%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO193+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n009.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 03:48:30 EDT 2022 % Result : Theorem 23.73s 6.85s % Output : Proof 54.97s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO193+3 : TPTP v8.1.0. Released v4.0.0. % 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 17 21:50:23 EDT 2022 % 0.13/0.34 % CPUTime : % 0.48/0.59 ____ _ % 0.48/0.59 ___ / __ \_____(_)___ ________ __________ % 0.48/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.59 % 0.48/0.59 A Theorem Prover for First-Order Logic % 0.48/0.59 (ePrincess v.1.0) % 0.48/0.59 % 0.48/0.59 (c) Philipp Rümmer, 2009-2015 % 0.48/0.59 (c) Peter Backeman, 2014-2015 % 0.48/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.59 Bug reports to peter@backeman.se % 0.48/0.59 % 0.48/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.59 % 0.48/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.79/0.96 Prover 0: Preprocessing ... % 2.43/1.17 Prover 0: Warning: ignoring some quantifiers % 2.43/1.20 Prover 0: Constructing countermodel ... % 19.58/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 19.69/6.01 Prover 1: Preprocessing ... % 20.64/6.17 Prover 1: Constructing countermodel ... % 20.88/6.24 Prover 1: gave up % 20.88/6.24 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 21.09/6.27 Prover 2: Preprocessing ... % 21.83/6.44 Prover 2: Warning: ignoring some quantifiers % 21.83/6.45 Prover 2: Constructing countermodel ... % 23.73/6.85 Prover 2: proved (612ms) % 23.73/6.85 Prover 0: stopped % 23.73/6.85 % 23.73/6.85 No countermodel exists, formula is valid % 23.73/6.85 % SZS status Theorem for theBenchmark % 23.73/6.85 % 23.73/6.85 Generating proof ... Warning: ignoring some quantifiers % 53.75/19.41 found it (size 615) % 53.75/19.41 % 53.75/19.41 % SZS output start Proof for theBenchmark % 53.75/19.41 Assumed formulas after preprocessing and simplification: % 53.75/19.41 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = 0) & intersection_point(v2, v1) = v4 & intersection_point(v0, v1) = v3 & apart_point_and_line(v4, v0) = v5 & apart_point_and_line(v3, v2) = 0 & convergent_lines(v2, v1) = 0 & convergent_lines(v0, v2) = 0 & convergent_lines(v0, v1) = 0 & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v8, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v12 = 0) & distinct_lines(v7, v8) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (unorthogonal_lines(v7, v9) = v11) | ~ (apart_point_and_line(v6, v7) = v10) | ~ (distinct_lines(v7, v8) = 0) | ? [v12] : ((v12 = 0 & unorthogonal_lines(v8, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v7, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v6, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v8) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v9) = v10) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v7, v8) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v8, v9) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v6, v9) = 0) | ( ~ (v12 = 0) & distinct_points(v6, v7) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = 0 | ~ (apart_point_and_line(v6, v9) = v11) | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_points(v6, v7) = 0) | ? [v12] : ((v12 = 0 & apart_point_and_line(v7, v9) = 0) | (v12 = 0 & apart_point_and_line(v7, v8) = 0) | ( ~ (v12 = 0) & distinct_lines(v8, v9) = v12))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v8, v7) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ? [v11] : ((v11 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & apart_point_and_line(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (convergent_lines(v6, v8) = v10) | ~ (distinct_lines(v7, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_lines(v7, v8) = v10) | ~ (distinct_lines(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (distinct_points(v7, v8) = v10) | ~ (distinct_points(v6, v8) = v9) | ? [v11] : ( ~ (v11 = 0) & distinct_points(v6, v7) = v11)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & convergent_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v6, v8) = v10) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v7, v8) = v10) | ~ (convergent_lines(v6, v8) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v6, v7) = v11) | ( ~ (v11 = 0) & convergent_lines(v6, v7) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (convergent_lines(v6, v8) = v10) | ~ (convergent_lines(v6, v7) = v9) | ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v11 = 0) & unorthogonal_lines(v7, v8) = v11) | ( ~ (v11 = 0) & convergent_lines(v7, v8) = v11))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | unorthogonal_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v8, v7) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (apart_point_and_line(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v7) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v6, v8) = 0) | (v10 = 0 & convergent_lines(v7, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | apart_point_and_line(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (apart_point_and_line(v6, v7) = 0) | ~ (distinct_points(v6, v8) = v9) | apart_point_and_line(v8, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | convergent_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (convergent_lines(v6, v7) = 0) | ~ (distinct_lines(v7, v8) = v9) | convergent_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v7, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_lines(v6, v8) = v9) | ~ (distinct_lines(v6, v7) = 0) | distinct_lines(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v7, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v6, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (distinct_points(v6, v8) = v9) | ~ (distinct_points(v6, v7) = 0) | distinct_points(v7, v8) = 0) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_lines(v9, v8) = v7) | ~ (orthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (incident_point_and_line(v9, v8) = v7) | ~ (incident_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_lines(v9, v8) = v7) | ~ (parallel_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_lines(v9, v8) = v7) | ~ (equal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (equal_points(v9, v8) = v7) | ~ (equal_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (orthogonal_through_point(v9, v8) = v7) | ~ (orthogonal_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (unorthogonal_lines(v9, v8) = v7) | ~ (unorthogonal_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (parallel_through_point(v9, v8) = v7) | ~ (parallel_through_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (intersection_point(v9, v8) = v7) | ~ (intersection_point(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (line_connecting(v9, v8) = v7) | ~ (line_connecting(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (apart_point_and_line(v9, v8) = v7) | ~ (apart_point_and_line(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (convergent_lines(v9, v8) = v7) | ~ (convergent_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_lines(v9, v8) = v7) | ~ (distinct_lines(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (distinct_points(v9, v8) = v7) | ~ (distinct_points(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (unorthogonal_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & convergent_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (unorthogonal_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v7, v8) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v7, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & convergent_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v7, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v7, v8) = 0) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v6, v8) = 0 & convergent_lines(v6, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v7, v8) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v8) = v9) | ~ (convergent_lines(v6, v7) = 0) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = 0 & unorthogonal_lines(v7, v8) = 0 & convergent_lines(v7, v8) = 0) | (v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v8) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v6, v7) = v10))) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (distinct_lines(v8, v9) = 0) | ~ (distinct_points(v6, v7) = 0) | ? [v10] : ((v10 = 0 & apart_point_and_line(v7, v9) = 0) | (v10 = 0 & apart_point_and_line(v7, v8) = 0) | (v10 = 0 & apart_point_and_line(v6, v9) = 0) | (v10 = 0 & apart_point_and_line(v6, v8) = 0))) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (orthogonal_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (incident_point_and_line(v6, v7) = v8) | apart_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (parallel_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_lines(v6, v7) = v8) | distinct_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (equal_points(v6, v7) = v8) | distinct_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | orthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (unorthogonal_lines(v6, v7) = v8) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v6, v7) = v8) | incident_point_and_line(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | parallel_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | unorthogonal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & distinct_lines(v6, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | equal_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | equal_points(v6, v7) = 0) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (point(v8) = v7) | ~ (point(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (line(v8) = v7) | ~ (line(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & unorthogonal_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (orthogonal_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v7, v6) = v8) | ? [v9] : ( ~ (v9 = 0) & convergent_lines(v8, v7) = v9)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (parallel_through_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : ((v9 = 0 & point(v8) = 0) | ( ~ (v9 = 0) & line(v7) = v9) | ( ~ (v9 = 0) & line(v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v7) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (intersection_point(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v8, v6) = v9) | ( ~ (v9 = 0) & convergent_lines(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : ((v9 = 0 & line(v8) = 0) | ( ~ (v9 = 0) & point(v7) = v9) | ( ~ (v9 = 0) & point(v6) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v7, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (line_connecting(v6, v7) = v8) | ? [v9] : (( ~ (v9 = 0) & apart_point_and_line(v6, v8) = v9) | ( ~ (v9 = 0) & distinct_points(v6, v7) = v9))) & ! [v6] : ! [v7] : ( ~ (orthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (incident_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (parallel_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (equal_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & distinct_points(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (unorthogonal_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & orthogonal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (apart_point_and_line(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & incident_point_and_line(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v7) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & intersection_point(v6, v7) = v8 & apart_point_and_line(v8, v6) = v9)) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & point(v8) = 0 & intersection_point(v6, v7) = v8) | ( ~ (v8 = 0) & line(v7) = v8) | ( ~ (v8 = 0) & line(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (convergent_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & parallel_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | convergent_lines(v6, v7) = 0) & ! [v6] : ! [v7] : ( ~ (distinct_lines(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_lines(v6, v7) = v8)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v7, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ( ~ (v9 = 0) & line_connecting(v6, v7) = v8 & apart_point_and_line(v6, v8) = v9)) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ? [v9] : ((v9 = 0 & line(v8) = 0 & line_connecting(v6, v7) = v8) | ( ~ (v8 = 0) & point(v7) = v8) | ( ~ (v8 = 0) & point(v6) = v8))) & ! [v6] : ! [v7] : ( ~ (distinct_points(v6, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & equal_points(v6, v7) = v8)) & ! [v6] : ~ (convergent_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_lines(v6, v6) = 0) & ! [v6] : ~ (distinct_points(v6, v6) = 0) & ? [v6] : ? [v7] : ? [v8] : orthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : incident_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : equal_points(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : orthogonal_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : unorthogonal_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : parallel_through_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : intersection_point(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : line_connecting(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : apart_point_and_line(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : convergent_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_lines(v7, v6) = v8 & ? [v6] : ? [v7] : ? [v8] : distinct_points(v7, v6) = v8 & ? [v6] : ? [v7] : point(v6) = v7 & ? [v6] : ? [v7] : line(v6) = v7) % 53.91/19.49 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5 yields: % 53.91/19.49 | (1) ~ (all_0_0_0 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1 & intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 & apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & point(v0) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) & ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & line(v2) = 0 & line_connecting(v0, v1) = v2) | ( ~ (v2 = 0) & point(v1) = v2) | ( ~ (v2 = 0) & point(v0) = v2))) & ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) & ! [v0] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 & ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 & ? [v0] : ? [v1] : point(v0) = v1 & ? [v0] : ? [v1] : line(v0) = v1 % 53.91/19.53 | % 53.91/19.53 | Applying alpha-rule on (1) yields: % 53.91/19.53 | (2) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 54.35/19.53 | (3) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_lines(v0, v1) = v2)) % 54.35/19.53 | (4) ! [v0] : ! [v1] : ( ~ (equal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_lines(v0, v1) = v2)) % 54.35/19.53 | (5) ? [v0] : ? [v1] : ? [v2] : parallel_lines(v1, v0) = v2 % 54.35/19.53 | (6) convergent_lines(all_0_5_5, all_0_3_3) = 0 % 54.35/19.53 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) % 54.35/19.53 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 54.35/19.53 | (9) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & line(v2) = 0) | ( ~ (v3 = 0) & point(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3))) % 54.35/19.53 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 54.35/19.53 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 54.35/19.53 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_lines(v3, v2) = v1) | ~ (equal_lines(v3, v2) = v0)) % 54.35/19.53 | (13) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v1) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 54.35/19.53 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 54.35/19.53 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | apart_point_and_line(v0, v2) = 0) % 54.35/19.53 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 54.35/19.53 | (17) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 54.35/19.53 | (18) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ((v3 = 0 & point(v2) = 0 & intersection_point(v0, v1) = v2) | ( ~ (v2 = 0) & line(v1) = v2) | ( ~ (v2 = 0) & line(v0) = v2))) % 54.35/19.53 | (19) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 54.35/19.53 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 54.35/19.53 | (21) ! [v0] : ! [v1] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & orthogonal_lines(v0, v1) = v2)) % 54.35/19.53 | (22) ! [v0] : ! [v1] : ( ~ (orthogonal_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & unorthogonal_lines(v0, v1) = v2)) % 54.35/19.54 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 54.35/19.54 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 54.35/19.54 | (25) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (apart_point_and_line(v0, v1) = v2) | incident_point_and_line(v0, v1) = 0) % 54.35/19.54 | (26) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (incident_point_and_line(v0, v1) = v2) | apart_point_and_line(v0, v1) = 0) % 54.35/19.54 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 54.35/19.54 | (28) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 54.35/19.54 | (29) intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1 % 54.35/19.54 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 54.35/19.54 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 54.35/19.54 | (32) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 54.35/19.54 | (33) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : ((v3 = 0 & point(v2) = 0) | ( ~ (v3 = 0) & line(v1) = v3) | ( ~ (v3 = 0) & line(v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 54.35/19.54 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 54.35/19.54 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (convergent_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5)) % 54.35/19.54 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 54.35/19.54 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (point(v2) = v1) | ~ (point(v2) = v0)) % 54.35/19.54 | (38) apart_point_and_line(all_0_2_2, all_0_3_3) = 0 % 54.35/19.54 | (39) ! [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)) % 54.35/19.54 | (40) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 54.35/19.54 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) % 54.35/19.54 | (42) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (line(v2) = v1) | ~ (line(v2) = v0)) % 54.35/19.54 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 54.35/19.54 | (44) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 54.35/19.54 | (45) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 54.35/19.54 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0))) % 54.35/19.54 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (unorthogonal_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) % 54.35/19.54 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 54.35/19.54 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 54.35/19.54 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 54.35/19.54 | (51) ! [v0] : ! [v1] : ( ~ (distinct_lines(v0, v1) = 0) | convergent_lines(v0, v1) = 0) % 54.35/19.54 | (52) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | orthogonal_lines(v0, v1) = 0) % 54.35/19.54 | (53) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (orthogonal_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 54.35/19.54 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 54.35/19.54 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v0, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v1, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 54.35/19.54 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 54.35/19.54 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 54.35/19.55 | (58) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 54.35/19.55 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 54.35/19.55 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | parallel_lines(v0, v1) = 0) % 54.35/19.55 | (61) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (parallel_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 54.35/19.55 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 54.35/19.55 | (63) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 54.35/19.55 | (64) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 54.35/19.55 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 54.35/19.55 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 54.35/19.55 | (67) ? [v0] : ? [v1] : ? [v2] : equal_points(v1, v0) = v2 % 54.35/19.55 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 54.35/19.55 | (69) convergent_lines(all_0_3_3, all_0_4_4) = 0 % 54.35/19.55 | (70) ? [v0] : ? [v1] : ? [v2] : equal_lines(v1, v0) = v2 % 54.35/19.55 | (71) ! [v0] : ! [v1] : ! [v2] : ( ~ (intersection_point(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v2, v0) = v3) | ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3))) % 54.35/19.55 | (72) ! [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))) % 54.35/19.55 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = 0) | ~ (convergent_lines(v1, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 54.35/19.55 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 54.35/19.55 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v1) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) % 54.35/19.55 | (76) ! [v0] : ! [v1] : ( ~ (apart_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & incident_point_and_line(v0, v1) = v2)) % 54.35/19.55 | (77) ! [v0] : ! [v1] : ( ~ (incident_point_and_line(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & apart_point_and_line(v0, v1) = v2)) % 54.35/19.55 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 54.35/19.55 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = 0) | ~ (distinct_points(v0, v2) = v3) | apart_point_and_line(v2, v1) = 0) % 54.35/19.55 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) % 54.35/19.55 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 54.35/19.55 | (82) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_points(v0, v1) = v2) | equal_points(v0, v1) = 0) % 54.35/19.55 | (83) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_points(v0, v1) = v2) | distinct_points(v0, v1) = 0) % 54.35/19.55 | (84) ? [v0] : ? [v1] : ? [v2] : incident_point_and_line(v1, v0) = v2 % 54.35/19.55 | (85) ? [v0] : ? [v1] : line(v0) = v1 % 54.35/19.55 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v1, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v2, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) % 54.35/19.55 | (87) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & distinct_lines(v0, v1) = v3)) % 54.35/19.55 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_lines(v3, v2) = v1) | ~ (orthogonal_lines(v3, v2) = v0)) % 54.35/19.55 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 54.35/19.56 | (90) ~ (all_0_0_0 = 0) % 54.35/19.56 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 54.35/19.56 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (convergent_lines(v0, v2) = v4) | ~ (convergent_lines(v0, v1) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 54.35/19.56 | (93) ? [v0] : ? [v1] : ? [v2] : orthogonal_lines(v1, v0) = v2 % 54.35/19.56 | (94) intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2 % 54.35/19.56 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v4) | ~ (apart_point_and_line(v0, v1) = v3) | ? [v5] : ((v5 = 0 & convergent_lines(v1, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) % 54.35/19.56 | (96) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 54.35/19.56 | (97) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & equal_points(v0, v1) = v2)) % 54.35/19.56 | (98) ! [v0] : ! [v1] : ( ~ (equal_points(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & distinct_points(v0, v1) = v2)) % 54.35/19.56 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v3) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 54.35/19.56 | (100) apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0 % 54.35/19.56 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ~ (distinct_lines(v2, v3) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v2) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 54.35/19.56 | (102) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 54.35/19.56 | (103) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v1, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) % 54.35/19.56 | (104) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 54.35/19.56 | (105) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v0, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v1, v2) = v5) | ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5))) % 54.35/19.56 | (106) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v0, v1) = v4))) % 54.35/19.56 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (unorthogonal_lines(v0, v1) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0 & convergent_lines(v1, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v4 = 0) & convergent_lines(v0, v1) = v4))) % 54.35/19.56 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v1) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) % 54.35/19.56 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (equal_points(v3, v2) = v1) | ~ (equal_points(v3, v2) = v0)) % 54.35/19.56 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (convergent_lines(v1, v2) = 0) | ~ (convergent_lines(v0, v2) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v1) = 0 & convergent_lines(v0, v1) = 0) | (v4 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v4 = 0) & unorthogonal_lines(v1, v2) = v4))) % 54.35/19.56 | (111) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 54.35/19.56 | (112) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 54.35/19.56 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 54.35/19.56 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 54.35/19.56 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v2) = v5) | ~ (apart_point_and_line(v0, v3) = v4) | ? [v6] : ((v6 = 0 & apart_point_and_line(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6) | ( ~ (v6 = 0) & distinct_points(v0, v1) = v6))) % 54.35/19.56 | (116) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 54.35/19.57 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (distinct_lines(v2, v3) = 0) | ~ (distinct_points(v0, v1) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v1, v3) = 0) | (v4 = 0 & apart_point_and_line(v1, v2) = 0) | (v4 = 0 & apart_point_and_line(v0, v3) = 