%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO215+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n008.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Sat Jul 16 03:48:49 EDT 2022 % Result : Theorem 6.01s 2.06s % Output : Proof 12.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : GEO215+1 : TPTP v8.1.0. Released v3.3.0. % 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.13/0.33 % Computer : n008.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sat Jun 18 00:41:52 EDT 2022 % 0.13/0.34 % CPUTime : % 0.58/0.59 ____ _ % 0.58/0.59 ___ / __ \_____(_)___ ________ __________ % 0.58/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.59 % 0.58/0.59 A Theorem Prover for First-Order Logic % 0.58/0.59 (ePrincess v.1.0) % 0.58/0.59 % 0.58/0.59 (c) Philipp Rümmer, 2009-2015 % 0.58/0.59 (c) Peter Backeman, 2014-2015 % 0.58/0.59 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.59 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.59 Bug reports to peter@backeman.se % 0.58/0.59 % 0.58/0.59 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.59 % 0.58/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.72/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.73/0.96 Prover 0: Preprocessing ... % 2.05/1.12 Prover 0: Warning: ignoring some quantifiers % 2.05/1.14 Prover 0: Constructing countermodel ... % 3.11/1.37 Prover 0: gave up % 3.11/1.37 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 3.11/1.40 Prover 1: Preprocessing ... % 3.72/1.51 Prover 1: Constructing countermodel ... % 3.87/1.55 Prover 1: gave up % 3.87/1.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 3.87/1.58 Prover 2: Preprocessing ... % 4.58/1.76 Prover 2: Warning: ignoring some quantifiers % 4.58/1.78 Prover 2: Constructing countermodel ... % 6.01/2.06 Prover 2: proved (500ms) % 6.01/2.06 % 6.01/2.06 No countermodel exists, formula is valid % 6.01/2.06 % SZS status Theorem for theBenchmark % 6.01/2.06 % 6.01/2.06 Generating proof ... Warning: ignoring some quantifiers % 11.86/3.44 found it (size 196) % 11.86/3.44 % 11.86/3.44 % SZS output start Proof for theBenchmark % 11.86/3.44 Assumed formulas after preprocessing and simplification: % 11.86/3.44 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & unorthogonal_lines(v0, v2) = v3 & convergent_lines(v0, v1) = 0 & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v7, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v11 = 0) & distinct_lines(v6, v7) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (unorthogonal_lines(v6, v8) = v10) | ~ (apart_point_and_line(v5, v6) = v9) | ~ (distinct_lines(v6, v7) = 0) | ? [v11] : ((v11 = 0 & unorthogonal_lines(v7, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v6, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v5, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v7) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v8) = v9) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v6, v7) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v7, v8) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v5, v8) = 0) | ( ~ (v11 = 0) & distinct_points(v5, v6) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = 0 | ~ (apart_point_and_line(v5, v8) = v10) | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_points(v5, v6) = 0) | ? [v11] : ((v11 = 0 & apart_point_and_line(v6, v8) = 0) | (v11 = 0 & apart_point_and_line(v6, v7) = 0) | ( ~ (v11 = 0) & distinct_lines(v7, v8) = v11))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v7, v6) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (apart_point_and_line(v5, v6) = v8) | ? [v10] : ((v10 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & apart_point_and_line(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v6) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & apart_point_and_line(v5, v7) = 0) | ( ~ (v10 = 0) & distinct_lines(v6, v7) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (convergent_lines(v5, v7) = v9) | ~ (distinct_lines(v6, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (unorthogonal_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & convergent_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v6, v7) = v9) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (convergent_lines(v6, v7) = v9) | ~ (convergent_lines(v5, v7) = v8) | ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0) | (v10 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v10 = 0) & unorthogonal_lines(v5, v6) = v10) | ( ~ (v10 = 0) & convergent_lines(v5, v6) = v10))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v7, v6) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (apart_point_and_line(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v7) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v6) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = v8) | ~ (distinct_lines(v6, v7) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v5, v7) = 0) | (v9 = 0 & convergent_lines(v6, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | apart_point_and_line(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (apart_point_and_line(v5, v6) = 0) | ~ (distinct_points(v5, v7) = v8) | apart_point_and_line(v7, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | convergent_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (convergent_lines(v5, v6) = 0) | ~ (distinct_lines(v6, v7) = v8) | convergent_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v6, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_lines(v5, v7) = v8) | ~ (distinct_lines(v5, v6) = 0) | distinct_lines(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v6, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v5, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = 0 | ~ (distinct_points(v5, v7) = v8) | ~ (distinct_points(v5, v6) = 0) | distinct_points(v6, v7) = 0) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (orthogonal_through_point(v8, v7) = v6) | ~ (orthogonal_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (unorthogonal_lines(v8, v7) = v6) | ~ (unorthogonal_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (parallel_through_point(v8, v7) = v6) | ~ (parallel_through_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (intersection_point(v8, v7) = v6) | ~ (intersection_point(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (line_connecting(v8, v7) = v6) | ~ (line_connecting(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (apart_point_and_line(v8, v7) = v6) | ~ (apart_point_and_line(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (convergent_lines(v8, v7) = v6) | ~ (convergent_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_lines(v8, v7) = v6) | ~ (distinct_lines(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (distinct_points(v8, v7) = v6) | ~ (distinct_points(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (unorthogonal_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & convergent_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v6, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (unorthogonal_lines(v5, v6) = 0) | ~ (convergent_lines(v5, v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & convergent_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v6, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v5, v7) = 0 & convergent_lines(v5, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v6, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (convergent_lines(v5, v7) = v8) | ~ (convergent_lines(v5, v6) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & unorthogonal_lines(v6, v7) = 0 & convergent_lines(v6, v7) = 0) | (v9 = 0 & v8 = 0 & unorthogonal_lines(v5, v7) = 0) | ( ~ (v9 = 0) & unorthogonal_lines(v5, v6) = v9))) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (distinct_lines(v7, v8) = 0) | ~ (distinct_points(v5, v6) = 0) | ? [v9] : ((v9 = 0 & apart_point_and_line(v6, v8) = 0) | (v9 = 0 & apart_point_and_line(v6, v7) = 0) | (v9 = 0 & apart_point_and_line(v5, v8) = 0) | (v9 = 0 & apart_point_and_line(v5, v7) = 0))) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (unorthogonal_lines(v5, v6) = v7) | convergent_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : (v7 = 0 | ~ (convergent_lines(v5, v6) = v7) | unorthogonal_lines(v5, v6) = 0) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & unorthogonal_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (orthogonal_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (parallel_through_point(v6, v5) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v7, v6) = v8)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v6) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (intersection_point(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v7, v5) = v8) | ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v6, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (line_connecting(v5, v6) = v7) | ? [v8] : (( ~ (v8 = 0) & apart_point_and_line(v5, v7) = v8) | ( ~ (v8 = 0) & distinct_points(v5, v6) = v8))) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v6) = v8)) & ! [v5] : ! [v6] : ( ~ (convergent_lines(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & intersection_point(v5, v6) = v7 & apart_point_and_line(v7, v5) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v6, v7) = v8)) & ! [v5] : ! [v6] : ( ~ (distinct_points(v5, v6) = 0) | ? [v7] : ? [v8] : ( ~ (v8 = 0) & line_connecting(v5, v6) = v7 & apart_point_and_line(v5, v7) = v8)) & ! [v5] : ~ (convergent_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_lines(v5, v5) = 0) & ! [v5] : ~ (distinct_points(v5, v5) = 0) & ? [v5] : ? [v6] : ? [v7] : orthogonal_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : unorthogonal_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : parallel_through_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : intersection_point(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : line_connecting(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : apart_point_and_line(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : convergent_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_lines(v6, v5) = v7 & ? [v5] : ? [v6] : ? [v7] : distinct_points(v6, v5) = v7) % 12.40/3.50 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 12.40/3.50 | (1) ~ (all_0_0_0 = 0) & ~ (all_0_1_1 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1 & convergent_lines(all_0_4_4, all_0_3_3) = 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 | ~ (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) = 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] : ( ~ (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] : (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_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(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(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) = 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(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 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) & ! [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] : ( ~ (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] : ( ~ (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) & 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] : ( ~ (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] : ( ~ (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] : ~ (convergent_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_lines(v0, v0) = 0) & ! [v0] : ~ (distinct_points(v0, v0) = 0) & ? [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 % 12.59/3.53 | % 12.59/3.53 | Applying alpha-rule on (1) yields: % 12.59/3.53 | (2) ! [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))) % 12.59/3.53 | (3) ! [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))) % 12.59/3.53 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 12.59/3.53 | (5) ! [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)) % 12.59/3.53 | (6) ! [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))) % 12.59/3.53 | (7) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 12.59/3.53 | (8) ! [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))) % 12.59/3.53 | (9) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 12.59/3.53 | (10) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 12.59/3.53 | (11) ! [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))) % 12.59/3.54 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 12.59/3.54 | (13) ! [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)) % 12.59/3.54 | (14) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 12.59/3.54 | (15) ! [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))) % 12.59/3.54 | (16) ! [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))) % 12.59/3.54 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 12.59/3.54 | (18) ! [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))) % 12.59/3.54 | (19) ! [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))) % 12.59/3.54 | (20) ! [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))) % 12.59/3.54 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 12.59/3.54 | (22) ! [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)) % 12.59/3.54 | (23) ! [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))) % 12.59/3.54 | (24) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 12.59/3.54 | (25) ! [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))) % 12.59/3.54 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 12.59/3.54 | (27) ! [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) % 12.59/3.54 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 12.59/3.54 | (29) ! [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))) % 12.59/3.54 | (30) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 12.59/3.54 | (31) ! [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) % 12.59/3.54 | (32) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v1, v2) = v3)) % 12.59/3.54 | (33) ! [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))) % 12.59/3.54 | (34) ~ (all_0_1_1 = 0) % 12.59/3.55 | (35) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 12.59/3.55 | (36) ! [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))) % 12.59/3.55 | (37) ! [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))) % 12.59/3.55 | (38) ! [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))) % 12.59/3.55 | (39) ! [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))) % 12.59/3.55 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 12.59/3.55 | (41) ! [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)) % 12.59/3.55 | (42) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v0) = v3)) % 12.59/3.55 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 12.59/3.55 | (44) ! [v0] : ! [v1] : ( ~ (distinct_points(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & line_connecting(v0, v1) = v2 & apart_point_and_line(v0, v2) = v3)) % 12.59/3.55 | (45) ! [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))) % 12.59/3.55 | (46) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | ? [v2] : ? [v3] : ( ~ (v3 = 0) & intersection_point(v0, v1) = v2 & apart_point_and_line(v2, v1) = v3)) % 12.59/3.55 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v1) = 0) | ~ (distinct_lines(v1, v2) = v3) | convergent_lines(v0, v2) = 0) % 12.59/3.55 | (48) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 12.59/3.55 | (49) ! [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))) % 12.79/3.55 | (50) ! [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))) % 12.79/3.55 | (51) ! [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))) % 12.79/3.55 | (52) ! [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) % 12.79/3.55 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 12.79/3.55 | (54) ! [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))) % 12.79/3.55 | (55) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 12.79/3.55 | (56) ! [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))) % 12.79/3.55 | (57) ! [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))) % 12.79/3.55 | (58) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 12.79/3.55 | (59) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 % 12.79/3.55 | (60) ! [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))) % 12.79/3.56 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 12.79/3.56 | (62) ! [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))) % 12.79/3.56 | (63) ! [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))) % 12.79/3.56 | (64) ! [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))) % 12.79/3.56 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 12.79/3.56 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 12.79/3.56 | (67) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 12.79/3.56 | (68) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 12.79/3.56 | (69) ~ (all_0_0_0 = 0) % 12.79/3.56 | (70) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 12.79/3.56 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 12.79/3.56 | (72) ! [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))) % 12.79/3.56 | (73) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 12.79/3.56 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 12.79/3.56 | (75) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 12.79/3.56 | (76) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 12.79/3.56 | (77) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 12.79/3.56 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 12.79/3.56 | (79) ! [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))) % 12.79/3.56 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 12.79/3.56 | (81) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 12.79/3.56 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 12.79/3.56 | (83) ! [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)) % 12.79/3.56 | (84) ! [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) % 12.79/3.56 | (85) unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1 % 12.79/3.56 | (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))) % 12.79/3.56 | (87) ! [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)) % 12.79/3.56 | % 12.79/3.56 | Instantiating formula (16) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 12.79/3.56 | (88) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.56 | % 12.79/3.56 | Instantiating formula (2) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 12.79/3.56 | (89) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.56 | % 12.79/3.56 | Instantiating formula (19) with all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 12.79/3.56 | (90) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.56 | % 12.79/3.56 | Instantiating formula (46) with all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 12.79/3.56 | (91) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_3_3) = v1) % 12.79/3.56 | % 12.79/3.56 | Instantiating formula (42) with all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 12.79/3.56 | (92) ? [v0] : ? [v1] : ( ~ (v1 = 0) & intersection_point(all_0_4_4, all_0_3_3) = v0 & apart_point_and_line(v0, all_0_4_4) = v1) % 12.79/3.57 | % 12.79/3.57 | Instantiating (92) with all_26_0_32, all_26_1_33 yields: % 12.79/3.57 | (93) ~ (all_26_0_32 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_26_1_33 & apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (93) yields: % 12.79/3.57 | (94) ~ (all_26_0_32 = 0) % 12.79/3.57 | (95) intersection_point(all_0_4_4, all_0_3_3) = all_26_1_33 % 12.79/3.57 | (96) apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32 % 12.79/3.57 | % 12.79/3.57 | Instantiating (91) with all_28_0_34, all_28_1_35 yields: % 12.79/3.57 | (97) ~ (all_28_0_34 = 0) & intersection_point(all_0_4_4, all_0_3_3) = all_28_1_35 & apart_point_and_line(all_28_1_35, all_0_3_3) = all_28_0_34 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (97) yields: % 12.79/3.57 | (98) ~ (all_28_0_34 = 0) % 12.79/3.57 | (99) intersection_point(all_0_4_4, all_0_3_3) = all_28_1_35 % 12.79/3.57 | (100) apart_point_and_line(all_28_1_35, all_0_3_3) = all_28_0_34 % 12.79/3.57 | % 12.79/3.57 | Instantiating (90) with all_30_0_36, all_30_1_37 yields: % 12.79/3.57 | (101) (all_30_0_36 = 0 & all_30_1_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_30_1_37 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_30_1_37 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37) % 12.79/3.57 | % 12.79/3.57 | Instantiating (89) with all_31_0_38, all_31_1_39 yields: % 12.79/3.57 | (102) (all_31_0_38 = 0 & all_31_1_39 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_31_1_39 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_31_1_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_31_1_39) % 12.79/3.57 | % 12.79/3.57 | Instantiating (88) with all_34_0_43 yields: % 12.79/3.57 | (103) (all_34_0_43 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_34_0_43 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_34_0_43 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_34_0_43) | ( ~ (all_34_0_43 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_34_0_43) % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (103), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (104) (all_34_0_43 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_34_0_43 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_34_0_43 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_34_0_43) % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (104), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (105) (all_34_0_43 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_34_0_43 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (105), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (106) all_34_0_43 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (106) yields: % 12.79/3.57 | (107) all_34_0_43 = 0 % 12.79/3.57 | (108) all_0_0_0 = 0 % 12.79/3.57 | (109) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Equations (108) can reduce 69 to: % 12.79/3.57 | (110) $false % 12.79/3.57 | % 12.79/3.57 |-The branch is then unsatisfiable % 12.79/3.57 |-Branch two: % 12.79/3.57 | (111) all_34_0_43 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (111) yields: % 12.79/3.57 | (107) all_34_0_43 = 0 % 12.79/3.57 | (113) all_0_1_1 = 0 % 12.79/3.57 | (114) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Equations (113) can reduce 34 to: % 12.79/3.57 | (110) $false % 12.79/3.57 | % 12.79/3.57 |-The branch is then unsatisfiable % 12.79/3.57 |-Branch two: % 12.79/3.57 | (116) ~ (all_34_0_43 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_34_0_43 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (116) yields: % 12.79/3.57 | (117) ~ (all_34_0_43 = 0) % 12.79/3.57 | (118) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_34_0_43 % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (101), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (119) (all_30_0_36 = 0 & all_30_1_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_30_1_37 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (119), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (120) all_30_0_36 = 0 & all_30_1_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (120) yields: % 12.79/3.57 | (121) all_30_0_36 = 0 % 12.79/3.57 | (122) all_30_1_37 = 0 % 12.79/3.57 | (123) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | (109) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Instantiating