%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n028.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 03:48:47 EDT 2022 % Result : Theorem 6.56s 2.21s % Output : Proof 18.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0. % 0.03/0.13 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n028.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 18 13:59:44 EDT 2022 % 0.12/0.34 % CPUTime : % 0.54/0.60 ____ _ % 0.54/0.60 ___ / __ \_____(_)___ ________ __________ % 0.54/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.54/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.54/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.54/0.60 % 0.54/0.60 A Theorem Prover for First-Order Logic % 0.54/0.60 (ePrincess v.1.0) % 0.54/0.60 % 0.54/0.61 (c) Philipp Rümmer, 2009-2015 % 0.54/0.61 (c) Peter Backeman, 2014-2015 % 0.54/0.61 (contributions by Angelo Brillout, Peter Baumgartner) % 0.54/0.61 Free software under GNU Lesser General Public License (LGPL). % 0.54/0.61 Bug reports to peter@backeman.se % 0.54/0.61 % 0.54/0.61 For more information, visit http://user.uu.se/~petba168/breu/ % 0.54/0.61 % 0.54/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.75/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 1.76/0.99 Prover 0: Preprocessing ... % 2.04/1.15 Prover 0: Warning: ignoring some quantifiers % 2.25/1.17 Prover 0: Constructing countermodel ... % 3.84/1.61 Prover 0: gave up % 3.84/1.61 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 4.23/1.64 Prover 1: Preprocessing ... % 4.47/1.73 Prover 1: Constructing countermodel ... % 4.88/1.80 Prover 1: gave up % 4.88/1.80 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 5.01/1.82 Prover 2: Preprocessing ... % 5.52/1.96 Prover 2: Warning: ignoring some quantifiers % 5.52/1.97 Prover 2: Constructing countermodel ... % 6.56/2.21 Prover 2: proved (415ms) % 6.56/2.21 % 6.56/2.21 No countermodel exists, formula is valid % 6.56/2.21 % SZS status Theorem for theBenchmark % 6.56/2.21 % 6.56/2.21 Generating proof ... Warning: ignoring some quantifiers % 16.87/4.62 found it (size 848) % 16.87/4.62 % 16.87/4.62 % SZS output start Proof for theBenchmark % 16.87/4.62 Assumed formulas after preprocessing and simplification: % 17.08/4.62 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = 0) & ~ (v3 = 0) & unorthogonal_lines(v1, v2) = v4 & unorthogonal_lines(v0, v1) = 0 & distinct_lines(v0, v2) = v3 & ! [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 | ~ (distinct_lines(v6, v7) = v9) | ~ (distinct_lines(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_lines(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = 0 | ~ (distinct_points(v6, v7) = v9) | ~ (distinct_points(v5, v7) = v8) | ? [v10] : ( ~ (v10 = 0) & distinct_points(v5, v6) = v10)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | ~ (intersection_point(v5, v6) = v8) | ~ (distinct_points(v7, v8) = v9) | ? [v10] : ? [v11] : (( ~ (v11 = 0) & ~ (v10 = 0) & apart_point_and_line(v7, v6) = v11 & apart_point_and_line(v7, v5) = v10) | ( ~ (v10 = 0) & convergent_lines(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 | ~ (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] : ( ~ (line_connecting(v5, v6) = v8) | ~ (apart_point_and_line(v7, v8) = 0) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = 0 & distinct_points(v7, v6) = 0 & distinct_points(v7, v5) = 0) | ( ~ (v9 = 0) & distinct_points(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] : (v7 = 0 | ~ (distinct_lines(v5, v6) = v7) | ? [v8] : ( ~ (v8 = 0) & convergent_lines(v5, v6) = v8)) & ! [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] : ( ~ (convergent_lines(v5, v6) = 0) | distinct_lines(v5, v6) = 0) & ! [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) % 17.21/4.68 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 17.21/4.68 | (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_3_3) = 0 & distinct_lines(all_0_4_4, all_0_2_2) = all_0_1_1 & ! [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 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(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 | ~ (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] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(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] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) & ! [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] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) & ! [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 % 17.21/4.71 | % 17.21/4.71 | Applying alpha-rule on (1) yields: % 17.21/4.71 | (2) ? [v0] : ? [v1] : ? [v2] : distinct_points(v1, v0) = v2 % 17.21/4.71 | (3) ! [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))) % 17.21/4.71 | (4) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (distinct_lines(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v0, v1) = v3)) % 17.21/4.71 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v0, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v1, v2) = 0) % 17.21/4.71 | (6) ? [v0] : ? [v1] : ? [v2] : apart_point_and_line(v1, v0) = v2 % 17.21/4.71 | (7) ! [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)) % 17.21/4.71 | (8) ! [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))) % 17.21/4.71 | (9) ? [v0] : ? [v1] : ? [v2] : distinct_lines(v1, v0) = v2 % 17.21/4.71 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (convergent_lines(v3, v2) = v1) | ~ (convergent_lines(v3, v2) = v0)) % 17.21/4.71 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (unorthogonal_lines(v3, v2) = v1) | ~ (unorthogonal_lines(v3, v2) = v0)) % 17.21/4.71 | (12) ! [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))) % 17.21/4.71 | (13) ! [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) % 17.21/4.71 | (14) ! [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))) % 17.21/4.72 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_lines(v1, v2) = v3) | ~ (distinct_lines(v0, v1) = 0) | distinct_lines(v0, v2) = 0) % 17.21/4.72 | (16) ! [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))) % 17.21/4.72 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_lines(v1, v2) = v4) | ~ (distinct_lines(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_lines(v0, v1) = v5)) % 17.21/4.72 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (parallel_through_point(v3, v2) = v1) | ~ (parallel_through_point(v3, v2) = v0)) % 17.21/4.72 | (19) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (convergent_lines(v0, v1) = v2) | unorthogonal_lines(v0, v1) = 0) % 17.21/4.72 | (20) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | ~ (unorthogonal_lines(v0, v1) = v2) | convergent_lines(v0, v1) = 0) % 17.21/4.72 | (21) ~ (all_0_0_0 = 0) % 17.21/4.72 | (22) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 % 17.21/4.72 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (apart_point_and_line(v3, v2) = v1) | ~ (apart_point_and_line(v3, v2) = v0)) % 17.21/4.72 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v1, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v0, v2) = 0) % 17.21/4.72 | (25) ! [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))) % 17.21/4.72 | (26) ! [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) % 17.21/4.72 | (27) ! [v0] : ~ (convergent_lines(v0, v0) = 0) % 17.21/4.72 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (distinct_points(v1, v2) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & distinct_points(v0, v1) = v5)) % 17.21/4.72 | (29) ! [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))) % 17.21/4.72 | (30) ! [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))) % 17.21/4.72 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_lines(v3, v2) = v1) | ~ (distinct_lines(v3, v2) = v0)) % 17.21/4.72 | (32) ! [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))) % 17.21/4.72 | (33) ! [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))) % 17.21/4.72 | (34) ! [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)) % 17.21/4.72 | (35) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.21/4.72 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (distinct_points(v3, v2) = v1) | ~ (distinct_points(v3, v2) = v0)) % 17.21/4.72 | (37) ! [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))) % 17.21/4.72 | (38) distinct_lines(all_0_4_4, all_0_2_2) = all_0_1_1 % 17.21/4.72 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 17.21/4.72 | (40) ! [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))) % 17.21/4.72 | (41) ? [v0] : ? [v1] : ? [v2] : intersection_point(v1, v0) = v2 % 17.61/4.72 | (42) ! [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))) % 17.61/4.72 | (43) ~ (all_0_1_1 = 0) % 17.61/4.72 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & apart_point_and_line(v0, v2) = v3)) % 17.61/4.73 | (45) ! [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))) % 17.61/4.73 | (46) ? [v0] : ? [v1] : ? [v2] : orthogonal_through_point(v1, v0) = v2 % 17.61/4.73 | (47) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (line_connecting(v0, v1) = v3) | ~ (apart_point_and_line(v2, v3) = 0) | ? [v4] : ? [v5] : ((v5 = 0 & v4 = 0 & distinct_points(v2, v1) = 0 & distinct_points(v2, v0) = 0) | ( ~ (v4 = 0) & distinct_points(v0, v1) = v4))) % 17.61/4.73 | (48) ! [v0] : ~ (distinct_points(v0, v0) = 0) % 17.61/4.73 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v1, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v0, v2) = 0) % 17.61/4.73 | (50) ! [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))) % 17.61/4.73 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (orthogonal_through_point(v3, v2) = v1) | ~ (orthogonal_through_point(v3, v2) = v0)) % 17.61/4.73 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (intersection_point(v0, v1) = v3) | ~ (distinct_points(v2, v3) = v4) | ? [v5] : ? [v6] : (( ~ (v6 = 0) & ~ (v5 = 0) & apart_point_and_line(v2, v1) = v6 & apart_point_and_line(v2, v0) = v5) | ( ~ (v5 = 0) & convergent_lines(v0, v1) = v5))) % 17.61/4.73 | (53) ! [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))) % 17.61/4.73 | (54) ? [v0] : ? [v1] : ? [v2] : unorthogonal_lines(v1, v0) = v2 % 17.61/4.73 | (55) ! [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))) % 17.61/4.73 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | v3 = 0 | ~ (apart_point_and_line(v2, v1) = v4) | ~ (distinct_points(v0, v2) = v3) | ? [v5] : ( ~ (v5 = 0) & apart_point_and_line(v0, v1) = v5)) % 17.61/4.73 | (57) ! [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))) % 17.61/4.73 | (58) ? [v0] : ? [v1] : ? [v2] : convergent_lines(v1, v0) = v2 % 17.61/4.73 | (59) ! [v0] : ! [v1] : ( ~ (convergent_lines(v0, v1) = 0) | distinct_lines(v0, v1) = 0) % 17.61/4.73 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (parallel_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & convergent_lines(v2, v1) = v3)) % 17.61/4.73 | (61) ! [v0] : ~ (distinct_lines(v0, v0) = 0) % 17.61/4.73 | (62) ! [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))) % 17.61/4.73 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (intersection_point(v3, v2) = v1) | ~ (intersection_point(v3, v2) = v0)) % 17.61/4.73 | (64) ! [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) % 17.61/4.73 | (65) ? [v0] : ? [v1] : ? [v2] : parallel_through_point(v1, v0) = v2 % 17.61/4.73 | (66) ! [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))) % 17.61/4.73 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (line_connecting(v3, v2) = v1) | ~ (line_connecting(v3, v2) = v0)) % 17.61/4.73 | (68) ? [v0] : ? [v1] : ? [v2] : line_connecting(v1, v0) = v2 % 17.61/4.73 | (69) ! [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))) % 17.61/4.73 | (70) ! [v0] : ! [v1] : ! [v2] : ( ~ (orthogonal_through_point(v1, v0) = v2) | ? [v3] : ( ~ (v3 = 0) & unorthogonal_lines(v2, v1) = v3)) % 17.61/4.73 | (71) ! [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))) % 17.61/4.73 | (72) ! [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) % 17.61/4.74 | (73) ! [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))) % 17.61/4.74 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (convergent_lines(v0, v2) = v3) | ~ (convergent_lines(v0, v1) = 0) | convergent_lines(v1, v2) = 0) % 17.61/4.74 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (distinct_points(v0, v2) = v3) | ~ (distinct_points(v0, v1) = 0) | distinct_points(v1, v2) = 0) % 17.61/4.74 | (76) ! [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))) % 17.61/4.74 | (77) ! [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))) % 17.61/4.74 | (78) ! [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))) % 17.61/4.74 | (79) ! [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))) % 17.61/4.74 | (80) ! [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))) % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (45) with all_0_0_0, all_0_0_0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 17.61/4.74 | (81) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)) % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (20) with all_0_0_0, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 17.61/4.74 | (82) all_0_0_0 = 0 | convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (45) with 0, 0, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.61/4.74 | (83) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (79) with 0, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.61/4.74 | (84) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)) % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (33) 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, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.61/4.74 | (85) ? [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) & convergent_lines(all_0_4_4, all_0_3_3) = v0)) % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (17) with all_0_1_1, all_0_1_1, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms distinct_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 17.61/4.74 | (86) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.74 | % 17.61/4.74 | Instantiating formula (4) with all_0_1_1, all_0_2_2, all_0_4_4 and discharging atoms distinct_lines(all_0_4_4, all_0_2_2) = all_0_1_1, yields: % 17.61/4.74 | (87) all_0_1_1 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0) % 17.61/4.74 | % 17.61/4.74 | Instantiating (85) with all_26_0_32, all_26_1_33 yields: % 17.61/4.74 | (88) (all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_26_1_33 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_26_1_33 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33) % 17.61/4.74 | % 17.61/4.74 | Instantiating (84) with all_27_0_34, all_27_1_35 yields: % 17.61/4.74 | (89) (all_27_0_34 = 0 & all_27_1_35 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_27_1_35 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_27_1_35 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35) % 17.61/4.74 | % 17.61/4.74 | Instantiating (83) with all_28_0_36 yields: % 17.61/4.74 | (90) (all_28_0_36 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_28_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_28_0_36) | ( ~ (all_28_0_36 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_28_0_36) % 17.61/4.74 | % 17.61/4.74 | Instantiating (81) with all_29_0_37 yields: % 17.61/4.74 | (91) (all_29_0_37 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_29_0_37 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_29_0_37) | ( ~ (all_29_0_37 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37) % 17.61/4.74 | % 17.61/4.74 +-Applying beta-rule and splitting (82), into two cases. % 17.61/4.74 |-Branch one: % 17.61/4.74 | (92) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.61/4.74 | % 17.61/4.74 +-Applying beta-rule and splitting (87), into two cases. % 17.61/4.74 |-Branch one: % 17.61/4.74 | (93) all_0_1_1 = 0 % 17.61/4.74 | % 17.61/4.75 | Equations (93) can reduce 43 to: % 17.61/4.75 | (94) $false % 17.61/4.75 | % 17.61/4.75 |-The branch is then unsatisfiable % 17.61/4.75 |-Branch two: % 17.61/4.75 | (43) ~ (all_0_1_1 = 0) % 17.61/4.75 | (96) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0) % 17.61/4.75 | % 17.61/4.75 | Instantiating (96) with all_36_0_38 yields: % 17.61/4.75 | (97) ~ (all_36_0_38 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 17.61/4.75 | % 17.61/4.75 | Applying alpha-rule on (97) yields: % 17.61/4.75 | (98) ~ (all_36_0_38 = 0) % 17.61/4.75 | (99) convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 17.61/4.75 | % 17.61/4.75 +-Applying beta-rule and splitting (86), into two cases. % 17.61/4.75 |-Branch one: % 17.61/4.75 | (93) all_0_1_1 = 0 % 17.61/4.75 | % 17.61/4.75 | Equations (93) can reduce 43 to: % 17.61/4.75 | (94) $false % 17.61/4.75 | % 17.61/4.75 |-The branch is then unsatisfiable % 17.61/4.75 |-Branch two: % 17.61/4.75 | (43) ~ (all_0_1_1 = 0) % 17.61/4.75 | (103) ? [v0] : ( ~ (v0 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.75 | % 17.61/4.75 | Instantiating (103) with all_41_0_39 yields: % 17.61/4.75 | (104) ~ (all_41_0_39 = 0) & distinct_lines(all_0_4_4, all_0_4_4) = all_41_0_39 % 17.61/4.75 | % 17.61/4.75 | Applying alpha-rule on (104) yields: % 17.61/4.75 | (105) ~ (all_41_0_39 = 0) % 17.61/4.75 | (106) distinct_lines(all_0_4_4, all_0_4_4) = all_41_0_39 % 17.61/4.75 | % 17.61/4.75 +-Applying beta-rule and splitting (88), into two cases. % 17.61/4.75 |-Branch one: % 17.61/4.75 | (107) (all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | (all_26_1_33 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) % 17.61/4.75 | % 17.61/4.75 +-Applying beta-rule and splitting (107), into two cases. % 17.61/4.75 |-Branch one: % 17.61/4.75 | (108) all_26_0_32 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.61/4.75 | % 17.61/4.75 | Applying alpha-rule on (108) yields: % 17.61/4.75 | (109) all_26_0_32 = 0 % 17.61/4.75 | (110) all_26_1_33 = 0 % 17.61/4.75 | (111) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.61/4.75 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (10) with all_0_4_4, all_0_2_2, 0, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.61/4.75 | (113) all_36_0_38 = 0 % 17.61/4.75 | % 17.61/4.75 | Equations (113) can reduce 98 to: % 17.61/4.75 | (94) $false % 17.61/4.75 | % 17.61/4.75 |-The branch is then unsatisfiable % 17.61/4.75 |-Branch two: % 17.61/4.75 | (115) all_26_1_33 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.61/4.75 | % 17.61/4.75 | Applying alpha-rule on (115) yields: % 17.61/4.75 | (110) all_26_1_33 = 0 % 17.61/4.75 | (117) all_0_0_0 = 0 % 17.61/4.75 | (92) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.61/4.75 | % 17.61/4.75 | Equations (117) can reduce 21 to: % 17.61/4.75 | (94) $false % 17.61/4.75 | % 17.61/4.75 |-The branch is then unsatisfiable % 17.61/4.75 |-Branch two: % 17.61/4.75 | (120) ~ (all_26_1_33 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33 % 17.61/4.75 | % 17.61/4.75 | Applying alpha-rule on (120) yields: % 17.61/4.75 | (121) ~ (all_26_1_33 = 0) % 17.61/4.75 | (122) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33 % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (40) with 0, 0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 17.61/4.75 | (123) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (69) with 0, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 17.61/4.75 | (124) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (55) with all_0_0_0, 0, all_0_2_2, all_0_3_3, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 17.61/4.75 | (125) ? [v0] : ((v0 = 0 & all_0_0_0 = 0) | (v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (78) with all_0_0_0, all_0_2_2, all_0_2_2, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 17.61/4.75 | (126) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & all_0_0_0 = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (40) with all_36_0_38, 0, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 17.61/4.75 | (127) ? [v0] : ((v0 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (7) with all_36_0_38, all_36_0_38, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 17.61/4.75 | (128) all_36_0_38 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (40) with all_36_0_38, all_36_0_38, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 17.61/4.75 | (129) ? [v0] : ((v0 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (3) with all_36_0_38, all_0_0_0, all_0_2_2, all_0_4_4, all_0_3_3 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_2_2) = all_36_0_38, yields: % 17.61/4.75 | (130) ? [v0] : ((v0 = 0 & all_36_0_38 = 0 & unorthogonal_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_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (19) with all_36_0_38, all_0_2_2, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 17.61/4.75 | (131) all_36_0_38 = 0 | unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (7) with all_26_1_33, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.61/4.75 | (132) all_26_1_33 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (40) with all_26_1_33, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.61/4.75 | (133) ? [v0] : ((v0 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.75 | % 17.61/4.75 | Instantiating formula (55) with 0, all_26_1_33, all_0_3_3, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.61/4.75 | (134) ? [v0] : ((v0 = 0 & all_26_1_33 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.76 | % 17.61/4.76 | Instantiating formula (73) with all_26_1_33, all_0_3_3, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.61/4.76 | (135) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & all_26_1_33 = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)) % 17.61/4.76 | % 17.61/4.76 | Instantiating formula (4) with all_41_0_39, all_0_4_4, all_0_4_4 and discharging atoms distinct_lines(all_0_4_4, all_0_4_4) = all_41_0_39, yields: % 17.61/4.76 | (136) all_41_0_39 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.76 | % 17.61/4.76 | Instantiating (135) with all_53_0_40, all_53_1_41 yields: % 17.61/4.76 | (137) (all_53_0_40 = 0 & all_53_1_41 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_53_1_41 = 0 & all_26_1_33 = 0) | ( ~ (all_53_1_41 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_53_1_41) % 17.61/4.76 | % 17.61/4.76 | Instantiating (134) with all_54_0_42 yields: % 17.61/4.76 | (138) (all_54_0_42 = 0 & all_26_1_33 = 0) | (all_54_0_42 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_54_0_42 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_54_0_42) | ( ~ (all_54_0_42 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_54_0_42) % 17.61/4.76 | % 17.61/4.76 | Instantiating (133) with all_55_0_43 yields: % 17.61/4.76 | (139) (all_55_0_43 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_55_0_43 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_55_0_43) | ( ~ (all_55_0_43 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_55_0_43) % 17.61/4.76 | % 17.61/4.76 | Instantiating (130) with all_56_0_44 yields: % 17.61/4.76 | (140) (all_56_0_44 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_56_0_44 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_56_0_44 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44) | ( ~ (all_56_0_44 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44) % 17.61/4.76 | % 17.61/4.76 | Instantiating (127) with all_57_0_45 yields: % 17.61/4.76 | (141) (all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_57_0_45 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45) | ( ~ (all_57_0_45 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45) % 17.61/4.76 | % 17.61/4.76 | Instantiating (129) with all_58_0_46 yields: % 17.61/4.76 | (142) (all_58_0_46 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_58_0_46 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_58_0_46) | ( ~ (all_58_0_46 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_58_0_46) % 17.61/4.76 | % 17.61/4.76 | Instantiating (126) with all_59_0_47, all_59_1_48 yields: % 17.61/4.76 | (143) (all_59_0_47 = 0 & all_59_1_48 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_59_1_48 = 0 & all_0_0_0 = 0) | ( ~ (all_59_1_48 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48) % 17.61/4.76 | % 17.61/4.76 | Instantiating (125) with all_60_0_49 yields: % 17.61/4.76 | (144) (all_60_0_49 = 0 & all_0_0_0 = 0) | (all_60_0_49 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_60_0_49 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_60_0_49) | ( ~ (all_60_0_49 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_60_0_49) % 17.61/4.76 | % 17.61/4.76 | Instantiating (124) with all_61_0_50, all_61_1_51 yields: % 17.61/4.76 | (145) (all_61_0_50 = 0 & all_61_1_51 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_61_1_51 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_61_1_51 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_61_1_51) % 17.61/4.76 | % 17.61/4.76 | Instantiating (123) with all_62_0_52 yields: % 17.61/4.76 | (146) (all_62_0_52 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_62_0_52 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_62_0_52) | ( ~ (all_62_0_52 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_62_0_52) % 17.61/4.76 | % 17.61/4.76 +-Applying beta-rule and splitting (131), into two cases. % 17.61/4.76 |-Branch one: % 17.61/4.76 | (111) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.61/4.76 | % 17.61/4.76 +-Applying beta-rule and splitting (132), into two cases. % 17.61/4.76 |-Branch one: % 17.61/4.76 | (110) all_26_1_33 = 0 % 17.61/4.76 | % 17.61/4.76 | Equations (110) can reduce 121 to: % 17.61/4.76 | (94) $false % 17.61/4.76 | % 17.61/4.76 |-The branch is then unsatisfiable % 17.61/4.76 |-Branch two: % 17.61/4.76 | (121) ~ (all_26_1_33 = 0) % 17.61/4.76 | (151) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.76 | % 17.61/4.76 | Instantiating (151) with all_71_0_53 yields: % 17.61/4.76 | (152) ~ (all_71_0_53 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53 % 17.61/4.76 | % 17.61/4.76 | Applying alpha-rule on (152) yields: % 17.61/4.76 | (153) ~ (all_71_0_53 = 0) % 17.61/4.76 | (154) convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53 % 17.61/4.76 | % 17.61/4.76 +-Applying beta-rule and splitting (128), into two cases. % 17.61/4.76 |-Branch one: % 17.61/4.76 | (113) all_36_0_38 = 0 % 17.61/4.76 | % 17.61/4.76 | Equations (113) can reduce 98 to: % 17.61/4.76 | (94) $false % 17.61/4.76 | % 17.61/4.76 |-The branch is then unsatisfiable % 17.61/4.76 |-Branch two: % 17.61/4.76 | (98) ~ (all_36_0_38 = 0) % 17.61/4.76 | (151) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.76 | % 17.61/4.76 | Instantiating (151) with all_76_0_54 yields: % 17.61/4.76 | (159) ~ (all_76_0_54 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_76_0_54 % 17.61/4.76 | % 17.61/4.76 | Applying alpha-rule on (159) yields: % 17.61/4.76 | (160) ~ (all_76_0_54 = 0) % 17.61/4.76 | (161) convergent_lines(all_0_4_4, all_0_4_4) = all_76_0_54 % 17.61/4.76 | % 17.61/4.76 +-Applying beta-rule and splitting (136), into two cases. % 17.61/4.76 |-Branch one: % 17.61/4.76 | (162) all_41_0_39 = 0 % 17.61/4.76 | % 17.61/4.76 | Equations (162) can reduce 105 to: % 17.61/4.76 | (94) $false % 17.61/4.76 | % 17.61/4.76 |-The branch is then unsatisfiable % 17.61/4.76 |-Branch two: % 17.61/4.76 | (105) ~ (all_41_0_39 = 0) % 17.61/4.76 | (151) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0) % 17.61/4.76 | % 17.61/4.76 | Instantiating (151) with all_81_0_55 yields: % 17.61/4.76 | (166) ~ (all_81_0_55 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_81_0_55 % 17.61/4.76 | % 17.61/4.76 | Applying alpha-rule on (166) yields: % 17.61/4.76 | (167) ~ (all_81_0_55 = 0) % 17.61/4.76 | (168) convergent_lines(all_0_4_4, all_0_4_4) = all_81_0_55 % 17.61/4.76 | % 17.61/4.76 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_76_0_54, all_81_0_55 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_81_0_55, convergent_lines(all_0_4_4, all_0_4_4) = all_76_0_54, yields: % 17.61/4.76 | (169) all_81_0_55 = all_76_0_54 % 17.61/4.76 | % 17.61/4.76 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_71_0_53, all_81_0_55 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_81_0_55, convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, yields: % 17.61/4.76 | (170) all_81_0_55 = all_71_0_53 % 17.61/4.76 | % 17.61/4.77 | Combining equations (169,170) yields a new equation: % 17.61/4.77 | (171) all_76_0_54 = all_71_0_53 % 17.61/4.77 | % 17.61/4.77 | Simplifying 171 yields: % 17.61/4.77 | (172) all_76_0_54 = all_71_0_53 % 17.61/4.77 | % 17.61/4.77 | Equations (172) can reduce 160 to: % 17.61/4.77 | (153) ~ (all_71_0_53 = 0) % 17.61/4.77 | % 17.61/4.77 | From (172) and (161) follows: % 17.61/4.77 | (154) convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53 % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (45) with 0, all_0_0_0, all_0_2_2, all_0_4_4, all_0_3_3 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) = 0, yields: % 17.61/4.77 | (175) ? [v0] : ((v0 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (45) with 0, 0, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.61/4.77 | (176) ? [v0] : ((v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (79) with 0, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.61/4.77 | (177) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (55) with 0, 0, all_0_2_2, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 17.61/4.77 | (178) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (55) with 0, all_36_0_38, all_0_2_2, all_0_4_4, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 17.61/4.77 | (179) ? [v0] : ((v0 = 0 & all_36_0_38 = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (79) with 0, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.61/4.77 | (180) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (73) with all_36_0_38, all_0_2_2, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 17.61/4.77 | (181) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & all_36_0_38 = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (73) with all_26_1_33, all_0_3_3, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.61/4.77 | (182) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (40) with all_71_0_53, all_71_0_53, all_0_4_4, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, yields: % 17.61/4.77 | (183) ? [v0] : ((v0 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (73) with all_71_0_53, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, yields: % 17.61/4.77 | (184) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (73) with all_71_0_53, all_0_4_4, all_0_2_2, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_2_2) = 0, convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, yields: % 17.61/4.77 | (185) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = v0)) % 17.61/4.77 | % 17.61/4.77 | Instantiating formula (19) with all_71_0_53, all_0_4_4, all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, yields: % 17.61/4.77 | (186) all_71_0_53 = 0 | unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 17.61/4.77 | % 17.61/4.77 | Instantiating (185) with all_92_0_56, all_92_1_57 yields: % 17.61/4.77 | (187) (all_92_0_56 = 0 & all_92_1_57 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_92_1_57 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_92_1_57 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_92_1_57) % 17.61/4.77 | % 17.61/4.77 | Instantiating (184) with all_93_0_58, all_93_1_59 yields: % 17.61/4.77 | (188) (all_93_0_58 = 0 & all_93_1_59 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_93_1_59 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_93_1_59 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_93_1_59) % 17.61/4.77 | % 17.61/4.77 | Instantiating (183) with all_94_0_60 yields: % 17.61/4.77 | (189) (all_94_0_60 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_94_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_94_0_60) | ( ~ (all_94_0_60 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_94_0_60) % 17.61/4.77 | % 17.61/4.77 | Instantiating (182) with all_95_0_61, all_95_1_62 yields: % 17.61/4.77 | (190) (all_95_0_61 = 0 & all_95_1_62 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | (all_95_1_62 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_95_1_62 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_95_1_62) % 17.61/4.77 | % 17.61/4.77 | Instantiating (181) with all_96_0_63, all_96_1_64 yields: % 17.61/4.77 | (191) (all_96_0_63 = 0 & all_96_1_64 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_96_1_64 = 0 & all_36_0_38 = 0) | ( ~ (all_96_1_64 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_96_1_64) % 17.61/4.77 | % 17.61/4.77 | Instantiating (178) with all_97_0_65 yields: % 17.61/4.77 | (192) (all_97_0_65 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (all_97_0_65 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_97_0_65 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_97_0_65) | ( ~ (all_97_0_65 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_97_0_65) % 17.61/4.77 | % 17.61/4.77 | Instantiating (177) with all_98_0_66, all_98_1_67 yields: % 17.61/4.77 | (193) (all_98_0_66 = 0 & all_98_1_67 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_98_1_67 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_98_1_67 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_98_1_67) % 17.61/4.77 | % 17.61/4.77 | Instantiating (176) with all_99_0_68 yields: % 17.61/4.77 | (194) (all_99_0_68 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_99_0_68 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_99_0_68) | ( ~ (all_99_0_68 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_99_0_68) % 17.61/4.77 | % 17.61/4.77 | Instantiating (180) with all_100_0_69, all_100_1_70 yields: % 17.61/4.77 | (195) (all_100_0_69 = 0 & all_100_1_70 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | (all_100_1_70 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_100_1_70 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_100_1_70) % 17.61/4.77 | % 17.61/4.77 | Instantiating (179) with all_101_0_71 yields: % 17.61/4.77 | (196) (all_101_0_71 = 0 & all_36_0_38 = 0) | (all_101_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_101_0_71 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_101_0_71) | ( ~ (all_101_0_71 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_101_0_71) % 17.61/4.78 | % 17.61/4.78 | Instantiating (175) with all_102_0_72 yields: % 17.61/4.78 | (197) (all_102_0_72 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_102_0_72 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_102_0_72 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_102_0_72) | ( ~ (all_102_0_72 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_102_0_72) % 17.61/4.78 | % 17.61/4.78 +-Applying beta-rule and splitting (89), into two cases. % 17.61/4.78 |-Branch one: % 17.61/4.78 | (198) (all_27_0_34 = 0 & all_27_1_35 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_27_1_35 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 17.61/4.78 | % 17.61/4.78 +-Applying beta-rule and splitting (198), into two cases. % 17.61/4.78 |-Branch one: % 17.61/4.78 | (199) all_27_0_34 = 0 & all_27_1_35 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.61/4.78 | % 17.61/4.78 | Applying alpha-rule on (199) yields: % 17.61/4.78 | (200) all_27_0_34 = 0 % 17.61/4.78 | (201) all_27_1_35 = 0 % 17.61/4.78 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.61/4.78 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.61/4.78 | % 17.61/4.78 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.61/4.78 | (204) $false % 17.61/4.78 | % 17.61/4.78 |-The branch is then unsatisfiable % 17.61/4.78 |-Branch two: % 17.61/4.78 | (205) all_27_1_35 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.61/4.78 | % 17.61/4.78 | Applying alpha-rule on (205) yields: % 17.61/4.78 | (201) all_27_1_35 = 0 % 17.61/4.78 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.61/4.78 | % 17.61/4.78 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.61/4.78 | (110) all_26_1_33 = 0 % 17.61/4.78 | % 17.61/4.78 | Equations (110) can reduce 121 to: % 17.61/4.78 | (94) $false % 17.61/4.78 | % 17.61/4.78 |-The branch is then unsatisfiable % 17.61/4.78 |-Branch two: % 17.61/4.78 | (210) ~ (all_27_1_35 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (210) yields: % 17.87/4.78 | (211) ~ (all_27_1_35 = 0) % 17.87/4.78 | (212) convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35 % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (186), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (213) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (90), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (214) (all_28_0_36 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_28_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_28_0_36) % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (214), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (215) all_28_0_36 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (215) yields: % 17.87/4.78 | (216) all_28_0_36 = 0 % 17.87/4.78 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.78 | % 17.87/4.78 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_27_1_35, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.78 | (218) all_27_1_35 = all_26_1_33 % 17.87/4.78 | % 17.87/4.78 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_27_1_35 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.87/4.78 | (201) all_27_1_35 = 0 % 17.87/4.78 | % 17.87/4.78 | Combining equations (201,218) yields a new equation: % 17.87/4.78 | (110) all_26_1_33 = 0 % 17.87/4.78 | % 17.87/4.78 | Equations (110) can reduce 121 to: % 17.87/4.78 | (94) $false % 17.87/4.78 | % 17.87/4.78 |-The branch is then unsatisfiable % 17.87/4.78 |-Branch two: % 17.87/4.78 | (222) ~ (all_28_0_36 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_28_0_36 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (222) yields: % 17.87/4.78 | (223) ~ (all_28_0_36 = 0) % 17.87/4.78 | (224) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_28_0_36 % 17.87/4.78 | % 17.87/4.78 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_28_0_36 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_28_0_36, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.78 | (216) all_28_0_36 = 0 % 17.87/4.78 | % 17.87/4.78 | Equations (216) can reduce 223 to: % 17.87/4.78 | (94) $false % 17.87/4.78 | % 17.87/4.78 |-The branch is then unsatisfiable % 17.87/4.78 |-Branch two: % 17.87/4.78 | (227) ~ (all_28_0_36 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_28_0_36 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (227) yields: % 17.87/4.78 | (223) ~ (all_28_0_36 = 0) % 17.87/4.78 | (229) convergent_lines(all_0_4_4, all_0_4_4) = all_28_0_36 % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (189), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (230) (all_94_0_60 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_94_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_94_0_60) % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (230), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (231) all_94_0_60 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (231) yields: % 17.87/4.78 | (232) all_94_0_60 = 0 % 17.87/4.78 | (233) all_71_0_53 = 0 % 17.87/4.78 | (213) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.78 | % 17.87/4.78 | Equations (233) can reduce 153 to: % 17.87/4.78 | (94) $false % 17.87/4.78 | % 17.87/4.78 |-The branch is then unsatisfiable % 17.87/4.78 |-Branch two: % 17.87/4.78 | (236) ~ (all_94_0_60 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_94_0_60 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (236) yields: % 17.87/4.78 | (237) ~ (all_94_0_60 = 0) % 17.87/4.78 | (238) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_94_0_60 % 17.87/4.78 | % 17.87/4.78 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_94_0_60 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_94_0_60, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.78 | (232) all_94_0_60 = 0 % 17.87/4.78 | % 17.87/4.78 | Equations (232) can reduce 237 to: % 17.87/4.78 | (94) $false % 17.87/4.78 | % 17.87/4.78 |-The branch is then unsatisfiable % 17.87/4.78 |-Branch two: % 17.87/4.78 | (241) ~ (all_94_0_60 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_94_0_60 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (241) yields: % 17.87/4.78 | (237) ~ (all_94_0_60 = 0) % 17.87/4.78 | (243) convergent_lines(all_0_4_4, all_0_4_4) = all_94_0_60 % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (139), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (244) (all_55_0_43 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_55_0_43 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_55_0_43) % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (244), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (245) all_55_0_43 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (245) yields: % 17.87/4.78 | (246) all_55_0_43 = 0 % 17.87/4.78 | (110) all_26_1_33 = 0 % 17.87/4.78 | (35) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.78 | % 17.87/4.78 | Equations (110) can reduce 121 to: % 17.87/4.78 | (94) $false % 17.87/4.78 | % 17.87/4.78 |-The branch is then unsatisfiable % 17.87/4.78 |-Branch two: % 17.87/4.78 | (250) ~ (all_55_0_43 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_55_0_43 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (250) yields: % 17.87/4.78 | (251) ~ (all_55_0_43 = 0) % 17.87/4.78 | (252) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_55_0_43 % 17.87/4.78 | % 17.87/4.78 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_55_0_43 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_55_0_43, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.78 | (246) all_55_0_43 = 0 % 17.87/4.78 | % 17.87/4.78 | Equations (246) can reduce 251 to: % 17.87/4.78 | (94) $false % 17.87/4.78 | % 17.87/4.78 |-The branch is then unsatisfiable % 17.87/4.78 |-Branch two: % 17.87/4.78 | (255) ~ (all_55_0_43 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_55_0_43 % 17.87/4.78 | % 17.87/4.78 | Applying alpha-rule on (255) yields: % 17.87/4.78 | (251) ~ (all_55_0_43 = 0) % 17.87/4.78 | (257) convergent_lines(all_0_4_4, all_0_4_4) = all_55_0_43 % 17.87/4.78 | % 17.87/4.78 +-Applying beta-rule and splitting (138), into two cases. % 17.87/4.78 |-Branch one: % 17.87/4.78 | (258) (all_54_0_42 = 0 & all_26_1_33 = 0) | (all_54_0_42 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_54_0_42 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_54_0_42) % 17.87/4.78 | % 17.87/4.79 +-Applying beta-rule and splitting (258), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (259) (all_54_0_42 = 0 & all_26_1_33 = 0) | (all_54_0_42 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (259), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (260) all_54_0_42 = 0 & all_26_1_33 = 0 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (260) yields: % 17.87/4.79 | (261) all_54_0_42 = 0 % 17.87/4.79 | (110) all_26_1_33 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (110) can reduce 121 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (264) all_54_0_42 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (264) yields: % 17.87/4.79 | (261) all_54_0_42 = 0 % 17.87/4.79 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_27_1_35, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.79 | (218) all_27_1_35 = all_26_1_33 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_27_1_35 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.87/4.79 | (201) all_27_1_35 = 0 % 17.87/4.79 | % 17.87/4.79 | Combining equations (201,218) yields a new equation: % 17.87/4.79 | (110) all_26_1_33 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (110) can reduce 121 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (271) ~ (all_54_0_42 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (271) yields: % 17.87/4.79 | (272) ~ (all_54_0_42 = 0) % 17.87/4.79 | (273) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_54_0_42 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_54_0_42, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.79 | (261) all_54_0_42 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (261) can reduce 272 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (276) ~ (all_54_0_42 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (276) yields: % 17.87/4.79 | (272) ~ (all_54_0_42 = 0) % 17.87/4.79 | (278) convergent_lines(all_0_4_4, all_0_4_4) = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (196), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (279) (all_101_0_71 = 0 & all_36_0_38 = 0) | (all_101_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_101_0_71 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_101_0_71) % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (279), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (280) (all_101_0_71 = 0 & all_36_0_38 = 0) | (all_101_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (280), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (281) all_101_0_71 = 0 & all_36_0_38 = 0 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (281) yields: % 17.87/4.79 | (282) all_101_0_71 = 0 % 17.87/4.79 | (113) all_36_0_38 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (113) can reduce 98 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (285) all_101_0_71 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (285) yields: % 17.87/4.79 | (282) all_101_0_71 = 0 % 17.87/4.79 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_2_2, 0, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.87/4.79 | (113) all_36_0_38 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (113) can reduce 98 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (290) ~ (all_101_0_71 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_101_0_71 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (290) yields: % 17.87/4.79 | (291) ~ (all_101_0_71 = 0) % 17.87/4.79 | (292) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_101_0_71 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_101_0_71 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_101_0_71, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.79 | (282) all_101_0_71 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (282) can reduce 291 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (295) ~ (all_101_0_71 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_101_0_71 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (295) yields: % 17.87/4.79 | (291) ~ (all_101_0_71 = 0) % 17.87/4.79 | (297) convergent_lines(all_0_4_4, all_0_4_4) = all_101_0_71 % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (142), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (298) (all_58_0_46 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_58_0_46 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_58_0_46) % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (298), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (299) all_58_0_46 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (299) yields: % 17.87/4.79 | (300) all_58_0_46 = 0 % 17.87/4.79 | (113) all_36_0_38 = 0 % 17.87/4.79 | (111) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (113) can reduce 98 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (304) ~ (all_58_0_46 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_58_0_46 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (304) yields: % 17.87/4.79 | (305) ~ (all_58_0_46 = 0) % 17.87/4.79 | (306) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_58_0_46 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_58_0_46 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_58_0_46, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.79 | (300) all_58_0_46 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (300) can reduce 305 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (309) ~ (all_58_0_46 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_58_0_46 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (309) yields: % 17.87/4.79 | (305) ~ (all_58_0_46 = 0) % 17.87/4.79 | (311) convergent_lines(all_0_4_4, all_0_4_4) = all_58_0_46 % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (194), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (312) (all_99_0_68 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_99_0_68 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_99_0_68) % 17.87/4.79 | % 17.87/4.79 +-Applying beta-rule and splitting (312), into two cases. % 17.87/4.79 |-Branch one: % 17.87/4.79 | (313) all_99_0_68 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (313) yields: % 17.87/4.79 | (314) all_99_0_68 = 0 % 17.87/4.79 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_2_2, 0, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.87/4.79 | (113) all_36_0_38 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (113) can reduce 98 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (318) ~ (all_99_0_68 = 0) & unorthogonal_lines(all_0_4_4, all_0_4_4) = all_99_0_68 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (318) yields: % 17.87/4.79 | (319) ~ (all_99_0_68 = 0) % 17.87/4.79 | (320) unorthogonal_lines(all_0_4_4, all_0_4_4) = all_99_0_68 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (11) with all_0_4_4, all_0_4_4, 0, all_99_0_68 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = all_99_0_68, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.79 | (314) all_99_0_68 = 0 % 17.87/4.79 | % 17.87/4.79 | Equations (314) can reduce 319 to: % 17.87/4.79 | (94) $false % 17.87/4.79 | % 17.87/4.79 |-The branch is then unsatisfiable % 17.87/4.79 |-Branch two: % 17.87/4.79 | (323) ~ (all_99_0_68 = 0) & convergent_lines(all_0_4_4, all_0_4_4) = all_99_0_68 % 17.87/4.79 | % 17.87/4.79 | Applying alpha-rule on (323) yields: % 17.87/4.79 | (319) ~ (all_99_0_68 = 0) % 17.87/4.79 | (325) convergent_lines(all_0_4_4, all_0_4_4) = all_99_0_68 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_27_1_35, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_27_1_35, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.79 | (218) all_27_1_35 = all_26_1_33 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_101_0_71, all_71_0_53 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_101_0_71, convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, yields: % 17.87/4.79 | (327) all_101_0_71 = all_71_0_53 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_94_0_60, all_99_0_68 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_99_0_68, convergent_lines(all_0_4_4, all_0_4_4) = all_94_0_60, yields: % 17.87/4.79 | (328) all_99_0_68 = all_94_0_60 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_58_0_46, all_71_0_53 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_71_0_53, convergent_lines(all_0_4_4, all_0_4_4) = all_58_0_46, yields: % 17.87/4.79 | (329) all_71_0_53 = all_58_0_46 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_58_0_46, all_94_0_60 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_94_0_60, convergent_lines(all_0_4_4, all_0_4_4) = all_58_0_46, yields: % 17.87/4.79 | (330) all_94_0_60 = all_58_0_46 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_55_0_43, all_94_0_60 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_94_0_60, convergent_lines(all_0_4_4, all_0_4_4) = all_55_0_43, yields: % 17.87/4.79 | (331) all_94_0_60 = all_55_0_43 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_54_0_42, all_99_0_68 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_99_0_68, convergent_lines(all_0_4_4, all_0_4_4) = all_54_0_42, yields: % 17.87/4.79 | (332) all_99_0_68 = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Instantiating formula (10) with all_0_4_4, all_0_4_4, all_28_0_36, all_101_0_71 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = all_101_0_71, convergent_lines(all_0_4_4, all_0_4_4) = all_28_0_36, yields: % 17.87/4.79 | (333) all_101_0_71 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Combining equations (327,333) yields a new equation: % 17.87/4.79 | (334) all_71_0_53 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Simplifying 334 yields: % 17.87/4.79 | (335) all_71_0_53 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Combining equations (328,332) yields a new equation: % 17.87/4.79 | (336) all_94_0_60 = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Simplifying 336 yields: % 17.87/4.79 | (337) all_94_0_60 = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Combining equations (337,331) yields a new equation: % 17.87/4.79 | (338) all_55_0_43 = all_54_0_42 % 17.87/4.79 | % 17.87/4.79 | Combining equations (330,331) yields a new equation: % 17.87/4.79 | (339) all_58_0_46 = all_55_0_43 % 17.87/4.79 | % 17.87/4.79 | Simplifying 339 yields: % 17.87/4.79 | (340) all_58_0_46 = all_55_0_43 % 17.87/4.79 | % 17.87/4.79 | Combining equations (329,335) yields a new equation: % 17.87/4.79 | (341) all_58_0_46 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Simplifying 341 yields: % 17.87/4.79 | (342) all_58_0_46 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Combining equations (340,342) yields a new equation: % 17.87/4.79 | (343) all_55_0_43 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Simplifying 343 yields: % 17.87/4.79 | (344) all_55_0_43 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Combining equations (344,338) yields a new equation: % 17.87/4.79 | (345) all_54_0_42 = all_28_0_36 % 17.87/4.79 | % 17.87/4.79 | Equations (345) can reduce 272 to: % 17.87/4.79 | (223) ~ (all_28_0_36 = 0) % 17.87/4.79 | % 17.87/4.79 | Equations (218) can reduce 211 to: % 17.87/4.79 | (121) ~ (all_26_1_33 = 0) % 17.87/4.79 | % 17.87/4.79 | From (218) and (212) follows: % 17.87/4.79 | (122) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33 % 17.87/4.79 | % 17.87/4.80 | From (345) and (278) follows: % 17.87/4.80 | (229) convergent_lines(all_0_4_4, all_0_4_4) = all_28_0_36 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (79) with 0, all_0_4_4, all_0_3_3, all_0_4_4 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.80 | (350) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = v0)) % 17.87/4.80 | % 17.87/4.80 | Instantiating (350) with all_146_0_73, all_146_1_74 yields: % 17.87/4.80 | (351) (all_146_0_73 = 0 & all_146_1_74 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_146_1_74 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_146_1_74 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_146_1_74) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (91), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (352) (all_29_0_37 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_29_0_37 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_29_0_37) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (352), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (353) all_29_0_37 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (353) yields: % 17.87/4.80 | (354) all_29_0_37 = 0 % 17.87/4.80 | (117) all_0_0_0 = 0 % 17.87/4.80 | (92) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (117) can reduce 21 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (358) ~ (all_29_0_37 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_29_0_37 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (358) yields: % 17.87/4.80 | (359) ~ (all_29_0_37 = 0) % 17.87/4.80 | (360) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_29_0_37 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (20) with all_29_0_37, all_0_3_3, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_29_0_37, yields: % 17.87/4.80 | (361) all_29_0_37 = 0 | convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (361), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.80 | (204) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (364) ~ (convergent_lines(all_0_3_3, all_0_3_3) = 0) % 17.87/4.80 | (354) all_29_0_37 = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (354) can reduce 359 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (367) ~ (all_29_0_37 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (367) yields: % 17.87/4.80 | (359) ~ (all_29_0_37 = 0) % 17.87/4.80 | (369) convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37 % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (137), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (370) (all_53_0_40 = 0 & all_53_1_41 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_53_1_41 = 0 & all_26_1_33 = 0) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (370), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (371) all_53_0_40 = 0 & all_53_1_41 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (371) yields: % 17.87/4.80 | (372) all_53_0_40 = 0 % 17.87/4.80 | (373) all_53_1_41 = 0 % 17.87/4.80 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.80 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.80 | (204) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (377) all_53_1_41 = 0 & all_26_1_33 = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (377) yields: % 17.87/4.80 | (373) all_53_1_41 = 0 % 17.87/4.80 | (110) all_26_1_33 = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (110) can reduce 121 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (381) ~ (all_53_1_41 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_53_1_41 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (381) yields: % 17.87/4.80 | (382) ~ (all_53_1_41 = 0) % 17.87/4.80 | (383) convergent_lines(all_0_4_4, all_0_3_3) = all_53_1_41 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_53_1_41, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_53_1_41, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.80 | (384) all_53_1_41 = all_26_1_33 % 17.87/4.80 | % 17.87/4.80 | Equations (384) can reduce 382 to: % 17.87/4.80 | (121) ~ (all_26_1_33 = 0) % 17.87/4.80 | % 17.87/4.80 | From (384) and (383) follows: % 17.87/4.80 | (122) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (74) with all_29_0_37, all_0_3_3, all_0_2_2, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_2_2) = 0, convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, yields: % 17.87/4.80 | (387) all_29_0_37 = 0 | convergent_lines(all_0_2_2, all_0_3_3) = 0 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (7) with all_26_1_33, all_29_0_37, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.80 | (388) all_29_0_37 = 0 | all_26_1_33 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0) % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (40) with all_26_1_33, all_29_0_37, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.80 | (389) ? [v0] : ((v0 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (40) with all_29_0_37, all_29_0_37, all_0_3_3, all_0_3_3, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, yields: % 17.87/4.80 | (390) ? [v0] : ((v0 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = v0)) % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (55) with 0, all_29_0_37, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, yields: % 17.87/4.80 | (391) ? [v0] : ((v0 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (19) with all_29_0_37, all_0_3_3, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, yields: % 17.87/4.80 | (392) all_29_0_37 = 0 | unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.80 | % 17.87/4.80 | Instantiating (391) with all_163_0_82 yields: % 17.87/4.80 | (393) (all_163_0_82 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (all_163_0_82 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_163_0_82 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_163_0_82) | ( ~ (all_163_0_82 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_163_0_82) % 17.87/4.80 | % 17.87/4.80 | Instantiating (390) with all_164_0_83 yields: % 17.87/4.80 | (394) (all_164_0_83 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_164_0_83 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_164_0_83) | ( ~ (all_164_0_83 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_164_0_83) % 17.87/4.80 | % 17.87/4.80 | Instantiating (389) with all_165_0_84 yields: % 17.87/4.80 | (395) (all_165_0_84 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (all_165_0_84 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_165_0_84 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_165_0_84) | ( ~ (all_165_0_84 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_165_0_84) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (140), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (396) (all_56_0_44 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_56_0_44 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_56_0_44 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (396), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (397) (all_56_0_44 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_56_0_44 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (397), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (398) all_56_0_44 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (398) yields: % 17.87/4.80 | (399) all_56_0_44 = 0 % 17.87/4.80 | (113) all_36_0_38 = 0 % 17.87/4.80 | (111) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (113) can reduce 98 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (403) all_56_0_44 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (403) yields: % 17.87/4.80 | (399) all_56_0_44 = 0 % 17.87/4.80 | (117) all_0_0_0 = 0 % 17.87/4.80 | (92) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (117) can reduce 21 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (408) ~ (all_56_0_44 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (408) yields: % 17.87/4.80 | (409) ~ (all_56_0_44 = 0) % 17.87/4.80 | (410) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44 % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (388), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (354) all_29_0_37 = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (354) can reduce 359 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (359) ~ (all_29_0_37 = 0) % 17.87/4.80 | (414) all_26_1_33 = 0 | ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (414), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (110) all_26_1_33 = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (110) can reduce 121 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (121) ~ (all_26_1_33 = 0) % 17.87/4.80 | (418) ? [v0] : ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0) % 17.87/4.80 | % 17.87/4.80 | Instantiating (418) with all_204_0_106 yields: % 17.87/4.80 | (419) ~ (all_204_0_106 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_204_0_106 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (419) yields: % 17.87/4.80 | (420) ~ (all_204_0_106 = 0) % 17.87/4.80 | (421) convergent_lines(all_0_3_3, all_0_4_4) = all_204_0_106 % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (143), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (422) (all_59_0_47 = 0 & all_59_1_48 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_59_1_48 = 0 & all_0_0_0 = 0) % 17.87/4.80 | % 17.87/4.80 +-Applying beta-rule and splitting (422), into two cases. % 17.87/4.80 |-Branch one: % 17.87/4.80 | (423) all_59_0_47 = 0 & all_59_1_48 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (423) yields: % 17.87/4.80 | (424) all_59_0_47 = 0 % 17.87/4.80 | (425) all_59_1_48 = 0 % 17.87/4.80 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.80 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.80 | % 17.87/4.80 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 17.87/4.80 | (204) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (429) all_59_1_48 = 0 & all_0_0_0 = 0 % 17.87/4.80 | % 17.87/4.80 | Applying alpha-rule on (429) yields: % 17.87/4.80 | (425) all_59_1_48 = 0 % 17.87/4.80 | (117) all_0_0_0 = 0 % 17.87/4.80 | % 17.87/4.80 | Equations (117) can reduce 21 to: % 17.87/4.80 | (94) $false % 17.87/4.80 | % 17.87/4.80 |-The branch is then unsatisfiable % 17.87/4.80 |-Branch two: % 17.87/4.80 | (433) ~ (all_59_1_48 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (433) yields: % 17.87/4.81 | (434) ~ (all_59_1_48 = 0) % 17.87/4.81 | (435) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (11) with all_0_3_3, all_0_2_2, all_59_1_48, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 17.87/4.81 | (436) all_59_1_48 = all_0_0_0 % 17.87/4.81 | % 17.87/4.81 | Equations (436) can reduce 434 to: % 17.87/4.81 | (21) ~ (all_0_0_0 = 0) % 17.87/4.81 | % 17.87/4.81 | From (436) and (435) follows: % 17.87/4.81 | (22) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (141), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (439) (all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_57_0_45 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45) % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (439), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (440) (all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (440), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (441) all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (441) yields: % 17.87/4.81 | (442) all_57_0_45 = 0 % 17.87/4.81 | (113) all_36_0_38 = 0 % 17.87/4.81 | (111) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (113) can reduce 98 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (446) all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (446) yields: % 17.87/4.81 | (442) all_57_0_45 = 0 % 17.87/4.81 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (11) 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: % 17.87/4.81 | (117) all_0_0_0 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (117) can reduce 21 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (451) ~ (all_57_0_45 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (451) yields: % 17.87/4.81 | (452) ~ (all_57_0_45 = 0) % 17.87/4.81 | (453) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (11) with all_0_3_3, all_0_4_4, all_57_0_45, all_56_0_44 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45, unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 17.87/4.81 | (454) all_57_0_45 = all_56_0_44 % 17.87/4.81 | % 17.87/4.81 | Equations (454) can reduce 452 to: % 17.87/4.81 | (409) ~ (all_56_0_44 = 0) % 17.87/4.81 | % 17.87/4.81 | From (454) and (453) follows: % 17.87/4.81 | (410) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (19) with all_204_0_106, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_204_0_106, yields: % 17.87/4.81 | (457) all_204_0_106 = 0 | unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (457), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_56_0_44 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.81 | (399) all_56_0_44 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (399) can reduce 409 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (461) ~ (unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) % 17.87/4.81 | (462) all_204_0_106 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (462) can reduce 420 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (464) ~ (all_57_0_45 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (464) yields: % 17.87/4.81 | (452) ~ (all_57_0_45 = 0) % 17.87/4.81 | (466) convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_57_0_45, all_204_0_106 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_204_0_106, convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45, yields: % 17.87/4.81 | (467) all_204_0_106 = all_57_0_45 % 17.87/4.81 | % 17.87/4.81 | Equations (467) can reduce 420 to: % 17.87/4.81 | (452) ~ (all_57_0_45 = 0) % 17.87/4.81 | % 17.87/4.81 | From (467) and (421) follows: % 17.87/4.81 | (466) convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (19) with all_57_0_45, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45, yields: % 17.87/4.81 | (470) all_57_0_45 = 0 | unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (470), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_56_0_44 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_56_0_44, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.81 | (399) all_56_0_44 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (399) can reduce 409 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (461) ~ (unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) % 17.87/4.81 | (442) all_57_0_45 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (442) can reduce 452 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (477) ~ (all_56_0_44 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (477) yields: % 17.87/4.81 | (409) ~ (all_56_0_44 = 0) % 17.87/4.81 | (479) convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (392), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (188), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (481) (all_93_0_58 = 0 & all_93_1_59 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_93_1_59 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (481), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (482) all_93_0_58 = 0 & all_93_1_59 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (482) yields: % 17.87/4.81 | (483) all_93_0_58 = 0 % 17.87/4.81 | (484) all_93_1_59 = 0 % 17.87/4.81 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | (486) convergent_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (10) with all_0_3_3, all_0_4_4, 0, all_56_0_44 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.81 | (399) all_56_0_44 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (399) can reduce 409 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (489) all_93_1_59 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (489) yields: % 17.87/4.81 | (484) all_93_1_59 = 0 % 17.87/4.81 | (233) all_71_0_53 = 0 % 17.87/4.81 | (213) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Combining equations (335,233) yields a new equation: % 17.87/4.81 | (493) all_28_0_36 = 0 % 17.87/4.81 | % 17.87/4.81 | Simplifying 493 yields: % 17.87/4.81 | (216) all_28_0_36 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (216) can reduce 223 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (496) ~ (all_93_1_59 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_93_1_59 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (496) yields: % 17.87/4.81 | (497) ~ (all_93_1_59 = 0) % 17.87/4.81 | (498) convergent_lines(all_0_4_4, all_0_3_3) = all_93_1_59 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (387), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (499) convergent_lines(all_0_2_2, all_0_3_3) = 0 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (394), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (500) (all_164_0_83 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_164_0_83 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_164_0_83) % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (500), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (501) all_164_0_83 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (501) yields: % 17.87/4.81 | (502) all_164_0_83 = 0 % 17.87/4.81 | (354) all_29_0_37 = 0 % 17.87/4.81 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (354) can reduce 359 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (506) ~ (all_164_0_83 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_164_0_83 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (506) yields: % 17.87/4.81 | (507) ~ (all_164_0_83 = 0) % 17.87/4.81 | (508) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_164_0_83 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (11) with all_0_3_3, all_0_3_3, 0, all_164_0_83 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_164_0_83, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.81 | (502) all_164_0_83 = 0 % 17.87/4.81 | % 17.87/4.81 | Equations (502) can reduce 507 to: % 17.87/4.81 | (94) $false % 17.87/4.81 | % 17.87/4.81 |-The branch is then unsatisfiable % 17.87/4.81 |-Branch two: % 17.87/4.81 | (511) ~ (all_164_0_83 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_164_0_83 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (511) yields: % 17.87/4.81 | (507) ~ (all_164_0_83 = 0) % 17.87/4.81 | (513) convergent_lines(all_0_3_3, all_0_3_3) = all_164_0_83 % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (351), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (514) (all_146_0_73 = 0 & all_146_1_74 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0) | (all_146_1_74 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) % 17.87/4.81 | % 17.87/4.81 +-Applying beta-rule and splitting (514), into two cases. % 17.87/4.81 |-Branch one: % 17.87/4.81 | (515) all_146_0_73 = 0 & all_146_1_74 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 & convergent_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Applying alpha-rule on (515) yields: % 17.87/4.81 | (516) all_146_0_73 = 0 % 17.87/4.81 | (517) all_146_1_74 = 0 % 17.87/4.81 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | (486) convergent_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.81 | % 17.87/4.81 | Instantiating formula (10) with all_0_3_3, all_0_4_4, 0, all_56_0_44 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.81 | (399) all_56_0_44 = 0 % 17.87/4.81 | % 17.87/4.82 | Equations (399) can reduce 409 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (522) all_146_1_74 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (522) yields: % 17.87/4.82 | (517) all_146_1_74 = 0 % 17.87/4.82 | (524) convergent_lines(all_0_4_4, all_0_4_4) = 0 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (27) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields: % 17.87/4.82 | (204) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (526) ~ (all_146_1_74 = 0) & convergent_lines(all_0_4_4, all_0_3_3) = all_146_1_74 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (526) yields: % 17.87/4.82 | (527) ~ (all_146_1_74 = 0) % 17.87/4.82 | (528) convergent_lines(all_0_4_4, all_0_3_3) = all_146_1_74 % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (144), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (529) (all_60_0_49 = 0 & all_0_0_0 = 0) | (all_60_0_49 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_60_0_49 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_60_0_49) % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (529), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (530) (all_60_0_49 = 0 & all_0_0_0 = 0) | (all_60_0_49 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (530), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (531) all_60_0_49 = 0 & all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (531) yields: % 17.87/4.82 | (532) all_60_0_49 = 0 % 17.87/4.82 | (117) all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (117) can reduce 21 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (535) all_60_0_49 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (535) yields: % 17.87/4.82 | (532) all_60_0_49 = 0 % 17.87/4.82 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (11) 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: % 17.87/4.82 | (117) all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (117) can reduce 21 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (540) ~ (all_60_0_49 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (540) yields: % 17.87/4.82 | (541) ~ (all_60_0_49 = 0) % 17.87/4.82 | (542) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (11) with all_0_3_3, all_0_3_3, 0, all_60_0_49 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_60_0_49, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.82 | (532) all_60_0_49 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (532) can reduce 541 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (545) ~ (all_60_0_49 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (545) yields: % 17.87/4.82 | (541) ~ (all_60_0_49 = 0) % 17.87/4.82 | (547) convergent_lines(all_0_3_3, all_0_3_3) = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (146), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (548) (all_62_0_52 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_62_0_52 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_62_0_52) % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (548), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (549) all_62_0_52 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (549) yields: % 17.87/4.82 | (550) all_62_0_52 = 0 % 17.87/4.82 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (11) 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: % 17.87/4.82 | (117) all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (117) can reduce 21 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (554) ~ (all_62_0_52 = 0) & unorthogonal_lines(all_0_3_3, all_0_3_3) = all_62_0_52 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (554) yields: % 17.87/4.82 | (555) ~ (all_62_0_52 = 0) % 17.87/4.82 | (556) unorthogonal_lines(all_0_3_3, all_0_3_3) = all_62_0_52 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (11) with all_0_3_3, all_0_3_3, 0, all_62_0_52 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = all_62_0_52, unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.82 | (550) all_62_0_52 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (550) can