0) | (v4 = 0 & apart_point_and_line(v0, v2) = 0))) % 54.35/19.57 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v2, v1) = v3) | ~ (apart_point_and_line(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 54.35/19.57 | (119) ? [v0] : ? [v1] : point(v0) = v1 % 54.35/19.57 | (120) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 54.35/19.57 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v2) = v4) | ~ (distinct_lines(v1, v2) = 0) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v1) = 0))) % 54.35/19.57 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (apart_point_and_line(v1, v3) = v5) | ~ (apart_point_and_line(v1, v2) = v4) | ~ (distinct_points(v0, v1) = 0) | ? [v6] : ((v6 = 0 & apart_point_and_line(v0, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v2, v3) = v6))) % 54.35/19.57 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v2) = 0) % 54.35/19.57 | (124) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & parallel_lines(v0, v1) = v2)) % 54.35/19.57 | (125) ! [v0] : ! [v1] : ( ~ (parallel_lines(v0, v1) = 0) | ? [v2] : ( ~ (v2 = 0) & convergent_lines(v0, v1) = v2)) % 54.35/19.57 | (126) convergent_lines(all_0_5_5, all_0_4_4) = 0 % 54.35/19.57 | (127) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 54.35/19.57 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v4) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v5] : ( ~ (v5 = 0) & convergent_lines(v1, v2) = v5)) % 54.35/19.57 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (distinct_lines(v1, v2) = 0) | ? [v4] : ((v4 = 0 & apart_point_and_line(v0, v2) = 0) | (v4 = 0 & convergent_lines(v1, v2) = 0))) % 54.35/19.57 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & convergent_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) % 54.35/19.57 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_lines(v3, v2) = v1) | ~ (parallel_lines(v3, v2) = v0)) % 54.35/19.57 | (132) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (incident_point_and_line(v3, v2) = v1) | ~ (incident_point_and_line(v3, v2) = v0)) % 54.35/19.57 | (133) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 54.35/19.57 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (unorthogonal_lines(v1, v2) = v4) | ~ (convergent_lines(v0, v2) = v3) | ? [v5] : ((v5 = 0 & v4 = 0 & convergent_lines(v1, v2) = 0) | (v5 = 0 & v3 = 0 & unorthogonal_lines(v0, v2) = 0) | ( ~ (v5 = 0) & unorthogonal_lines(v0, v1) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) % 54.35/19.57 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (line_connecting(v0, v1) = v2) | ? [v3] : (( ~ (v3 = 0) & apart_point_and_line(v1, v2) = v3) | ( ~ (v3 = 0) & distinct_points(v0, v1) = v3))) % 54.35/19.57 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (unorthogonal_lines(v0, v2) = v3) | ~ (convergent_lines(v1, v2) = 0) | unorthogonal_lines(v0, v1) = 0) % 54.35/19.57 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (unorthogonal_lines(v1, v2) = 0) | ~ (unorthogonal_lines(v0, v1) = v3) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & unorthogonal_lines(v0, v2) = 0 & convergent_lines(v0, v2) = 0) | (v4 = 0 & v3 = 0 & convergent_lines(v0, v1) = 0) | ( ~ (v4 = 0) & convergent_lines(v1, v2) = v4))) % 54.35/19.57 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | equal_lines(v0, v1) = 0) % 54.35/19.57 | (139) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (equal_lines(v0, v1) = v2) | distinct_lines(v0, v1) = 0) % 54.35/19.57 | (140) ! [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))) % 54.35/19.57 | (141) ! [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)) % 54.35/19.57 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v0, v1) = v3) | ~ (convergent_lines(v1, v2) = v4) | ? [v5] : ((v5 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v5 = 0) & distinct_lines(v1, v2) = v5))) % 54.35/19.57 | (143) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 54.35/19.57 | (144) ! [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))) % 54.35/19.57 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 54.35/19.57 | (146) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 54.35/19.57 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v5 = 0 | v4 = 0 | ~ (unorthogonal_lines(v2, v3) = v5) | ~ (apart_point_and_line(v0, v1) = v4) | ? [v6] : ((v6 = 0 & unorthogonal_lines(v1, v3) = 0) | (v6 = 0 & apart_point_and_line(v0, v2) = 0) | ( ~ (v6 = 0) & distinct_lines(v1, v2) = v6))) % 54.35/19.57 | % 54.35/19.57 | Instantiating formula (13) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 54.35/19.57 | (148) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 54.35/19.57 | % 54.35/19.57 | Instantiating formula (71) with all_0_1_1, all_0_4_4, all_0_3_3 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 54.35/19.57 | (149) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 54.35/19.57 | % 54.35/19.57 | Instantiating formula (13) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 54.35/19.58 | (150) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (71) with all_0_2_2, all_0_4_4, all_0_5_5 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 54.35/19.58 | (151) ? [v0] : (( ~ (v0 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = v0)) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (95) with all_0_0_0, all_0_0_0, all_0_5_5, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.35/19.58 | (152) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (65) with all_0_0_0, all_0_0_0, all_0_5_5, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.35/19.58 | (153) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (127) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 54.35/19.58 | (154) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (32) with all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 54.35/19.58 | (155) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_3_3, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_3_3) = v1) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (127) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields: % 54.35/19.58 | (156) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (32) with all_0_3_3, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_3_3) = 0, yields: % 54.35/19.58 | (157) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_5_5) = v1) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (127) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 54.35/19.58 | (158) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_4_4) = v1) % 54.35/19.58 | % 54.35/19.58 | Instantiating formula (32) with all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 54.35/19.58 | (159) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_5_5, all_0_4_4) = v0 & apart_point_and_line(v0, all_0_5_5) = v1) % 54.35/19.58 | % 54.35/19.58 | Instantiating (159) with all_42_0_53, all_42_1_54 yields: % 54.35/19.58 | (160) ~ (all_42_0_53 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_42_1_54 & apart_point_and_line(all_42_1_54, all_0_5_5) = all_42_0_53 % 54.35/19.58 | % 54.35/19.58 | Applying alpha-rule on (160) yields: % 54.35/19.58 | (161) ~ (all_42_0_53 = 0) % 54.35/19.58 | (162) intersection_point(all_0_5_5, all_0_4_4) = all_42_1_54 % 54.35/19.58 | (163) apart_point_and_line(all_42_1_54, all_0_5_5) = all_42_0_53 % 54.35/19.58 | % 54.35/19.58 | Instantiating (155) with all_46_0_58, all_46_1_59 yields: % 54.35/19.58 | (164) ~ (all_46_0_58 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_46_1_59 & apart_point_and_line(all_46_1_59, all_0_3_3) = all_46_0_58 % 54.35/19.58 | % 54.35/19.58 | Applying alpha-rule on (164) yields: % 54.35/19.58 | (165) ~ (all_46_0_58 = 0) % 54.35/19.58 | (166) intersection_point(all_0_3_3, all_0_4_4) = all_46_1_59 % 54.35/19.58 | (167) apart_point_and_line(all_46_1_59, all_0_3_3) = all_46_0_58 % 54.35/19.58 | % 54.35/19.58 | Instantiating (154) with all_48_0_60, all_48_1_61 yields: % 54.35/19.58 | (168) ~ (all_48_0_60 = 0) & intersection_point(all_0_3_3, all_0_4_4) = all_48_1_61 & apart_point_and_line(all_48_1_61, all_0_4_4) = all_48_0_60 % 54.35/19.58 | % 54.35/19.58 | Applying alpha-rule on (168) yields: % 54.35/19.58 | (169) ~ (all_48_0_60 = 0) % 54.35/19.58 | (170) intersection_point(all_0_3_3, all_0_4_4) = all_48_1_61 % 54.35/19.58 | (171) apart_point_and_line(all_48_1_61, all_0_4_4) = all_48_0_60 % 54.35/19.58 | % 54.35/19.58 | Instantiating (151) with all_51_0_63 yields: % 54.35/19.58 | (172) ( ~ (all_51_0_63 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_51_0_63) | ( ~ (all_51_0_63 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_51_0_63) % 54.35/19.58 | % 54.35/19.58 | Instantiating (150) with all_52_0_64 yields: % 54.35/19.58 | (173) ( ~ (all_52_0_64 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64) | ( ~ (all_52_0_64 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_52_0_64) % 54.35/19.58 | % 54.35/19.58 | Instantiating (157) with all_63_0_78, all_63_1_79 yields: % 54.35/19.58 | (174) ~ (all_63_0_78 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_63_1_79 & apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78 % 54.35/19.58 | % 54.35/19.58 | Applying alpha-rule on (174) yields: % 54.35/19.58 | (175) ~ (all_63_0_78 = 0) % 54.35/19.58 | (176) intersection_point(all_0_5_5, all_0_3_3) = all_63_1_79 % 54.35/19.58 | (177) apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78 % 54.35/19.58 | % 54.35/19.58 | Instantiating (156) with all_65_0_80, all_65_1_81 yields: % 54.35/19.58 | (178) ~ (all_65_0_80 = 0) & intersection_point(all_0_5_5, all_0_3_3) = all_65_1_81 & apart_point_and_line(all_65_1_81, all_0_3_3) = all_65_0_80 % 54.35/19.58 | % 54.35/19.58 | Applying alpha-rule on (178) yields: % 54.35/19.58 | (179) ~ (all_65_0_80 = 0) % 54.35/19.58 | (180) intersection_point(all_0_5_5, all_0_3_3) = all_65_1_81 % 54.35/19.58 | (181) apart_point_and_line(all_65_1_81, all_0_3_3) = all_65_0_80 % 54.35/19.58 | % 54.35/19.58 | Instantiating (148) with all_68_0_83 yields: % 54.35/19.58 | (182) ( ~ (all_68_0_83 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_68_0_83) | ( ~ (all_68_0_83 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_83) % 54.35/19.58 | % 54.35/19.58 | Instantiating (158) with all_69_0_84, all_69_1_85 yields: % 54.35/19.58 | (183) ~ (all_69_0_84 = 0) & intersection_point(all_0_5_5, all_0_4_4) = all_69_1_85 & apart_point_and_line(all_69_1_85, all_0_4_4) = all_69_0_84 % 54.35/19.58 | % 54.35/19.58 | Applying alpha-rule on (183) yields: % 54.35/19.58 | (184) ~ (all_69_0_84 = 0) % 54.35/19.58 | (185) intersection_point(all_0_5_5, all_0_4_4) = all_69_1_85 % 54.35/19.58 | (186) apart_point_and_line(all_69_1_85, all_0_4_4) = all_69_0_84 % 54.35/19.58 | % 54.35/19.58 | Instantiating (149) with all_73_0_89 yields: % 54.35/19.58 | (187) ( ~ (all_73_0_89 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_73_0_89) | ( ~ (all_73_0_89 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_73_0_89) % 54.35/19.58 | % 54.35/19.58 +-Applying beta-rule and splitting (152), into two cases. % 54.35/19.58 |-Branch one: % 54.35/19.58 | (188) all_0_0_0 = 0 % 54.35/19.58 | % 54.35/19.58 | Equations (188) can reduce 90 to: % 54.35/19.58 | (189) $false % 54.35/19.58 | % 54.35/19.58 |-The branch is then unsatisfiable % 54.35/19.58 |-Branch two: % 54.35/19.58 | (90) ~ (all_0_0_0 = 0) % 54.35/19.58 | (191) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 54.35/19.58 | % 54.35/19.58 +-Applying beta-rule and splitting (153), into two cases. % 54.35/19.58 |-Branch one: % 54.35/19.58 | (188) all_0_0_0 = 0 % 54.35/19.58 | % 54.35/19.58 | Equations (188) can reduce 90 to: % 54.35/19.58 | (189) $false % 54.35/19.58 | % 54.35/19.58 |-The branch is then unsatisfiable % 54.35/19.58 |-Branch two: % 54.35/19.58 | (90) ~ (all_0_0_0 = 0) % 54.35/19.58 | (195) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.35/19.59 | % 54.35/19.59 +-Applying beta-rule and splitting (173), into two cases. % 54.35/19.59 |-Branch one: % 54.35/19.59 | (196) ~ (all_52_0_64 = 0) & apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64 % 54.35/19.59 | % 54.35/19.59 | Applying alpha-rule on (196) yields: % 54.35/19.59 | (197) ~ (all_52_0_64 = 0) % 54.35/19.59 | (198) apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64 % 54.35/19.59 | % 54.35/19.59 +-Applying beta-rule and splitting (172), into two cases. % 54.35/19.59 |-Branch one: % 54.35/19.59 | (199) ~ (all_51_0_63 = 0) & apart_point_and_line(all_0_2_2, all_0_5_5) = all_51_0_63 % 54.35/19.59 | % 54.35/19.59 | Applying alpha-rule on (199) yields: % 54.35/19.59 | (200) ~ (all_51_0_63 = 0) % 54.35/19.59 | (201) apart_point_and_line(all_0_2_2, all_0_5_5) = all_51_0_63 % 54.35/19.59 | % 54.35/19.59 +-Applying beta-rule and splitting (187), into two cases. % 54.35/19.59 |-Branch one: % 54.35/19.59 | (202) ~ (all_73_0_89 = 0) & apart_point_and_line(all_0_1_1, all_0_3_3) = all_73_0_89 % 54.35/19.59 | % 54.35/19.59 | Applying alpha-rule on (202) yields: % 54.35/19.59 | (203) ~ (all_73_0_89 = 0) % 54.35/19.59 | (204) apart_point_and_line(all_0_1_1, all_0_3_3) = all_73_0_89 % 54.35/19.59 | % 54.35/19.59 +-Applying beta-rule and splitting (182), into two cases. % 54.35/19.59 |-Branch one: % 54.35/19.59 | (205) ~ (all_68_0_83 = 