line(v5) = v6 & unequally_directed_lines(v4, v6) = v7))) & ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & equally_directed_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (unequally_directed_lines(v4, v5) = 0) | ? [v6] : ((v6 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v6 = 0) & unequally_directed_opposite_lines(v4, v5) = v6))) & ! [v4] : ! [v5] : ( ~ (unequally_directed_opposite_lines(v4, v5) = 0) | ? [v6] : ( ~ (v6 = 0) & equally_directed_opposite_lines(v4, v5) = v6)) & ! [v4] : ! [v5] : ( ~ (unequally_directed_opposite_lines(v4, v5) = 0) | ? [v6] : (reverse_line(v5) = v6 & unequally_directed_lines(v4, v6) = 0)) & ! [v4] : ! [v5] : ( ~ (unequally_directed_opposite_lines(v4, v5) = 0) | ? [v6] : ((v6 = 0 & convergent_lines(v4, v5) = 0) | ( ~ (v6 = 0) & unequally_directed_lines(v4, v5) = v6))) & ! [v4] : ( ~ (line(v4) = 0) | ? [v5] : (line(v5) = 0 & reverse_line(v4) = v5)) & ! [v4] : ~ (distinct_lines(v4, v4) = 0) & ! [v4] : ~ (distinct_points(v4, v4) = 0) & ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : between_on_line(v7, v6, v5, v4) = v8 & ? [v4] : ? [v5] : ? [v6] : ? [v7] : before_on_line(v6, v5, v4) = v7 & ? [v4] : ? [v5] : ? [v6] : ? [v7] : divides_points(v6, v5, v4) = v7 & ? [v4] : ? [v5] : ? [v6] : parallel_through_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : intersection_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : distinct_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : line_connecting(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : distinct_points(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : incident_point_and_line(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : convergent_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : apart_point_and_line(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : equally_directed_opposite_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : equally_directed_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : left_convergent_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : right_convergent_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : left_apart_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : right_apart_point(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : unequally_directed_lines(v5, v4) = v6 & ? [v4] : ? [v5] : ? [v6] : unequally_directed_opposite_lines(v5, v4) = v6 & ? [v4] : ? [v5] : point(v4) = v5 & ? [v4] : ? [v5] : line(v4) = v5 & ? [v4] : ? [v5] : reverse_line(v4) = v5 & ((v3 = 0 & ~ (v2 = 0)) | (v2 = 0 & ~ (v3 = 0)))) % 26.81/7.98 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 26.81/7.98 | (1) unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = all_0_0_0 & unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_1_1 & ! [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 & ((all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0))) % 26.81/8.03 | % 26.81/8.03 | Applying alpha-rule on (1) yields: % 26.81/8.03 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 26.81/8.03 | (3) ! [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)) % 26.81/8.03 | (4) ! [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))) % 26.81/8.03 | (5) ? [v0] : ? [v1] : ? [v2] : unequally_directed_opposite_lines(v1, v0) = v2 % 26.81/8.03 | (6) ! [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))) % 26.81/8.03 | (7) ! [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))) % 26.81/8.03 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 26.81/8.03 | (9) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ((v2 = 0 & line(v1) = 0) | ( ~ (v2 = 0) & line(v0) = v2))) % 26.81/8.03 | (10) ! [v0] : ! [v1] : ( ~ (right_apart_point(v0, v1) = 0) | ? [v2] : (left_apart_point(v0, v2) = 0 & reverse_line(v1) = v2)) % 26.81/8.03 | (11) ! [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))) % 26.81/8.03 | (12) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 26.81/8.03 | (13) ? [v0] : ? [v1] : ? [v2] : right_apart_point(v1, v0) = v2 % 26.81/8.03 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v1) = v3) | ~ (left_apart_point(v0, v2) = 0) | left_apart_point(v1, v2) = 0) % 26.81/8.03 | (15) ! [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))) % 26.81/8.03 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 26.81/8.03 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) % 26.81/8.03 | (18) ! [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))) % 26.81/8.03 | (19) ! [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))) % 26.81/8.03 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_opposite_lines(v3, v2) = v1) | ~ (unequally_directed_opposite_lines(v3, v2) = v0)) % 26.81/8.03 | (21) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 26.81/8.03 | (22) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 % 26.81/8.03 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unequally_directed_lines(v3, v2) = v1) | ~ (unequally_directed_lines(v3, v2) = v0)) % 26.81/8.03 | (24) ! [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))) % 26.81/8.04 | (25) ! [v0] : ! [v1] : ~ (left_apart_point(v0, v1) = 0) % 26.81/8.04 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) % 26.81/8.04 | (27) ! [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))) % 26.81/8.04 | (28) unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = all_0_0_0 % 26.81/8.04 | (29) ! [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))) % 26.81/8.04 | (30) ? [v0] : ? [v1] : ? [v2] : unequally_directed_lines(v1, v0) = v2 % 26.81/8.04 | (31) ! [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))) % 26.81/8.04 | (32) ! [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))) % 26.81/8.04 | (33) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | (unequally_directed_lines(v0, v1) = 0 & unequally_directed_opposite_lines(v0, v1) = 0)) % 26.81/8.04 | (34) ! [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))) % 26.81/8.04 | (35) ? [v0] : ? [v1] : ? [v2] : equally_directed_opposite_lines(v1, v0) = v2 % 26.81/8.04 | (36) ! [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))) % 26.81/8.04 | (37) ! [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))) % 26.81/8.04 | (38) ! [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))) % 26.81/8.04 | (39) ! [v0] : ! [v1] : ( ~ (reverse_line(v0) = v1) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 26.81/8.04 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_apart_point(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_apart_point(v0, v1) = 0) % 26.81/8.04 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 26.81/8.04 | (42) ! [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))) % 26.81/8.04 | (43) ! [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))) % 26.81/8.04 | (44) ! [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))) % 26.81/8.04 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (reverse_line(v2) = v1) | ~ (reverse_line(v2) = v0)) % 26.81/8.04 | (46) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 26.81/8.04 | (47) ! [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))) % 26.81/8.04 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_apart_point(v3, v2) = v1) | ~ (left_apart_point(v3, v2) = v0)) % 26.81/8.04 | (49) ! [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))) % 26.81/8.04 | (50) ! [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))) % 26.81/8.04 | (51) ! [v0] : ( ~ (line(v0) = 0) | ? [v1] : (line(v1) = 0 & reverse_line(v0) = v1)) % 26.81/8.04 | (52) ! [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))) % 26.81/8.04 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 26.81/8.04 | (54) ! [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))) % 26.81/8.04 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 26.81/8.04 | (56) ! [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)) % 26.81/8.04 | (57) ! [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))) % 26.81/8.04 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (divides_points(v4, v3, v2) = v1) | ~ (divides_points(v4, v3, v2) = v0)) % 26.81/8.04 | (59) ! [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)) % 26.81/8.04 | (60) ! [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))) % 26.81/8.05 | (61) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 26.81/8.05 | (62) ! [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))) % 26.81/8.05 | (63) ! [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))) % 26.81/8.05 | (64) ! [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)) % 26.81/8.05 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_apart_point(v1, v2) = v3) | ~ (left_apart_point(v0, v2) = 0) | distinct_points(v0, v1) = 0) % 26.81/8.05 | (66) ? [v0] : ? [v1] : ? [v2] : left_convergent_lines(v1, v0) = v2 % 26.81/8.05 | (67) ! [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)) % 26.81/8.05 | (68) ! [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))) % 26.81/8.05 | (69) ! [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))) % 26.81/8.05 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = v3) | unequally_directed_lines(v0, v1) = 0) % 26.81/8.05 | (71) ! [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))) % 26.81/8.05 | (72) ! [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))) % 26.81/8.05 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v0, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) % 26.81/8.05 | (74) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : between_on_line(v3, v2, v1, v0) = v4 % 26.81/8.05 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (reverse_line(v1) = v2) | ~ (unequally_directed_lines(v0, v2) = 0) | unequally_directed_opposite_lines(v0, v1) = 0) % 26.81/8.05 | (76) ! [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))) % 26.81/8.05 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 26.81/8.05 | (78) ! [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))) % 26.81/8.05 | (79) ! [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))) % 26.81/8.05 | (80) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_opposite_lines(v0, v1) = v2) | equally_directed_opposite_lines(v0, v1) = 0) % 26.81/8.05 | (81) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_opposite_lines(v0, v1) = v2) | unequally_directed_opposite_lines(v0, v1) = 0) % 26.81/8.05 | (82) ! [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))) % 26.81/8.05 | (83) ! [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)) % 26.81/8.05 | (84) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 26.81/8.05 | (85) ? [v0] : ? [v1] : ? [v2] : equally_directed_lines(v1, v0) = v2 % 26.81/8.05 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) % 26.81/8.05 | (87) ! [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)) % 26.81/8.05 | (88) ! [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))) % 26.81/8.05 | (89) ! [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))) % 26.81/8.05 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2) | right_convergent_lines(v0, v1) = 0) % 26.81/8.05 | (91) ! [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))) % 26.81/8.05 | (92) (all_0_0_0 = 0 & ~ (all_0_1_1 = 0)) | (all_0_1_1 = 0 & ~ (all_0_0_0 = 0)) % 26.81/8.05 | (93) ? [v0] : ? [v1] : reverse_line(v0) = v1 % 26.81/8.05 | (94) unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_1_1 % 26.81/8.05 | (95) ! [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))) % 26.81/8.05 | (96) ! [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))) % 26.81/8.05 | (97) ? [v0] : ? [v1] : ? [v2] : ? [v3] : before_on_line(v2, v1, v0) = v3 % 26.81/8.05 | (98) ! [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))) % 26.81/8.06 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_convergent_lines(v3, v2) = v1) | ~ (right_convergent_lines(v3, v2) = v0)) % 26.81/8.06 | (100) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 26.81/8.06 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (left_convergent_lines(v0, v2) = 0) | ~ (reverse_line(v1) = v2)) % 26.81/8.06 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 26.81/8.06 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v2) = v3) | ~ (left_convergent_lines(v0, v1) = 0) | unequally_directed_lines(v1, v2) = 0) % 26.81/8.06 | (104) ? [v0] : ? [v1] : ? [v2] : left_apart_point(v1, v0) = v2 % 26.81/8.06 | (105) ! [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))) % 26.81/8.06 | (106) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_opposite_lines(v0, v1) = v2)) % 26.81/8.06 | (107) ! [v0] : ! [v1] : ( ~ (equally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_opposite_lines(v0, v1) = v2)) % 26.81/8.06 | (108) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 26.81/8.06 | (109) ! [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))) % 26.81/8.06 | (110) ! [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))) % 26.81/8.06 | (111) ! [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))) % 26.81/8.06 | (112) ! [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)) % 26.81/8.06 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 26.81/8.06 | (114) ! [v0] : ! [v1] : (v1 = 0 | ~ (equally_directed_lines(v0, v0) = v1)) % 26.81/8.06 | (115) ! [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))) % 26.81/8.06 | (116) ! [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))) % 26.81/8.06 | (117) ? [v0] : ? [v1] : point(v0) = v1 % 26.81/8.06 | (118) ! [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))) % 26.81/8.06 | (119) ! [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))) % 26.81/8.06 | (120) ! [v0] : ! [v1] : ( ~ (right_convergent_lines(v0, v1) = 0) | ? [v2] : (left_convergent_lines(v0, v2) = 0 & reverse_line(v1) = v2)) % 26.81/8.06 | (121) ! [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)) % 26.81/8.06 | (122) ! [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)) % 26.81/8.06 | (123) ! [v0] : ! [v1] : ( ~ (unequally_directed_opposite_lines(v0, v1) = 0) | ? [v2] : (reverse_line(v1) = v2 & unequally_directed_lines(v0, v2) = 0)) % 26.81/8.06 | (124) ! [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))) % 26.81/8.06 | (125) ! [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))) % 26.81/8.06 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 26.81/8.06 | (127) ! [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))) % 26.81/8.06 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (between_on_line(v5, v4, v3, v2) = v1) | ~ (between_on_line(v5, v4, v3, v2) = v0)) % 26.81/8.06 | (129) ! [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))) % 26.81/8.06 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 