reduce 555 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (559) ~ (all_62_0_52 = 0) & convergent_lines(all_0_3_3, all_0_3_3) = all_62_0_52 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (559) yields: % 17.87/4.82 | (555) ~ (all_62_0_52 = 0) % 17.87/4.82 | (561) convergent_lines(all_0_3_3, all_0_3_3) = all_62_0_52 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (10) with all_0_3_3, all_0_3_3, all_62_0_52, all_29_0_37 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_62_0_52, convergent_lines(all_0_3_3, all_0_3_3) = all_29_0_37, yields: % 17.87/4.82 | (562) all_62_0_52 = all_29_0_37 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (10) with all_0_3_3, all_0_3_3, all_62_0_52, all_164_0_83 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_164_0_83, convergent_lines(all_0_3_3, all_0_3_3) = all_62_0_52, yields: % 17.87/4.82 | (563) all_164_0_83 = all_62_0_52 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (10) with all_0_3_3, all_0_3_3, all_60_0_49, all_164_0_83 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = all_164_0_83, convergent_lines(all_0_3_3, all_0_3_3) = all_60_0_49, yields: % 17.87/4.82 | (564) all_164_0_83 = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_146_1_74, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_146_1_74, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.82 | (565) all_146_1_74 = all_26_1_33 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (10) with all_0_4_4, all_0_3_3, all_93_1_59, all_146_1_74 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_146_1_74, convergent_lines(all_0_4_4, all_0_3_3) = all_93_1_59, yields: % 17.87/4.82 | (566) all_146_1_74 = all_93_1_59 % 17.87/4.82 | % 17.87/4.82 | Combining equations (563,564) yields a new equation: % 17.87/4.82 | (567) all_62_0_52 = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 | Simplifying 567 yields: % 17.87/4.82 | (568) all_62_0_52 = all_60_0_49 % 17.87/4.82 | % 17.87/4.82 | Combining equations (565,566) yields a new equation: % 17.87/4.82 | (569) all_93_1_59 = all_26_1_33 % 17.87/4.82 | % 17.87/4.82 | Combining equations (568,562) yields a new equation: % 17.87/4.82 | (570) all_60_0_49 = all_29_0_37 % 17.87/4.82 | % 17.87/4.82 | Simplifying 570 yields: % 17.87/4.82 | (571) all_60_0_49 = all_29_0_37 % 17.87/4.82 | % 17.87/4.82 | Equations (569) can reduce 497 to: % 17.87/4.82 | (121) ~ (all_26_1_33 = 0) % 17.87/4.82 | % 17.87/4.82 | Equations (571) can reduce 541 to: % 17.87/4.82 | (359) ~ (all_29_0_37 = 0) % 17.87/4.82 | % 17.87/4.82 | From (569) and (498) follows: % 17.87/4.82 | (122) convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33 % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (143), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (422) (all_59_0_47 = 0 & all_59_1_48 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_59_1_48 = 0 & all_0_0_0 = 0) % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (422), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (423) all_59_0_47 = 0 & all_59_1_48 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (423) yields: % 17.87/4.82 | (424) all_59_0_47 = 0 % 17.87/4.82 | (425) all_59_1_48 = 0 % 17.87/4.82 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.82 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 17.87/4.82 | (204) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (429) all_59_1_48 = 0 & all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (429) yields: % 17.87/4.82 | (425) all_59_1_48 = 0 % 17.87/4.82 | (117) all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (117) can reduce 21 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (433) ~ (all_59_1_48 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (433) yields: % 17.87/4.82 | (434) ~ (all_59_1_48 = 0) % 17.87/4.82 | (435) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (11) with all_0_3_3, all_0_2_2, all_59_1_48, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_59_1_48, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 17.87/4.82 | (436) all_59_1_48 = all_0_0_0 % 17.87/4.82 | % 17.87/4.82 | Equations (436) can reduce 434 to: % 17.87/4.82 | (21) ~ (all_0_0_0 = 0) % 17.87/4.82 | % 17.87/4.82 | From (436) and (435) follows: % 17.87/4.82 | (22) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (141), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (439) (all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_57_0_45 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45) % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (439), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (440) (all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) | (all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (440), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (441) all_57_0_45 = 0 & all_36_0_38 = 0 & unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (441) yields: % 17.87/4.82 | (442) all_57_0_45 = 0 % 17.87/4.82 | (113) all_36_0_38 = 0 % 17.87/4.82 | (111) unorthogonal_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (113) can reduce 98 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (446) all_57_0_45 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (446) yields: % 17.87/4.82 | (442) all_57_0_45 = 0 % 17.87/4.82 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (11) 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: % 17.87/4.82 | (117) all_0_0_0 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (117) can reduce 21 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.82 | (451) ~ (all_57_0_45 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.82 | % 17.87/4.82 | Applying alpha-rule on (451) yields: % 17.87/4.82 | (452) ~ (all_57_0_45 = 0) % 17.87/4.82 | (453) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (20) with all_57_0_45, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_57_0_45, yields: % 17.87/4.82 | (607) all_57_0_45 = 0 | convergent_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.82 | % 17.87/4.82 +-Applying beta-rule and splitting (607), into two cases. % 17.87/4.82 |-Branch one: % 17.87/4.82 | (486) convergent_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.82 | % 17.87/4.82 | Instantiating formula (10) with all_0_3_3, all_0_4_4, 0, all_56_0_44 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, convergent_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.82 | (399) all_56_0_44 = 0 % 17.87/4.82 | % 17.87/4.82 | Equations (399) can reduce 409 to: % 17.87/4.82 | (94) $false % 17.87/4.82 | % 17.87/4.82 |-The branch is then unsatisfiable % 17.87/4.82 |-Branch two: % 17.87/4.83 | (611) ~ (convergent_lines(all_0_3_3, all_0_4_4) = 0) % 17.87/4.83 | (442) all_57_0_45 = 0 % 17.87/4.83 | % 17.87/4.83 | Equations (442) can reduce 452 to: % 17.87/4.83 | (94) $false % 17.87/4.83 | % 17.87/4.83 |-The branch is then unsatisfiable % 17.87/4.83 |-Branch two: % 17.87/4.83 | (464) ~ (all_57_0_45 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.83 | % 17.87/4.83 | Applying alpha-rule on (464) yields: % 17.87/4.83 | (452) ~ (all_57_0_45 = 0) % 17.87/4.83 | (466) convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45 % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_57_0_45, all_56_0_44 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_57_0_45, convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 17.87/4.83 | (454) all_57_0_45 = all_56_0_44 % 17.87/4.83 | % 17.87/4.83 | Equations (454) can reduce 452 to: % 17.87/4.83 | (409) ~ (all_56_0_44 = 0) % 17.87/4.83 | % 17.87/4.83 | From (454) and (466) follows: % 17.87/4.83 | (479) convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44 % 17.87/4.83 | % 17.87/4.83 +-Applying beta-rule and splitting (145), into two cases. % 17.87/4.83 |-Branch one: % 17.87/4.83 | (620) (all_61_0_50 = 0 & all_61_1_51 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_61_1_51 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) % 17.87/4.83 | % 17.87/4.83 +-Applying beta-rule and splitting (620), into two cases. % 17.87/4.83 |-Branch one: % 17.87/4.83 | (621) all_61_0_50 = 0 & all_61_1_51 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.83 | % 17.87/4.83 | Applying alpha-rule on (621) yields: % 17.87/4.83 | (622) all_61_0_50 = 0 % 17.87/4.83 | (623) all_61_1_51 = 0 % 17.87/4.83 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.83 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 17.87/4.83 | (204) $false % 17.87/4.83 | % 17.87/4.83 |-The branch is then unsatisfiable % 17.87/4.83 |-Branch two: % 17.87/4.83 | (627) all_61_1_51 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.83 | % 17.87/4.83 | Applying alpha-rule on (627) yields: % 17.87/4.83 | (623) all_61_1_51 = 0 % 17.87/4.83 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (11) 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: % 17.87/4.83 | (117) all_0_0_0 = 0 % 17.87/4.83 | % 17.87/4.83 | Equations (117) can reduce 21 to: % 17.87/4.83 | (94) $false % 17.87/4.83 | % 17.87/4.83 |-The branch is then unsatisfiable % 17.87/4.83 |-Branch two: % 17.87/4.83 | (632) ~ (all_61_1_51 = 0) & unorthogonal_lines(all_0_3_3, all_0_2_2) = all_61_1_51 % 17.87/4.83 | % 17.87/4.83 | Applying alpha-rule on (632) yields: % 17.87/4.83 | (633) ~ (all_61_1_51 = 0) % 17.87/4.83 | (634) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_61_1_51 % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (11) with all_0_3_3, all_0_2_2, all_61_1_51, all_0_0_0 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_61_1_51, unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, yields: % 17.87/4.83 | (635) all_61_1_51 = all_0_0_0 % 17.87/4.83 | % 17.87/4.83 | Equations (635) can reduce 633 to: % 17.87/4.83 | (21) ~ (all_0_0_0 = 0) % 17.87/4.83 | % 17.87/4.83 | From (635) and (634) follows: % 17.87/4.83 | (22) unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0 % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (45) with 0, 0, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.87/4.83 | (638) ? [v0] : ((v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (3) with all_26_1_33, 0, all_0_3_3, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, yields: % 17.87/4.83 | (639) ? [v0] : ((v0 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (69) with 0, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 17.87/4.83 | (640) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (55) with 0, 0, all_0_3_3, all_0_4_4, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_3_3) = 0, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 17.87/4.83 | (641) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (55) with 0, 0, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 17.87/4.83 | (642) ? [v0] : ((v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (30) with 0, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = 0, convergent_lines(all_0_3_3, all_0_2_2) = 0, yields: % 17.87/4.83 | (643) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (v0 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (32) with all_0_0_0, all_0_2_2, all_0_3_3, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_2_2) = all_0_0_0, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 17.87/4.83 | (644) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, 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_2_2, all_0_3_3) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (32) with 0, all_0_3_3, all_0_3_3, all_0_2_2 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_3_3) = 0, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 17.87/4.83 | (645) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (v0 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (40) with all_28_0_36, all_56_0_44, all_0_4_4, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, convergent_lines(all_0_4_4, all_0_4_4) = all_28_0_36, yields: % 17.87/4.83 | (646) ? [v0] : ((v0 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & all_28_0_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (24) with all_56_0_44, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = 0, convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 17.87/4.83 | (647) all_56_0_44 = 0 | convergent_lines(all_0_2_2, all_0_4_4) = 0 % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (30) with all_56_0_44, all_0_4_4, all_0_3_3, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = 0, convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 17.87/4.83 | (648) ? [v0] : ? [v1] : ((v1 = 0 & v0 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (v0 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (55) with 0, all_56_0_44, all_0_4_4, all_0_4_4, all_0_3_3 and discharging atoms unorthogonal_lines(all_0_4_4, all_0_4_4) = 0, convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 17.87/4.83 | (649) ? [v0] : ((v0 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (v0 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (v0 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = v0) | ( ~ (v0 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = v0)) % 17.87/4.83 | % 17.87/4.83 | Instantiating formula (19) with all_56_0_44, all_0_4_4, all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 17.87/4.83 | (650) all_56_0_44 = 0 | unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.83 | % 17.87/4.83 | Instantiating (648) with all_237_0_224, all_237_1_225 yields: % 17.87/4.83 | (651) (all_237_0_224 = 0 & all_237_1_225 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_237_1_225 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | ( ~ (all_237_1_225 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225) % 17.87/4.83 | % 17.87/4.83 | Instantiating (646) with all_239_0_228 yields: % 17.87/4.83 | (652) (all_239_0_228 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (all_239_0_228 = 0 & all_28_0_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_239_0_228 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_239_0_228) | ( ~ (all_239_0_228 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_239_0_228) % 17.87/4.83 | % 17.87/4.83 | Instantiating (645) with all_240_0_229, all_240_1_230 yields: % 17.87/4.83 | (653) (all_240_0_229 = 0 & all_240_1_230 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_240_1_230 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_240_1_230 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230) % 17.87/4.83 | % 17.87/4.83 | Instantiating (649) with all_241_0_231 yields: % 17.87/4.83 | (654) (all_241_0_231 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (all_241_0_231 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_241_0_231 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_241_0_231) | ( ~ (all_241_0_231 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_241_0_231) % 17.87/4.83 | % 17.87/4.83 | Instantiating (643) with all_242_0_232, all_242_1_233 yields: % 17.87/4.83 | (655) (all_242_0_232 = 0 & all_242_1_233 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_242_1_233 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_242_1_233 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233) % 17.87/4.83 | % 17.87/4.83 | Instantiating (642) with all_244_0_235 yields: % 17.87/4.83 | (656) (all_244_0_235 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_244_0_235 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_244_0_235 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_244_0_235) | ( ~ (all_244_0_235 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_244_0_235) % 17.87/4.83 | % 17.87/4.83 | Instantiating (641) with all_250_0_241 yields: % 17.87/4.83 | (657) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241) | ( ~ (all_250_0_241 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241) % 17.87/4.83 | % 17.87/4.83 | Instantiating (640) with all_251_0_242, all_251_1_243 yields: % 17.87/4.83 | (658) (all_251_0_242 = 0 & all_251_1_243 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_251_1_243 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | ( ~ (all_251_1_243 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243) % 17.87/4.83 | % 17.87/4.83 | Instantiating (644) with all_254_0_247, all_254_1_248 yields: % 17.87/4.83 | (659) (all_254_0_247 = 0 & all_254_1_248 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_254_1_248 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | ( ~ (all_254_1_248 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_254_1_248) % 17.87/4.83 | % 17.87/4.83 | Instantiating (639) with all_256_0_251 yields: % 17.87/4.83 | (660) (all_256_0_251 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (all_256_0_251 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_256_0_251 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_256_0_251) | ( ~ (all_256_0_251 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_256_0_251) % 17.87/4.83 | % 17.87/4.83 | Instantiating (638) with all_258_0_254 yields: % 17.87/4.83 | (661) (all_258_0_254 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_258_0_254 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_258_0_254 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_258_0_254) | ( ~ (all_258_0_254 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_258_0_254) % 17.87/4.83 | % 17.87/4.83 +-Applying beta-rule and splitting (650), into two cases. % 17.87/4.83 |-Branch one: % 17.87/4.83 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.83 | % 17.87/4.83 +-Applying beta-rule and splitting (197), into two cases. % 17.87/4.83 |-Branch one: % 17.87/4.83 | (663) (all_102_0_72 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_102_0_72 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_102_0_72 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_102_0_72) % 17.87/4.83 | % 17.87/4.83 +-Applying beta-rule and splitting (663), into two cases. % 17.87/4.83 |-Branch one: % 17.87/4.84 | (664) (all_102_0_72 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) | (all_102_0_72 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (664), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (665) all_102_0_72 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (665) yields: % 17.87/4.84 | (666) all_102_0_72 = 0 % 17.87/4.84 | (117) all_0_0_0 = 0 % 17.87/4.84 | (92) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (117) can reduce 21 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (670) all_102_0_72 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (670) yields: % 17.87/4.84 | (666) all_102_0_72 = 0 % 17.87/4.84 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (10) with all_0_4_4, all_0_2_2, 0, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.87/4.84 | (113) all_36_0_38 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (113) can reduce 98 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (675) ~ (all_102_0_72 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_102_0_72 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (675) yields: % 17.87/4.84 | (676) ~ (all_102_0_72 = 0) % 17.87/4.84 | (677) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_102_0_72 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_102_0_72 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_102_0_72, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.84 | (666) all_102_0_72 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (666) can reduce 676 