0) & apart_point_and_line(all_0_1_1, all_0_4_4) = all_68_0_83 % 54.35/19.59 | % 54.35/19.59 | Applying alpha-rule on (205) yields: % 54.35/19.59 | (206) ~ (all_68_0_83 = 0) % 54.35/19.59 | (207) apart_point_and_line(all_0_1_1, all_0_4_4) = all_68_0_83 % 54.35/19.59 | % 54.35/19.59 | Instantiating formula (24) with all_0_3_3, all_0_4_4, all_48_1_61, all_0_1_1 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_48_1_61, intersection_point(all_0_3_3, all_0_4_4) = all_0_1_1, yields: % 54.35/19.59 | (208) all_48_1_61 = all_0_1_1 % 54.35/19.59 | % 54.35/19.59 | Instantiating formula (24) with all_0_3_3, all_0_4_4, all_46_1_59, all_48_1_61 and discharging atoms intersection_point(all_0_3_3, all_0_4_4) = all_48_1_61, intersection_point(all_0_3_3, all_0_4_4) = all_46_1_59, yields: % 54.64/19.59 | (209) all_48_1_61 = all_46_1_59 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (24) with all_0_5_5, all_0_3_3, all_63_1_79, all_65_1_81 and discharging atoms intersection_point(all_0_5_5, all_0_3_3) = all_65_1_81, intersection_point(all_0_5_5, all_0_3_3) = all_63_1_79, yields: % 54.64/19.59 | (210) all_65_1_81 = all_63_1_79 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (24) with all_0_5_5, all_0_4_4, all_69_1_85, all_0_2_2 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_69_1_85, intersection_point(all_0_5_5, all_0_4_4) = all_0_2_2, yields: % 54.64/19.59 | (211) all_69_1_85 = all_0_2_2 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (24) with all_0_5_5, all_0_4_4, all_42_1_54, all_69_1_85 and discharging atoms intersection_point(all_0_5_5, all_0_4_4) = all_69_1_85, intersection_point(all_0_5_5, all_0_4_4) = all_42_1_54, yields: % 54.64/19.59 | (212) all_69_1_85 = all_42_1_54 % 54.64/19.59 | % 54.64/19.59 | Combining equations (211,212) yields a new equation: % 54.64/19.59 | (213) all_42_1_54 = all_0_2_2 % 54.64/19.59 | % 54.64/19.59 | Combining equations (208,209) yields a new equation: % 54.64/19.59 | (214) all_46_1_59 = all_0_1_1 % 54.64/19.59 | % 54.64/19.59 | Combining equations (214,209) yields a new equation: % 54.64/19.59 | (208) all_48_1_61 = all_0_1_1 % 54.64/19.59 | % 54.64/19.59 | Combining equations (213,212) yields a new equation: % 54.64/19.59 | (211) all_69_1_85 = all_0_2_2 % 54.64/19.59 | % 54.64/19.59 | From (211) and (186) follows: % 54.64/19.59 | (217) apart_point_and_line(all_0_2_2, all_0_4_4) = all_69_0_84 % 54.64/19.59 | % 54.64/19.59 | From (210) and (181) follows: % 54.64/19.59 | (218) apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80 % 54.64/19.59 | % 54.64/19.59 | From (208) and (171) follows: % 54.64/19.59 | (219) apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60 % 54.64/19.59 | % 54.64/19.59 | From (214) and (167) follows: % 54.64/19.59 | (220) apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58 % 54.64/19.59 | % 54.64/19.59 | From (213) and (163) follows: % 54.64/19.59 | (221) apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (54) with all_0_1_1, all_0_3_3, all_46_0_58, all_73_0_89 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_73_0_89, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.59 | (222) all_73_0_89 = all_46_0_58 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (54) with all_0_1_1, all_0_4_4, all_48_0_60, all_68_0_83 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_68_0_83, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.59 | (223) all_68_0_83 = all_48_0_60 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (54) with all_0_2_2, all_0_4_4, all_69_0_84, all_52_0_64 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_69_0_84, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.59 | (224) all_69_0_84 = all_52_0_64 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (54) with all_0_2_2, all_0_5_5, all_42_0_53, all_51_0_63 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_51_0_63, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.59 | (225) all_51_0_63 = all_42_0_53 % 54.64/19.59 | % 54.64/19.59 | Equations (222) can reduce 203 to: % 54.64/19.59 | (165) ~ (all_46_0_58 = 0) % 54.64/19.59 | % 54.64/19.59 | Equations (224) can reduce 184 to: % 54.64/19.59 | (197) ~ (all_52_0_64 = 0) % 54.64/19.59 | % 54.64/19.59 | Equations (223) can reduce 206 to: % 54.64/19.59 | (169) ~ (all_48_0_60 = 0) % 54.64/19.59 | % 54.64/19.59 | Equations (225) can reduce 200 to: % 54.64/19.59 | (161) ~ (all_42_0_53 = 0) % 54.64/19.59 | % 54.64/19.59 | From (222) and (204) follows: % 54.64/19.59 | (220) apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58 % 54.64/19.59 | % 54.64/19.59 | From (223) and (207) follows: % 54.64/19.59 | (219) apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60 % 54.64/19.59 | % 54.64/19.59 | From (224) and (217) follows: % 54.64/19.59 | (198) apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64 % 54.64/19.59 | % 54.64/19.59 | From (225) and (201) follows: % 54.64/19.59 | (221) apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53 % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (65) with all_65_0_80, all_0_0_0, all_0_3_3, all_0_5_5, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.59 | (234) all_65_0_80 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (65) with all_0_0_0, all_65_0_80, all_0_5_5, all_0_3_3, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.59 | (235) all_65_0_80 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (115) with all_65_0_80, all_0_0_0, all_0_5_5, all_0_3_3, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.59 | (236) all_65_0_80 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (115) with all_0_0_0, all_65_0_80, all_0_3_3, all_0_5_5, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.59 | (237) all_65_0_80 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (95) with all_65_0_80, all_65_0_80, all_0_3_3, all_0_3_3, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, yields: % 54.64/19.59 | (238) all_65_0_80 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (65) with all_65_0_80, all_65_0_80, all_0_3_3, all_0_3_3, all_63_1_79, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, yields: % 54.64/19.59 | (239) all_65_0_80 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.59 | % 54.64/19.59 | Instantiating formula (65) with all_63_0_78, all_0_0_0, all_0_5_5, all_0_5_5, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.59 | (240) all_63_0_78 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_0_0_0, all_63_0_78, all_0_5_5, all_0_5_5, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (241) all_63_0_78 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_63_0_78, all_65_0_80, all_0_5_5, all_0_3_3, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, yields: % 54.64/19.60 | (242) all_65_0_80 = 0 | all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_65_0_80, all_63_0_78, all_0_3_3, all_0_5_5, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, yields: % 54.64/19.60 | (243) all_65_0_80 = 0 | all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_63_0_78, all_65_0_80, all_0_5_5, all_0_3_3, all_63_1_79, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, yields: % 54.64/19.60 | (244) all_65_0_80 = 0 | all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_65_0_80, all_63_0_78, all_0_3_3, all_0_5_5, all_63_1_79, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, yields: % 54.64/19.60 | (245) all_65_0_80 = 0 | all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_63_0_78, all_63_0_78, all_0_5_5, all_0_5_5, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, yields: % 54.64/19.60 | (246) all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_63_0_78, all_63_0_78, all_0_5_5, all_0_5_5, all_63_1_79, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, yields: % 54.64/19.60 | (247) all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_46_0_58, all_0_0_0, all_0_3_3, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (248) all_46_0_58 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_46_0_58, all_0_0_0, all_0_3_3, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (249) all_46_0_58 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_0_0_0, all_46_0_58, all_0_5_5, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (250) all_46_0_58 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (118) with all_46_0_58, all_0_1_1, all_0_3_3, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_3_3) = 0, yields: % 54.64/19.60 | (251) all_46_0_58 = 0 | distinct_points(all_0_2_2, all_0_1_1) = 0 % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_46_0_58, all_65_0_80, all_0_3_3, all_0_3_3, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (252) all_65_0_80 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_65_0_80, all_46_0_58, all_0_3_3, all_0_3_3, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (253) all_65_0_80 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_46_0_58, all_63_0_78, all_0_3_3, all_0_5_5, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (254) all_63_0_78 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_63_0_78, all_46_0_58, all_0_5_5, all_0_3_3, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (255) all_63_0_78 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (115) with all_46_0_58, all_63_0_78, all_0_5_5, all_0_3_3, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (256) all_63_0_78 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (115) with all_63_0_78, all_46_0_58, all_0_3_3, all_0_5_5, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (257) all_63_0_78 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_46_0_58, all_46_0_58, all_0_3_3, all_0_3_3, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (258) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_46_0_58, all_46_0_58, all_0_3_3, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, yields: % 54.64/19.60 | (259) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_48_0_60, all_0_0_0, all_0_4_4, all_0_5_5, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (260) all_48_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (95) with all_0_0_0, all_48_0_60, all_0_5_5, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (261) all_48_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_48_0_60, all_0_0_0, all_0_4_4, all_0_5_5, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (262) all_48_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_0_0_0, all_48_0_60, all_0_5_5, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, yields: % 54.64/19.60 | (263) all_48_0_60 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_48_0_60, all_65_0_80, all_0_4_4, all_0_3_3, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (264) all_65_0_80 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_65_0_80, all_48_0_60, all_0_3_3, all_0_4_4, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (265) all_65_0_80 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (115) with all_48_0_60, all_65_0_80, all_0_3_3, all_0_4_4, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (266) all_65_0_80 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (115) with all_65_0_80, all_48_0_60, all_0_4_4, all_0_3_3, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (267) all_65_0_80 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_48_0_60, all_63_0_78, all_0_4_4, all_0_5_5, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (268) all_63_0_78 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (65) with all_63_0_78, all_48_0_60, all_0_5_5, all_0_4_4, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (269) all_63_0_78 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (115) with all_48_0_60, all_63_0_78, all_0_5_5, all_0_4_4, all_0_1_1, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.60 | (270) all_63_0_78 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.60 | % 54.64/19.60 | Instantiating formula (115) with all_63_0_78, all_48_0_60, all_0_4_4, all_0_5_5, all_63_1_79, all_0_1_1 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.61 | (271) all_63_0_78 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (95) with all_46_0_58, all_48_0_60, all_0_3_3, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.61 | (272) all_48_0_60 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_48_0_60, all_46_0_58, all_0_4_4, all_0_3_3, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.61 | (273) all_48_0_60 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_46_0_58, all_48_0_60, all_0_3_3, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.61 | (274) all_48_0_60 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (95) with all_48_0_60, all_48_0_60, all_0_4_4, all_0_4_4, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.61 | (275) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_48_0_60, all_48_0_60, all_0_4_4, all_0_4_4, all_0_1_1, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, yields: % 54.64/19.61 | (276) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_52_0_64, all_0_0_0, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (277) all_52_0_64 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_0_0_0, all_52_0_64, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (278) all_52_0_64 