26.81/8.06 | (131) ! [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))) % 26.81/8.06 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (left_convergent_lines(v3, v2) = v1) | ~ (left_convergent_lines(v3, v2) = v0)) % 26.81/8.06 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | equally_directed_lines(v2, v1) = 0) % 27.27/8.06 | (134) ! [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))) % 27.27/8.06 | (135) ! [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))) % 27.27/8.06 | (136) ! [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))) % 27.27/8.06 | (137) ! [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))) % 27.27/8.06 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 27.27/8.06 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_lines(v3, v2) = v1) | ~ (equally_directed_lines(v3, v2) = v0)) % 27.27/8.07 | (140) ! [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))) % 27.27/8.07 | (141) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 27.27/8.07 | (142) ! [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))) % 27.27/8.07 | (143) ? [v0] : ? [v1] : line(v0) = v1 % 27.27/8.07 | (144) ! [v0] : ! [v1] : ( ~ (unequally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equally_directed_lines(v0, v1) = v2)) % 27.27/8.07 | (145) ! [v0] : ! [v1] : ( ~ (equally_directed_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unequally_directed_lines(v0, v1) = v2)) % 27.27/8.07 | (146) ! [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))) % 27.27/8.07 | (147) ! [v0] : ! [v1] : ~ (left_convergent_lines(v0, v1) = 0) % 27.27/8.07 | (148) ! [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))) % 27.27/8.07 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unequally_directed_lines(v1, v2) = v3) | ~ (unequally_directed_lines(v0, v1) = 0) | unequally_directed_lines(v0, v2) = 0) % 27.27/8.07 | (150) ? [v0] : ? [v1] : ? [v2] : right_convergent_lines(v1, v0) = v2 % 27.27/8.07 | (151) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 27.27/8.07 | (152) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 27.27/8.07 | (153) ! [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))) % 27.27/8.07 | (154) ! [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))) % 27.27/8.07 | (155) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equally_directed_opposite_lines(v3, v2) = v1) | ~ (equally_directed_opposite_lines(v3, v2) = v0)) % 27.27/8.07 | (156) ! [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))) % 27.27/8.07 | (157) ? [v0] : ? [v1] : ? [v2] : ? [v3] : divides_points(v2, v1, v0) = v3 % 27.27/8.07 | (158) ! [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))) % 27.27/8.07 | (159) ! [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))) % 27.27/8.07 | (160) ! [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))) % 27.27/8.07 | (161) ! [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)) % 27.27/8.07 | (162) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 27.27/8.07 | (163) ! [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))) % 27.27/8.07 | (164) ! [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))) % 27.27/8.07 | (165) ! [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))) % 27.27/8.07 | (166) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 27.27/8.07 | (167) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | ? [v3] : (reverse_line(v1) = v3 & unequally_directed_lines(v0, v3) = 0)) % 27.27/8.07 | (168) ! [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))) % 27.27/8.07 | (169) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (right_apart_point(v3, v2) = v1) | ~ (right_apart_point(v3, v2) = v0)) % 27.27/8.07 | (170) ! [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))) % 27.27/8.07 | (171) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (before_on_line(v4, v3, v2) = v1) | ~ (before_on_line(v4, v3, v2) = v0)) % 27.27/8.07 | (172) ! [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)) % 27.27/8.07 | (173) ! [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))) % 27.27/8.07 | (174) ! [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))) % 27.27/8.07 | (175) ! [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))) % 27.27/8.08 | (176) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unequally_directed_lines(v0, v1) = v2) | equally_directed_lines(v0, v1) = 0) % 27.27/8.08 | (177) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equally_directed_lines(v0, v1) = v2) | unequally_directed_lines(v0, v1) = 0) % 27.27/8.08 | (178) ! [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))) % 27.27/8.08 | (179) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (left_convergent_lines(v0, v1) = 0) | ~ (unequally_directed_lines(v1, v2) = v3) | left_convergent_lines(v0, v2) = 0) % 27.27/8.08 | (180) ! [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)) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (180) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 27.27/8.08 | (181) all_0_0_0 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_2_2, v0) = v1) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (96) with all_0_0_0, all_0_3_3, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = all_0_0_0, yields: % 27.27/8.08 | (182) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0)) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (180) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 27.27/8.08 | (183) all_0_1_1 = 0 | ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_2_2) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (96) with all_0_1_1, all_0_2_2, all_0_3_3 and discharging atoms unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = all_0_1_1, yields: % 27.27/8.08 | (184) ? [v0] : ((v0 = 0 & all_0_1_1 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = v0)) % 27.27/8.08 | % 27.27/8.08 | Instantiating (184) with all_52_0_71 yields: % 27.27/8.08 | (185) (all_52_0_71 = 0 & all_0_1_1 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_52_0_71 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_52_0_71) % 27.27/8.08 | % 27.27/8.08 | Instantiating (182) with all_53_0_72 yields: % 27.27/8.08 | (186) (all_53_0_72 = 0 & all_0_0_0 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_53_0_72 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_53_0_72) % 27.27/8.08 | % 27.27/8.08 +-Applying beta-rule and splitting (92), into two cases. % 27.27/8.08 |-Branch one: % 27.27/8.08 | (187) all_0_0_0 = 0 & ~ (all_0_1_1 = 0) % 27.27/8.08 | % 27.27/8.08 | Applying alpha-rule on (187) yields: % 27.27/8.08 | (188) all_0_0_0 = 0 % 27.27/8.08 | (189) ~ (all_0_1_1 = 0) % 27.27/8.08 | % 27.27/8.08 | From (188) and (28) follows: % 27.27/8.08 | (190) unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.08 | % 27.27/8.08 +-Applying beta-rule and splitting (183), into two cases. % 27.27/8.08 |-Branch one: % 27.27/8.08 | (191) all_0_1_1 = 0 % 27.27/8.08 | % 27.27/8.08 | Equations (191) can reduce 189 to: % 27.27/8.08 | (192) $false % 27.27/8.08 | % 27.27/8.08 |-The branch is then unsatisfiable % 27.27/8.08 |-Branch two: % 27.27/8.08 | (189) ~ (all_0_1_1 = 0) % 27.27/8.08 | (194) ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_2_2) = v0 & unequally_directed_lines(all_0_3_3, v0) = v1) % 27.27/8.08 | % 27.27/8.08 | Instantiating (194) with all_68_0_73, all_68_1_74 yields: % 27.27/8.08 | (195) ~ (all_68_0_73 = 0) & reverse_line(all_0_2_2) = all_68_1_74 & unequally_directed_lines(all_0_3_3, all_68_1_74) = all_68_0_73 % 27.27/8.08 | % 27.27/8.08 | Applying alpha-rule on (195) yields: % 27.27/8.08 | (196) ~ (all_68_0_73 = 0) % 27.27/8.08 | (197) reverse_line(all_0_2_2) = all_68_1_74 % 27.27/8.08 | (198) unequally_directed_lines(all_0_3_3, all_68_1_74) = all_68_0_73 % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (70) with all_68_0_73, all_68_1_74, all_0_2_2, all_0_3_3 and discharging atoms reverse_line(all_0_2_2) = all_68_1_74, unequally_directed_lines(all_0_3_3, all_68_1_74) = all_68_0_73, yields: % 27.27/8.08 | (199) all_68_0_73 = 0 | unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (59) with all_68_0_73, all_68_0_73, all_68_1_74, all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_68_1_74) = all_68_0_73, yields: % 27.27/8.08 | (200) all_68_0_73 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (167) with all_68_0_73, all_68_1_74, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_68_1_74) = all_68_0_73, yields: % 27.27/8.08 | (201) all_68_0_73 = 0 | ? [v0] : (reverse_line(all_68_1_74) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (123) with all_0_3_3, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.08 | (202) ? [v0] : (reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (173) with all_0_3_3, all_0_2_2 and discharging atoms unequally_directed_opposite_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.08 | (203) ? [v0] : ((v0 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = v0)) % 27.27/8.08 | % 27.27/8.08 | Instantiating (203) with all_75_0_75 yields: % 27.27/8.08 | (204) (all_75_0_75 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_75_0_75 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_75_0_75) % 27.27/8.08 | % 27.27/8.08 | Instantiating (202) with all_79_0_78 yields: % 27.27/8.08 | (205) reverse_line(all_0_3_3) = all_79_0_78 & unequally_directed_lines(all_0_2_2, all_79_0_78) = 0 % 27.27/8.08 | % 27.27/8.08 | Applying alpha-rule on (205) yields: % 27.27/8.08 | (206) reverse_line(all_0_3_3) = all_79_0_78 % 27.27/8.08 | (207) unequally_directed_lines(all_0_2_2, all_79_0_78) = 0 % 27.27/8.08 | % 27.27/8.08 +-Applying beta-rule and splitting (199), into two cases. % 27.27/8.08 |-Branch one: % 27.27/8.08 | (208) unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.27/8.08 | % 27.27/8.08 +-Applying beta-rule and splitting (201), into two cases. % 27.27/8.08 |-Branch one: % 27.27/8.08 | (209) all_68_0_73 = 0 % 27.27/8.08 | % 27.27/8.08 | Equations (209) can reduce 196 to: % 27.27/8.08 | (192) $false % 27.27/8.08 | % 27.27/8.08 |-The branch is then unsatisfiable % 27.27/8.08 |-Branch two: % 27.27/8.08 | (196) ~ (all_68_0_73 = 0) % 27.27/8.08 | (212) ? [v0] : (reverse_line(all_68_1_74) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) % 27.27/8.08 | % 27.27/8.08 +-Applying beta-rule and splitting (200), into two cases. % 27.27/8.08 |-Branch one: % 27.27/8.08 | (209) all_68_0_73 = 0 % 27.27/8.08 | % 27.27/8.08 | Equations (209) can reduce 196 to: % 27.27/8.08 | (192) $false % 27.27/8.08 | % 27.27/8.08 |-The branch is then unsatisfiable % 27.27/8.08 |-Branch two: % 27.27/8.08 | (196) ~ (all_68_0_73 = 0) % 27.27/8.08 | (216) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = v0) % 27.27/8.08 | % 27.27/8.08 | Instantiating (216) with all_115_0_88 yields: % 27.27/8.08 | (217) ~ (all_115_0_88 = 0) & unequally_directed_lines(all_0_3_3, all_0_3_3) = all_115_0_88 % 27.27/8.08 | % 27.27/8.08 | Applying alpha-rule on (217) yields: % 27.27/8.08 | (218) ~ (all_115_0_88 = 0) % 27.27/8.08 | (219) unequally_directed_lines(all_0_3_3, all_0_3_3) = all_115_0_88 % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (38) with 0, all_79_0_78, all_79_0_78, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms reverse_line(all_0_3_3) = all_79_0_78, unequally_directed_lines(all_0_2_2, all_79_0_78) = 0, yields: % 27.27/8.08 | (220) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_3_3, all_79_0_78) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = v0)) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (57) with all_68_0_73, all_68_1_74, all_79_0_78, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms reverse_line(all_0_2_2) = all_68_1_74, reverse_line(all_0_3_3) = all_79_0_78, unequally_directed_lines(all_0_2_2, all_79_0_78) = 0, unequally_directed_lines(all_0_3_3, all_68_1_74) = all_68_0_73, yields: % 27.27/8.08 | (221) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_2_2, all_68_1_74) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & all_68_0_73 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = v0)) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (170) with all_115_0_88, all_79_0_78, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms reverse_line(all_0_3_3) = all_79_0_78, unequally_directed_lines(all_0_2_2, all_79_0_78) = 0, unequally_directed_lines(all_0_3_3, all_0_3_3) = all_115_0_88, yields: % 27.27/8.08 | (222) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & reverse_line(all_0_3_3) = v1 & unequally_directed_lines(all_0_2_2, v1) = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | (v1 = 0 & all_115_0_88 = 0 & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = v0)) % 27.27/8.08 | % 27.27/8.08 | Instantiating formula (73) with all_115_0_88, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_2_2) = 0, unequally_directed_lines(all_0_3_3, all_0_3_3) = all_115_0_88, yields: % 27.27/8.09 | (223) all_115_0_88 = 0 | unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (167) with all_115_0_88, all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_115_0_88, yields: % 27.27/8.09 | (224) all_115_0_88 = 0 | ? [v0] : (reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) % 27.27/8.09 | % 27.27/8.09 | Instantiating (222) with all_140_0_112, all_140_1_113, all_140_2_114 yields: % 27.27/8.09 | (225) (all_140_0_112 = 0 & all_140_2_114 = 0 & reverse_line(all_0_3_3) = all_140_1_113 & unequally_directed_lines(all_0_2_2, all_140_1_113) = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | (all_140_1_113 = 0 & all_115_0_88 = 0 & reverse_line(all_0_3_3) = all_140_2_114 & unequally_directed_lines(all_0_3_3, all_140_2_114) = 0) | ( ~ (all_140_2_114 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_140_2_114) % 27.27/8.09 | % 27.27/8.09 | Instantiating (220) with all_151_0_138, all_151_1_139 yields: % 27.27/8.09 | (226) (all_151_0_138 = 0 & all_151_1_139 = 0 & unequally_directed_lines(all_0_3_3, all_79_0_78) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_151_1_139 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_151_1_139 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_151_1_139) % 27.27/8.09 | % 27.27/8.09 | Instantiating (221) with all_162_0_155, all_162_1_156 yields: % 27.27/8.09 | (227) (all_162_0_155 = 0 & all_162_1_156 = 0 & unequally_directed_lines(all_0_2_2, all_68_1_74) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0) | (all_162_1_156 = 0 & all_68_0_73 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_162_1_156 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_162_1_156) % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (223), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (228) unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (204), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (229) all_75_0_75 = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (229) yields: % 27.27/8.09 | (230) all_75_0_75 = 0 % 27.27/8.09 | (231) convergent_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (186), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (232) all_53_0_72 = 0 & all_0_0_0 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (232) yields: % 27.27/8.09 | (233) all_53_0_72 = 0 % 27.27/8.09 | (188) all_0_0_0 = 0 % 27.27/8.09 | (228) unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (224), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (236) all_115_0_88 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (236) can reduce 218 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (218) ~ (all_115_0_88 = 0) % 27.27/8.09 | (239) ? [v0] : (reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (225), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (240) (all_140_0_112 = 0 & all_140_2_114 = 0 & reverse_line(all_0_3_3) = all_140_1_113 & unequally_directed_lines(all_0_2_2, all_140_1_113) = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | (all_140_1_113 = 0 & all_115_0_88 = 0 & reverse_line(all_0_3_3) = all_140_2_114 & unequally_directed_lines(all_0_3_3, all_140_2_114) = 0) % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (240), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (241) all_140_0_112 = 0 & all_140_2_114 = 0 & reverse_line(all_0_3_3) = all_140_1_113 & unequally_directed_lines(all_0_2_2, all_140_1_113) = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (241) yields: % 27.27/8.09 | (228) unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | (243) reverse_line(all_0_3_3) = all_140_1_113 % 27.27/8.09 | (244) all_140_0_112 = 0 % 27.27/8.09 | (245) all_140_2_114 = 0 % 27.27/8.09 | (246) unequally_directed_lines(all_0_2_2, all_140_1_113) = 0 % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (226), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (247) (all_151_0_138 = 0 & all_151_1_139 = 0 & unequally_directed_lines(all_0_3_3, all_79_0_78) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_151_1_139 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (247), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (248) all_151_0_138 = 0 & all_151_1_139 = 0 & unequally_directed_lines(all_0_3_3, all_79_0_78) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (248) yields: % 27.27/8.09 | (249) all_151_0_138 = 0 % 27.27/8.09 | (250) all_151_1_139 = 0 % 27.27/8.09 | (251) unequally_directed_lines(all_0_3_3, all_79_0_78) = 0 % 27.27/8.09 | (252) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (23) with all_0_3_3, all_0_3_3, 0, all_115_0_88 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = all_115_0_88, unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields: % 27.27/8.09 | (236) all_115_0_88 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (236) can reduce 218 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (255) all_151_1_139 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (255) yields: % 27.27/8.09 | (250) all_151_1_139 = 0 % 27.27/8.09 | (228) unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (227), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (258) (all_162_0_155 = 0 & all_162_1_156 = 0 & unequally_directed_lines(all_0_2_2, all_68_1_74) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0) | (all_162_1_156 = 0 & all_68_0_73 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) % 27.27/8.09 | % 27.27/8.09 +-Applying beta-rule and splitting (258), into two cases. % 27.27/8.09 |-Branch one: % 27.27/8.09 | (259) all_162_0_155 = 0 & all_162_1_156 = 0 & unequally_directed_lines(all_0_2_2, all_68_1_74) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (259) yields: % 27.27/8.09 | (260) all_162_0_155 = 0 % 27.27/8.09 | (261) all_162_1_156 = 0 % 27.27/8.09 | (262) unequally_directed_lines(all_0_2_2, all_68_1_74) = 0 % 27.27/8.09 | (263) unequally_directed_lines(all_0_2_2, all_0_2_2) = 0 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (144) with all_0_2_2, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_2_2) = 0, yields: % 27.27/8.09 | (264) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_2_2, all_0_2_2) = v0) % 27.27/8.09 | % 27.27/8.09 | Instantiating (264) with all_466_0_1281 yields: % 27.27/8.09 | (265) ~ (all_466_0_1281 = 0) & equally_directed_lines(all_0_2_2, all_0_2_2) = all_466_0_1281 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (265) yields: % 27.27/8.09 | (266) ~ (all_466_0_1281 = 0) % 27.27/8.09 | (267) equally_directed_lines(all_0_2_2, all_0_2_2) = all_466_0_1281 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (114) with all_466_0_1281, all_0_2_2 and discharging atoms equally_directed_lines(all_0_2_2, all_0_2_2) = all_466_0_1281, yields: % 27.27/8.09 | (268) all_466_0_1281 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (268) can reduce 266 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (270) all_162_1_156 = 0 & all_68_0_73 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (270) yields: % 27.27/8.09 | (261) all_162_1_156 = 0 % 27.27/8.09 | (209) all_68_0_73 = 0 % 27.27/8.09 | (208) unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (209) can reduce 196 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (275) ~ (all_162_1_156 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_162_1_156 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (275) yields: % 27.27/8.09 | (276) ~ (all_162_1_156 = 0) % 27.27/8.09 | (277) unequally_directed_lines(all_0_2_2, all_0_3_3) = all_162_1_156 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (23) with all_0_2_2, all_0_3_3, 0, all_162_1_156 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_3_3) = all_162_1_156, unequally_directed_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.09 | (261) all_162_1_156 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (261) can reduce 276 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (280) ~ (all_151_1_139 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_151_1_139 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (280) yields: % 27.27/8.09 | (281) ~ (all_151_1_139 = 0) % 27.27/8.09 | (282) unequally_directed_lines(all_0_2_2, all_0_3_3) = all_151_1_139 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (23) with all_0_2_2, all_0_3_3, 0, all_151_1_139 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_3_3) = all_151_1_139, unequally_directed_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.09 | (250) all_151_1_139 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (250) can reduce 281 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (285) all_140_1_113 = 0 & all_115_0_88 = 0 & reverse_line(all_0_3_3) = all_140_2_114 & unequally_directed_lines(all_0_3_3, all_140_2_114) = 0 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (285) yields: % 27.27/8.09 | (286) all_140_1_113 = 0 % 27.27/8.09 | (236) all_115_0_88 = 0 % 27.27/8.09 | (288) reverse_line(all_0_3_3) = all_140_2_114 % 27.27/8.09 | (289) unequally_directed_lines(all_0_3_3, all_140_2_114) = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (236) can reduce 218 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (291) ~ (all_140_2_114 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_140_2_114 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (291) yields: % 27.27/8.09 | (292) ~ (all_140_2_114 = 0) % 27.27/8.09 | (293) unequally_directed_lines(all_0_2_2, all_0_3_3) = all_140_2_114 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (23) with all_0_2_2, all_0_3_3, 0, all_140_2_114 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_3_3) = all_140_2_114, unequally_directed_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.09 | (245) all_140_2_114 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (245) can reduce 292 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (296) ~ (all_53_0_72 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_53_0_72 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (296) yields: % 27.27/8.09 | (297) ~ (all_53_0_72 = 0) % 27.27/8.09 | (298) convergent_lines(all_0_2_2, all_0_3_3) = all_53_0_72 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (16) with all_0_2_2, all_0_3_3, 0, all_53_0_72 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = all_53_0_72, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.09 | (233) all_53_0_72 = 0 % 27.27/8.09 | % 27.27/8.09 | Equations (233) can reduce 297 to: % 27.27/8.09 | (192) $false % 27.27/8.09 | % 27.27/8.09 |-The branch is then unsatisfiable % 27.27/8.09 |-Branch two: % 27.27/8.09 | (301) ~ (all_75_0_75 = 0) & unequally_directed_lines(all_0_2_2, all_0_3_3) = all_75_0_75 % 27.27/8.09 | % 27.27/8.09 | Applying alpha-rule on (301) yields: % 27.27/8.09 | (302) ~ (all_75_0_75 = 0) % 27.27/8.09 | (303) unequally_directed_lines(all_0_2_2, all_0_3_3) = all_75_0_75 % 27.27/8.09 | % 27.27/8.09 | Instantiating formula (23) with all_0_2_2, all_0_3_3, 0, all_75_0_75 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_3_3) = all_75_0_75, unequally_directed_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.27/8.09 | (230) all_75_0_75 = 0 % 27.27/8.09 | % 27.40/8.09 | Equations (230) can reduce 302 to: % 27.40/8.09 | (192) $false % 27.40/8.09 | % 27.40/8.09 |-The branch is then unsatisfiable % 27.40/8.09 |-Branch two: % 27.40/8.09 | (306) ~ (unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) % 27.40/8.09 | (236) all_115_0_88 = 0 % 27.40/8.09 | % 27.40/8.09 | Equations (236) can reduce 218 to: % 27.40/8.09 | (192) $false % 27.40/8.09 | % 27.40/8.09 |-The branch is then unsatisfiable % 27.40/8.09 |-Branch two: % 27.40/8.09 | (309) ~ (unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) % 27.40/8.09 | (209) all_68_0_73 = 0 % 27.40/8.09 | % 27.40/8.09 | Equations (209) can reduce 196 to: % 27.40/8.09 | (192) $false % 27.40/8.09 | % 27.40/8.09 |-The branch is then unsatisfiable % 27.40/8.09 |-Branch two: % 27.40/8.10 | (312) all_0_1_1 = 0 & ~ (all_0_0_0 = 0) % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (312) yields: % 27.40/8.10 | (191) all_0_1_1 = 0 % 27.40/8.10 | (314) ~ (all_0_0_0 = 0) % 27.40/8.10 | % 27.40/8.10 | From (191) and (94) follows: % 27.40/8.10 | (315) unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (181), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (188) all_0_0_0 = 0 % 27.40/8.10 | % 27.40/8.10 | Equations (188) can reduce 314 to: % 27.40/8.10 | (192) $false % 27.40/8.10 | % 27.40/8.10 |-The branch is then unsatisfiable % 27.40/8.10 |-Branch two: % 27.40/8.10 | (314) ~ (all_0_0_0 = 0) % 27.40/8.10 | (319) ? [v0] : ? [v1] : ( ~ (v1 = 0) & reverse_line(all_0_3_3) = v0 & unequally_directed_lines(all_0_2_2, v0) = v1) % 27.40/8.10 | % 27.40/8.10 | Instantiating (319) with all_68_0_1540, all_68_1_1541 yields: % 27.40/8.10 | (320) ~ (all_68_0_1540 = 0) & reverse_line(all_0_3_3) = all_68_1_1541 & unequally_directed_lines(all_0_2_2, all_68_1_1541) = all_68_0_1540 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (320) yields: % 27.40/8.10 | (321) ~ (all_68_0_1540 = 0) % 27.40/8.10 | (322) reverse_line(all_0_3_3) = all_68_1_1541 % 27.40/8.10 | (323) unequally_directed_lines(all_0_2_2, all_68_1_1541) = all_68_0_1540 % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (70) with all_68_0_1540, all_68_1_1541, all_0_3_3, all_0_2_2 and discharging atoms reverse_line(all_0_3_3) = all_68_1_1541, unequally_directed_lines(all_0_2_2, all_68_1_1541) = all_68_0_1540, yields: % 27.40/8.10 | (324) all_68_0_1540 = 0 | unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (59) with all_68_0_1540, all_68_0_1540, all_68_1_1541, all_0_2_2, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_2_2, all_68_1_1541) = all_68_0_1540, yields: % 27.40/8.10 | (325) all_68_0_1540 = 0 | ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_2_2) = v0) % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (167) with all_68_0_1540, all_68_1_1541, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_2_2, all_68_1_1541) = all_68_0_1540, yields: % 27.40/8.10 | (326) all_68_0_1540 = 0 | ? [v0] : (reverse_line(all_68_1_1541) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0) % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (123) with all_0_2_2, all_0_3_3 and discharging atoms unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.10 | (327) ? [v0] : (reverse_line(all_0_2_2) = v0 & unequally_directed_lines(all_0_3_3, v0) = 0) % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (173) with all_0_2_2, all_0_3_3 and discharging atoms unequally_directed_opposite_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.10 | (328) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = v0)) % 27.40/8.10 | % 27.40/8.10 | Instantiating (328) with all_75_0_1542 yields: % 27.40/8.10 | (329) (all_75_0_1542 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_75_0_1542 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_75_0_1542) % 27.40/8.10 | % 27.40/8.10 | Instantiating (327) with all_79_0_1545 yields: % 27.40/8.10 | (330) reverse_line(all_0_2_2) = all_79_0_1545 & unequally_directed_lines(all_0_3_3, all_79_0_1545) = 0 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (330) yields: % 27.40/8.10 | (331) reverse_line(all_0_2_2) = all_79_0_1545 % 27.40/8.10 | (332) unequally_directed_lines(all_0_3_3, all_79_0_1545) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (324), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (228) unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (326), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (334) all_68_0_1540 = 0 % 27.40/8.10 | % 27.40/8.10 | Equations (334) can reduce 321 to: % 27.40/8.10 | (192) $false % 27.40/8.10 | % 27.40/8.10 |-The branch is then unsatisfiable % 27.40/8.10 |-Branch two: % 27.40/8.10 | (321) ~ (all_68_0_1540 = 0) % 27.40/8.10 | (337) ? [v0] : (reverse_line(all_68_1_1541) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0) % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (325), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (334) all_68_0_1540 = 0 % 27.40/8.10 | % 27.40/8.10 | Equations (334) can reduce 321 to: % 27.40/8.10 | (192) $false % 27.40/8.10 | % 27.40/8.10 |-The branch is then unsatisfiable % 27.40/8.10 |-Branch two: % 27.40/8.10 | (321) ~ (all_68_0_1540 = 0) % 27.40/8.10 | (341) ? [v0] : ( ~ (v0 = 0) & unequally_directed_lines(all_0_2_2, all_0_2_2) = v0) % 27.40/8.10 | % 27.40/8.10 | Instantiating (341) with all_115_0_1555 yields: % 27.40/8.10 | (342) ~ (all_115_0_1555 = 