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (680) ~ (all_102_0_72 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_102_0_72 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (680) yields: % 17.87/4.84 | (676) ~ (all_102_0_72 = 0) % 17.87/4.84 | (682) convergent_lines(all_0_3_3, all_0_4_4) = all_102_0_72 % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (192), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (683) (all_97_0_65 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (all_97_0_65 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) | ( ~ (all_97_0_65 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_97_0_65) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (683), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (684) (all_97_0_65 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) | (all_97_0_65 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (684), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (685) all_97_0_65 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (685) yields: % 17.87/4.84 | (686) all_97_0_65 = 0 % 17.87/4.84 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (11) 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: % 17.87/4.84 | (117) all_0_0_0 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (117) can reduce 21 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (690) all_97_0_65 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (690) yields: % 17.87/4.84 | (686) all_97_0_65 = 0 % 17.87/4.84 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (10) with all_0_4_4, all_0_2_2, 0, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 17.87/4.84 | (113) all_36_0_38 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (113) can reduce 98 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (695) ~ (all_97_0_65 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_97_0_65 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (695) yields: % 17.87/4.84 | (696) ~ (all_97_0_65 = 0) % 17.87/4.84 | (697) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_97_0_65 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_97_0_65 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_97_0_65, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.84 | (686) all_97_0_65 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (686) can reduce 696 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (700) ~ (all_97_0_65 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_97_0_65 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (700) yields: % 17.87/4.84 | (696) ~ (all_97_0_65 = 0) % 17.87/4.84 | (702) convergent_lines(all_0_3_3, all_0_4_4) = all_97_0_65 % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (393), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (703) (all_163_0_82 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (all_163_0_82 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_163_0_82 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_163_0_82) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (703), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (704) (all_163_0_82 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (all_163_0_82 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (704), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (705) all_163_0_82 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (705) yields: % 17.87/4.84 | (706) all_163_0_82 = 0 % 17.87/4.84 | (354) all_29_0_37 = 0 % 17.87/4.84 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (354) can reduce 359 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (710) all_163_0_82 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (710) yields: % 17.87/4.84 | (706) all_163_0_82 = 0 % 17.87/4.84 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.87/4.84 | (110) all_26_1_33 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (110) can reduce 121 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (715) ~ (all_163_0_82 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_163_0_82 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (715) yields: % 17.87/4.84 | (716) ~ (all_163_0_82 = 0) % 17.87/4.84 | (717) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_163_0_82 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_163_0_82 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_163_0_82, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.84 | (706) all_163_0_82 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (706) can reduce 716 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (720) ~ (all_163_0_82 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_163_0_82 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (720) yields: % 17.87/4.84 | (716) ~ (all_163_0_82 = 0) % 17.87/4.84 | (722) convergent_lines(all_0_3_3, all_0_4_4) = all_163_0_82 % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (395), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (723) (all_165_0_84 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (all_165_0_84 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_165_0_84 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_165_0_84) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (723), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (724) (all_165_0_84 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) | (all_165_0_84 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (724), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (725) all_165_0_84 = 0 & all_29_0_37 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (725) yields: % 17.87/4.84 | (726) all_165_0_84 = 0 % 17.87/4.84 | (354) all_29_0_37 = 0 % 17.87/4.84 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (354) can reduce 359 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (730) all_165_0_84 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (730) yields: % 17.87/4.84 | (726) all_165_0_84 = 0 % 17.87/4.84 | (110) all_26_1_33 = 0 % 17.87/4.84 | (35) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (110) can reduce 121 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (735) ~ (all_165_0_84 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_165_0_84 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (735) yields: % 17.87/4.84 | (736) ~ (all_165_0_84 = 0) % 17.87/4.84 | (737) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_165_0_84 % 17.87/4.84 | % 17.87/4.84 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_165_0_84 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_165_0_84, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.84 | (726) all_165_0_84 = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (726) can reduce 736 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (740) ~ (all_165_0_84 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_165_0_84 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (740) yields: % 17.87/4.84 | (736) ~ (all_165_0_84 = 0) % 17.87/4.84 | (742) convergent_lines(all_0_3_3, all_0_4_4) = all_165_0_84 % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (660), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (743) (all_256_0_251 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (all_256_0_251 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_256_0_251 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_256_0_251) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (743), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (744) (all_256_0_251 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) | (all_256_0_251 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) % 17.87/4.84 | % 17.87/4.84 +-Applying beta-rule and splitting (744), into two cases. % 17.87/4.84 |-Branch one: % 17.87/4.84 | (745) all_256_0_251 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Applying alpha-rule on (745) yields: % 17.87/4.84 | (746) all_256_0_251 = 0 % 17.87/4.84 | (110) all_26_1_33 = 0 % 17.87/4.84 | (35) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.84 | Equations (110) can reduce 121 to: % 17.87/4.84 | (94) $false % 17.87/4.84 | % 17.87/4.84 |-The branch is then unsatisfiable % 17.87/4.84 |-Branch two: % 17.87/4.84 | (750) all_256_0_251 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.84 | % 17.87/4.85 | Applying alpha-rule on (750) yields: % 17.87/4.85 | (746) all_256_0_251 = 0 % 17.87/4.85 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.85 | % 17.87/4.85 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.85 | (204) $false % 17.87/4.85 | % 17.87/4.85 |-The branch is then unsatisfiable % 17.87/4.85 |-Branch two: % 17.87/4.85 | (754) ~ (all_256_0_251 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_256_0_251 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (754) yields: % 17.87/4.85 | (755) ~ (all_256_0_251 = 0) % 17.87/4.85 | (756) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_256_0_251 % 17.87/4.85 | % 17.87/4.85 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_256_0_251 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_256_0_251, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.85 | (746) all_256_0_251 = 0 % 17.87/4.85 | % 17.87/4.85 | Equations (746) can reduce 755 to: % 17.87/4.85 | (94) $false % 17.87/4.85 | % 17.87/4.85 |-The branch is then unsatisfiable % 17.87/4.85 |-Branch two: % 17.87/4.85 | (759) ~ (all_256_0_251 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_256_0_251 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (759) yields: % 17.87/4.85 | (755) ~ (all_256_0_251 = 0) % 17.87/4.85 | (761) convergent_lines(all_0_3_3, all_0_4_4) = all_256_0_251 % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (661), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (762) (all_258_0_254 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_258_0_254 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_258_0_254 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_258_0_254) % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (762), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (763) (all_258_0_254 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_258_0_254 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (763), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (764) all_258_0_254 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (764) yields: % 17.87/4.85 | (765) all_258_0_254 = 0 % 17.87/4.85 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 17.87/4.85 | % 17.87/4.85 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 17.87/4.85 | (204) $false % 17.87/4.85 | % 17.87/4.85 |-The branch is then unsatisfiable % 17.87/4.85 |-Branch two: % 17.87/4.85 | (768) all_258_0_254 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (768) yields: % 17.87/4.85 | (765) all_258_0_254 = 0 % 17.87/4.85 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 17.87/4.85 | % 17.87/4.85 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 17.87/4.85 | (110) all_26_1_33 = 0 % 17.87/4.85 | % 17.87/4.85 | Equations (110) can reduce 121 to: % 17.87/4.85 | (94) $false % 17.87/4.85 | % 17.87/4.85 |-The branch is then unsatisfiable % 17.87/4.85 |-Branch two: % 17.87/4.85 | (773) ~ (all_258_0_254 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_258_0_254 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (773) yields: % 17.87/4.85 | (774) ~ (all_258_0_254 = 0) % 17.87/4.85 | (775) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_258_0_254 % 17.87/4.85 | % 17.87/4.85 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_258_0_254 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_258_0_254, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 17.87/4.85 | (765) all_258_0_254 = 0 % 17.87/4.85 | % 17.87/4.85 | Equations (765) can reduce 774 to: % 17.87/4.85 | (94) $false % 17.87/4.85 | % 17.87/4.85 |-The branch is then unsatisfiable % 17.87/4.85 |-Branch two: % 17.87/4.85 | (778) ~ (all_258_0_254 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_258_0_254 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (778) yields: % 17.87/4.85 | (774) ~ (all_258_0_254 = 0) % 17.87/4.85 | (780) convergent_lines(all_0_3_3, all_0_4_4) = all_258_0_254 % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (647), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (781) convergent_lines(all_0_2_2, all_0_4_4) = 0 % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (652), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (782) (all_239_0_228 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (all_239_0_228 = 0 & all_28_0_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_239_0_228 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_239_0_228) % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (782), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (783) (all_239_0_228 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (all_239_0_228 = 0 & all_28_0_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) % 17.87/4.85 | % 17.87/4.85 +-Applying beta-rule and splitting (783), into two cases. % 17.87/4.85 |-Branch one: % 17.87/4.85 | (784) all_239_0_228 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 17.87/4.85 | % 17.87/4.85 | Applying alpha-rule on (784) yields: % 17.87/4.85 | (785) all_239_0_228 = 0 % 17.87/4.85 | (399) all_56_0_44 = 0 % 17.87/4.85 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Equations (399) can reduce 409 to: % 18.21/4.85 | (94) $false % 18.21/4.85 | % 18.21/4.85 |-The branch is then unsatisfiable % 18.21/4.85 |-Branch two: % 18.21/4.85 | (789) all_239_0_228 = 0 & all_28_0_36 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Applying alpha-rule on (789) yields: % 18.21/4.85 | (785) all_239_0_228 = 0 % 18.21/4.85 | (216) all_28_0_36 = 0 % 18.21/4.85 | (213) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Equations (216) can reduce 223 to: % 18.21/4.85 | (94) $false % 18.21/4.85 | % 18.21/4.85 |-The branch is then unsatisfiable % 18.21/4.85 |-Branch two: % 18.21/4.85 | (794) ~ (all_239_0_228 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_239_0_228 % 18.21/4.85 | % 18.21/4.85 | Applying alpha-rule on (794) yields: % 18.21/4.85 | (795) ~ (all_239_0_228 = 0) % 18.21/4.85 | (796) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_239_0_228 % 18.21/4.85 | % 18.21/4.85 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_239_0_228 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_239_0_228, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 18.21/4.85 | (785) all_239_0_228 = 0 % 18.21/4.85 | % 18.21/4.85 | Equations (785) can reduce 795 to: % 18.21/4.85 | (94) $false % 18.21/4.85 | % 18.21/4.85 |-The branch is then unsatisfiable % 18.21/4.85 |-Branch two: % 18.21/4.85 | (799) ~ (all_239_0_228 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_239_0_228 % 18.21/4.85 | % 18.21/4.85 | Applying alpha-rule on (799) yields: % 18.21/4.85 | (795) ~ (all_239_0_228 = 0) % 18.21/4.85 | (801) convergent_lines(all_0_3_3, all_0_4_4) = all_239_0_228 % 18.21/4.85 | % 18.21/4.85 +-Applying beta-rule and splitting (654), into two cases. % 18.21/4.85 |-Branch one: % 18.21/4.85 | (802) (all_241_0_231 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (all_241_0_231 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) | ( ~ (all_241_0_231 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_241_0_231) % 18.21/4.85 | % 18.21/4.85 +-Applying beta-rule and splitting (802), into two cases. % 18.21/4.85 |-Branch one: % 18.21/4.85 | (803) (all_241_0_231 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) | (all_241_0_231 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0) % 18.21/4.85 | % 18.21/4.85 +-Applying beta-rule and splitting (803), into two cases. % 18.21/4.85 |-Branch one: % 18.21/4.85 | (804) all_241_0_231 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Applying alpha-rule on (804) yields: % 18.21/4.85 | (805) all_241_0_231 = 0 % 18.21/4.85 | (399) all_56_0_44 = 0 % 18.21/4.85 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Equations (399) can reduce 409 to: % 18.21/4.85 | (94) $false % 18.21/4.85 | % 18.21/4.85 |-The branch is then unsatisfiable % 18.21/4.85 |-Branch two: % 18.21/4.85 | (809) all_241_0_231 = 0 & convergent_lines(all_0_4_4, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Applying alpha-rule on (809) yields: % 18.21/4.85 | (805) all_241_0_231 = 0 % 18.21/4.85 | (524) convergent_lines(all_0_4_4, all_0_4_4) = 0 % 18.21/4.85 | % 18.21/4.85 | Instantiating formula (27) with all_0_4_4 and discharging atoms convergent_lines(all_0_4_4, all_0_4_4) = 0, yields: % 18.21/4.85 | (204) $false % 18.21/4.85 | % 18.21/4.85 |-The branch is then unsatisfiable % 18.21/4.85 |-Branch two: % 18.21/4.85 | (813) ~ (all_241_0_231 = 0) & unorthogonal_lines(all_0_3_3, all_0_4_4) = all_241_0_231 % 18.21/4.85 | % 18.21/4.85 | Applying alpha-rule on (813) yields: % 18.21/4.85 | (814) ~ (all_241_0_231 = 0) % 18.21/4.85 | (815) unorthogonal_lines(all_0_3_3, all_0_4_4) = all_241_0_231 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (11) with all_0_3_3, all_0_4_4, 0, all_241_0_231 and discharging atoms unorthogonal_lines(all_0_3_3, all_0_4_4) = all_241_0_231, unorthogonal_lines(all_0_3_3, all_0_4_4) = 0, yields: % 18.21/4.86 | (805) all_241_0_231 = 0 % 18.21/4.86 | % 18.21/4.86 | Equations (805) can reduce 814 to: % 18.21/4.86 | (94) $false % 18.21/4.86 | % 18.21/4.86 |-The branch is then unsatisfiable % 18.21/4.86 |-Branch two: % 18.21/4.86 | (818) ~ (all_241_0_231 = 0) & convergent_lines(all_0_3_3, all_0_4_4) = all_241_0_231 % 18.21/4.86 | % 18.21/4.86 | Applying alpha-rule on (818) yields: % 18.21/4.86 | (814) ~ (all_241_0_231 = 0) % 18.21/4.86 | (820) convergent_lines(all_0_3_3, all_0_4_4) = all_241_0_231 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_256_0_251, all_56_0_44 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_256_0_251, convergent_lines(all_0_3_3, all_0_4_4) = all_56_0_44, yields: % 18.21/4.86 | (821) all_256_0_251 = all_56_0_44 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_241_0_231, all_258_0_254 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_258_0_254, convergent_lines(all_0_3_3, all_0_4_4) = all_241_0_231, yields: % 18.21/4.86 | (822) all_258_0_254 = all_241_0_231 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_239_0_228, all_256_0_251 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_256_0_251, convergent_lines(all_0_3_3, all_0_4_4) = all_239_0_228, yields: % 18.21/4.86 | (823) all_256_0_251 = all_239_0_228 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_165_0_84, all_241_0_231 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_241_0_231, convergent_lines(all_0_3_3, all_0_4_4) = all_165_0_84, yields: % 18.21/4.86 | (824) all_241_0_231 = all_165_0_84 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_165_0_84, all_239_0_228 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_239_0_228, convergent_lines(all_0_3_3, all_0_4_4) = all_165_0_84, yields: % 18.21/4.86 | (825) all_239_0_228 = all_165_0_84 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_163_0_82, all_256_0_251 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_256_0_251, convergent_lines(all_0_3_3, all_0_4_4) = all_163_0_82, yields: % 18.21/4.86 | (826) all_256_0_251 = all_163_0_82 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_102_0_72, all_239_0_228 