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_52_0_64, all_0_0_0, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (279) all_52_0_64 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_0_0_0, all_52_0_64, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (280) all_52_0_64 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_52_0_64, all_65_0_80, all_0_4_4, all_0_3_3, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (281) all_65_0_80 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_65_0_80, all_52_0_64, all_0_3_3, all_0_4_4, all_63_1_79, all_0_2_2 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (282) all_65_0_80 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_52_0_64, all_65_0_80, all_0_3_3, all_0_4_4, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (283) all_65_0_80 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_52_0_64, all_63_0_78, all_0_4_4, all_0_5_5, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (284) all_63_0_78 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_63_0_78, all_52_0_64, all_0_5_5, all_0_4_4, all_63_1_79, all_0_2_2 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (285) all_63_0_78 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_52_0_64, all_63_0_78, all_0_5_5, all_0_4_4, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (286) all_63_0_78 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_63_0_78, all_52_0_64, all_0_4_4, all_0_5_5, all_63_1_79, all_0_2_2 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (287) all_63_0_78 = 0 | all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_52_0_64, all_46_0_58, all_0_4_4, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (288) all_52_0_64 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_46_0_58, all_52_0_64, all_0_3_3, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (289) all_52_0_64 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_52_0_64, all_46_0_58, all_0_3_3, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (290) all_52_0_64 = 0 | all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_52_0_64, all_48_0_60, all_0_4_4, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (291) all_52_0_64 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_48_0_60, all_52_0_64, all_0_4_4, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (292) all_52_0_64 = 0 | all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (95) with all_52_0_64, all_52_0_64, all_0_4_4, all_0_4_4, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (293) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_52_0_64, all_52_0_64, all_0_4_4, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, yields: % 54.64/19.61 | (294) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_42_0_53, all_0_0_0, all_0_5_5, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (295) all_42_0_53 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_0_0_0, all_42_0_53, all_0_5_5, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (296) all_42_0_53 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_42_0_53, all_65_0_80, all_0_5_5, all_0_3_3, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (297) all_65_0_80 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_65_0_80, all_42_0_53, all_0_3_3, all_0_5_5, all_63_1_79, all_0_2_2 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (298) all_65_0_80 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (115) with all_42_0_53, all_65_0_80, all_0_3_3, all_0_5_5, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_3_3) = all_65_0_80, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (299) all_65_0_80 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_42_0_53, all_63_0_78, all_0_5_5, all_0_5_5, all_0_2_2, all_63_1_79 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (300) all_63_0_78 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.61 | % 54.64/19.61 | Instantiating formula (65) with all_63_0_78, all_42_0_53, all_0_5_5, all_0_5_5, all_63_1_79, all_0_2_2 and discharging atoms apart_point_and_line(all_63_1_79, all_0_5_5) = all_63_0_78, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.61 | (301) all_63_0_78 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_42_0_53, all_46_0_58, all_0_5_5, all_0_3_3, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (302) all_46_0_58 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_46_0_58, all_42_0_53, all_0_3_3, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (303) all_46_0_58 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (115) with all_42_0_53, all_46_0_58, all_0_3_3, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_3_3) = all_46_0_58, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (304) all_46_0_58 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_42_0_53, all_48_0_60, all_0_5_5, all_0_4_4, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (305) all_48_0_60 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_48_0_60, all_42_0_53, all_0_4_4, all_0_5_5, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (306) all_48_0_60 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (115) with all_42_0_53, all_48_0_60, all_0_4_4, all_0_5_5, all_0_2_2, all_0_1_1 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (307) all_48_0_60 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (115) with all_48_0_60, all_42_0_53, all_0_5_5, all_0_4_4, all_0_1_1, all_0_2_2 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (308) all_48_0_60 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (95) with all_42_0_53, all_52_0_64, all_0_5_5, all_0_4_4, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (309) all_52_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (95) with all_52_0_64, all_42_0_53, all_0_4_4, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (310) all_52_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_42_0_53, all_52_0_64, all_0_5_5, all_0_4_4, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (311) all_52_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_52_0_64, all_42_0_53, all_0_4_4, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (312) all_52_0_64 = 0 | all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (95) with all_42_0_53, all_42_0_53, all_0_5_5, all_0_5_5, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (313) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 54.64/19.62 | % 54.64/19.62 | Instantiating formula (65) with all_42_0_53, all_42_0_53, all_0_5_5, all_0_5_5, all_0_2_2, all_0_2_2 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, yields: % 54.64/19.62 | (314) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (246), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (315) all_63_0_78 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (315) can reduce 175 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (175) ~ (all_63_0_78 = 0) % 54.64/19.62 | (191) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (240), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (315) all_63_0_78 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (315) can reduce 175 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (175) ~ (all_63_0_78 = 0) % 54.64/19.62 | (322) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (245), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (323) all_65_0_80 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (323) can reduce 179 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (179) ~ (all_65_0_80 = 0) % 54.64/19.62 | (326) all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (322), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (188) all_0_0_0 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (188) can reduce 90 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (90) ~ (all_0_0_0 = 0) % 54.64/19.62 | (330) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (275), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (331) all_48_0_60 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (331) can reduce 169 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (169) ~ (all_48_0_60 = 0) % 54.64/19.62 | (334) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (313), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (335) all_42_0_53 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (335) can reduce 161 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (161) ~ (all_42_0_53 = 0) % 54.64/19.62 | (191) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (238), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (323) all_65_0_80 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (323) can reduce 179 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (179) ~ (all_65_0_80 = 0) % 54.64/19.62 | (342) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (258), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (343) all_46_0_58 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (343) can reduce 165 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (165) ~ (all_46_0_58 = 0) % 54.64/19.62 | (342) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (293), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (347) all_52_0_64 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (347) can reduce 197 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (197) ~ (all_52_0_64 = 0) % 54.64/19.62 | (334) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (239), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (323) all_65_0_80 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (323) can reduce 179 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (179) ~ (all_65_0_80 = 0) % 54.64/19.62 | (354) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (234), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (323) all_65_0_80 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (323) can reduce 179 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (179) ~ (all_65_0_80 = 0) % 54.64/19.62 | (358) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (242), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (323) all_65_0_80 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (323) can reduce 179 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (179) ~ (all_65_0_80 = 0) % 54.64/19.62 | (362) all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (358), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (188) all_0_0_0 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (188) can reduce 90 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (90) ~ (all_0_0_0 = 0) % 54.64/19.62 | (366) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (362), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (315) all_63_0_78 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (315) can reduce 175 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (175) ~ (all_63_0_78 = 0) % 54.64/19.62 | (370) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (243), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (323) all_65_0_80 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (323) can reduce 179 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (179) ~ (all_65_0_80 = 0) % 54.64/19.62 | (374) all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0)) % 54.64/19.62 | % 54.64/19.62 +-Applying beta-rule and splitting (260), into two cases. % 54.64/19.62 |-Branch one: % 54.64/19.62 | (331) all_48_0_60 = 0 % 54.64/19.62 | % 54.64/19.62 | Equations (331) can reduce 169 to: % 54.64/19.62 | (189) $false % 54.64/19.62 | % 54.64/19.62 |-The branch is then unsatisfiable % 54.64/19.62 |-Branch two: % 54.64/19.62 | (169) ~ (all_48_0_60 = 0) % 54.64/19.62 | (378) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (261), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (382) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (272), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (386) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (264), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (390) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (265), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (394) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (262), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (398) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (263), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (402) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (273), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (406) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (266), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (410) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (267), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (414) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (268), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (315) all_63_0_78 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (315) can reduce 175 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (175) ~ (all_63_0_78 = 0) % 54.64/19.63 | (418) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (235), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (422) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (269), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (315) all_63_0_78 