0) & unequally_directed_lines(all_0_2_2, all_0_2_2) = all_115_0_1555 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (342) yields: % 27.40/8.10 | (343) ~ (all_115_0_1555 = 0) % 27.40/8.10 | (344) unequally_directed_lines(all_0_2_2, all_0_2_2) = all_115_0_1555 % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (167) with all_115_0_1555, all_0_2_2, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_2_2) = all_115_0_1555, yields: % 27.40/8.10 | (345) all_115_0_1555 = 0 | ? [v0] : (reverse_line(all_0_2_2) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0) % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (73) with all_115_0_1555, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_2_2) = all_115_0_1555, unequally_directed_lines(all_0_2_2, all_0_3_3) = 0, yields: % 27.40/8.10 | (346) all_115_0_1555 = 0 | unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (38) with 0, all_79_0_1545, all_79_0_1545, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms reverse_line(all_0_2_2) = all_79_0_1545, unequally_directed_lines(all_0_3_3, all_79_0_1545) = 0, yields: % 27.40/8.10 | (347) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_2_2, all_79_0_1545) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = v0)) % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (57) with all_68_0_1540, all_68_1_1541, all_79_0_1545, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms reverse_line(all_0_2_2) = all_79_0_1545, reverse_line(all_0_3_3) = all_68_1_1541, unequally_directed_lines(all_0_2_2, all_68_1_1541) = all_68_0_1540, unequally_directed_lines(all_0_3_3, all_79_0_1545) = 0, yields: % 27.40/8.10 | (348) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unequally_directed_lines(all_0_3_3, all_68_1_1541) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & all_68_0_1540 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = v0)) % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (170) with all_115_0_1555, all_79_0_1545, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms reverse_line(all_0_2_2) = all_79_0_1545, unequally_directed_lines(all_0_2_2, all_0_2_2) = all_115_0_1555, unequally_directed_lines(all_0_3_3, all_79_0_1545) = 0, yields: % 27.40/8.10 | (349) ? [v0] : ? [v1] : ? [v2] : ((v2 = 0 & v0 = 0 & reverse_line(all_0_2_2) = v1 & unequally_directed_lines(all_0_3_3, v1) = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | (v1 = 0 & all_115_0_1555 = 0 & reverse_line(all_0_2_2) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0) | ( ~ (v0 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = v0)) % 27.40/8.10 | % 27.40/8.10 | Instantiating (347) with all_146_0_1596, all_146_1_1597 yields: % 27.40/8.10 | (350) (all_146_0_1596 = 0 & all_146_1_1597 = 0 & unequally_directed_lines(all_0_2_2, all_79_0_1545) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0) | (all_146_1_1597 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_146_1_1597 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_146_1_1597) % 27.40/8.10 | % 27.40/8.10 | Instantiating (348) with all_179_0_1662, all_179_1_1663 yields: % 27.40/8.10 | (351) (all_179_0_1662 = 0 & all_179_1_1663 = 0 & unequally_directed_lines(all_0_3_3, all_68_1_1541) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_179_1_1663 = 0 & all_68_0_1540 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_179_1_1663 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_179_1_1663) % 27.40/8.10 | % 27.40/8.10 | Instantiating (349) with all_181_0_1667, all_181_1_1668, all_181_2_1669 yields: % 27.40/8.10 | (352) (all_181_0_1667 = 0 & all_181_2_1669 = 0 & reverse_line(all_0_2_2) = all_181_1_1668 & unequally_directed_lines(all_0_3_3, all_181_1_1668) = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | (all_181_1_1668 = 0 & all_115_0_1555 = 0 & reverse_line(all_0_2_2) = all_181_2_1669 & unequally_directed_lines(all_0_2_2, all_181_2_1669) = 0) | ( ~ (all_181_2_1669 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_181_2_1669) % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (346), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (208) unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (329), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (354) all_75_0_1542 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (354) yields: % 27.40/8.10 | (355) all_75_0_1542 = 0 % 27.40/8.10 | (356) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (185), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (357) all_52_0_71 = 0 & all_0_1_1 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (357) yields: % 27.40/8.10 | (358) all_52_0_71 = 0 % 27.40/8.10 | (191) all_0_1_1 = 0 % 27.40/8.10 | (208) unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (345), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (361) all_115_0_1555 = 0 % 27.40/8.10 | % 27.40/8.10 | Equations (361) can reduce 343 to: % 27.40/8.10 | (192) $false % 27.40/8.10 | % 27.40/8.10 |-The branch is then unsatisfiable % 27.40/8.10 |-Branch two: % 27.40/8.10 | (343) ~ (all_115_0_1555 = 0) % 27.40/8.10 | (364) ? [v0] : (reverse_line(all_0_2_2) = v0 & unequally_directed_lines(all_0_2_2, v0) = 0) % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (352), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (365) (all_181_0_1667 = 0 & all_181_2_1669 = 0 & reverse_line(all_0_2_2) = all_181_1_1668 & unequally_directed_lines(all_0_3_3, all_181_1_1668) = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) | (all_181_1_1668 = 0 & all_115_0_1555 = 0 & reverse_line(all_0_2_2) = all_181_2_1669 & unequally_directed_lines(all_0_2_2, all_181_2_1669) = 0) % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (365), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (366) all_181_0_1667 = 0 & all_181_2_1669 = 0 & reverse_line(all_0_2_2) = all_181_1_1668 & unequally_directed_lines(all_0_3_3, all_181_1_1668) = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (366) yields: % 27.40/8.10 | (367) all_181_0_1667 = 0 % 27.40/8.10 | (368) unequally_directed_lines(all_0_3_3, all_181_1_1668) = 0 % 27.40/8.10 | (369) reverse_line(all_0_2_2) = all_181_1_1668 % 27.40/8.10 | (370) all_181_2_1669 = 0 % 27.40/8.10 | (208) unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (350), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (372) (all_146_0_1596 = 0 & all_146_1_1597 = 0 & unequally_directed_lines(all_0_2_2, all_79_0_1545) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0) | (all_146_1_1597 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (372), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (373) all_146_0_1596 = 0 & all_146_1_1597 = 0 & unequally_directed_lines(all_0_2_2, all_79_0_1545) = 0 & unequally_directed_lines(all_0_2_2, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (373) yields: % 27.40/8.10 | (374) all_146_0_1596 = 0 % 27.40/8.10 | (375) all_146_1_1597 = 0 % 27.40/8.10 | (376) unequally_directed_lines(all_0_2_2, all_79_0_1545) = 0 % 27.40/8.10 | (263) unequally_directed_lines(all_0_2_2, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Instantiating formula (23) with all_0_2_2, all_0_2_2, 0, all_115_0_1555 and discharging atoms unequally_directed_lines(all_0_2_2, all_0_2_2) = all_115_0_1555, unequally_directed_lines(all_0_2_2, all_0_2_2) = 0, yields: % 27.40/8.10 | (361) all_115_0_1555 = 0 % 27.40/8.10 | % 27.40/8.10 | Equations (361) can reduce 343 to: % 