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_239_0_228, convergent_lines(all_0_3_3, all_0_4_4) = all_102_0_72, yields: % 18.21/4.86 | (827) all_239_0_228 = all_102_0_72 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (10) with all_0_3_3, all_0_4_4, all_97_0_65, all_258_0_254 and discharging atoms convergent_lines(all_0_3_3, all_0_4_4) = all_258_0_254, convergent_lines(all_0_3_3, all_0_4_4) = all_97_0_65, yields: % 18.21/4.86 | (828) all_258_0_254 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Combining equations (822,828) yields a new equation: % 18.21/4.86 | (829) all_241_0_231 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Simplifying 829 yields: % 18.21/4.86 | (830) all_241_0_231 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Combining equations (821,826) yields a new equation: % 18.21/4.86 | (831) all_163_0_82 = all_56_0_44 % 18.21/4.86 | % 18.21/4.86 | Combining equations (823,826) yields a new equation: % 18.21/4.86 | (832) all_239_0_228 = all_163_0_82 % 18.21/4.86 | % 18.21/4.86 | Simplifying 832 yields: % 18.21/4.86 | (833) all_239_0_228 = all_163_0_82 % 18.21/4.86 | % 18.21/4.86 | Combining equations (824,830) yields a new equation: % 18.21/4.86 | (834) all_165_0_84 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Simplifying 834 yields: % 18.21/4.86 | (835) all_165_0_84 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Combining equations (833,827) yields a new equation: % 18.21/4.86 | (836) all_163_0_82 = all_102_0_72 % 18.21/4.86 | % 18.21/4.86 | Simplifying 836 yields: % 18.21/4.86 | (837) all_163_0_82 = all_102_0_72 % 18.21/4.86 | % 18.21/4.86 | Combining equations (825,827) yields a new equation: % 18.21/4.86 | (838) all_165_0_84 = all_102_0_72 % 18.21/4.86 | % 18.21/4.86 | Simplifying 838 yields: % 18.21/4.86 | (839) all_165_0_84 = all_102_0_72 % 18.21/4.86 | % 18.21/4.86 | Combining equations (839,835) yields a new equation: % 18.21/4.86 | (840) all_102_0_72 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Simplifying 840 yields: % 18.21/4.86 | (841) all_102_0_72 = all_97_0_65 % 18.21/4.86 | % 18.21/4.86 | Combining equations (837,831) yields a new equation: % 18.21/4.86 | (842) all_102_0_72 = all_56_0_44 % 18.21/4.86 | % 18.21/4.86 | Simplifying 842 yields: % 18.21/4.86 | (843) all_102_0_72 = all_56_0_44 % 18.21/4.86 | % 18.21/4.86 | Combining equations (843,841) yields a new equation: % 18.21/4.86 | (844) all_97_0_65 = all_56_0_44 % 18.21/4.86 | % 18.21/4.86 | Equations (844) can reduce 696 to: % 18.21/4.86 | (409) ~ (all_56_0_44 = 0) % 18.21/4.86 | % 18.21/4.86 +-Applying beta-rule and splitting (187), into two cases. % 18.21/4.86 |-Branch one: % 18.21/4.86 | (846) (all_92_0_56 = 0 & all_92_1_57 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_92_1_57 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) % 18.21/4.86 | % 18.21/4.86 +-Applying beta-rule and splitting (846), into two cases. % 18.21/4.86 |-Branch one: % 18.21/4.86 | (847) all_92_0_56 = 0 & all_92_1_57 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0 % 18.21/4.86 | % 18.21/4.86 | Applying alpha-rule on (847) yields: % 18.21/4.86 | (848) all_92_0_56 = 0 % 18.21/4.86 | (849) all_92_1_57 = 0 % 18.21/4.86 | (850) unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 % 18.21/4.86 | (781) convergent_lines(all_0_2_2, all_0_4_4) = 0 % 18.21/4.86 | % 18.21/4.86 +-Applying beta-rule and splitting (659), into two cases. % 18.21/4.86 |-Branch one: % 18.21/4.86 | (852) (all_254_0_247 = 0 & all_254_1_248 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_254_1_248 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0) % 18.21/4.86 | % 18.21/4.86 +-Applying beta-rule and splitting (852), into two cases. % 18.21/4.86 |-Branch one: % 18.21/4.86 | (853) all_254_0_247 = 0 & all_254_1_248 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.21/4.86 | % 18.21/4.86 | Applying alpha-rule on (853) yields: % 18.21/4.86 | (854) all_254_0_247 = 0 % 18.21/4.86 | (855) all_254_1_248 = 0 % 18.21/4.86 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 18.21/4.86 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.21/4.86 | % 18.21/4.86 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 18.21/4.86 | (204) $false % 18.21/4.86 | % 18.21/4.86 |-The branch is then unsatisfiable % 18.21/4.86 |-Branch two: % 18.21/4.86 | (859) all_254_1_248 = 0 & all_0_0_0 = 0 & convergent_lines(all_0_3_3, all_0_2_2) = 0 % 18.21/4.86 | % 18.21/4.86 | Applying alpha-rule on (859) yields: % 18.21/4.86 | (855) all_254_1_248 = 0 % 18.21/4.86 | (117) all_0_0_0 = 0 % 18.21/4.86 | (92) convergent_lines(all_0_3_3, all_0_2_2) = 0 % 18.21/4.86 | % 18.21/4.86 | Equations (117) can reduce 21 to: % 18.21/4.86 | (94) $false % 18.21/4.86 | % 18.21/4.86 |-The branch is then unsatisfiable % 18.21/4.86 |-Branch two: % 18.21/4.86 | (864) ~ (all_254_1_248 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_254_1_248 % 18.21/4.86 | % 18.21/4.86 | Applying alpha-rule on (864) yields: % 18.21/4.86 | (865) ~ (all_254_1_248 = 0) % 18.21/4.86 | (866) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_254_1_248 % 18.21/4.86 | % 18.21/4.86 +-Applying beta-rule and splitting (657), into two cases. % 18.21/4.86 |-Branch one: % 18.21/4.86 | (867) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241) % 18.21/4.86 | % 18.21/4.86 +-Applying beta-rule and splitting (867), into two cases. % 18.21/4.86 |-Branch one: % 18.21/4.87 | (868) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 18.21/4.87 | % 18.21/4.87 +-Applying beta-rule and splitting (868), into two cases. % 18.21/4.87 |-Branch one: % 18.21/4.87 | (869) all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.21/4.87 | % 18.21/4.87 | Applying alpha-rule on (869) yields: % 18.21/4.87 | (870) all_250_0_241 = 0 % 18.21/4.87 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.21/4.87 | % 18.21/4.87 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_254_1_248 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_254_1_248, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.21/4.87 | (855) all_254_1_248 = 0 % 18.21/4.87 | % 18.21/4.87 | Equations (855) can reduce 865 to: % 18.21/4.87 | (94) $false % 18.21/4.87 | % 18.21/4.87 |-The branch is then unsatisfiable % 18.21/4.87 |-Branch two: % 18.21/4.87 | (874) all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.21/4.87 | % 18.21/4.87 | Applying alpha-rule on (874) yields: % 18.21/4.87 | (870) all_250_0_241 = 0 % 18.21/4.87 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.21/4.87 | % 18.21/4.87 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 18.21/4.87 | (110) all_26_1_33 = 0 % 18.21/4.87 | % 18.21/4.87 | Equations (110) can reduce 121 to: % 18.21/4.87 | (94) $false % 18.21/4.87 | % 18.21/4.87 |-The branch is then unsatisfiable % 18.21/4.87 |-Branch two: % 18.21/4.87 | (879) ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.21/4.87 | % 18.21/4.87 | Applying alpha-rule on (879) yields: % 18.21/4.87 | (880) ~ (all_250_0_241 = 0) % 18.21/4.87 | (881) unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.21/4.87 | % 18.21/4.87 | Instantiating formula (11) with all_0_2_2, all_0_4_4, 0, all_250_0_241 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241, unorthogonal_lines(all_0_2_2, all_0_4_4) = 0, yields: % 18.21/4.87 | (870) all_250_0_241 = 0 % 18.21/4.87 | % 18.21/4.87 | Equations (870) can reduce 880 to: % 18.21/4.87 | (94) $false % 18.21/4.87 | % 18.21/4.87 |-The branch is then unsatisfiable % 18.21/4.87 |-Branch two: % 18.21/4.87 | (884) ~ (all_250_0_241 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.21/4.87 | % 18.21/4.87 | Applying alpha-rule on (884) yields: % 18.21/4.87 | (880) ~ (all_250_0_241 = 0) % 18.21/4.87 | (886) convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.21/4.87 | % 18.21/4.87 | Instantiating formula (10) with all_0_2_2, all_0_4_4, all_250_0_241, 0 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241, convergent_lines(all_0_2_2, all_0_4_4) = 0, yields: % 18.21/4.87 | (870) all_250_0_241 = 0 % 18.21/4.87 | % 18.21/4.87 | Equations (870) can reduce 880 to: % 18.21/4.87 | (94) $false % 18.21/4.87 | % 18.21/4.87 |-The branch is then unsatisfiable % 18.21/4.87 |-Branch two: % 18.21/4.87 | (889) all_92_1_57 = 0 & all_71_0_53 = 0 & unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 18.21/4.87 | % 18.21/4.87 | Applying alpha-rule on (889) yields: % 18.21/4.87 | (849) all_92_1_57 = 0 % 18.21/4.87 | (233) all_71_0_53 = 0 % 18.21/4.87 | (213) unorthogonal_lines(all_0_4_4, all_0_4_4) = 0 % 18.21/4.87 | % 18.21/4.87 | Combining equations (335,233) yields a new equation: % 18.21/4.87 | (493) all_28_0_36 = 0 % 18.21/4.87 | % 18.21/4.87 | Simplifying 493 yields: % 18.21/4.87 | (216) all_28_0_36 = 0 % 18.21/4.87 | % 18.21/4.87 | Equations (216) can reduce 223 to: % 18.21/4.87 | (94) $false % 18.21/4.87 | % 18.21/4.87 |-The branch is then unsatisfiable % 18.21/4.87 |-Branch two: % 18.21/4.87 | (896) ~ (all_92_1_57 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_92_1_57 % 18.21/4.87 | % 18.21/4.87 | Applying alpha-rule on (896) yields: % 18.21/4.87 | (897) ~ (all_92_1_57 = 0) % 18.21/4.87 | (898) convergent_lines(all_0_4_4, all_0_2_2) = all_92_1_57 % 18.21/4.87 | % 18.21/4.87 | Instantiating formula (10) with all_0_4_4, all_0_2_2, all_92_1_57, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_92_1_57, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 18.29/4.87 | (899) all_92_1_57 = all_36_0_38 % 18.29/4.87 | % 18.29/4.87 | From (899) and (898) follows: % 18.29/4.87 | (99) convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (190), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (901) (all_95_0_61 = 0 & all_95_1_62 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | (all_95_1_62 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0) % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (901), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (902) all_95_0_61 = 0 & all_95_1_62 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | % 18.29/4.87 | Applying alpha-rule on (902) yields: % 18.29/4.87 | (903) all_95_0_61 = 0 % 18.29/4.87 | (904) all_95_1_62 = 0 % 18.29/4.87 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | (499) convergent_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (653), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (907) (all_240_0_229 = 0 & all_240_1_230 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_240_1_230 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (907), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (908) all_240_0_229 = 0 & all_240_1_230 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | % 18.29/4.87 | Applying alpha-rule on (908) yields: % 18.29/4.87 | (909) all_240_0_229 = 0 % 18.29/4.87 | (910) all_240_1_230 = 0 % 18.29/4.87 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (656), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (912) (all_244_0_235 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_244_0_235 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | ( ~ (all_244_0_235 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_244_0_235) % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (912), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (913) (all_244_0_235 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_244_0_235 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (913), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (914) all_244_0_235 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | % 18.29/4.87 | Applying alpha-rule on (914) yields: % 18.29/4.87 | (915) all_244_0_235 = 0 % 18.29/4.87 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (651), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (917) (all_237_0_224 = 0 & all_237_1_225 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_237_1_225 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (917), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (918) all_237_0_224 = 0 & all_237_1_225 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0 % 18.29/4.87 | % 18.29/4.87 | Applying alpha-rule on (918) yields: % 18.29/4.87 | (919) all_237_0_224 = 0 % 18.29/4.87 | (920) all_237_1_225 = 0 % 18.29/4.87 | (850) unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 % 18.29/4.87 | (781) convergent_lines(all_0_2_2, all_0_4_4) = 0 % 18.29/4.87 | % 18.29/4.87 +-Applying beta-rule and splitting (658), into two cases. % 18.29/4.87 |-Branch one: % 18.29/4.87 | (923) (all_251_0_242 = 0 & all_251_1_243 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_251_1_243 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) % 18.29/4.87 | % 18.29/4.88 +-Applying beta-rule and splitting (923), into two cases. % 18.29/4.88 |-Branch one: % 18.29/4.88 | (924) all_251_0_242 = 0 & all_251_1_243 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (924) yields: % 18.29/4.88 | (925) all_251_0_242 = 0 % 18.29/4.88 | (926) all_251_1_243 = 0 % 18.29/4.88 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 18.29/4.88 | (204) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (930) all_251_1_243 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (930) yields: % 18.29/4.88 | (926) all_251_1_243 = 0 % 18.29/4.88 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 +-Applying beta-rule and splitting (655), into two cases. % 18.29/4.88 |-Branch one: % 18.29/4.88 | (933) (all_242_0_232 = 0 & all_242_1_233 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_242_1_233 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) % 18.29/4.88 | % 18.29/4.88 +-Applying beta-rule and splitting (933), into two cases. % 18.29/4.88 |-Branch one: % 18.29/4.88 | (934) all_242_0_232 = 0 & all_242_1_233 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (934) yields: % 18.29/4.88 | (935) all_242_0_232 = 0 % 18.29/4.88 | (936) all_242_1_233 = 0 % 18.29/4.88 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.88 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 18.29/4.88 | (204) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (940) all_242_1_233 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (940) yields: % 18.29/4.88 | (936) all_242_1_233 = 0 % 18.29/4.88 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) 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: % 18.29/4.88 | (117) all_0_0_0 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (117) can reduce 21 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (945) ~ (all_242_1_233 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (945) yields: % 18.29/4.88 | (946) ~ (all_242_1_233 = 0) % 18.29/4.88 | (947) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_242_1_233 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.88 | (936) all_242_1_233 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (936) can reduce 946 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (950) ~ (all_251_1_243 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (950) yields: % 18.29/4.88 | (951) ~ (all_251_1_243 = 0) % 18.29/4.88 | (952) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243 % 18.29/4.88 | % 18.29/4.88 +-Applying beta-rule and splitting (657), into two cases. % 18.29/4.88 |-Branch one: % 18.29/4.88 | (867) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241) % 18.29/4.88 | % 18.29/4.88 +-Applying beta-rule and splitting (867), into two cases. % 18.29/4.88 |-Branch one: % 18.29/4.88 | (868) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 18.29/4.88 | % 18.29/4.88 +-Applying beta-rule and splitting (868), into two cases. % 18.29/4.88 |-Branch one: % 18.29/4.88 | (869) all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (869) yields: % 18.29/4.88 | (870) all_250_0_241 = 0 % 18.29/4.88 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_251_1_243 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.88 | (926) all_251_1_243 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (926) can reduce 951 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (874) all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (874) yields: % 18.29/4.88 | (870) all_250_0_241 = 0 % 18.29/4.88 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 18.29/4.88 | (110) all_26_1_33 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (110) can reduce 121 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (879) ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (879) yields: % 18.29/4.88 | (880) ~ (all_250_0_241 = 0) % 18.29/4.88 | (881) unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) with all_0_2_2, all_0_4_4, 0, all_250_0_241 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241, unorthogonal_lines(all_0_2_2, all_0_4_4) = 0, yields: % 18.29/4.88 | (870) all_250_0_241 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (870) can reduce 880 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (884) ~ (all_250_0_241 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (884) yields: % 18.29/4.88 | (880) ~ (all_250_0_241 = 0) % 18.29/4.88 | (886) convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (10) with all_0_2_2, all_0_4_4, all_250_0_241, 0 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241, convergent_lines(all_0_2_2, all_0_4_4) = 0, yields: % 18.29/4.88 | (870) all_250_0_241 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (870) can reduce 880 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (975) all_237_1_225 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (975) yields: % 18.29/4.88 | (920) all_237_1_225 = 0 % 18.29/4.88 | (399) all_56_0_44 = 0 % 18.29/4.88 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (399) can reduce 409 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (980) ~ (all_237_1_225 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (980) yields: % 18.29/4.88 | (981) ~ (all_237_1_225 = 0) % 18.29/4.88 | (982) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_237_1_225 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.88 | (920) all_237_1_225 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (920) can reduce 981 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (985) all_244_0_235 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (985) yields: % 18.29/4.88 | (915) all_244_0_235 = 0 % 18.29/4.88 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 18.29/4.88 | (204) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (989) ~ (all_244_0_235 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_244_0_235 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (989) yields: % 18.29/4.88 | (990) ~ (all_244_0_235 = 0) % 18.29/4.88 | (991) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_244_0_235 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_244_0_235 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_244_0_235, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.88 | (915) all_244_0_235 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (915) can reduce 990 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (994) ~ (all_244_0_235 = 0) & convergent_lines(all_0_2_2, all_0_3_3) = all_244_0_235 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (994) yields: % 18.29/4.88 | (990) ~ (all_244_0_235 = 0) % 18.29/4.88 | (996) convergent_lines(all_0_2_2, all_0_3_3) = all_244_0_235 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (10) with all_0_2_2, all_0_3_3, all_244_0_235, 0 and discharging atoms