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (315) can reduce 175 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (175) ~ (all_63_0_78 = 0) % 54.64/19.63 | (426) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (270), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (315) all_63_0_78 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (315) can reduce 175 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (175) ~ (all_63_0_78 = 0) % 54.64/19.63 | (430) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (271), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (315) all_63_0_78 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (315) can reduce 175 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (175) ~ (all_63_0_78 = 0) % 54.64/19.63 | (434) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (278), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (347) all_52_0_64 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (347) can reduce 197 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (197) ~ (all_52_0_64 = 0) % 54.64/19.63 | (438) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (279), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (347) all_52_0_64 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (347) can reduce 197 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (197) ~ (all_52_0_64 = 0) % 54.64/19.63 | (442) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (236), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (446) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (244), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (323) all_65_0_80 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (323) can reduce 179 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (179) ~ (all_65_0_80 = 0) % 54.64/19.63 | (450) all_63_0_78 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (241), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (315) all_63_0_78 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (315) can reduce 175 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (175) ~ (all_63_0_78 = 0) % 54.64/19.63 | (454) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (274), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (458) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (326), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (315) all_63_0_78 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (315) can reduce 175 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (175) ~ (all_63_0_78 = 0) % 54.64/19.63 | (462) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (394), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (466) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (251), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (467) distinct_points(all_0_2_2, all_0_1_1) = 0 % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (378), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (188) all_0_0_0 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (188) can reduce 90 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (90) ~ (all_0_0_0 = 0) % 54.64/19.63 | (471) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (398), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (188) all_0_0_0 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (188) can reduce 90 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (90) ~ (all_0_0_0 = 0) % 54.64/19.63 | (475) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (410), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.63 | (331) all_48_0_60 = 0 % 54.64/19.63 | % 54.64/19.63 | Equations (331) can reduce 169 to: % 54.64/19.63 | (189) $false % 54.64/19.63 | % 54.64/19.63 |-The branch is then unsatisfiable % 54.64/19.63 |-Branch two: % 54.64/19.63 | (169) ~ (all_48_0_60 = 0) % 54.64/19.63 | (479) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.63 | % 54.64/19.63 +-Applying beta-rule and splitting (454), into two cases. % 54.64/19.63 |-Branch one: % 54.64/19.64 | (188) all_0_0_0 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (188) can reduce 90 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (90) ~ (all_0_0_0 = 0) % 54.64/19.64 | (483) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (259), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (343) all_46_0_58 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (343) can reduce 165 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (165) ~ (all_46_0_58 = 0) % 54.64/19.64 | (487) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (294), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (347) all_52_0_64 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (347) can reduce 197 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (197) ~ (all_52_0_64 = 0) % 54.64/19.64 | (491) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (309), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (347) all_52_0_64 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (347) can reduce 197 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (197) ~ (all_52_0_64 = 0) % 54.64/19.64 | (495) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (310), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (347) all_52_0_64 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (347) can reduce 197 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (197) ~ (all_52_0_64 = 0) % 54.64/19.64 | (499) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (314), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (335) all_42_0_53 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (335) can reduce 161 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (161) ~ (all_42_0_53 = 0) % 54.64/19.64 | (503) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (308), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (331) all_48_0_60 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (331) can reduce 169 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (169) ~ (all_48_0_60 = 0) % 54.64/19.64 | (507) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (307), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (331) all_48_0_60 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (331) can reduce 169 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (169) ~ (all_48_0_60 = 0) % 54.64/19.64 | (511) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (288), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (347) all_52_0_64 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (347) can reduce 197 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (197) ~ (all_52_0_64 = 0) % 54.64/19.64 | (515) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (289), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (347) all_52_0_64 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (347) can reduce 197 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (197) ~ (all_52_0_64 = 0) % 54.64/19.64 | (519) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (290), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (347) all_52_0_64 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (347) can reduce 197 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (197) ~ (all_52_0_64 = 0) % 54.64/19.64 | (523) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (276), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (331) all_48_0_60 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (331) can reduce 169 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (169) ~ (all_48_0_60 = 0) % 54.64/19.64 | (527) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (247), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (531) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (248), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (343) all_46_0_58 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (343) can reduce 165 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (165) ~ (all_46_0_58 = 0) % 54.64/19.64 | (535) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (253), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (539) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (254), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (543) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (255), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (547) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (281), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (551) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (282), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (555) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (283), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (559) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (286), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (563) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (284), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (567) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (256), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (571) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (257), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (575) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (285), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (579) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (287), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (315) all_63_0_78 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (315) can reduce 175 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (175) ~ (all_63_0_78 = 0) % 54.64/19.64 | (583) all_52_0_64 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (252), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (587) all_46_0_58 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (249), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (343) all_46_0_58 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (343) can reduce 165 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (165) ~ (all_46_0_58 = 0) % 54.64/19.64 | (591) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (250), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (343) all_46_0_58 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (343) can reduce 165 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (165) ~ (all_46_0_58 = 0) % 54.64/19.64 | (595) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (237), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (599) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.64 | % 54.64/19.64 +-Applying beta-rule and splitting (297), into two cases. % 54.64/19.64 |-Branch one: % 54.64/19.64 | (323) all_65_0_80 = 0 % 54.64/19.64 | % 54.64/19.64 | Equations (323) can reduce 179 to: % 54.64/19.64 | (189) $false % 54.64/19.64 | % 54.64/19.64 |-The branch is then unsatisfiable % 54.64/19.64 |-Branch two: % 54.64/19.64 | (179) ~ (all_65_0_80 = 0) % 54.64/19.64 | (603) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (298), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (323) all_65_0_80 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (323) can reduce 179 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (179) ~ (all_65_0_80 = 0) % 54.64/19.65 | (607) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (296), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (335) all_42_0_53 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (335) can reduce 161 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (161) ~ (all_42_0_53 = 0) % 54.64/19.65 | (611) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (299), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (323) all_65_0_80 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (323) can reduce 179 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (179) ~ (all_65_0_80 = 0) % 54.64/19.65 | (615) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (295), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (335) all_42_0_53 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (335) can reduce 161 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (161) ~ (all_42_0_53 = 0) % 54.64/19.65 | (619) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (291), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (347) all_52_0_64 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (347) can reduce 197 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (197) ~ (all_52_0_64 = 0) % 54.64/19.65 | (623) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (292), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (347) all_52_0_64 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (347) can reduce 197 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (197) ~ (all_52_0_64 = 0) % 54.64/19.65 | (627) all_48_0_60 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (280), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (347) all_52_0_64 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (347) can reduce 197 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (197) ~ (all_52_0_64 = 0) % 54.64/19.65 | (631) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (277), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (347) all_52_0_64 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (347) can