formula (78) with all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields: % 12.79/3.57 | (108) all_0_0_0 = 0 % 12.79/3.57 | % 12.79/3.57 | Equations (108) can reduce 69 to: % 12.79/3.57 | (110) $false % 12.79/3.57 | % 12.79/3.57 |-The branch is then unsatisfiable % 12.79/3.57 |-Branch two: % 12.79/3.57 | (127) all_30_1_37 = 0 & all_0_1_1 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (127) yields: % 12.79/3.57 | (122) all_30_1_37 = 0 % 12.79/3.57 | (113) all_0_1_1 = 0 % 12.79/3.57 | (114) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Equations (113) can reduce 34 to: % 12.79/3.57 | (110) $false % 12.79/3.57 | % 12.79/3.57 |-The branch is then unsatisfiable % 12.79/3.57 |-Branch two: % 12.79/3.57 | (132) ~ (all_30_1_37 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (132) yields: % 12.79/3.57 | (133) ~ (all_30_1_37 = 0) % 12.79/3.57 | (134) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37 % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (102), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (135) (all_31_0_38 = 0 & all_31_1_39 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_31_1_39 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) % 12.79/3.57 | % 12.79/3.57 +-Applying beta-rule and splitting (135), into two cases. % 12.79/3.57 |-Branch one: % 12.79/3.57 | (136) all_31_0_38 = 0 & all_31_1_39 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (136) yields: % 12.79/3.57 | (137) all_31_0_38 = 0 % 12.79/3.57 | (138) all_31_1_39 = 0 % 12.79/3.57 | (139) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | (114) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Instantiating formula (78) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields: % 12.79/3.57 | (113) all_0_1_1 = 0 % 12.79/3.57 | % 12.79/3.57 | Equations (113) can reduce 34 to: % 12.79/3.57 | (110) $false % 12.79/3.57 | % 12.79/3.57 |-The branch is then unsatisfiable % 12.79/3.57 |-Branch two: % 12.79/3.57 | (143) all_31_1_39 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (143) yields: % 12.79/3.57 | (138) all_31_1_39 = 0 % 12.79/3.57 | (108) all_0_0_0 = 0 % 12.79/3.57 | (109) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.57 | % 12.79/3.57 | Equations (108) can reduce 69 to: % 12.79/3.57 | (110) $false % 12.79/3.57 | % 12.79/3.57 |-The branch is then unsatisfiable % 12.79/3.57 |-Branch two: % 12.79/3.57 | (148) ~ (all_31_1_39 = 0) & unorthogonal_lines(all_0_4_4, all_0_3_3) = all_31_1_39 % 12.79/3.57 | % 12.79/3.57 | Applying alpha-rule on (148) yields: % 12.79/3.57 | (149) ~ (all_31_1_39 = 0) % 12.79/3.57 | (150) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_31_1_39 % 12.79/3.57 | % 12.79/3.57 | Instantiating formula (78) with all_0_4_4, all_0_3_3, all_31_1_39, all_34_0_43 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_34_0_43, unorthogonal_lines(all_0_4_4, all_0_3_3) = all_31_1_39, yields: % 12.79/3.57 | (151) all_34_0_43 = all_31_1_39 % 12.79/3.57 | % 12.79/3.57 | Instantiating formula (78) with all_0_4_4, all_0_3_3, all_30_1_37, all_34_0_43 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_34_0_43, unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37, yields: % 12.79/3.57 | (152) all_34_0_43 = all_30_1_37 % 12.79/3.57 | % 12.79/3.57 | Instantiating formula (21) with all_0_4_4, all_0_3_3, all_26_1_33, all_28_1_35 and discharging atoms intersection_point(all_0_4_4, all_0_3_3) = all_28_1_35, intersection_point(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 12.79/3.57 | (153) all_28_1_35 = all_26_1_33 % 12.79/3.57 | % 12.79/3.57 | Combining equations (151,152) yields a new equation: % 12.79/3.57 | (154) all_31_1_39 = all_30_1_37 % 12.79/3.57 | % 12.79/3.57 | Simplifying 154 yields: % 12.79/3.57 | (155) all_31_1_39 = all_30_1_37 % 12.79/3.58 | % 12.79/3.58 | Equations (155) can reduce 149 to: % 12.79/3.58 | (133) ~ (all_30_1_37 = 0) % 12.79/3.58 | % 12.79/3.58 | From (155) and (150) follows: % 12.79/3.58 | (134) unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37 % 12.79/3.58 | % 12.79/3.58 | From (153) and (100) follows: % 12.79/3.58 | (158) apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34 % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (11) with all_0_0_0, all_28_0_34, all_0_2_2, all_0_3_3, all_0_3_3, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (159) all_28_0_34 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (11) with all_0_1_1, all_28_0_34, all_0_2_2, all_0_4_4, all_0_3_3, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (160) all_28_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (86) with all_0_1_1, all_28_0_34, all_0_2_2, all_0_3_3, all_0_4_4, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (161) all_28_0_34 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (11) with all_30_1_37, all_28_0_34, all_0_3_3, all_0_4_4, all_0_3_3, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37, apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (162) all_30_1_37 = 0 | all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (86) with all_30_1_37, all_28_0_34, all_0_3_3, all_0_3_3, all_0_4_4, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37, apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (163) all_30_1_37 = 0 | all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (6) with all_28_0_34, all_28_0_34, all_0_3_3, all_0_3_3, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (164) all_28_0_34 = 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)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (39) with all_28_0_34, all_28_0_34, all_0_3_3, all_0_3_3, all_26_1_33, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, yields: % 12.79/3.58 | (165) all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (11) with