convergent_lines(all_0_2_2, all_0_3_3) = all_244_0_235, convergent_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.88 | (915) all_244_0_235 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (915) can reduce 990 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (999) all_240_1_230 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (999) yields: % 18.29/4.88 | (910) all_240_1_230 = 0 % 18.29/4.88 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 18.29/4.88 | (204) $false % 18.29/4.88 | % 18.29/4.88 |-The branch is then unsatisfiable % 18.29/4.88 |-Branch two: % 18.29/4.88 | (1003) ~ (all_240_1_230 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230 % 18.29/4.88 | % 18.29/4.88 | Applying alpha-rule on (1003) yields: % 18.29/4.88 | (1004) ~ (all_240_1_230 = 0) % 18.29/4.88 | (1005) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230 % 18.29/4.88 | % 18.29/4.88 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_240_1_230 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.88 | (910) all_240_1_230 = 0 % 18.29/4.88 | % 18.29/4.88 | Equations (910) can reduce 1004 to: % 18.29/4.88 | (94) $false % 18.29/4.88 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1008) all_95_1_62 = 0 & all_26_1_33 = 0 & unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1008) yields: % 18.29/4.89 | (904) all_95_1_62 = 0 % 18.29/4.89 | (110) all_26_1_33 = 0 % 18.29/4.89 | (35) unorthogonal_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Equations (110) can reduce 121 to: % 18.29/4.89 | (94) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1013) ~ (all_95_1_62 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_95_1_62 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1013) yields: % 18.29/4.89 | (1014) ~ (all_95_1_62 = 0) % 18.29/4.89 | (1015) convergent_lines(all_0_4_4, all_0_2_2) = all_95_1_62 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (10) with all_0_4_4, all_0_2_2, all_95_1_62, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_95_1_62, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 18.29/4.89 | (1016) all_95_1_62 = all_36_0_38 % 18.29/4.89 | % 18.29/4.89 | Equations (1016) can reduce 1014 to: % 18.29/4.89 | (98) ~ (all_36_0_38 = 0) % 18.29/4.89 | % 18.29/4.89 | From (1016) and (1015) follows: % 18.29/4.89 | (99) convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (191), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (1019) (all_96_0_63 = 0 & all_96_1_64 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_96_1_64 = 0 & all_36_0_38 = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (1019), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (1020) all_96_0_63 = 0 & all_96_1_64 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1020) yields: % 18.29/4.89 | (1021) all_96_0_63 = 0 % 18.29/4.89 | (1022) all_96_1_64 = 0 % 18.29/4.89 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 18.29/4.89 | (204) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1026) all_96_1_64 = 0 & all_36_0_38 = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1026) yields: % 18.29/4.89 | (1022) all_96_1_64 = 0 % 18.29/4.89 | (113) all_36_0_38 = 0 % 18.29/4.89 | % 18.29/4.89 | Equations (113) can reduce 98 to: % 18.29/4.89 | (94) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1030) ~ (all_96_1_64 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_96_1_64 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1030) yields: % 18.29/4.89 | (1031) ~ (all_96_1_64 = 0) % 18.29/4.89 | (1032) convergent_lines(all_0_4_4, all_0_2_2) = all_96_1_64 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (10) with all_0_4_4, all_0_2_2, all_96_1_64, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_96_1_64, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 18.29/4.89 | (1033) all_96_1_64 = all_36_0_38 % 18.29/4.89 | % 18.29/4.89 | Equations (1033) can reduce 1031 to: % 18.29/4.89 | (98) ~ (all_36_0_38 = 0) % 18.29/4.89 | % 18.29/4.89 | From (1033) and (1032) follows: % 18.29/4.89 | (99) convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (193), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (1036) (all_98_0_66 = 0 & all_98_1_67 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_98_1_67 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (1036), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (1037) all_98_0_66 = 0 & all_98_1_67 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1037) yields: % 18.29/4.89 | (1038) all_98_0_66 = 0 % 18.29/4.89 | (1039) all_98_1_67 = 0 % 18.29/4.89 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 18.29/4.89 | (204) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1043) all_98_1_67 = 0 & convergent_lines(all_0_4_4, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1043) yields: % 18.29/4.89 | (1039) all_98_1_67 = 0 % 18.29/4.89 | (112) convergent_lines(all_0_4_4, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (10) with all_0_4_4, all_0_2_2, 0, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, convergent_lines(all_0_4_4, all_0_2_2) = 0, yields: % 18.29/4.89 | (113) all_36_0_38 = 0 % 18.29/4.89 | % 18.29/4.89 | Equations (113) can reduce 98 to: % 18.29/4.89 | (94) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1048) ~ (all_98_1_67 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_98_1_67 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1048) yields: % 18.29/4.89 | (1049) ~ (all_98_1_67 = 0) % 18.29/4.89 | (1050) convergent_lines(all_0_4_4, all_0_2_2) = all_98_1_67 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (10) with all_0_4_4, all_0_2_2, all_98_1_67, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_98_1_67, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 18.29/4.89 | (1051) all_98_1_67 = all_36_0_38 % 18.29/4.89 | % 18.29/4.89 | From (1051) and (1050) follows: % 18.29/4.89 | (99) convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (195), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (1053) (all_100_0_69 = 0 & all_100_1_70 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0) | (all_100_1_70 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (1053), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (1054) all_100_0_69 = 0 & all_100_1_70 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 & convergent_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1054) yields: % 18.29/4.89 | (1055) all_100_0_69 = 0 % 18.29/4.89 | (1056) all_100_1_70 = 0 % 18.29/4.89 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | (499) convergent_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (651), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (917) (all_237_0_224 = 0 & all_237_1_225 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0) | (all_237_1_225 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (917), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (918) all_237_0_224 = 0 & all_237_1_225 = 0 & unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 & convergent_lines(all_0_2_2, all_0_4_4) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (918) yields: % 18.29/4.89 | (919) all_237_0_224 = 0 % 18.29/4.89 | (920) all_237_1_225 = 0 % 18.29/4.89 | (850) unorthogonal_lines(all_0_2_2, all_0_4_4) = 0 % 18.29/4.89 | (781) convergent_lines(all_0_2_2, all_0_4_4) = 0 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (658), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (923) (all_251_0_242 = 0 & all_251_1_243 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) | (all_251_1_243 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (923), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (924) all_251_0_242 = 0 & all_251_1_243 = 0 & unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (924) yields: % 18.29/4.89 | (925) all_251_0_242 = 0 % 18.29/4.89 | (926) all_251_1_243 = 0 % 18.29/4.89 | (202) unorthogonal_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.89 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 18.29/4.89 | (204) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (930) all_251_1_243 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (930) yields: % 18.29/4.89 | (926) all_251_1_243 = 0 % 18.29/4.89 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (653), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (907) (all_240_0_229 = 0 & all_240_1_230 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_240_1_230 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (907), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (908) all_240_0_229 = 0 & all_240_1_230 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (908) yields: % 18.29/4.89 | (909) all_240_0_229 = 0 % 18.29/4.89 | (910) all_240_1_230 = 0 % 18.29/4.89 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (655), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (933) (all_242_0_232 = 0 & all_242_1_233 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0) | (all_242_1_233 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0) % 18.29/4.89 | % 18.29/4.89 +-Applying beta-rule and splitting (933), into two cases. % 18.29/4.89 |-Branch one: % 18.29/4.89 | (934) all_242_0_232 = 0 & all_242_1_233 = 0 & unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 & convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (934) yields: % 18.29/4.89 | (935) all_242_0_232 = 0 % 18.29/4.89 | (936) all_242_1_233 = 0 % 18.29/4.89 | (426) unorthogonal_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 18.29/4.89 | (204) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (940) all_242_1_233 = 0 & unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (940) yields: % 18.29/4.89 | (936) all_242_1_233 = 0 % 18.29/4.89 | (448) unorthogonal_lines(all_0_3_3, all_0_2_2) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (11) 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: % 18.29/4.89 | (117) all_0_0_0 = 0 % 18.29/4.89 | % 18.29/4.89 | Equations (117) can reduce 21 to: % 18.29/4.89 | (94) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (945) ~ (all_242_1_233 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (945) yields: % 18.29/4.89 | (946) ~ (all_242_1_233 = 0) % 18.29/4.89 | (947) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_242_1_233 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_242_1_233, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.89 | (936) all_242_1_233 = 0 % 18.29/4.89 | % 18.29/4.89 | Equations (936) can reduce 946 to: % 18.29/4.89 | (94) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (999) all_240_1_230 = 0 & convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (999) yields: % 18.29/4.89 | (910) all_240_1_230 = 0 % 18.29/4.89 | (203) convergent_lines(all_0_3_3, all_0_3_3) = 0 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (27) with all_0_3_3 and discharging atoms convergent_lines(all_0_3_3, all_0_3_3) = 0, yields: % 18.29/4.89 | (204) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (1003) ~ (all_240_1_230 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230 % 18.29/4.89 | % 18.29/4.89 | Applying alpha-rule on (1003) yields: % 18.29/4.89 | (1004) ~ (all_240_1_230 = 0) % 18.29/4.89 | (1005) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230 % 18.29/4.89 | % 18.29/4.89 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_240_1_230 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_240_1_230, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.89 | (910) all_240_1_230 = 0 % 18.29/4.89 | % 18.29/4.89 | Equations (910) can reduce 1004 to: % 18.29/4.89 | (94) $false % 18.29/4.89 | % 18.29/4.89 |-The branch is then unsatisfiable % 18.29/4.89 |-Branch two: % 18.29/4.89 | (950) ~ (all_251_1_243 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (950) yields: % 18.29/4.90 | (951) ~ (all_251_1_243 = 0) % 18.29/4.90 | (952) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243 % 18.29/4.90 | % 18.29/4.90 +-Applying beta-rule and splitting (657), into two cases. % 18.29/4.90 |-Branch one: % 18.29/4.90 | (867) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) | ( ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241) % 18.29/4.90 | % 18.29/4.90 +-Applying beta-rule and splitting (867), into two cases. % 18.29/4.90 |-Branch one: % 18.29/4.90 | (868) (all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0) | (all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0) % 18.29/4.90 | % 18.29/4.90 +-Applying beta-rule and splitting (868), into two cases. % 18.29/4.90 |-Branch one: % 18.29/4.90 | (869) all_250_0_241 = 0 & unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (869) yields: % 18.29/4.90 | (870) all_250_0_241 = 0 % 18.29/4.90 | (871) unorthogonal_lines(all_0_2_2, all_0_3_3) = 0 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_251_1_243 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_251_1_243, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.90 | (926) all_251_1_243 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (926) can reduce 951 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (874) all_250_0_241 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (874) yields: % 18.29/4.90 | (870) all_250_0_241 = 0 % 18.29/4.90 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 18.29/4.90 | (110) all_26_1_33 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (110) can reduce 121 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (879) ~ (all_250_0_241 = 0) & unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (879) yields: % 18.29/4.90 | (880) ~ (all_250_0_241 = 0) % 18.29/4.90 | (881) unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (11) with all_0_2_2, all_0_4_4, 0, all_250_0_241 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_4_4) = all_250_0_241, unorthogonal_lines(all_0_2_2, all_0_4_4) = 0, yields: % 18.29/4.90 | (870) all_250_0_241 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (870) can reduce 880 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (884) ~ (all_250_0_241 = 0) & convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (884) yields: % 18.29/4.90 | (880) ~ (all_250_0_241 = 0) % 18.29/4.90 | (886) convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (10) with all_0_2_2, all_0_4_4, all_250_0_241, 0 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = all_250_0_241, convergent_lines(all_0_2_2, all_0_4_4) = 0, yields: % 18.29/4.90 | (870) all_250_0_241 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (870) can reduce 880 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (975) all_237_1_225 = 0 & all_56_0_44 = 0 & unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (975) yields: % 18.29/4.90 | (920) all_237_1_225 = 0 % 18.29/4.90 | (399) all_56_0_44 = 0 % 18.29/4.90 | (458) unorthogonal_lines(all_0_3_3, all_0_4_4) = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (399) can reduce 409 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (980) ~ (all_237_1_225 = 0) & unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (980) yields: % 18.29/4.90 | (981) ~ (all_237_1_225 = 0) % 18.29/4.90 | (982) unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (11) with all_0_2_2, all_0_3_3, 0, all_237_1_225 and discharging atoms unorthogonal_lines(all_0_2_2, all_0_3_3) = all_237_1_225, unorthogonal_lines(all_0_2_2, all_0_3_3) = 0, yields: % 18.29/4.90 | (920) all_237_1_225 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (920) can reduce 981 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1141) all_100_1_70 = 0 & convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (1141) yields: % 18.29/4.90 | (1056) all_100_1_70 = 0 % 18.29/4.90 | (207) convergent_lines(all_0_4_4, all_0_3_3) = 0 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (10) with all_0_4_4, all_0_3_3, 0, all_26_1_33 and discharging atoms convergent_lines(all_0_4_4, all_0_3_3) = all_26_1_33, convergent_lines(all_0_4_4, all_0_3_3) = 0, yields: % 18.29/4.90 | (110) all_26_1_33 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (110) can reduce 121 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1146) ~ (all_100_1_70 = 0) & convergent_lines(all_0_4_4, all_0_2_2) = all_100_1_70 % 18.29/4.90 | % 18.29/4.90 | Applying alpha-rule on (1146) yields: % 18.29/4.90 | (1147) ~ (all_100_1_70 = 0) % 18.29/4.90 | (1148) convergent_lines(all_0_4_4, all_0_2_2) = all_100_1_70 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (10) with all_0_4_4, all_0_2_2, all_100_1_70, all_36_0_38 and discharging atoms convergent_lines(all_0_4_4, all_0_2_2) = all_100_1_70, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 18.29/4.90 | (1149) all_100_1_70 = all_36_0_38 % 18.29/4.90 | % 18.29/4.90 | Equations (1149) can reduce 1147 to: % 18.29/4.90 | (98) ~ (all_36_0_38 = 0) % 18.29/4.90 | % 18.29/4.90 | From (1149) and (1148) follows: % 18.29/4.90 | (99) convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (24) with all_36_0_38, all_0_2_2, all_0_4_4, all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_4_4) = 0, convergent_lines(all_0_4_4, all_0_2_2) = all_36_0_38, yields: % 18.29/4.90 | (1152) all_36_0_38 = 0 | convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.90 | % 18.29/4.90 +-Applying beta-rule and splitting (1152), into two cases. % 18.29/4.90 |-Branch one: % 18.29/4.90 | (427) convergent_lines(all_0_2_2, all_0_2_2) = 0 % 18.29/4.90 | % 18.29/4.90 | Instantiating formula (27) with all_0_2_2 and discharging atoms convergent_lines(all_0_2_2, all_0_2_2) = 0, yields: % 18.29/4.90 | (204) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1155) ~ (convergent_lines(all_0_2_2, all_0_2_2) = 0) % 18.29/4.90 | (113) all_36_0_38 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (113) can reduce 98 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1158) ~ (convergent_lines(all_0_2_2, all_0_4_4) = 0) % 18.29/4.90 | (399) all_56_0_44 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (399) can reduce 409 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (461) ~ (unorthogonal_lines(all_0_3_3, all_0_4_4) = 0) % 18.29/4.90 | (399) all_56_0_44 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (399) can reduce 409 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1164) ~ (convergent_lines(all_0_2_2, all_0_3_3) = 0) % 18.29/4.90 | (354) all_29_0_37 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (354) can reduce 359 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1167) ~ (unorthogonal_lines(all_0_3_3, all_0_3_3) = 0) % 18.29/4.90 | (354) all_29_0_37 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (354) can reduce 359 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1170) ~ (unorthogonal_lines(all_0_4_4, all_0_4_4) = 0) % 18.29/4.90 | (233) all_71_0_53 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (233) can reduce 153 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1173) ~ (unorthogonal_lines(all_0_4_4, all_0_2_2) = 0) % 18.29/4.90 | (113) all_36_0_38 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (113) can reduce 98 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 |-Branch two: % 18.29/4.90 | (1176) ~ (convergent_lines(all_0_3_3, all_0_2_2) = 0) % 18.29/4.90 | (117) all_0_0_0 = 0 % 18.29/4.90 | % 18.29/4.90 | Equations (117) can reduce 21 to: % 18.29/4.90 | (94) $false % 18.29/4.90 | % 18.29/4.90 |-The branch is then unsatisfiable % 18.29/4.90 % SZS output end Proof for theBenchmark % 18.29/4.90 % 18.29/4.90 4281ms %------------------------------------------------------------------------------