reduce 197 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (197) ~ (all_52_0_64 = 0) % 54.64/19.65 | (635) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (311), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (347) all_52_0_64 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (347) can reduce 197 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (197) ~ (all_52_0_64 = 0) % 54.64/19.65 | (639) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (300), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (315) all_63_0_78 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (315) can reduce 175 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (175) ~ (all_63_0_78 = 0) % 54.64/19.65 | (643) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (301), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (315) all_63_0_78 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (315) can reduce 175 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (175) ~ (all_63_0_78 = 0) % 54.64/19.65 | (647) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (302), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (343) all_46_0_58 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (343) can reduce 165 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (165) ~ (all_46_0_58 = 0) % 54.64/19.65 | (651) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (303), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (343) all_46_0_58 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (343) can reduce 165 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (165) ~ (all_46_0_58 = 0) % 54.64/19.65 | (655) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (305), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (659) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (304), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (343) all_46_0_58 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (343) can reduce 165 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (165) ~ (all_46_0_58 = 0) % 54.64/19.65 | (663) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (306), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (667) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (312), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (347) all_52_0_64 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (347) can reduce 197 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (197) ~ (all_52_0_64 = 0) % 54.64/19.65 | (671) all_42_0_53 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (382), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (188) all_0_0_0 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (188) can reduce 90 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (90) ~ (all_0_0_0 = 0) % 54.64/19.65 | (675) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (390), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (679) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (402), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (188) all_0_0_0 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (188) can reduce 90 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (90) ~ (all_0_0_0 = 0) % 54.64/19.65 | (683) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (414), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (687) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (418), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (691) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (422), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (188) all_0_0_0 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (188) can reduce 90 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (90) ~ (all_0_0_0 = 0) % 54.64/19.65 | (695) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (426), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (699) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.64/19.65 | % 54.64/19.65 +-Applying beta-rule and splitting (430), into two cases. % 54.64/19.65 |-Branch one: % 54.64/19.65 | (331) all_48_0_60 = 0 % 54.64/19.65 | % 54.64/19.65 | Equations (331) can reduce 169 to: % 54.64/19.65 | (189) $false % 54.64/19.65 | % 54.64/19.65 |-The branch is then unsatisfiable % 54.64/19.65 |-Branch two: % 54.64/19.65 | (169) ~ (all_48_0_60 = 0) % 54.64/19.65 | (703) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.93/19.65 | % 54.93/19.65 +-Applying beta-rule and splitting (434), into two cases. % 54.93/19.65 |-Branch one: % 54.93/19.65 | (331) all_48_0_60 = 0 % 54.93/19.65 | % 54.93/19.65 | Equations (331) can reduce 169 to: % 54.93/19.65 | (189) $false % 54.93/19.65 | % 54.93/19.65 |-The branch is then unsatisfiable % 54.93/19.65 |-Branch two: % 54.93/19.65 | (169) ~ (all_48_0_60 = 0) % 54.93/19.65 | (707) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.93/19.65 | % 54.93/19.65 +-Applying beta-rule and splitting (438), into two cases. % 54.93/19.65 |-Branch one: % 54.93/19.65 | (188) all_0_0_0 = 0 % 54.93/19.65 | % 54.93/19.65 | Equations (188) can reduce 90 to: % 54.93/19.65 | (189) $false % 54.93/19.65 | % 54.93/19.65 |-The branch is then unsatisfiable % 54.93/19.65 |-Branch two: % 54.93/19.65 | (90) ~ (all_0_0_0 = 0) % 54.93/19.65 | (711) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.93/19.65 | % 54.93/19.65 | Instantiating (711) with all_529_0_1466 yields: % 54.93/19.65 | (712) (all_529_0_1466 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (all_529_0_1466 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_529_0_1466 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466) | ( ~ (all_529_0_1466 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_529_0_1466) % 54.93/19.65 | % 54.93/19.65 +-Applying beta-rule and splitting (442), into two cases. % 54.93/19.65 |-Branch one: % 54.93/19.65 | (188) all_0_0_0 = 0 % 54.93/19.65 | % 54.93/19.66 | Equations (188) can reduce 90 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (90) ~ (all_0_0_0 = 0) % 54.93/19.66 | (716) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (446), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (188) all_0_0_0 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (188) can reduce 90 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (90) ~ (all_0_0_0 = 0) % 54.93/19.66 | (720) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_63_1_79) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (495), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (675) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (499), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (471) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (507), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (732) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.93/19.66 | % 54.93/19.66 | Instantiating (732) with all_557_0_1473 yields: % 54.93/19.66 | (733) (all_557_0_1473 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_557_0_1473 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_557_0_1473 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_557_0_1473) | ( ~ (all_557_0_1473 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_557_0_1473) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (511), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (737) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (535), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (188) all_0_0_0 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (188) can reduce 90 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (90) ~ (all_0_0_0 = 0) % 54.93/19.66 | (741) ? [v0] : ((v0 = 0 & convergent_lines(all_0_5_5, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (583), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (347) all_52_0_64 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (347) can reduce 197 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (197) ~ (all_52_0_64 = 0) % 54.93/19.66 | (745) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (611), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (188) all_0_0_0 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (188) can reduce 90 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (90) ~ (all_0_0_0 = 0) % 54.93/19.66 | (749) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (615), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (753) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (671), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (757) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (551), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (347) all_52_0_64 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (347) can reduce 197 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (197) ~ (all_52_0_64 = 0) % 54.93/19.66 | (761) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (555), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (347) all_52_0_64 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (347) can reduce 197 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (197) ~ (all_52_0_64 = 0) % 54.93/19.66 | (765) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (659), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (769) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (663), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (773) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (712), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (774) (all_529_0_1466 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (all_529_0_1466 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (all_529_0_1466 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (774), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (775) (all_529_0_1466 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (all_529_0_1466 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (775), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (776) all_529_0_1466 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0 % 54.93/19.66 | % 54.93/19.66 | Applying alpha-rule on (776) yields: % 54.93/19.66 | (777) all_529_0_1466 = 0 % 54.93/19.66 | (778) apart_point_and_line(all_0_1_1, all_0_4_4) = 0 % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (623), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (331) all_48_0_60 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (331) can reduce 169 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (169) ~ (all_48_0_60 = 0) % 54.93/19.66 | (782) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (627), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (331) all_48_0_60 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (331) can reduce 169 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (169) ~ (all_48_0_60 = 0) % 54.93/19.66 | (786) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.93/19.66 | % 54.93/19.66 | Instantiating formula (54) with all_0_1_1, all_0_4_4, 0, all_48_0_60 and discharging atoms apart_point_and_line(all_0_1_1, all_0_4_4) = all_48_0_60, apart_point_and_line(all_0_1_1, all_0_4_4) = 0, yields: % 54.93/19.66 | (331) all_48_0_60 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (331) can reduce 169 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (789) all_529_0_1466 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0 % 54.93/19.66 | % 54.93/19.66 | Applying alpha-rule on (789) yields: % 54.93/19.66 | (777) all_529_0_1466 = 0 % 54.93/19.66 | (791) apart_point_and_line(all_0_2_2, all_0_5_5) = 0 % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (603), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (795) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (607), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (799) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.93/19.66 | % 54.93/19.66 +-Applying beta-rule and splitting (639), into two cases. % 54.93/19.66 |-Branch one: % 54.93/19.66 | (335) all_42_0_53 = 0 % 54.93/19.66 | % 54.93/19.66 | Equations (335) can reduce 161 to: % 54.93/19.66 | (189) $false % 54.93/19.66 | % 54.93/19.66 |-The branch is then unsatisfiable % 54.93/19.66 |-Branch two: % 54.93/19.66 | (161) ~ (all_42_0_53 = 0) % 54.93/19.66 | (803) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_2_2) = v0)) % 54.97/19.66 | % 54.97/19.66 +-Applying beta-rule and splitting (651), into two cases. % 54.97/19.66 |-Branch one: % 54.97/19.66 | (335) all_42_0_53 = 0 % 54.97/19.66 | % 54.97/19.66 | Equations (335) can reduce 161 to: % 54.97/19.66 | (189) $false % 54.97/19.66 | % 54.97/19.66 |-The branch is then unsatisfiable % 54.97/19.66 |-Branch two: % 54.97/19.66 | (161) ~ (all_42_0_53 = 0) % 54.97/19.66 | (807) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.97/19.66 | % 54.97/19.66 +-Applying beta-rule and splitting (655), into two cases. % 54.97/19.66 |-Branch one: % 54.97/19.66 | (335) all_42_0_53 = 0 % 54.97/19.66 | % 54.97/19.66 | Equations (335) can reduce 161 to: % 54.97/19.66 | (189) $false % 54.97/19.66 | % 54.97/19.66 |-The branch is then unsatisfiable % 54.97/19.66 |-Branch two: % 54.97/19.66 | (161) ~ (all_42_0_53 = 0) % 54.97/19.66 | (811) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.97/19.66 | % 54.97/19.66 +-Applying beta-rule and splitting (667), into two