all_0_0_0, all_26_0_32, all_0_2_2, all_0_3_3, all_0_4_4, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (166) all_26_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (86) with all_0_0_0, all_26_0_32, all_0_2_2, all_0_4_4, all_0_3_3, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (167) all_26_0_32 = 0 | all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (11) with all_0_1_1, all_26_0_32, all_0_2_2, all_0_4_4, all_0_4_4, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (168) all_26_0_32 = 0 | all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (11) with all_30_1_37, all_26_0_32, all_0_3_3, all_0_4_4, all_0_4_4, all_26_1_33 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = all_30_1_37, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (169) all_30_1_37 = 0 | all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (6) with all_26_0_32, all_28_0_34, all_0_4_4, all_0_3_3, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (170) all_28_0_34 = 0 | all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (6) with all_28_0_34, all_26_0_32, all_0_3_3, all_0_4_4, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (171) all_28_0_34 = 0 | all_26_0_32 = 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)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (39) with all_26_0_32, all_28_0_34, all_0_4_4, all_0_3_3, all_26_1_33, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (172) all_28_0_34 = 0 | all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (39) with all_28_0_34, all_26_0_32, all_0_3_3, all_0_4_4, all_26_1_33, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (173) all_28_0_34 = 0 | all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (6) with all_26_0_32, all_26_0_32, all_0_4_4, all_0_4_4, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (174) all_26_0_32 = 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)) % 12.79/3.58 | % 12.79/3.58 | Instantiating formula (39) with all_26_0_32, all_26_0_32, all_0_4_4, all_0_4_4, all_26_1_33, all_26_1_33 and discharging atoms apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, yields: % 12.79/3.58 | (175) all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.58 | % 12.79/3.58 +-Applying beta-rule and splitting (175), into two cases. % 12.79/3.58 |-Branch one: % 12.79/3.58 | (176) all_26_0_32 = 0 % 12.79/3.58 | % 12.79/3.58 | Equations (176) can reduce 94 to: % 12.79/3.58 | (110) $false % 12.79/3.58 | % 12.79/3.58 |-The branch is then unsatisfiable % 12.79/3.58 |-Branch two: % 12.79/3.58 | (94) ~ (all_26_0_32 = 0) % 12.79/3.59 | (179) ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (165), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (183) ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (174), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (176) all_26_0_32 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (176) can reduce 94 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (94) ~ (all_26_0_32 = 0) % 12.79/3.59 | (187) ? [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)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (164), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (191) ? [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)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (170), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (195) all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (171), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (199) all_26_0_32 = 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)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (168), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (176) all_26_0_32 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (176) can reduce 94 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (94) ~ (all_26_0_32 = 0) % 12.79/3.59 | (203) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (162), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (122) all_30_1_37 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (122) can reduce 133 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (133) ~ (all_30_1_37 = 0) % 12.79/3.59 | (207) all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (172), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (211) all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (167), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (176) all_26_0_32 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (176) can reduce 94 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (94) ~ (all_26_0_32 = 0) % 12.79/3.59 | (215) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (159), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (219) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (173), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (180) all_28_0_34 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (180) can reduce 98 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (98) ~ (all_28_0_34 = 0) % 12.79/3.59 | (223) all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.59 | % 12.79/3.59 +-Applying beta-rule and splitting (169), into two cases. % 12.79/3.59 |-Branch one: % 12.79/3.59 | (122) all_30_1_37 = 0 % 12.79/3.59 | % 12.79/3.59 | Equations (122) can reduce 133 to: % 12.79/3.59 | (110) $false % 12.79/3.59 | % 12.79/3.59 |-The branch is then unsatisfiable % 12.79/3.59 |-Branch two: % 12.79/3.59 | (133) ~ (all_30_1_37 = 0) % 12.79/3.59 | (227) all_26_0_32 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (160), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (180) all_28_0_34 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (180) can reduce 98 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (98) ~ (all_28_0_34 = 0) % 12.79/3.60 | (231) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (161), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (180) all_28_0_34 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (180) can reduce 