27.40/8.10 | (192) $false % 27.40/8.10 | % 27.40/8.10 |-The branch is then unsatisfiable % 27.40/8.10 |-Branch two: % 27.40/8.10 | (380) all_146_1_1597 = 0 & unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 | Applying alpha-rule on (380) yields: % 27.40/8.10 | (375) all_146_1_1597 = 0 % 27.40/8.10 | (208) unequally_directed_lines(all_0_3_3, all_0_2_2) = 0 % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (351), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (383) (all_179_0_1662 = 0 & all_179_1_1663 = 0 & unequally_directed_lines(all_0_3_3, all_68_1_1541) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0) | (all_179_1_1663 = 0 & all_68_0_1540 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) % 27.40/8.10 | % 27.40/8.10 +-Applying beta-rule and splitting (383), into two cases. % 27.40/8.10 |-Branch one: % 27.40/8.10 | (384) all_179_0_1662 = 0 & all_179_1_1663 = 0 & unequally_directed_lines(all_0_3_3, all_68_1_1541) = 0 & unequally_directed_lines(all_0_3_3, all_0_3_3) = 0 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (384) yields: % 27.40/8.11 | (385) all_179_0_1662 = 0 % 27.40/8.11 | (386) all_179_1_1663 = 0 % 27.40/8.11 | (387) unequally_directed_lines(all_0_3_3, all_68_1_1541) = 0 % 27.40/8.11 | (252) unequally_directed_lines(all_0_3_3, all_0_3_3) = 0 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (144) with all_0_3_3, all_0_3_3 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_3_3) = 0, yields: % 27.40/8.11 | (389) ? [v0] : ( ~ (v0 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = v0) % 27.40/8.11 | % 27.40/8.11 | Instantiating (389) with all_481_0_2050 yields: % 27.40/8.11 | (390) ~ (all_481_0_2050 = 0) & equally_directed_lines(all_0_3_3, all_0_3_3) = all_481_0_2050 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (390) yields: % 27.40/8.11 | (391) ~ (all_481_0_2050 = 0) % 27.40/8.11 | (392) equally_directed_lines(all_0_3_3, all_0_3_3) = all_481_0_2050 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (114) with all_481_0_2050, all_0_3_3 and discharging atoms equally_directed_lines(all_0_3_3, all_0_3_3) = all_481_0_2050, yields: % 27.40/8.11 | (393) all_481_0_2050 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (393) can reduce 391 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (395) all_179_1_1663 = 0 & all_68_0_1540 = 0 & unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (395) yields: % 27.40/8.11 | (386) all_179_1_1663 = 0 % 27.40/8.11 | (334) all_68_0_1540 = 0 % 27.40/8.11 | (228) unequally_directed_lines(all_0_2_2, all_0_3_3) = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (334) can reduce 321 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (400) ~ (all_179_1_1663 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_179_1_1663 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (400) yields: % 27.40/8.11 | (401) ~ (all_179_1_1663 = 0) % 27.40/8.11 | (402) unequally_directed_lines(all_0_3_3, all_0_2_2) = all_179_1_1663 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (23) with all_0_3_3, all_0_2_2, 0, all_179_1_1663 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_2_2) = all_179_1_1663, unequally_directed_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.11 | (386) all_179_1_1663 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (386) can reduce 401 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (405) ~ (all_146_1_1597 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_146_1_1597 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (405) yields: % 27.40/8.11 | (406) ~ (all_146_1_1597 = 0) % 27.40/8.11 | (407) unequally_directed_lines(all_0_3_3, all_0_2_2) = all_146_1_1597 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (23) with all_0_3_3, all_0_2_2, 0, all_146_1_1597 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_2_2) = all_146_1_1597, unequally_directed_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.11 | (375) all_146_1_1597 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (375) can reduce 406 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (410) all_181_1_1668 = 0 & all_115_0_1555 = 0 & reverse_line(all_0_2_2) = all_181_2_1669 & unequally_directed_lines(all_0_2_2, all_181_2_1669) = 0 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (410) yields: % 27.40/8.11 | (411) all_181_1_1668 = 0 % 27.40/8.11 | (361) all_115_0_1555 = 0 % 27.40/8.11 | (413) reverse_line(all_0_2_2) = all_181_2_1669 % 27.40/8.11 | (414) unequally_directed_lines(all_0_2_2, all_181_2_1669) = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (361) can reduce 343 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (416) ~ (all_181_2_1669 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_181_2_1669 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (416) yields: % 27.40/8.11 | (417) ~ (all_181_2_1669 = 0) % 27.40/8.11 | (418) unequally_directed_lines(all_0_3_3, all_0_2_2) = all_181_2_1669 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (23) with all_0_3_3, all_0_2_2, 0, all_181_2_1669 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_2_2) = all_181_2_1669, unequally_directed_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.11 | (370) all_181_2_1669 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (370) can reduce 417 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (421) ~ (all_52_0_71 = 0) & convergent_lines(all_0_3_3, all_0_2_2) = all_52_0_71 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (421) yields: % 27.40/8.11 | (422) ~ (all_52_0_71 = 0) % 27.40/8.11 | (423) convergent_lines(all_0_3_3, all_0_2_2) = all_52_0_71 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (16) with all_0_3_3, all_0_2_2, 0, all_52_0_71 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = all_52_0_71, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.11 | (358) all_52_0_71 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (358) can reduce 422 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (426) ~ (all_75_0_1542 = 0) & unequally_directed_lines(all_0_3_3, all_0_2_2) = all_75_0_1542 % 27.40/8.11 | % 27.40/8.11 | Applying alpha-rule on (426) yields: % 27.40/8.11 | (427) ~ (all_75_0_1542 = 0) % 27.40/8.11 | (428) unequally_directed_lines(all_0_3_3, all_0_2_2) = all_75_0_1542 % 27.40/8.11 | % 27.40/8.11 | Instantiating formula (23) with all_0_3_3, all_0_2_2, 0, all_75_0_1542 and discharging atoms unequally_directed_lines(all_0_3_3, all_0_2_2) = all_75_0_1542, unequally_directed_lines(all_0_3_3, all_0_2_2) = 0, yields: % 27.40/8.11 | (355) all_75_0_1542 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (355) can reduce 427 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (309) ~ (unequally_directed_lines(all_0_3_3, all_0_2_2) = 0) % 27.40/8.11 | (361) all_115_0_1555 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (361) can reduce 343 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 |-Branch two: % 27.40/8.11 | (306) ~ (unequally_directed_lines(all_0_2_2, all_0_3_3) = 0) % 27.40/8.11 | (334) all_68_0_1540 = 0 % 27.40/8.11 | % 27.40/8.11 | Equations (334) can reduce 321 to: % 27.40/8.11 | (192) $false % 27.40/8.11 | % 27.40/8.11 |-The branch is then unsatisfiable % 27.40/8.11 % SZS output end Proof for theBenchmark % 27.40/8.11 % 27.40/8.11 7500ms %------------------------------------------------------------------------------