cases. % 54.97/19.66 |-Branch one: % 54.97/19.66 | (335) all_42_0_53 = 0 % 54.97/19.66 | % 54.97/19.66 | Equations (335) can reduce 161 to: % 54.97/19.66 | (189) $false % 54.97/19.66 | % 54.97/19.66 |-The branch is then unsatisfiable % 54.97/19.66 |-Branch two: % 54.97/19.66 | (161) ~ (all_42_0_53 = 0) % 54.97/19.66 | (815) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.97/19.66 | % 54.97/19.66 +-Applying beta-rule and splitting (643), into two cases. % 54.97/19.66 |-Branch one: % 54.97/19.66 | (335) all_42_0_53 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (335) can reduce 161 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (161) ~ (all_42_0_53 = 0) % 54.97/19.67 | (819) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (647), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (335) all_42_0_53 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (335) can reduce 161 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (161) ~ (all_42_0_53 = 0) % 54.97/19.67 | (823) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (54) with all_0_2_2, all_0_5_5, 0, all_42_0_53 and discharging atoms apart_point_and_line(all_0_2_2, all_0_5_5) = all_42_0_53, apart_point_and_line(all_0_2_2, all_0_5_5) = 0, yields: % 54.97/19.67 | (335) all_42_0_53 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (335) can reduce 161 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (826) ~ (all_529_0_1466 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466 % 54.97/19.67 | % 54.97/19.67 | Applying alpha-rule on (826) yields: % 54.97/19.67 | (827) ~ (all_529_0_1466 = 0) % 54.97/19.67 | (828) distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466 % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (733), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (829) (all_557_0_1473 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_557_0_1473 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) | ( ~ (all_557_0_1473 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_557_0_1473) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (829), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (830) (all_557_0_1473 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (all_557_0_1473 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (830), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (831) all_557_0_1473 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0 % 54.97/19.67 | % 54.97/19.67 | Applying alpha-rule on (831) yields: % 54.97/19.67 | (832) all_557_0_1473 = 0 % 54.97/19.67 | (833) apart_point_and_line(all_0_1_1, all_0_5_5) = 0 % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (591), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (90) ~ (all_0_0_0 = 0) % 54.97/19.67 | (837) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (595), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (90) ~ (all_0_0_0 = 0) % 54.97/19.67 | (841) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_1_1) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (599), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (90) ~ (all_0_0_0 = 0) % 54.97/19.67 | (845) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_1_1, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_1_1) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (619), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (90) ~ (all_0_0_0 = 0) % 54.97/19.67 | (849) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_5_5) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (631), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (90) ~ (all_0_0_0 = 0) % 54.97/19.67 | (853) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_0_1_1) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (635), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (90) ~ (all_0_0_0 = 0) % 54.97/19.67 | (857) ? [v0] : ((v0 = 0 & apart_point_and_line(all_0_1_1, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_1_1, all_0_2_2) = v0)) % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (54) with all_0_1_1, all_0_5_5, 0, all_0_0_0 and discharging atoms apart_point_and_line(all_0_1_1, all_0_5_5) = all_0_0_0, apart_point_and_line(all_0_1_1, all_0_5_5) = 0, yields: % 54.97/19.67 | (188) all_0_0_0 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (188) can reduce 90 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (860) all_557_0_1473 = 0 & apart_point_and_line(all_0_2_2, all_0_4_4) = 0 % 54.97/19.67 | % 54.97/19.67 | Applying alpha-rule on (860) yields: % 54.97/19.67 | (832) all_557_0_1473 = 0 % 54.97/19.67 | (862) apart_point_and_line(all_0_2_2, all_0_4_4) = 0 % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (559), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (347) all_52_0_64 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (347) can reduce 197 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (197) ~ (all_52_0_64 = 0) % 54.97/19.67 | (866) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (563), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (347) all_52_0_64 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (347) can reduce 197 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (197) ~ (all_52_0_64 = 0) % 54.97/19.67 | (870) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (567), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (347) all_52_0_64 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (347) can reduce 197 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (197) ~ (all_52_0_64 = 0) % 54.97/19.67 | (874) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_5_5, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_63_1_79, all_0_2_2) = v0)) % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (579), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (347) all_52_0_64 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (347) can reduce 197 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (197) ~ (all_52_0_64 = 0) % 54.97/19.67 | (878) ? [v0] : ((v0 = 0 & apart_point_and_line(all_63_1_79, all_0_4_4) = 0) | (v0 = 0 & apart_point_and_line(all_0_2_2, all_0_5_5) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = v0) | ( ~ (v0 = 0) & distinct_points(all_0_2_2, all_63_1_79) = v0)) % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (54) with all_0_2_2, all_0_4_4, 0, all_52_0_64 and discharging atoms apart_point_and_line(all_0_2_2, all_0_4_4) = all_52_0_64, apart_point_and_line(all_0_2_2, all_0_4_4) = 0, yields: % 54.97/19.67 | (347) all_52_0_64 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (347) can reduce 197 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (881) ~ (all_557_0_1473 = 0) & distinct_lines(all_0_4_4, all_0_5_5) = all_557_0_1473 % 54.97/19.67 | % 54.97/19.67 | Applying alpha-rule on (881) yields: % 54.97/19.67 | (882) ~ (all_557_0_1473 = 0) % 54.97/19.67 | (883) distinct_lines(all_0_4_4, all_0_5_5) = all_557_0_1473 % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (62) with all_0_4_4, all_0_5_5, all_529_0_1466, all_557_0_1473 and discharging atoms distinct_lines(all_0_4_4, all_0_5_5) = all_557_0_1473, distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466, yields: % 54.97/19.67 | (884) all_557_0_1473 = all_529_0_1466 % 54.97/19.67 | % 54.97/19.67 | Equations (884) can reduce 882 to: % 54.97/19.67 | (827) ~ (all_529_0_1466 = 0) % 54.97/19.67 | % 54.97/19.67 | From (884) and (883) follows: % 54.97/19.67 | (828) distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466 % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (31) with all_529_0_1466, all_0_5_5, all_0_4_4, all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = 0, distinct_lines(all_0_4_4, all_0_5_5) = all_529_0_1466, yields: % 54.97/19.67 | (887) all_529_0_1466 = 0 | convergent_lines(all_0_5_5, all_0_5_5) = 0 % 54.97/19.67 | % 54.97/19.67 +-Applying beta-rule and splitting (887), into two cases. % 54.97/19.67 |-Branch one: % 54.97/19.67 | (888) convergent_lines(all_0_5_5, all_0_5_5) = 0 % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (40) with all_0_5_5 and discharging atoms convergent_lines(all_0_5_5, all_0_5_5) = 0, yields: % 54.97/19.67 | (889) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (890) ~ (convergent_lines(all_0_5_5, all_0_5_5) = 0) % 54.97/19.67 | (777) all_529_0_1466 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (777) can reduce 827 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (893) ~ (all_557_0_1473 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_557_0_1473 % 54.97/19.67 | % 54.97/19.67 | Applying alpha-rule on (893) yields: % 54.97/19.67 | (882) ~ (all_557_0_1473 = 0) % 54.97/19.67 | (895) distinct_points(all_0_2_2, all_0_1_1) = all_557_0_1473 % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (145) with all_0_2_2, all_0_1_1, 0, all_557_0_1473 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_557_0_1473, distinct_points(all_0_2_2, all_0_1_1) = 0, yields: % 54.97/19.67 | (832) all_557_0_1473 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (832) can reduce 882 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.67 |-Branch two: % 54.97/19.67 | (898) ~ (all_529_0_1466 = 0) & distinct_points(all_0_2_2, all_0_1_1) = all_529_0_1466 % 54.97/19.67 | % 54.97/19.67 | Applying alpha-rule on (898) yields: % 54.97/19.67 | (827) ~ (all_529_0_1466 = 0) % 54.97/19.67 | (900) distinct_points(all_0_2_2, all_0_1_1) = all_529_0_1466 % 54.97/19.67 | % 54.97/19.67 | Instantiating formula (145) with all_0_2_2, all_0_1_1, 0, all_529_0_1466 and discharging atoms distinct_points(all_0_2_2, all_0_1_1) = all_529_0_1466, distinct_points(all_0_2_2, all_0_1_1) = 0, yields: % 54.97/19.67 | (777) all_529_0_1466 = 0 % 54.97/19.67 | % 54.97/19.67 | Equations (777) can reduce 827 to: % 54.97/19.67 | (189) $false % 54.97/19.67 | % 54.97/19.67 |-The branch is then unsatisfiable % 54.97/19.68 |-Branch two: % 54.97/19.68 | (903) ~ (distinct_points(all_0_2_2, all_0_1_1) = 0) % 54.97/19.68 | (343) all_46_0_58 = 0 % 54.97/19.68 | % 54.97/19.68 | Equations (343) can reduce 165 to: % 54.97/19.68 | (189) $false % 54.97/19.68 | % 54.97/19.68 |-The branch is then unsatisfiable % 54.97/19.68 |-Branch two: % 54.97/19.68 | (906) ~ (all_68_0_83 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_83 % 54.97/19.68 | % 54.97/19.68 | Applying alpha-rule on (906) yields: % 54.97/19.68 | (206) ~ (all_68_0_83 = 0) % 54.97/19.68 | (908) convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_83 % 54.97/19.68 | % 54.97/19.68 | Instantiating formula (143) with all_0_3_3, all_0_4_4, all_68_0_83, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_68_0_83, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 54.97/19.68 | (909) all_68_0_83 = 0 % 54.97/19.68 | % 54.97/19.68 | Equations (909) can reduce 206 to: % 54.97/19.68 | (189) $false % 54.97/19.68 | % 54.97/19.68 |-The branch is then unsatisfiable % 54.97/19.68 |-Branch two: % 54.97/19.68 | (911) ~ (all_73_0_89 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_73_0_89 % 54.97/19.68 | % 54.97/19.68 | Applying alpha-rule on (911) yields: % 54.97/19.68 | (203) ~ (all_73_0_89 = 0) % 54.97/19.68 | (913) convergent_lines(all_0_3_3, all_0_4_4) = all_73_0_89 % 54.97/19.68 | % 54.97/19.68 | Instantiating formula (143) with all_0_3_3, all_0_4_4, all_73_0_89, 0 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_73_0_89, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 54.97/19.68 | (914) all_73_0_89 = 0 % 54.97/19.68 | % 54.97/19.68 | Equations (914) can reduce 203 to: % 54.97/19.68 | (189) $false % 54.97/19.68 | % 54.97/19.68 |-The branch is then unsatisfiable % 54.97/19.68 |-Branch two: % 54.97/19.68 | (916) ~ (all_51_0_63 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_51_0_63 % 54.97/19.68 | % 54.97/19.68 | Applying alpha-rule on (916) yields: % 54.97/19.68 | (200) ~ (all_51_0_63 = 0) % 54.97/19.68 | (918) convergent_lines(all_0_5_5, all_0_4_4) = all_51_0_63 % 54.97/19.68 | % 54.97/19.68 | Instantiating formula (143) with all_0_5_5, all_0_4_4, all_51_0_63, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_51_0_63, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 54.97/19.68 | (919) all_51_0_63 = 0 % 54.97/19.68 | % 54.97/19.68 | Equations (919) can reduce 200 to: % 54.97/19.68 | (189) $false % 54.97/19.68 | % 54.97/19.68 |-The branch is then unsatisfiable % 54.97/19.68 |-Branch two: % 54.97/19.68 | (921) ~ (all_52_0_64 = 0) & convergent_lines(all_0_5_5, all_0_4_4) = all_52_0_64 % 54.97/19.68 | % 54.97/19.68 | Applying alpha-rule on (921) yields: % 54.97/19.68 | (197) ~ (all_52_0_64 = 0) % 54.97/19.68 | (923) convergent_lines(all_0_5_5, all_0_4_4) = all_52_0_64 % 54.97/19.68 | % 54.97/19.68 | Instantiating formula (143) with all_0_5_5, all_0_4_4, all_52_0_64, 0 and discharging atoms convergent_lines(all_0_5_5, all_0_4_4) = all_52_0_64, convergent_lines(all_0_5_5, all_0_4_4) = 0, yields: % 54.97/19.68 | (347) all_52_0_64 = 0 % 54.97/19.68 | % 54.97/19.68 | Equations (347) can reduce 197 to: % 54.97/19.68 | (189) $false % 54.97/19.68 | % 54.97/19.68 |-The branch is then unsatisfiable % 54.97/19.68 % SZS output end Proof for theBenchmark % 54.97/19.68 % 54.97/19.68 19074ms %------------------------------------------------------------------------------