98 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (98) ~ (all_28_0_34 = 0) % 12.79/3.60 | (235) all_0_1_1 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (163), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (122) all_30_1_37 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (122) can reduce 133 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (133) ~ (all_30_1_37 = 0) % 12.79/3.60 | (239) all_28_0_34 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (166), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (176) all_26_0_32 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (176) can reduce 94 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (94) ~ (all_26_0_32 = 0) % 12.79/3.60 | (243) all_0_0_0 = 0 | ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (195), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (176) all_26_0_32 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (176) can reduce 94 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (94) ~ (all_26_0_32 = 0) % 12.79/3.60 | (247) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (199), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (176) all_26_0_32 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (176) can reduce 94 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (94) ~ (all_26_0_32 = 0) % 12.79/3.60 | (251) ? [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)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (203), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (113) all_0_1_1 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (113) can reduce 34 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (34) ~ (all_0_1_1 = 0) % 12.79/3.60 | (255) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (207), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (180) all_28_0_34 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (180) can reduce 98 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (98) ~ (all_28_0_34 = 0) % 12.79/3.60 | (259) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (211), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (176) all_26_0_32 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (176) can reduce 94 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (94) ~ (all_26_0_32 = 0) % 12.79/3.60 | (263) ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (215), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (108) all_0_0_0 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (108) can reduce 69 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (69) ~ (all_0_0_0 = 0) % 12.79/3.60 | (267) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.60 | % 12.79/3.60 | Instantiating (267) with all_171_0_87 yields: % 12.79/3.60 | (268) (all_171_0_87 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_171_0_87 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (all_171_0_87 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_171_0_87) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (219), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (108) all_0_0_0 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (108) can reduce 69 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (69) ~ (all_0_0_0 = 0) % 12.79/3.60 | (272) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_3_3) = v0)) % 12.79/3.60 | % 12.79/3.60 +-Applying beta-rule and splitting (223), into two cases. % 12.79/3.60 |-Branch one: % 12.79/3.60 | (176) all_26_0_32 = 0 % 12.79/3.60 | % 12.79/3.60 | Equations (176) can reduce 94 to: % 12.79/3.60 | (110) $false % 12.79/3.60 | % 12.79/3.60 |-The branch is then unsatisfiable % 12.79/3.60 |-Branch two: % 12.79/3.60 | (94) ~ (all_26_0_32 = 0) % 12.79/3.60 | (276) ? [v0] : ((v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0) | ( ~ (v0 = 0) & distinct_points(all_26_1_33, all_26_1_33) = v0)) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (227), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (176) all_26_0_32 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (176) can reduce 94 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (94) ~ (all_26_0_32 = 0) % 12.79/3.61 | (280) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0)) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (231), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (113) all_0_1_1 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (113) can reduce 34 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (34) ~ (all_0_1_1 = 0) % 12.79/3.61 | (284) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = v0)) % 12.79/3.61 | % 12.79/3.61 | Instantiating (284) with all_187_0_91 yields: % 12.79/3.61 | (285) (all_187_0_91 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (all_187_0_91 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (all_187_0_91 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_187_0_91) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (235), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (113) all_0_1_1 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (113) can reduce 34 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (34) ~ (all_0_1_1 = 0) % 12.79/3.61 | (289) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (239), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (180) all_28_0_34 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (180) can reduce 98 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (98) ~ (all_28_0_34 = 0) % 12.79/3.61 | (293) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (243), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (108) all_0_0_0 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (108) can reduce 69 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (69) ~ (all_0_0_0 = 0) % 12.79/3.61 | (297) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) | ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_3_3) = v0)) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (268), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (298) (all_171_0_87 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_171_0_87 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (298), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (299) all_171_0_87 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (299) yields: % 12.79/3.61 | (300) all_171_0_87 = 0 % 12.79/3.61 | (139) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (78) with all_0_4_4, all_0_2_2, 0, all_0_1_1 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = all_0_1_1, unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields: % 12.79/3.61 | (113) all_0_1_1 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (113) can reduce 34 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (304) all_171_0_87 = 0 & apart_point_and_line(all_26_1_33, all_0_3_3) = 0 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (304) yields: % 12.79/3.61 | (300) all_171_0_87 = 0 % 12.79/3.61 | (306) apart_point_and_line(all_26_1_33, all_0_3_3) = 0 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (74) with all_26_1_33, all_0_3_3, 0, all_28_0_34 and discharging atoms apart_point_and_line(all_26_1_33, all_0_3_3) = all_28_0_34, apart_point_and_line(all_26_1_33, all_0_3_3) = 0, yields: % 12.79/3.61 | (180) all_28_0_34 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (180) can reduce 98 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (309) ~ (all_171_0_87 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_171_0_87 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (309) yields: % 12.79/3.61 | (310) ~ (all_171_0_87 = 0) % 12.79/3.61 | (311) distinct_lines(all_0_3_3, all_0_4_4) = all_171_0_87 % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (285), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (312) (all_187_0_91 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (all_187_0_91 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0) % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (312), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (313) all_187_0_91 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (313) yields: % 12.79/3.61 | (314) all_187_0_91 = 0 % 12.79/3.61 | (123) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (78) with all_0_3_3, all_0_2_2, 0, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, unorthogonal_lines(all_0_3_3, all_0_2_2) = 0, yields: % 12.79/3.61 | (108) all_0_0_0 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (108) can reduce 69 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (318) all_187_0_91 = 0 & apart_point_and_line(all_26_1_33, all_0_4_4) = 0 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (318) yields: % 12.79/3.61 | (314) all_187_0_91 = 0 % 12.79/3.61 | (320) apart_point_and_line(all_26_1_33, all_0_4_4) = 0 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (74) with all_26_1_33, all_0_4_4, 0, all_26_0_32 and discharging atoms apart_point_and_line(all_26_1_33, all_0_4_4) = all_26_0_32, apart_point_and_line(all_26_1_33, all_0_4_4) = 0, yields: % 12.79/3.61 | (176) all_26_0_32 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (176) can reduce 94 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (323) ~ (all_187_0_91 = 0) & distinct_lines(all_0_3_3, all_0_4_4) = all_187_0_91 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (323) yields: % 12.79/3.61 | (324) ~ (all_187_0_91 = 0) % 12.79/3.61 | (325) distinct_lines(all_0_3_3, all_0_4_4) = all_187_0_91 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (28) with all_0_3_3, all_0_4_4, all_171_0_87, all_187_0_91 and discharging atoms distinct_lines(all_0_3_3, all_0_4_4) = all_187_0_91, distinct_lines(all_0_3_3, all_0_4_4) = all_171_0_87, yields: % 12.79/3.61 | (326) all_187_0_91 = all_171_0_87 % 12.79/3.61 | % 12.79/3.61 | Equations (326) can reduce 324 to: % 12.79/3.61 | (310) ~ (all_171_0_87 = 0) % 12.79/3.61 | % 12.79/3.61 | From (326) and (325) follows: % 12.79/3.61 | (311) distinct_lines(all_0_3_3, all_0_4_4) = all_171_0_87 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (47) with all_171_0_87, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = 0, distinct_lines(all_0_3_3, all_0_4_4) = all_171_0_87, yields: % 12.79/3.61 | (329) all_171_0_87 = 0 | convergent_lines(all_0_4_4, all_0_4_4) = 0 % 12.79/3.61 | % 12.79/3.61 +-Applying beta-rule and splitting (329), into two cases. % 12.79/3.61 |-Branch one: % 12.79/3.61 | (330) convergent_lines(all_0_4_4, all_0_4_4) = 0 % 12.79/3.61 | % 12.79/3.61 | Instantiating formula (10) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields: % 12.79/3.61 | (331) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (332) ~ (convergent_lines(all_0_4_4, all_0_4_4) = 0) % 12.79/3.61 | (300) all_171_0_87 = 0 % 12.79/3.61 | % 12.79/3.61 | Equations (300) can reduce 310 to: % 12.79/3.61 | (110) $false % 12.79/3.61 | % 12.79/3.61 |-The branch is then unsatisfiable % 12.79/3.61 |-Branch two: % 12.79/3.61 | (335) ~ (all_34_0_43 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_34_0_43 % 12.79/3.61 | % 12.79/3.61 | Applying alpha-rule on (335) yields: % 12.79/3.61 | (117) ~ (all_34_0_43 = 0) % 12.79/3.61 | (337) convergent_lines(all_0_4_4, all_0_3_3) = all_34_0_43 % 12.79/3.61 | % 12.79/3.62 | Instantiating formula (61) with all_0_4_4, all_0_3_3, all_34_0_43, 0 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_34_0_43, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 12.79/3.62 | (107) all_34_0_43 = 0 % 12.79/3.62 | % 12.79/3.62 | Equations (107) can reduce 117 to: % 12.79/3.62 | (110) $false % 12.79/3.62 | % 12.79/3.62 |-The branch is then unsatisfiable % 12.79/3.62 % SZS output end Proof for theBenchmark % 12.79/3.62 % 12.79/3.62 3015ms %------------------------------------------------------------------------------